Crystal Radio and Crystal Set Systems

Table of contents :
Crystal radio set design and optimization with measurements on diodes, audio transformers, headphones, inductors, variable capacitors......Page 1
Crystal Radio Set Design Technical Help......Page 4
Crystal Radio Set: Better sensitivity, selectivity and volume; less audio distortion......Page 15
Measure effective impedance of headphones or a speaker>......Page 23
Compare the sensitivity and impedance of headphones or speakers even if their parameters differ greatly. No lab test equipment is needed......Page 27
The best diode and audio transformer for a crystal set, and a simple way to approximate diode saturation current......Page 30
Audio transformer power loss and optimal impedance matching......Page 34
Diode detector Simulation using SPICE......Page 49
Do diodes have a specific knee voltage or is it just a matter of scale?......Page 53
Current and voltage weveforms in a half-wave AM peak detector, at several input-power levels......Page 56
Optimum diode for any crystal set......Page 63
Detector Linear-to-Square-Law Crossover Point (LSLCP), and a new diode detector equivalent circuit......Page 66
Measurent of sensitivity, selectivity and input/output impedance of Crystal Radios......Page 72
Directivity of the inverted L antenna and how one might enhance it......Page 81
Sensitivity measurements of headphone and earphone receiver elements......Page 83
No-loss audio transformer simulator with independently adjustable input and output impedances......Page 88
AM diode detector equations relating diode parameters to the LSLCP and sensitivity......Page 94
Diode saturation current and ideality factor measurement, with measured values for various diode types......Page 101
Increase diode detector weak-signal performance; determine if it is functioning above or below its linear-to-square-law crossover point......Page 106
3 dB more audio output from a crystal radio without using an external power source......Page 110
Mystery Crystal Radio circuit analysis......Page 114
Measure the impedance of an AM-band antenna-ground system......Page 118
Single-tuned four-band crystal radio set using a two-value tank inductor......Page 122
Double-tuned four-band crystal radio set......Page 135
Variable capacitor Q measurement, diode problems, RF loss in slide switches and dielectrics; sensitivity and selectivity in crystal radio sets......Page 138
Amplify a crystal radio's output without using batteries or socket power......Page 147
Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank......Page 152
Measurements of weak-signal detection efficiency (below the linear to square-law crossover point) of 15 germanium and Schottky diodes based upon their saturation currents and ideality factors, with application to crystal radio sets......Page 169
Diode detector weak-signal sensitivity improvement from input-impedance mismatching in crystal radio sets......Page 175
Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets......Page 179

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Crystal radio set design and optimization with measurements on diodes, audio transformers, headphones, inductors, variable capacitors http://bentongue.com/xtalset/xtalset.html

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The main purpose of these Articles is to show how Engineering Principles may be applied to the design of crystal radios.  Measurement techniques and actual measurements are described.  They relate to selectivity, sensitivity, inductor (coil) and capacitor Q (quality factor), impedance matching, the diode SPICE parameters saturation current and ideality factor, audio transformer characteristics, earphone and antenna to ground system parameters. The design of some crystal radios that embody these principles are shown, along with performance measurements.  Some original technical concepts such as the linear-to-square-law crossover point of a diode detector, contra-wound inductors and the 'benny' are presented. Please note:  If any terms or concepts used here are unclear or obscure, please check out Article # 00 for possible explanations.  If there still is a problem, e-mail me and I'll try to assist (Use the link below to the Front Page for my Email address). Second note: The two dates following the Article titles are, respectively, the original publication date and the date of the last revision.

Content of Articles in Section A of this Site Practical design considerations, helpful Definitions of Terms and useful Explanations of Concepts used in this Site: 04/25/00;  11/06/07  A New Way to Look at Crystal Radio Design. Get Greater Sensitivity to very Weak Signals and Greater Volume, less Audio Distortion and Improved Selectivity for Strong Signals: 07/15/99;  02/12/06  To maximize volume from headphones or a speaker, measure and use effective impedance. No lab test equipment is needed: 07/15/99;  06/21/03 Compare the impedance and sensitivity of headphones, earphones and/or speakers even if they differ greatly in impedance. No lab test equipment is needed: 07/15/99;  06/29/00 The best diode and audio transformer for a crystal radio, and a way to measure diode saturation current: 10/02/99;  08/22/02 Low-loss Impedance matching for magnetic and piezo-electric headphones, measurements on several audio transformers, and a transformer loss measurement method: 10/22/99;  03/30/08 A Crystal Radio Diode Detector Simulation using SPICE: 01/02/00;  11/23/01 Diode Voltage vs Current Curves:  Does an Actual Knee Voltage really Exist?: 01/08/00;  05/25/00 https://web.archive.org/web/20140810112324/http://bentongue.com/xtalset/xtalset.html[06.08.2019 20:25:32]

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Crystal radio set design and optimization with measurements on diodes, audio transformers, headphones, inductors, variable capacitors

Crystal Radio Diode Detector Power Loss with Current with Voltage Waveforms, as Determined from a SPICE Simulation: 02/13/00;  11/25/01 Build the Diode Detector Bias Box: a simple and easy way to determine if one's diode is optimum for weak signal reception, or should have a higher or lower axis-crossing resistance (0.026*n/Is): 03/30/00;  01/24/07 A New Diode Detector Equivalent Circuit, with a Discussion of the Linear to Square Law Crossover Point: the signal level at which the detector is functioning midway between linear and square-law operation: 04/04/00;  10/27/2002 A Procedure for Measuring the Sensitivity (Insertion Power Loss), Selectivity and Input and Output Impedance of a Crystal Radio: 07/21/00;  04/10/2003 Directivity of the Inverted L Antenna with speculation as to why it Occurs and how it might be enhanced: 07/29/00;  11/20/2005 How to Measure the Electric to Acoustic Transduction Power Loss of Magnetic and Ceramic Earphone Elements, with Measurements of some Headphone Receiver Elements: 08/30/00;  10/28/2004 A Zero Loss, Unilateral 'Ideal' Audio Transformer Simulator plus... This device makes it very easy to determine the optimum audio transformer input and output resistances for any diode/headphone combination. No test equipment necessary: 01/05/01;  01/17/2010 Quantitative insights into Diode Detector Operation derived from Simulation in SPICE, and some Interesting new Equations relating diode SPICE parameters to weak signal sensitivity: 4/10/2001;  12/07/2008 A Procedure for Measuring the Saturation Current Is, and Ideality Factor n, of a Diode along with Measurements on various diodes: 03/28/01;  02/10/2004 New ways to Increase Diode Detector Sensitivity to Weak Signals, and a way to determine if a diode detector is operating above or below its linear-to-square-law crossover point: 04/10/01;  11/29/2006 Get 3 dB More Output for Greater Volume on Strong Stations plus...: 07/09/01;  04/06/07 An explanation of how the "Mystery Crystal Radio" works: 08/11/01;  12/29/02 How to Measure the Impedance of an AM Band Antenna-Ground System, what one can do with the results, along with some measurements: 11/24/01;  04/16/2004 Design, construction and measurement of a single-tuned crystal radio set using a twovalue inductor, along with a discussion of the cause of 'hash', short-wave ghost-signal and spurious FM reception. A way is presented to determine if the signal operating the detector is above or below its linear-to-square-law crossover point: 02/07/2002;  08/20/2006 How to Make a Very Efficient Double-Tuned, Four-Band, MW Crystal Radio Set using two Version 'b' Single-Tuned, Four-Band, MW Crystal Sets 02/07/2002;  07/27/2002 Sensitivity and selectivity issues in crystal radio sets including diode problems; measurements of the Q of variable and fixed capacitors, RF loss in slide switches and loss tangent of various dielectrics: 03/25/2002;  06/10/2008 A new approach to amplifying the output of a crystal radio set, using energy extracted from the RF carrier to power a micro-power IC to drive headphones or a speaker: 07/04/2002;  02/25/2003 Highly sensitive and selective single-tuned four-band crystal radio set using a new contra wound dual-value inductor, and having a 'sharp selectivity setting'; along with a way to measure the unloaded Q of an L/C resonator: 02/10/2003;  10/23/2006 Measurement of the Sensitivity of a Crystal Radio Set when tuned to a Weak Fixed Signal, as a function of the Parameters of the Detector Diode; including Output Measurements on 15 diode types: 08/14/2003;  08/19/2006

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Crystal radio set design and optimization with measurements on diodes, audio transformers, headphones, inductors, variable capacitors

How to Reduce Diode Detector Weak-Signal Insertion Power Loss to Less than that Possible when the Input is Impedance Matched  Originally released as Article #15, later withdrawn.  Republished as Article #28: 03/04/05 About Maximizing the Q of Solenoid Inductors that use Ferrite Rod Cores, including charts of Magnetic flux density and lines, with some actual Q and inductance measurements: 10/07/06, 01/07/08

Return to the Front Page of the Site 020814

First published: 10 Jul 1999;  Revised: 01/06/10

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Crystal Radio Set Design Technical Help http://www.bentongue.com/xtalset/0def_exp/0def_exp.htmlGo

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Practical design considerations, helpful definitions of terms and useful explanations of some concepts used in this Site By Ben H. Tongue 

1.  An explanation as to why some diodes that work well in a broadcast band crystal set cause low sensitivity and selectivity when used at Short Waves:  The parasitic (approximately fixed) series resistance Rs of a diode is in series with the parallel active elements. The nonlinear active elements are the junction resistance Rj, which is a function of current through the diode, and the junction capacitance Cj, which is a function of the voltage across it.

The nonlinear junction resistance effect is what we use to get detection. The nonlinear capacitance effect is used when the diode is designed to be a voltage variable capacitor (a varactor diode). The parasitic series resistance of some 1N34 diodes can be pretty high, and in series with the junction capacitance, make that capacitance have a rather low Q at high frequencies.  This capacitance is, in a crystal radio set, effectively in parallel with the RF tank. The tank usually has a small value tuning capacitor itself, so the overall tank circuit Q is reduced at high frequencies.  This is the main reason why diodes having large values for Rs and CJ perform poorly at high frequencies. 

2.  An explanation of the meaning and use of dB and dBm:  In the acronym dBm, "d" means one-tenth.  "B" refers to the Bel and is named after Alexander Graham Bell.  The Bel is used to express the ratio of two powers, say (Output Power)/(Input Power).  Let's call this power ratio "(pr)".  Mathematically, a power ratio, expressed in Bels, is equal to the logarithm of the ratio of the two powers.  B=log (pr).  If the two powers are equal, the power ratio expressed in Bels is 0 B.  This is because the log of one is zero.  Another illustration:  Assume that the power ratio is twenty. (Pr)=20.  The logarithm of 20 is about 1.3. This power ratio in Bels is 1.3 B.  One decibel is equal to 0.1 Bel.  That is, 10 dB=1 B.  If we express the two power ratios mentioned above (1 and 20) in dB, we get 0 dB and about 13 dB. So far, we have seen that the decibel is used to express the ratio of two powers, it is not a measure of a power level itself.  A convenient way to express an actual power level using dB is to use a standard implied reference power for one of the powers.  dBW does this.  It expresses the ratio of a power to the reference power (One Watt in this case).  dBm uses a reference power of one milliwatt.  A power level of, say 100 milliwatts, can be said to be a power level of +20 dBm (twenty dB above one milliwatt).  Why?  (100 milliwatts)/(1 milliwatt)=100.  The logarithm of 100 is 2.  10 times 2 equals 20. The convenient thing about using dB comes from a property of logarithms:  The logarithm of the product of two numbers is equal to the sum of the logarithm of each number, taken separately.  An illustration:  If one has a power source of, say 2.5 mW and amplifies it through an amplifier having a

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Crystal Radio Set Design Technical Help

power gain of, say 80 times, the output power is 2.5 X 80=200 mW.  2.5 mW expressed in dBm is +4 about dBm.  A power gain of 80 times is about +19 dB.  The output power is 4+19=+23 dBm.

3.  Maximum Available Power:  If one has a voltage source Vs with an inaccessible internal resistance Rs, the load resistance to which the most power (Pa) can be delivered is equal to Rs.  Pa is called the 'maximum available power' from the  source Vs, Rs.  Any load resistance other than one equal to the source resistance, Rs, will absorb less power.  This applies whether the voltage is DC or AC (RMS).  The formula for power absorbed in a resistance is "voltage-squared divided by resistance".  In the impedance matched condition, because of the 2 to 1 voltage division between the source resistance and load resistance, one-half of the internal voltage Vs will be lost across the internal source resistance.  The other half will appear across the load resistance.  The actual power available to the load will be, as indicated in the preceding relation: Pa = [(Vs/2)^2]/Rs = (Vs^2)/(4*Rs).  Again, in the impedance matched condition, the total power delivered to the series combination of source and load resistance is divided up into two halves.  One half is unavoidably lost in the internal source resistance.  The other half is delivered as "useful output power" to the load resistance. The 'maximum available power' approach is useful when measuring the insertion power-loss of twoport devices such as transformers, amplifiers and crystal radio sets, which may not exhibit an input or output impedance that is matched to the power source.  The input impedance may be, in fact a combination of resistive and reactive components.  If the Vs,Rs source is connected to a resistive load (Ro) of value equal to Rs ohms, it will receive and dissipate a power of Pa Watts.  This is the maximum available power from the Vs, Rs source, so we can say we have a 'no loss' situation.  Now, assume that a transformer or other two-port device is inserted between the Vs,Rs source and Ro, and that an output voltage Vo is developed across Ro.  The output power is (Vo^2)/Ro.  The 'insertion power loss' can now be calculated.  It is: 10*log (output power)/(maximum available input power) dB.  After substituting terms, the equation becomes:  Insertion power loss =10*log [(Vo/Vs)^2)*(4*Rs/Ro)] dB. If the input voltage is referred to by its peak value (Vsp) as it is in a SPICE simulation, instead of by its RMS value, the equation changes.  The RMS voltage of a sine wave is equal to the peak value of that wave divided by the "square root of 2".  Since the power equation squares the voltage, the equation for the 'available input power' changes to Pa = (Vsp^2)/(8Rs).

4.  Diode Saturation Current and Ideality Factor:  Saturation current is abbreviated as Is in all of these articles.  Assume that one connects a DC voltage source to a diode with the polarity of the voltage source such as to bias the diode in the back direction.  Increase the voltage from zero.  If the diode obeys the classic Shockley ideal equation exactly, the current will start increasing, but the increase will flatten out to a value called the saturation current as the voltage is further increased.  That is, as the voltage is increased, the current will asymptotically approach the saturation current for that diode.  A real world diode has several mechanisms that cause the current to actually keep increasing somewhat and not flatten out as the back direction voltage is further increased.  Diode manufacturers characterize this as reverse breakdown and specify that the back current will be less than a specified value, say 10 uA at a specified voltage, say 30 V, called the reverse breakdown voltage.  BTW there are other causes of excessive reverse current that are collectively referred to as reverse bias excess leakage current.  Some diodes have a sharp, controlled increase in reverse current at a specified voltage.  These diodes are called Zener diodes. Diode Saturation Current is a very important SPICE parameter that, along with the diode Ideality Factor n, determines the actual diode current when it is forward biased by at particular DC Voltage.  Id=Is*(e^(Vd/(0.026*n)-1) at room temperature.  This expression ignores the effect of the parasitic series resistance of the diode because it has little effect on the operation of crystal radio sets at the low currents usually encountered.  Here Id is the diode current, e is the base of the natural logarithms (2.7183...),  ^ means raise the preceding symbol to the power of the expression that follows (Sometimes e^ is written 'exp'), * means multiply the preceding and following symbols, VD is the voltage across the diode and n equals the "Ideality factor" of the diode.  At low signal levels, most detector diodes have an n of between 1.05 and 1.2).  The lower the value of n, the higher will be the weak signal sensitivity.  One can see that Is is a scaling factor for the actual curve generated by the factor (e^(VD/(0.026*n)-1). Diode ideality factor (n):  The value of n affects the low signal-level sensitivity of a diode detector and https://web.archive.org/web/20150103225019/http://www.bentongue.com/xtalset/0def_exp/0def_exp.html[06.08.2019 19:47:32]

Crystal Radio Set Design Technical Help

its RF and audio resistance values.  n can vary between 1.0 and 2.0.  The higher the value of n, the worse the low signal level detector sensitivity.  The low signal level RF and audio resistances of a diode detector vary directly with the value of n.  Schottky diodes usually have a value of n between 1.03 and 1.10.  Good germanium diodes have an n of about 1.07 to 1.14 when detecting weak signals.  Silicon pn junction diodes such as the 1N914 have values of n of about 1.8 at low currents and therefore have a lower potential sensitivity as diode detectors than Schottky and germanium point contact diodes.  The value of n in Schottky diodes seems to be approximately constant over the full range of currents and voltages encountered in crystal radio set operation, but varies with diode current in silicon p-n junction and germanium point contact diodes.  A way of thinking about n is to consider it as a factor that effectively reduces the applied signal voltage to a diode detector compared to the case of using an ideal diode having an n of 1.0.  Less applied signal, of course, results in less detected output. Here are a few bits of information relative to diodes: Typically, if a diode is biased at 0.0282*n volts in the forward direction, it will pass a current of 2 times its Is.  If it is biased at 0.0182*n volts in the reverse direction, it will pass a current of 0.5 times its Is.  If a diode is biased at 0.0616*n volts in the forward direction, it will pass a current of 10 times its Is.  If it is biased at -0.0592*n volts, it will pass a current of -0.9 times its Is. These values are predicted from the classic Shockley equation.  In the real world, reverse current can depart substantially from values predicted by the equation because of effects not modeled (the reverse current becomes higher).  Gold bonded germanium diodes usually depart somewhat from the predicted values when operated in the forward direction.  The effect appears as an increase of Is when measurements are made at currents above about 6 times the low-current Is. Values of Is and n determine the location of the apparent 'knee" on a linear graph of the diode forward current vs. forward voltage. See Article #7.  An easy way to estimate the approximate value of Is can be found in Article #4, section 2.  A method of measuring Is and n is given in Article #16. If one connects two identical diodes in parallel, the combo will behave as a single diode having twice the Is, and the same n as one of them.  If one connects two identical diodes in series, the combo will behave as a single diode having twice the n and the same Is as one of them.  This connection results in a diode having 3 dB less potential weak signal output than one of the diodes by itself.

5.  Explanation of why, in a diode detector, and by how much, the RF input resistance and audio output resistances change as a function of input signal power.  Refer to the second schematic in Article #1. The output load will be considered to be a resistor connected across the "Audio Output" terminals; call it Rl. No audio transformer is involved in the first part of this discussion.  Consider first, a diode detector that is well impedance-matched both at its input and its output when driven by a very low power RF input signal.   There will exist an appreciable power loss in the detector.  The input and output resistances of the diode detector will approximately equal each other and approach Rd (diode axis-crossing resistance)= 0.026*n/Is.  See part 3 above for a definition of terms.  For this illustration, let the diode have an Is of 38 nA and an n of 1.02.  Rd will be 700k Ohms.  This well impedance-matched condition will hold if the input power is raised from a low value, but only up to a point.  After that , the match will start to deteriorate.  At an input power about 15 dB above that of the square-law-linear crossover point, the match will have deteriorated to a VSWR of about 1.5:1  (VSWR = Voltage Standing Wave Ratio.).  A further increase of input signal power will result in a further increase of VSWR.  This means that the input and output resistances of the detector have changed from their previously well matched values.  The input resistance of the diode detector decreased from the value obtained in the well matched low power situation.  The output resistance increased.  The reason for this change is that a new law now governs input and output resistance when a diode detector is operated at a high enough power level to result in a low detector insertion power loss.  It now operates as a peak detector.  The rule here is that the CW RF input resistance of a diode peak-detector approaches ½ the value of its output load resistance.  Also, the audio output resistance approaches 2 times the value of the input AC source resistance.  Further, since the detector is now a peak detector, the DC output voltage approaches the "square root of 2" times larger than of the applied input RF RMS voltage. (It's equal to the peak value of that voltage).  These existence of these relationships is necessary so that in an ideal peak detector, the output power will equal the input power (No free lunch).  Summary: Output DC voltage equals sqrt2 times input RMS voltage.  Since the output power must https://web.archive.org/web/20150103225019/http://www.bentongue.com/xtalset/0def_exp/0def_exp.html[06.08.2019 19:47:32]

Crystal Radio Set Design Technical Help

equal the input power, and power equals voltage squared divided by resistance, the output load resistance must equal two times the source resistance, assuming impedance matched conditions prevail.  If we were to adjust the input RF source resistance to, say 495k ohms (reduce it by sqrt2) and the output load resistance to 990k ohms (increase it by sqrt2) by changing the input and output impedance transformation ratios, the insertion loss would become even lower than before the change and the input and output impedance matches would be very much improved (remember we are now dealing with high signal levels).  Note: It is assumed here that the peak reverse voltage applied to the diode when the signal is strong does not approach its peak reverse breakdown voltage rating. A good compromise impedance match, from one point of view, occurs if one sets the RF source resistance to 0.794*Rd and the audio load resistance to 1.26*Rd (Rd=axis-crossing resistance of the diode).  With this setup, theoretically, the impedance match at both input and output remains very good over the range of signals from barely readable to strong enough to produce close to peak detection.  A measure of impedance match is "Voltage Reflection Coefficient", and in this case it is always better than 18 dB (VSWR better than 1.3).  Excess insertion loss is less than 1/3 dB and selectivity is largely independent of the signal level.  This situation can be attained in a real-world crystal set using an audio transformer if one connects a parallel RC (a "benny") in series with the transformer primary.  The resistor plus the DC resistance of the transformer primary is adjusted to equal the average AC resistance looking into the transformer primary. This combination approximates the effect of a straight resistive load, as used in the discussion above.  To determine the average AC input resistance of the audio transformer (when loaded by phones), multiply its step-up impedance ratio by the average AC impedance of the phones.  See Article #2 for a method of determining the average AC resistance of phones. In the practical case of a real-world crystal set not using a "benny", the load the diode sees has a DC resistance component lower than its AC impedance. This unbalanced condition is worse when a transformer is used, as compared with phones only.  In this case, when going from reception of a weak to a strong signal, bad things start happening to selectivity:  As the RF signal strength starts increasing, the rectified DC current in the diode starts increasing faster than it does in the condition using a "benny". This causes the diode input and output resistances to fall. The result is a loaded down tank having reduced selectivity.  The use a "benny" prevents this, among other things from happening. Information presented in Article #28 shows that, if the diode load resistance is made equal to Rd and the RF source resistance is made equal to Rd/2, the weak signal output of the detector will be about 2 dB greater than if both ports are impedance-matched!  There is little benefit when strong signals are received, since both input and output ports become impedance matched. Here is an interesting conceptual view of a high signal level diode detector circuit:  Assume that it is driven with a sufficiently high level sine wave voltage so it operates in its peak detection mode, and is loaded with a parallel RC of a sufficiently long time const ant.  This detector may be thought of as a low loss impedance transformer with a two-to-one impedance step up from input to output, BUT having an AC input and a DC output, instead of the usual AC input and output.   The DC output power will approximately equal the AC input power and the DC output voltage will be about sqrt 2 times the RMS AC input voltage.

5A.  A comparison of conventional half-wave and half-wave voltage-doubling detectors:  Here is some info that may be of interest regarding conventional half-wave detectors vs. voltage doubling half-wave detectors when each is terminated with an output load of Ro. For illustration purposes we will assume the input voltage to the detector to be 1.0 volt RMS. The RF input resistance of the detector will be designated as Ri. All diodes have the same Is and n. It is assumed that good diodes such as a 5082-2835 Schottky, ITT FO-215 germanium or other are used. The info relates to the RF input resistance of detectors (it has a large effect upon selectivity) and their output audio resistance. See Point 4 in this Article for info on diode Is and n. A high input power level is defined as one that is high compared to that at the LSLCP of the detector. A low input power level is defined as on that is low compared to that at the LSLCP of the detector. See "Quick Summary" in Article #15 for info on LSLCP.

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Crystal Radio Set Design Technical Help

1) Conventional half-wave detector operating at a high input signal power level: The detector, in this case, operates as a peak detector. Since it is a passive device, its output power will approximately equal its input power, under impedance-matched conditions. The output DC voltage will approach sqrt2 times the input RMS voltage, since the peak value of a sine wave is sqrt2 times its RMS value. For the input power, (1.0^2)/Ri, to equal the output power, [(1.0*sqrt2)^2]/Ro, the input RF resistance (Ri) must equal 1/2 Ro. That is, Ri=Ro/2. This illustrates the direct interaction between the RF input resistance and output audio resistive load. At high input power levels selectivity drops when the resistive audio output load value is lowered.  The audio output resistance of the detector approaches 2 times the RF source resistance driving it. If the diode were an ideal diode, the word "approximately" should be eliminated, and "approaches" should be changed to "becomes" . 2) Conventional half-wave detector operating at a low input signal power level: The detector, in this case, does not operate as a peak detector, and exhibits significant power loss. At low input signal power levels Ri approaches 0.026*n/Is ohms (diode axis-crossing resistance) and becomes independent of the value of Ro. The audio output resistance of the detector approaches the same value as the axis-crossing resistance (see above). 3) Half-wave voltage doubling detector operating at a high input signal power level: The detector, in this case, operates as a peak detector. Since it is a passive device, its output power will approximately equal its input power, under impedance-matched conditions. The output DC voltage will approach 2.0*sqrt2 times the input RMS voltage, since the peak of a 1.0 volt RMS sine wave is sqrt2 times its RMS value. For the input power (1.0^2)/Ri to equal the output power [(1.0*2*sqrt2)^2]/Ro, the input RF resistance (Ri) must equal 1/8 Ro. That is, Ri=Ro/8. This illustrates the direct interaction between the RF input resistance and output audio resistive load. At high input power levels selectivity drops substantially if the output resistive audio load value is lowered. The audio output resistance of the detector approaches 8 times the RF source resistance driving it. This fact is seldom recognized and it may be the cause of some of the problems encountered by those experimenting with doublers. 4) Half-wave voltage-doubler operating at a low input signal power level: The detector, in this case, does not operate as a peak detector, and it has significant power loss. At low input signal power levels Ri approaches (0.026*n/Is)/2 ohms and becomes independent of the value of Ro. The audio output resistance of the detector approaches twice the axis-crossing resistance of the diode. 5) Summary:  At high input power levels, and with both input and output matched, power loss in both half wave and half wave voltage doubling detectors approaches zero dB.  Sound volume should be the same with either detector.  At low input power levels both detectors exhibit substantial power loss.  I believe, but have not proven, that at low input power levels the doubler has a higher power loss than the straight half wave detector, and should deliver less volume.

6.  Some misconceptions regarding Impedance matching and Crystal Radio Sets:  To understand the importance of impedance matching, one must first accept the concept of power.  A radio station accepts power from the mains and converts some of it to RF power which is radiated into space.  This power leaves the transmitting antenna at the speed of light and spreads out as it goes away from the antenna.  One can prove that power is radiated by substituting a LED diode for the regular diode, getting physically close enough to the station and then tuning it in.  The LED will light up (give off light power), showing that some power is being broadcast and that it can be picked up. Now back at home, if one tunes in the station one gets sound in the headphones.  What activates one's hearing system is the power of the perceived sound.  BTW, if one gets too much sound power in the ear for a long enough time, the power can be strong enough to break off some of the hair cells in the inner ear and reduce one's hearing sensitivity forever.  The theoretical best one can do with a crystal radio set setup is the following:  (1) Use an antenna-ground system to pick up as much as possible of the RF power passing through the air in its vicinity .  In general, a higher antenna will pick up more power from the passing RF waves than will a lower one.  (2) Convert the intelligence carrying AM sideband RF power into

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Crystal Radio Set Design Technical Help

audio electrical power.  (3) Convert the electrical audio power into sound power and get that power  into the ear. There are power losses at each of the three steps and our job is to minimize them in order to get as much of the sideband RF power passing through the vicinity of the antenna (capture area)  changed into audio power for our ears.  We want all of the "available power" at the antenna-ground system to be absorbed into the crystal radio set then  passed on through it to our headphones as sound.  However, some of it will be unavoidably lost in the RF tuned circuit.  If the input impedance of the crystal radio set is not correctly matched to the impedance of the antenna, some of the RF power hitting the input to the crystal radio set will be reflected back to the antenna-ground system and be lost. An impedance-matched condition occurs when the resistance component of the input impedance of the crystal radio set equals the source resistance component of the impedance of the antenna-ground system.  Also, the reactive (inductive or capacitive) component of the impedance of the antenna-ground system must see an opposite reactive (capacitive or inductive) impedance in order to be canceled out.  In the impedance-matched condition, all of the maximum available power (See section on "Maximum Available Power" above) intercepted by the antenna-ground system is made available for use in the crystal radio set and none is reflected back towards the antenna to be lost. Now we are at the point where confusion often exists:  The voltage concept vs. the power concept.  Let's assume that the diode detector has a RF input resistance of 90,000 Ohms.  Assume that the antennaloaded resonant resistance of the tuned circuit driving it is 10,000 Ohms.  If one uses voltage concepts only, one might think that this represents a low loss condition.  NOT SO!  After all,  9/10 of the actual source voltage is actually applied to the detector.  If one impedance matches the 10k ohm source RF resistance to the diode 90k ohm RF resistance via RF impedance step-up transformation (maybe connecting the antenna to a tap on the tuned circuit, and leaving the diode on the top), good things happen.  (We will assume here that, in the impedance transformation to follow, the ratio of loaded-tounloaded Q of the tuned circuits is not changed.)   For an impedance match, the tuned circuit resonant resistance should be transformed up by 9 times.  If this was done by a separate transformer (for ease of understanding) it would have a turns ratio of 1:3, stepping up the equivalent source voltage by 3 times and changing the equivalent source resistance to 90,000 Ohms.  What now?  Before matching, the diode got 9/10 of the source voltage applied to it.  Now it gets 1/2 the new equivalent source voltage (remember the equivalent voltage is 3 times the original source internal voltage).  The 1/2 comes from the 2:1 voltage division between the resistance of the equivalent source of 90,000 Ohms and the detector input resistance of 90,000 Ohms.  The ratio of the new detector voltage to the old  is: 3 times 1/2 divided by 0.9 = 1.67 times.  This equates to a 4.44 dB increase in power applied to the detector.  If the input signal to the detector is so weak that the detector is operating in the square-law region, the audio output power  will increase by 8.88 dB!  This is about a doubling of volume.

6A.   A Short tutorial on some aspects of audio transformer utilization in crystal sets. See Section 3 of Article 14 here

7.  Caution to observe when cutting the leads of a glass Agilent 5082-2835 Schottky diode (or any other glass diode):  When it is necessary to cut the leads of a glass packaged diode close to the glass body, use a tool that gives a scissors type of cut.  Diagonal cutters give a sudden physical shock to the diode that can damage its electrical performance.  This physical shock is greater than one might expect because of the use of plated steel instead of  more ductile copper wire. Steel is used, in part, because of its lower heat conductivity, to reduce the possibility of heat damage during soldering.

8.  Several different ways to look at a diode detector: A diode detector can be thought of as a mixer, if one thinks of its input signal as consisting of two identical signals of equal power, in phase with each other.  It is well known that if a common AM mixer is fed with two signals of frequencies f1 and f2 Hz, most of the output it generates will consist of the second harmonic of each signal and two more signals at other frequencies.  One is at the sum frequency (f1+f2) Hz and one at the difference frequency (f1-f2).  Additional mixer products can be generated, but

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Crystal Radio Set Design Technical Help

they will be weaker than those mentioned and will be neglected in this discussion.  In the case of an AM diode detector, we may consider that its input signal of power P Watts is in reality the sum of two equal in-phase signals, each of power P/2 and that there will be four output components, as stated above. They are: The two second harmonic components (both of the same frequency and phase). The sum frequency component (f1+f2) Hz, which will be of the same frequency and phase as the second harmonic components since f1=f2. The difference frequency component (f1-f2) at a frequency of zero Hz. If we filter out the harmonic and sum components as well as the two original signals from the output in a non-dissipative manner, only the zero Hz signal will remain; and we call it the detected DC output. A diode detector can be thought of as a "Black Box".  If the DC output impedance of the detector is matched to its load resistor and an AC signal power source of P Watts 'available power' is impedance matched to the input AC impedance of the diode detector, the DC output power can closely approach the 'available power, P watts', from the AC source.  This gives us another way to look at a detector.  It can be considered to be a "Black Box" that changes incident CW AC power of frequency 'f' Hz into output power of frequency zero Hz (DC).  This is called the detected DC output.  If the input power is large enough, the power loss in the black box can approach zero. Reduced input power levels result in an increased insertion power loss in the AC to DC power conversion of the "black box).

9.  Using surface mount components in crystal radio sets:  A convenient way to connect to the tiny leads of small surface-mount diode and IC devices is to first solder them to a "Surfboard".  Pigtail leads can them be soldered through holes drilled in the Surfboard conducting races for connection to a circuit. A surface mount device such as the OPA-349 integrated circuit (Eight lead SOIC package) can be soldered to a surfboard such as that manufactured by Capital Advanced Technologies: http://www.capitaladvanced.com .  Their Surfboards #9081 or #9082 are suitable and are available from various distributors such as Alltronics, Digi-Key, etc. Surface mount diodes manufactured using the SOT-23 package can be handled using Surfboard #6103.  Diodes using the smaller SOT-323 package can be handled using Surfboard #330003.  This includes many Agilent surface mount diodes useful in crystal radio sets.  Packages containing multiple diodes exist that use the SOT-363 six lead package.  They can be handled using Surfboard #330006.  Agilent produces many of their Schottky diodes in dual, triple and quad form in the SOT-363 package. It is recommended that anyone considering using Surfboards visit the above mentioned Website and read "Application Notes" and the "How-to Index".

10.  How to modify the tone quality delivered by headphones:  It is interesting to note that driving magnetic headphone elements with a high source resistance tends to improve the treble (making it sound brighter or tinny) and reduce the bass response, compared to the response when the AC source resistance matches the effective impedance of the elements.  Conversely, driving the headphone elements from a low resistance source tends to roll off the treble (making it sound dull) and relatively speaking, increase the bass.  With piezo ceramic or crystal elements, a high source resistance tends to reduce the treble and improve the bass response, compared to the response where the source resistance matches the effective impedance of the elements.  A low source resistance tends to reduce the bass and emphasize the treble.  Some piezo elements sound scratchy.  This condition can be minimized by driving the elements from a lower resistance source. Here are some practical experimental ways to vary the audio source resistance of a crystal radio set when receiving weak-to-medium-strength signals.  A medium strength signal is defined as one at the crossover point between linear to square law operation (LSLCP).  See Figs. 2 & 3 in Article #15A. See the last paragraph of Article #17 for a way to determine if a diode detector is operating below or above its LSLCP.

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Crystal Radio Set Design Technical Help

Change the diode to one having a lower saturation current, such as from a germanium diode (1N34A) to one or several paralleled Schottky diodes such as the Agilent 5082-2835.  Schottky diodes described as "zero bias detectors' have a high saturation current and are not suitable for most crystal radio set use.  Schottky diodes described as "power rectifiers' usually have a high saturation current as well as a high junction capacitance.  A high diode junction capacitance will reduce treble response.  Too large a diode RF bypass capacitor in the crystal radio set can also reduce treble response.  A side benefit from a change to a diode having a lower saturation current value, on some crystal radio sets is an increase in selectivity.  This is because the RF load resistance presented by the diode to the tank is raised when the diode saturation current value is reduced.  This reduced loading raises the tank Q and hence, increases selectivity. Use an audio transformer between the detector output and the phones.  A smaller step-down transformer impedance transformation ratio will raise the transformed diode source resistance seen by the phones.  A larger ratio will decrease it. If the headphone elements are in series, reconnecting them in parallel will reduce their impedance to 1/4 the previous value.  This has the same effect as increasing the effective source resistance driving the headphones.  If they are in parallel, series connecting them has the effect of decreasing the effective source resistance. Audio transformers having too low a shunt inductance will reduce bass response.  When using magnetic headphone elements, this can be partially compensated for by connecting the transformer to the headphones using a suitable series-connected capacitor. Refer to Articles #2, #3,#5 and #14 for more info.  For a convenient way to vary the audio impedance driving the phones, consider the 'BT-Ulti-Match' described in Part 4 of Article #5. Note: Bullet points 2 and 3 will also change tone quality when receiving strong signals.

11. Long term resistance drift and frequency dependence of the AC resistance of low power resistors, etc:  From my early experience in the manufacturing of Blonder-Tongue products, the following is some insight relative to run-of -the-mill commercial carbon-composition resistors that we used: The process used by the resistor manufacturer is an important factor in the determination of long term resistance drift. Allen-Bradley (A-B) used their 'hot-mold' process, producing a more dense product then did the other manufacturers, as far as I know. The value of this carbon comp. resistor drifts the least, as a rule. Stackpole composition. resistors used their 'cold-mold' process and seem to drift more than do the A-B units. Composition carbon resistors mfg. by the Speer company, using their 'cold-mold' process drift more than the Stackpole resistors, as a rule. The IRC resistors that look like carbon comp. units actually are made by another process. They are called metallized resistors. My impression is that their drift is similar to the of Stackpole resistors. I have found that the IRC resistors usually generate much more low frequency noise when passing a DC current than the others. It seems, as a general rule, that the high value resistors drift in value more, over time, than the low value ones. The brand of resistor may be guessed by examining the smoothness and shininess of its surface finish, and looking at each end of the resistor to see where the wire exits. Allen Bradley resistors look the best. They have bright color code colors and a smooth shiny finish. At the wire exit point from the body one can usually see the appearance of a small shiny ring embedded in the plastic. Actually, this is part of the lead, shaped to be the contact electrode. Stackpole resistors look next best. They have somewhat duller colors on the color code and the surface is somewhat rougher and less shiny. The wires exit cleanly from the end of the resistor, no ring is visible. The Speer resistors have the dullest color code colors and a rougher surface than the Stackpole's. They usually look as if they have been wax impregnated. At the axial exit points from the body, a small copper colored dot may be seen next to the wire lead. This is actually the end of the lead, which was folded over and back on itself to form the electrode. The IRC socalled carbon comp. resistors can be identified by the visible 'mold-flash' marks on the body and ends. The colors are good, but the body is rough. Their end surfaces are slightly convex, not planar as in the case of the other resistors. Remember, these resistors usually made spec. when new, passed incoming inspection and standard aging tests. Unfortunately, no aging tests could be made that covered the span of many decades. https://web.archive.org/web/20150103225019/http://www.bentongue.com/xtalset/0def_exp/0def_exp.html[06.08.2019 19:47:32]

Crystal Radio Set Design Technical Help

It is interesting to note that the best resistors, from a long term resistance drift point of view turn out to be the A-B units. They also cost the most. The Speer units cost the least and the Stackpole's were in between. Ohmite carbon comp resistors I have seen looked like A-B units and were probably made by them. A fact of interest that some may not know is this: The AC resistance of carbon composition resistors, and film resistors, to a much lesser degree, decrease with increasing frequency (the Boella Effect). This effect is strongest in high value resistors, above, say, 22k ohms and above 50 MHz (film resistors). The effect is noticeable in 500k and 1 meg units at lower frequencies. Low value resistors having short leads and resistances in the mid 10s to mid hundreds of ohms are quite free of this effect up through many hundreds of MHz.  A typical graph of the ratio of AC-to-DC resistance vs frequency, of various values of conventional commercial axial-lead carbon film type resistors, taken from a Brell Components catalog is here . A chart providing similar info on carbon composition resistors, taken from the Radiotron Designer's Handbook, Fourth Edition, page 189 is here. An advantage of the old carbon comp resistors over the newer carbon-film and metal-film resistors is the fact that they can withstand much greater momentary power overloads. After being out of the carbon comp resistor business for many years, Stackpole re-entered it a couple of years ago for this very reason. For the same power rating, they usually have a higher voltage rating.

12. The effects from using the contra wound dual-value inductor configuration in crystal sets as compared to using a conventionally wound inductor, both using capacitive tuning Some quick facts: Crystal sets using a conventional single-valued tank coil usually suffer from poor selectivity and sensitivity at the high end of the BC band. Use of both connections of a contra wound dual-value inductor enables the achievement of much higher selectivity and sensitivity at the high end of the BC band (series connection for the low half and parallel for the high half of the BC band). There will be some small reduction in tank Q in the lower half of the BC band.  One reason is that distributed capacity is greater in the series-connected contra-coil than in the conventional solenoid (the close-space adjacent ends of the contra-coil windings have 1/2 the tank voltage across them). Tank Q at the high end of the BC band is noticeably improved. It is assumed that comparisons between conventional and contra wound inductors use coils having the same physical dimensions and wire specifications.  The inductance of the conventional solenoid is assumed to be about the same as that of the series-connected contra-coil. See 'The contra wound tank inductor' in Part 3 of Article #26 and the paragraph after Figs. 2 and 3 in Article #29 for descriptions of two different contra wound configurations. Discussion: Let us divide the BC band geometrically into two halves: This gives us 520-943 kHz for the low band and 943-1710 kHz as the high band. Assume, for ease of understanding, that the tank inductor for the conventional approach has an inductance of 250 uH. Conventional 250 uH inductor: The whole BC band of 520-1710 kHz can be tuned by a capacitance varying from 374.7 to 34.65 pF. contra wound 250/62.5 uH inductor: The low band of 520-943 kHz can be tuned, using the 250 uH series connection, by a capacitance varying from 374.7 to 113.94 pF. The high band of 943-1710 can be tuned, using the 62.5 pF parallel connection, by a capacitance varying from 455.76 to 138.60 pF. For the purposes of this discussion, let us assume that antenna matching (see Part 2 of Article #22) is

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Crystal Radio Set Design Technical Help

always adjusted to reflect a fixed shunt resistance of 230k ohms for driving the diode, over the full BC band.  230k ohms is also the RF input resistance of an ITT FO-215 germanium diode when fed a signal power well below its linear-to-square law crossover-point (see Article #10, points 1, 2 and 3 below Fig.1 in Article #15, Article 17A and Article #22). This setting approximates that for minimum insertion power loss (see Article #28). Reduction of insertion power loss at the high end of the BC band (1720 kHz): The total tuning capacitance needed when tuning a conventional 250 uH inductor to 1710 kHz is 39.9 pF. The value needed, using a contra wound approach is 138.6 pF. One can derive, from data values in Figs. 1 - 4 in Article 28, that the Q of the common 365 pF, non-ceramic insulated variable capacitor (capacitor B), at 1710 kHz comes out as follows: If one uses a conventional 250 uH inductor tuned by 20 pF stray capacity with 14.65 pF more from the variable capacitor, the capacitor Q comes out at about 460. If one uses a contra wound inductor that has 62.5 uH inductance with the two windings in parallel, tuned by 20 pF stray capacity with 118.6 pF more from variable capacitor B, the Q comes out at about 1770, 3.5 times as great! This translates directly to greater sensitivity and selectivity when using the commonly available 365 pF capacitor. From Fig. 3 in Article #24 we can see that, at 1710 kHz, the Q of capacitor A, a ceramic-insulated, with silver plated plates capacitor manufactured by Radio Condenser Corporation, or its successor TRW, has a Q of 9800. This is much higher than that of capacitor B when using a conventional 250 uH inductor. Changing to a contra wound coil while using the easily available capacitor B goes a long way toward a goal of reducing the effect of the variable capacitor on tank Q and loss at the high end of the band. Less selectivity variation and less insertion power loss: Conventional inductor: The 3 dB down RF bandwidth will vary from 3.69 kHz at 520 kHz to 39.9 kHz at 1710 kHz, a variation of 11.6 times . contra wound inductor: The 3 dB down RF bandwidth will vary from 3.69 kHz at 520 kHz to 12.15 kHz at 943 kHz in the low band, and from 3.04 kHz at 943 kHz to 9.99 kHz at 1710 kHz in the high band, an overall variation of 4.00 times. This is about 1/4 of the variation experienced when using a conventional inductor. If greater selectivity is needed at the high end of the BC band when using a conventional inductor, antenna coupling must be reduced and/or the diode must be tapped down on the tank to raise the loaded Q. Either approach results in a greater insertion power loss and a weaker or inaudible signal to the phones when tuning stations near the high end of the BC band . The low inductance (parallel connection) of the contra wound inductor enables a 4 times reduction in bandwidth at 1710 kHz, compared to results with conventional inductor. This reduces the need to tap the diode down on the tank and re-match the antenna when one needs to increase selectivity, as mentioned above. Note: One could use two separate conventional non-coupled inductors, one of 250 uH and the other of 62.5 uH, instead of a contra wound configuration. This is not recommended because the Q of the 62.5 uH inductor will probably be less than that of the 250 uH unit unless it is made physically as large as the contra wound coil.and employs larger diameter wire. Also, when using the contra wound approach the hot end of the inductor, when the two coils are connected in parallel, can be in the center of the overall unit, with the outer wire ends of the assembly placed at ground potential. This reduces electric field coupled losses from end mounting brackets and surroundings. The inductances of the two connection configurations (parallel and series) of a contra wound coil will depend upon how closely spaced the two windings are placed, but, the ratio of the inductance of the series to that of the parallel connection always remains at 4 times no matter how far or close together the windings are placed. Remember that overall distributed capacity is greater when using the parallel connection in the low band. About 1-2 wire diameter spacing between the two windings is recommended.

13. Comments on audio distortion in diode detectors. There seems to be four main causes of audio distortion in diode detectors.

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Crystal Radio Set Design Technical Help

Square-law detection: Second-order audio distortion occurs when receiving weak signals. This type of distortion is usually not irritating to the ear. Distortion when the signal is strong: This type of distortion occurs when the DC load on the diode is very different from the average value of its AC load. This is usually the case when an audio transformer is used without load resistance correction. The remedy is to use a ”benny” to equalize the DC resistance of the diode load to equal that of its average AC load. See second paragraph of Part 2 in Article #1. This type of distortion also occurs when using a piezo earphone without an appropriate shunt resistor. Distortion from using a diode having too low a saturation current (high axis-crossing resistance). This usually occurs when receiving weak signals: The remedy is to modify the crystal set to raise its audio load impedance (change the audio transformer) to achieve better impedance matching to the diode. Another approach is to forward bias the diode to lower its axis-crossing resistance (raise its effective saturation current) to better impedance match the existing audio load. See Article #9. Another solution is to use a different diode having an axis-crossing resistance that more closely impedance matches its source and load. See Table #2, second column for the axiscrossing resistances of some diodes. Distortion when using a diode having a low reverse breakdown voltage and having a sharp knee at breakdown (usually a microwave diode).  The peak reverse voltage on a diode can approach twice the detected DC voltage. When a signal is strong enough to cause this to happen on the peaks of modulation, a large reverse current can be drawn (reverse current is normally low) that clips the peaks of the detected envelope causing audio distortion and a weaker detected signal. A remedy is to change to another type of diode or reduce the strength of received strong signals. See attenuators SW1 and SW2 in Fig. 5, in Article #22. Some measurements of saturation current and ideality factor values for about 15 diodes be found in Articles #16 and 27. A suggested definition for “strong” and “weak” signals: A diode detector may be considered entering the "strong signal" mode of operation if it is operating at a signal power level about 10 dB or more above its LSLCP (Linear to square law crossover point). One can estimate that the diode detector is entering the "weak signal" mode of operation if it is operating at a signal power level about 10 dB or more below its LSLCP. A discussion of LSLCP may be found in Section 1, Article #15. A discussion of diode operation at its LSLCP may be found at the end of Article #17. #0  Published: 04/25/00;  Last revision: 11/06/2007 061410

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Crystal Radio Set: Better sensitivity, selectivity and volume; less audio distortion http://www.bentongue.com/xtalset/1nlxtlsd/1nlxtlsd.html

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A New Way to look at Crystal Radio Design. Get Greater Sensitivity to very Weak Signals, and Greater Volume, less Audio Distortion and Improved Selectivity on Strong Signals By Ben H. Tongue 

Quick introduction: Greater sensitivity to very weak signals can be attained by lowering the RF signal power level (linearto-square law point, or LSC point) at which the detector changes from the linear to the square-law mode of operation (See Article #10, Figs. 3 & 4 and part #3 for an explanation of the LSC point).  This is accomplished by connecting the highest impedance point of the RF tuned circuit to a diode having the proper Saturation Current (See Article #15A).  The output resistance of the detector should be impedance matched to the headphones, usually by a low-loss audio transformer, for maximum sensitivity.  Greater volume, less audio distortion and improved selectivity can be attained on strong signals by properly impedance matching the RF source resistance to the RF input resistance of the detector and also matching the output resistance of the detector to the effective impedance of the headphones. The DC and audio AC loads on the detector should also be made equal. This analysis does not involve the analysis of diode instantaneous voltage and current wave-forms, input voltage, output voltage, diode turn-on voltage or tuned circuit peak-clipping.  This analysis does consider the detector to be a black box having a linear input RF resistance and a linear output resistance, is driven from an AC power source and delivers power to an output load.  These resistances are independent of input signal power at low power levels (somewhat below the LSC point) and depend only upon the characteristics of the diode.  At high input power levels (somewhat above the LSC point), the input resistance is still linear and depends primarily on the output load resistance.  The output resistance depends primarily on the source resistance.   1. THEORY A crystal radio may be thought of as the cascaded connection of several basic components. Antenna-ground

system:  Signal source  RF tuned circuit:  Provides selectivity and impedance matching between the resistance of the antenna-ground circuit and the RF input resistance of the diode detector.  This tuned circuit has some power loss. Diode detector:  Characterized as a black box that accepts RF input power and converts it to DC output power.  It has an RF input resistance, an audio output resistance and a power insertion loss (dB).  These three characteristics are interrelated with the RF Input power, RF source resistance driving the detector, audio load resistance and the parameters of the diode used.  https://web.archive.org/web/20150305092538/http://www.bentongue.com/xtalset/1nlxtlsd/1nlxtlsd.html[06.08.2019 19:49:03]

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Crystal Radio Set: Better sensitivity, selectivity and volume; less audio distortion

Output transformer:  To impedance transform the effective headphone impedance to that required by the diode.  Audio load:  Headphones, what else?  We will consider these components one at a time.  See Part 1 of Article #10 for an overall view of the way we will be looking at diode detector operation.  The Antenna and RF Tuned Circuit will be combined into three components.  V1 and R1 represent the antenna induced voltage and resistance, impedance transformed by the tuned circuits and antenna reactance to the series-connected values seen by the diode detector.  X1 represents the reactance of the tuned circuit(s) seen at its output terminals.  Its impedance is considered to be substantially zero at harmonics of the frequency to which it is tuned.  Its impedance is also substantially zero at DC and at Audio frequencies.  R2 represents all the losses in the tuned circuits at resonance, as seen by the diode.  This is not the conventional way of viewing the signal source for a detector. 

The Detector will be represented as follows: The LC tank assures that the input is effectively shorted to ground at DC and at audio frequencies as well as all RF frequencies except that to which it is tuned.  The output is effectively shorted to ground at RF by C1.

The Output Transformer circuit will be represented as shown below.  The purpose of R3 and C2 will be covered later.

We start out with the assumption of no losses in the tuned circuits.  This condition makes R2 equal to infinity, not a practical assumption of course, but it will simplify what follows.  The input circuit then reduces to a simple series connection of the parallel tuned circuit, impedance transformed antenna voltage, and a series resistance. This resistance includes the effects of radiation, antenna, lead-in and ground circuit resistance.  A simple transformation enables us to eliminate R2 entirely by combining its effects into a changed value for R1 and a new value for V1.  The new value for V1 is: V1new = V1old* (R2old/(R1old + R2old)).  The new value for R1 is: R1new = (R1old*R2old)/(R1old + R2old).  With

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Crystal Radio Set: Better sensitivity, selectivity and volume; less audio distortion

this transformation the new value for R2 is infinity, so it can be eliminated from the circuit.  Of course, the maximum available power from the new source 'V1new, R1new' is less than what was available from the original source 'V1old, R1old' by the amount that was dissipated in R2.  From now on, V1new and R1new will be referred to as V1 and R1.  The RF Source Voltage (V1) is assumed to be un modulated CW. The transformed V1 (RMS) and R1 represent a Power Source of available power Pa = (V1^2)/(4*R1).  This is the most power it can deliver to a load.  It is also sometimes called the "Incident Power".  For the load to absorb this power, the load itself must equal R1, and then it is called an 'Impedance Matched Load'.  Changing the impedance transformation in the tuned circuit(s) changes the values of V1 and R1.  This does not change the available power.  That is still (V1^2)/(4*R1).  As an illustration, if V1 is doubled, R1 must quadruple thus keeping the power the same. The approach we will use in this analysis is to minimize impedance mismatch power loss between the transformed antenna resistance and the diode detector input RF resistance as well as between the detector audio output resistance and the headphones.  We will show that the diode detector power Loss (DDPL), for very weak signal levels, can be minimized by using a diode with as low a Saturation Current (Is) as possible if all else is equal.  In addition, the lower the ideality factor (n) of the diode, the greater will be the sensitivity to weak signals.  The limitation here is that if a diode with a lower Is used, the required diode RF source and audio load resistances go up in value.  That limit is reached when the diode is connected to the top (the highest impedance point) of the tuned circuit.  The high frequency audio cutoff point may be reduced because of unavoidable winding capacitance in the audio output transformer acting against the required higher transformed headphone effective impedance. The most important diode parameters to consider for Xtal radio operation are saturation current 'Is' and 'n'.  They show up in the Shockley diode equation:  Id = Is*(exp((Vd-Id*Rs)/(0.026*n)) -1), at room temperature.  In crystal radio applications, the Id*Rs term may be neglected because it is usually much smaller than V.  The equation then becomes: Id=Is*(exp(Vd/(0.026*n))-1).        (1) This equation provides a good approximation of the V/I relationship for most diodes, provided the parameters Is, n, and Rs are really constant.  Some diodes, especially germanium and silicon junction diodes seem to have Is and n values which increase at very high currents (higher than those usually encountered in crystal radio operation).  In some of these diodes, the values of Is and n also increase at very low currents, harming weak signal reception.  Is and n are usually constant in Silicon Schottky diodes, over the current range encountered in crystal radio use.   n = Ideality factor, sometimes called emission coefficient.  This parameter is usually between 1.05 and 1.15 for silicon Schottky and germanium diodes commonly used in crystal radios.   Vd = Diode voltage in Volts

Id = Diode current in Amps

Is = Diode Saturation current in Amps

Rs = Diode parasitic series resistance in ohms (usually small enough to have no effect in Xtal radios) Agilent specifies the values of Is, Rs and n for Schottky diodes in their catalog.  They are listed in the table of SPICE parameters.  To find some SPICE parameters for other diodes (germanium types etc.), one can use used a neat Computer Program written by Ray Waugh of Agilent.  To use it one measures the diode forward voltage at five different currents (0.1 mA, 1.0 mA, 4.8 mA, 5.0 mA and 5.2 mA). Ray&39;s program runs on Mathcad 6.0 or higher.  One enters the five voltages and voila, out come Is, n, and Rs.  Remember this caveat:  The program assumes that Is, n and Rs are constant and do not vary with diode current.  If they do vary, one can change the first two currents (0.1 and 1.0 mA) to cover a smaller range, say, two-to-one, that bracket a desired diode operating current and get the Is and n values for that current.  Ray told me that if anyone wants a copy of this program, it would be OK for me to supply it. A simplified method of approximating Is (n must be estimated) that does not require having https://web.archive.org/web/20150305092538/http://www.bentongue.com/xtalset/1nlxtlsd/1nlxtlsd.html[06.08.2019 19:49:03]

Crystal Radio Set: Better sensitivity, selectivity and volume; less audio distortion

Mathcad is described in article #4.  A complete description of a test set-up and calculation method for determining both n and Is is shown in Article #16. Here is what I have found experimentally through a SPICE simulation of a diode detector.  If a detector diode is fed by an RF source resistance of n*0.026/Is ohms and is loaded by an audio load resistance of n*0.026/Is, then both input and output ports are matched with a return loss of better than 18 dB,  assuming the signal is of weak to medium strength.  This satisfies the condition of very low mismatch but only holds true for diode rectified currents of up to about 5*Is.  An impedance matched diode detector insertion loss at a rectified current of 5*Is is about 3-4 dB. The input and output impedance match starts deteriorating with a DC rectified current of over about 5*Is because of the change from square law operation towards linear response at the higher input levels.  At the highest RF Power  input level point shown in the following graph, the rectified DC current is 500 nA and the input RF Return Loss (impedance match) is -12 dB.  Diode detector power loss is 1.39 dB.  At these high levels of Input Power, good matching conditions are restored if the Input Source Resistance is kept at n*0.026/Is and The Output Load Resistance is increased to 2*n*0.026/Is.  If this is done input return loss goes to -26 dB and the insertion loss reduces to 0.93 dB. Here is a graph of Diode Detector insertion power loss of an Agilent 5082-2835 or HSMS-2820 Schottky diode detector driven by a 1.182 megohm source and loaded by a 1.182 megohm load.  Note that these are very high resistance values for a usual Xtal radio.  The SPICE simulation was done using an Intusoft ICAP/4 simulator.  Is of the diode=22 nA, n=1.03.  The plot shows the insertion power loss as a function of the resultant rectified DC current.

  2. DISCUSSION In general, headphones should be impedance matched by a transformer to the output resistance of the diode detector.  To use a diode of such a low Is as 22 nA with, say, a Brandes Superior 12k Ohm AC impedance 2k Ohm DC resistance headphones, an impedance transformation of 1,182,000/12,000 = 98.5:1 is needed (this high a ratio is hard to get).  See Article #2, "Personalized Headphone Impedance" (PHI).  One should be cautious of some small (maximum dimension of less than one inch) , high transformation ratio transformers because they may have a high insertion power loss.  They also may also show the effects of nonlinear inductance because the initial permeability of the core is not high enough.  Their shunt inductance is usually so low at low xtal radio  DX  power levels, that the specified low frequency audio cut-off spec is not met.  At the transformer's rated power level, the shunt inductance is generally high enough so that the low frequency cut-off spec is met.  See Article #5 for info on various audio transformers. Headphones such as the 2000 DC ohm Brandes Superior  have an effective AC impedance of 12,000

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Crystal Radio Set: Better sensitivity, selectivity and volume; less audio distortion

ohms (PHI), but a DC resistance of 2000 ohms.  If the Brandes' impedance is incorrectly considered to be 12,000 ohms at DC and audio frequencies, and is used in a 12,000 ohm circuit (without a transformer), too high a diode DC current will be drawn because the DC resistance is really 2000 ohms, not 12,000.  This will load down the output RF tuned circuit thus reducing selectivity and also give increased insertion power loss.  For best selectivity and minimum audio distortion at medium and high signal levels, the DC load resistance on the diode should be the same as the AC audio load.  The solution to this problem is to place in series with the headphones a parallel combination of a 10,000 ohm resistor shunted by a cap large enough to bypass the lowest audio frequency of interest.  When a transformer is used;  the parallel RC*  (See R3 and C2 on the schematic above.) should be connected in series with the low end of the high impedance transformer primary winding.  In this case the resistor should equal the transformed effective headphone impedance (PHI).  Another advantage that accrues from adjusting the diode DC load to equal the AC load has to do with the way selectivity varies as a function of signal level.  When the diode DC load is much smaller than the AC load (the case when using a transformer and no parallel RC), selectivity starts to reduce more and more as signal strength increases above a moderate level.  The reason is that the detector rectified current increases very rapidly because of the low DC diode load resistance.  A high rectified DC current always reduces the input and output resistances of a diode detector.  Audio distortion may also appear.  Now make the DC load higher, say equal the AC diode load impedance and have the detector impedance matched at both input and output (at low signal levels).  What happens then?  As the signal strength increases above a moderate level, the selectivity will change by a much smaller amount because the RF resistance of the diode detector will not drop as much as it did when the DC load resistance was small.  The resistance does not drop as much because the DC rectified current is less because the DC diode load resistance has been set to a higher value than before.  Impedance matched conditions also result in less power loss with consequently higher sound volume.  If the headphone effective impedance over the frequency range 0.3-3.3 kHz is transformed to a value lower than the output resistance of the diode, these beneficial effects are reduced.  If no transformer is used, these effects may be hard to observe because the headphone effective impedance will probably be lower than the output resistance of the diode. Also, headphones usually have a resistive impedance component about 1/6 the average value, and that goes part way towards being equal to 80% of the effective impedance. * This may be the first time anyone has suggested placing a parallel RC in series with the diode to enable adjusting its DC load resistance equal its average AC load.  Some people call it a "benny".  What is the advantage of using a diode with a low Is?  We will see that if matched input and output impedance conditions are maintained, diodes with lower Is give higher crystal radio sensitivity (lower diode detector power loss) than diodes with higher Is, all else being equal.  The statement above is especially important when dealing with low power signals that themselves result in high DDPL.  The following graph shows the relationship between Diode Detector Power Loss at a relatively low DC Power Output Level  (-66 dBm) vs. diode Is for diodes having an n of 1.03.  Note that the graph data is valid only under the condition that the input and output are power matched.

NOTE: There is an error in the title of the graph. It should read: Detector Loss vs. Diode Is for a DC Power Output of -66 dBm. I

used the -66 dBm signal level for the graph because it is related to the weakest voice signal I can hear

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Crystal Radio Set: Better sensitivity, selectivity and volume; less audio distortion

with my most sensitive headphones, and still understand about 50% of the words.  Here is the listening experiment that I used to determine that power level.  I fed my headphones directly from a transistor radio through my FILVORA and reduced the volume until I judged I could understand about 50% of the words of a voice radio program.  This enabled me to determine the average impedance of the headphones. (See article #2).  I then measured the p-p audio voltage (Vpp_audio) on the headphones with an oscilloscope. Assume  the AM station was running at about 100% modulation.  The peak instantaneous audio voltage at the detector will be equal to Vpp_audio since the modulation is 100%.  Now make the assumption that a CW carrier is driving the detector at such a level that the DC output voltage (Vdc) at the detector is equal to Vpp_audio.  That DC  voltage across a resistor of value equal to the detector load resistance will deliver an output power of Pdc=10*log((1000*(Vdc^2))/Rload) dBm.  Since I could not get into the radio to measure the actual detector voltages and the audio load resistance,  I used the p-p voltage measured across my 1200 Ohm headphones in place of Vdc to calculate the instantaneous power at the modulation peaks.  Pp=10*log(1000*((Vpp_audio^2)/1200= -66 dBm.  This power, Pp is that used in calculating the graph above.  In my case Vpp_audio = 0.00055 Volts and effective headphone impedance = 1200 Ohms.  To calculate the actual audio power level I was using in the listening experiment, I assumed that the demodulated audio voltage was a sine wave (not a voice) with the same p-p value as the actual measured voice p-p voltage.  It was then a simple matter to use the p-p voltage of the assumed audio sine wave (Vpp_audio) and the effective impedance (PHI) of the headphones to calculate the power of the audio sine wave in dBm.  P=10*log ((1000*(Vpp_audio^2))/(8*PHI)) dBm.  This value comes out 9 dB less than the DC power of -66 dBm.  Of course there is an error here in assuming that a sine wave of a specific p-p voltage has the same RMS value as that of a broadcast voice waveform of an equal p-p value.  The "Audio Cyclopedia", in an article on VU meters, states that the actual power from a voice signal is 8-10 dB less than the power from a sine wave of the same p-p voltage.  I'll use 9 dB.  Bottom line:  The audio power from a voice voltage waveform is 18 dB less than the audio power from a sine wave voltage of p-p value equal to the p-p voltage of the voice waveform.  We can now calculate that the electrical power of weakest voice audio signal I can barely understand is -66 -9 -9 = -84 dBm.  This figure depends on the sensitivity of the headphones used and one's hearing acuity.  I used a  good sound powered headphone set in this test.  My hearing acuity is pretty poor. 

  3. PRACTICE Keep in mind that diodes have an unavoidable back leakage resistance.  Schottky diodes generally are very good in this respect.  An exception is the so-called "zero bias" detector diodes.  They have very high Is values and low reverse breakdown voltages and are generally not suitable for crystal radio.  Germanium and cats whisker diodes are worse than Schottkys and vary greatly. This reverse resistance increases detector loss and reduces selectivity. "n" in the diode equation is usually close to 1.05 for Schottky barrier diodes.  It is about 1.15 in Germanium diodes.  All diodes have a fixed parasitic series resistance Rs.  It is usually low enough to be ignored in crystal radios.  One problem with Schottky diodes having a low reverse breakdown voltage and low Is is that they are more vulnerable to damage from static electricity than diodes with a higher leakage resistance. Tuned circuit loss and bandwidth considerations:  A practical problem in using a diode of low Is is getting a high enough tuned circuit impedance for driving the diode.  Of course, the first thing to do is to tap the diode all the way up on the output tuned circuit.  An isolated tuned circuit having a  typical Q of 350 at a frequency of 1.0 MHz, with a circuit capacitance of say 100 pF, and not coupled to an antenna or detector diode will have a resonant resistance of about 560k ohms.  RF bandwidth will be fo/Q = 2.86 kHz.  If an antenna resistance is now coupled in sufficiently to drop the resonant resistance by half to 280k, all of the available received RF power will be dissipated in the resonator, resulting in a bandwidth of 5.72 kHz (loaded Q of 175).  If a diode is selected to match the now 280k ohm source resistance, it will present a 280k RF load resistance and result with a tuned circuit loaded Q of 87.5 giving an RF bandwidth of 11.4 kHz.  The overall power loss caused by the tuned circuit loss is 3 dB.  The diode will only receive 1/2 the maximum available-power at the antenna.  The diode should have an Is of about n*0.026/278k = 100 nA (assuming a Schottky barrier diode is used).  Note this:  Even though the the diode is driven from a perfectly matched source (parallel connected combo of 560k tuned circuit loss and 560k antenna resistances), now the antenna does not see a matched load.  It sees a https://web.archive.org/web/20150305092538/http://www.bentongue.com/xtalset/1nlxtlsd/1nlxtlsd.html[06.08.2019 19:49:03]

Crystal Radio Set: Better sensitivity, selectivity and volume; less audio distortion

parallel combo of the tuned circuit loss resistance of 560k and the 280k RF resistance of the diode.  This is a resistance of 187k ohms.  This mismatch power loss, included in the 3 dB above can be partially recovered by properly and equally mismatching the antenna and the diode.  If this is done by more lossless impedance transformation (technically, with an S parameter return loss of -11.7 dB), the total tuned-circuit power loss reduces to 2.63 dB, a reduction of 0.37 dB (pretty small, but it's there).  If the ratio of unloaded to loaded tuned circuit Q was less than the 4:1 ratio used here, the loss reduction would be larger. Audio impedance transformation:  One way to transform the 12k ohm effective impedance of a 2k ohm DC resistance Brandes Superior headset up to 280k ohms is to use an Antique Electronic Supply # P-T156, Stancor A53-C or similar 3:1 turns-ratio inter stage transformer.   I measure an insertion power loss of only 0.5 dB with the following connection (See Articles #4 and #5 for other options.):

Note that the impedance transformation ratio is 16:1 thus stepping up the impedance of the 12,000 ohm headphones to 192,000 ohms not 278,000 ohms.  This represents a mismatch of about 1.5:1. It will add a mismatch insertion power loss of only 0.15 dB. If the impedance mismatch had been 2:1, the insertion power loss would have been 0.5 dB.  A 4:1 mismatch gives an insertion loss of 1.9 dB. The lead grounding the transformer lamination stack and frame is used if the transformer is mounted on an insulated material.  It prevents the buildup of static charge on the frame during dry weather.  Discharge of it might cause a crackling sound in the headphones or damage the diode (I got the crackling sound until I made the grounding connection). The transformer windings start and stop leads should be connected as shown to minimize the effect of the primary to secondary winding capacitance.  If the f and s connections are reversed, the capacitance between the end of the secondary and the start of the primary winding will be across the primary and reduce the high frequency cut-off point.  The lower impedance (secondary) winding is usually wound on the bobbin first, then after winding on several layers of insulation film, the higher impedance (primary) is wound. To determine how to connect the leads of the transformer, connect the primary and secondary windings as shown. (Disregarding the s and f notations).  Connect an audio generator set to 1.0 kHz through a 200k ohm resistor. Load the secondary with a 12,000 Ohm resistor.  Probe the input and output voltages with a scope.  The output voltage should be about 0.25 of the input voltage. If the output voltage is about 0.5 that of the input, reverse the secondary leads.  Repeat the test at 20,000 Hz and note the input and output voltages.  Now reverse both the primary and secondary leads and repeat the 20 kHz test.  The connection that gives the largest output voltage at 20 kHz is the correct one. Note that R3 is shown above as a rheostat not a fixed resistor.  The nominal setting under the low signal level conditions discussed here is about 192k Ohms.  Setting it to zero has little effect on reception of these low level signals.  With this design approach, when receiving high level signals, RF selectivity is not reduced as much as when the DC resistance in the diode circuit is substantially below the effective impedance of the headset.  When receiving very strong signals, R3 should be set for minimum distortion. One last comment: These design values are not critical.  If impedances vary by several times from the

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Crystal Radio Set: Better sensitivity, selectivity and volume; less audio distortion

optimum values, usually only a small sensitivity reduction will occur. What is the effect on the volume in the headphones of a change of X dB?  Many years ago I did a study which determined, in a blinded condition, that a +1.0 dB or a -1.0 dB change in sound level was barely discernible by most people.  Half couldn't tell if the sound level was changed or not after being told that a change might have occurred.  Another study had the listener listen to a sound.  The sound was then turned off for several seconds and then on again at the same level, at a level of +3.0 dB or at a level of -3.0 dB.  After the delay, only half the listeners could tell whether the level of the sound had changed or not.  Incidentally, the listeners were not golden eared hi-fi listeners. 4. SUMMARY This design approach for crystal radios provides the following benefits: The volume from very low strength (DX) signals is increased (less detector power loss). Louder sound volume with less audio distortion when very strong signals are received. Improved high signal level selectivity without changing coupling or coil taps.  Less variation of selectivity with signal strength.  No need to tap the diode down on the output tuned circuit. Highest weak signal sensitivity is always achieved by connecting a good diode of the proper Is to the highest impedance point  (assuming that the correct audio impedance transformation to the headphones is used and that the transformer has low loss). Enables diodes with too high an Is to be used with strong signals without a large reduction in selectivity, by increasing R3.   Achieve the benefits by doing the following: 1. Use a diode with an appropriate Is to impedance match the resonant resistance of the "antenna loaded RF tuned circuit" that drives the diode.  See Article # 15 for new information on this. 2. Match the audio output resistance of the diode to the effective impedance of the headphones by using a low loss audio transformer.  See Article #5 for measurements on various transformers. 3. Use a bypassed adjustable  resistance in series with the cold end of the primary of audio transformer (sometimes called a "benny") to enable the diode DC load resistance to be made equal to the AC load impedance.  This can be used to reduce audio distortion and improve selectivity on strong signals (compared to having R3=0) when using diodes having reasonably low excess reverse leakage (most "good" diodes).  The Avago (formerly Agilent) 5082-2800 and HSMS-2800 Schottkys have high 75 volt peak inverse ratings and are not likely to overload when detecting strong signals when the "benny" is set to a high resistance.  Other diodes, such as some germaniums, sometimes have enough internal leakage so that the DC load resistor (R3) can be eliminated.   #1 Published: 07/15/99;  Last revision: 02/12/2006 060410

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Measure effective impedance of headphones or a speaker> http://www.bentongue.com/xtalset/2meaphi/2meaphi.html Go

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To maximize volume from headphones or a speaker, measure and use effective impedance for transformer impedance matching. No lab test equipment is needed By Ben H. Tongue

Quick Summary:  This article describes a way to determine the effective average impedance of a pair of  headphones or a speaker.  This is the optimum resistance with which to drive the headphones or speaker to obtain the maximum possible volume in crystal radio set and other applications. The magnitude of headphone or speaker impedance varies widely over the audio frequency range, being partly resistive and partly reactive.  A 'Fixed Insertion Loss Variable Output Resistance Attenuator'  (FILVORA) can be used to indicate the effective average value of this impedance, over that frequency range. The first section of this Article refers to the measurement of mono headphones and individual speakers by using a FILVORA.  The second section describes how to use the FILVORA to determine the effective average impedance of each element in a stereo headset.  The third section describes how the FILVORA was designed.

Section 1.

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Measure effective impedance of headphones or a speaker>

The circuit shown above has a fixed input resistance of 1000 ohms +/- about 5%, no matter what load is connected to the output or where the switch is set.  The output resistance at any switch point is about +/5% of the value shown with any impedance driving the input.  The insertion loss of the FILVORA is 26 dB.  Standard 5% tolerance resistors are used.  The use of resistors that differ by +/- 10% from the values shown should not have an appreciable impact on performance of this unit. To use the FILVORA, connect a source of audio voice or music to the input jack J1. (I use the output jack of a transistor radio for my source.)   Connect the plug of the mono headphone set or speaker to be measured to the output jack J2 of the FILVORA.  Adjust the switch for the loudest volume.  The correct setting indicates the effective impedance is very broad and somewhat hard to determine.  Call it P2.  Rotate the switch in one direction from P2 for a small reduction in volume to position P1 (generally a two positions movement), then in the other direction from P2 by two positions  to P3.  If the volume at P1 and P3 are the same, P2 indicates the effective impedance of the headset.  If the volume at P1 and P3 is not the same, increment both the P1 and P3 settings ccw or cc by one position.  When you obtain the same volume at the new P1 and P3 positions, you are done.  The effective headphone impedance is the calibration indication of the switch at point P2.  Sometimes equal volume settings cannot be obtained with switch settings five positions apart.  If this is the case, try to get equal volume settings four positions apart.  If this is done, the effective impedance is equal to the geometric mean of the settings of P1 and P3. (Take the square root of the product of the calibration readings at P1 and P3.) The effect of source impedance on tone quality.  It is interesting to note,  that with magnetic elements, setting the switch to a high source resistance tends to improve the treble and reduce the bass response, compared to the response where the source matches the effective impedance of the element.  Setting the switch to a low resistance does the reverse.  This setting rolls off the treble, and relatively speaking, improves the bass.  With piezo ceramic or crystal elements, a high source resistance tends to reduce the treble and improve the bass response, compared to the response where the source matches the effective impedance of the element.  A low source resistance tends to reduce the bass and emphasize the treble.

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Measure effective impedance of headphones or a speaker>

 Some piezo elements sound scratchy.  This condition can be minimized by driving the elements from a lower average impedance source. Here are some practical experimental ways to vary the audio source resistance of a crystal radio set when receiving medium strength to weak signals.  A medium strength signal is defined as one at the crossover point between linear to square law operation (LSLCP).  See the graphs in Article #15A. Change the diode to one having a lower saturation current, such as from a germanium to one or several paralleled Schottky diodes such as the Agilent 5082-2835.  Schottky diodes described as "zero bias detectors' have a high saturation current and are not suitable.  Schottky diodes described as "power rectifiers' usually have a high saturation current as well as a high junction capacitance.  A high diode junction capacitance will reduce treble response.  Too large a diode RF bypass capacitance will also reduce the treble response.  A side benefit from this change, on some crystal radio sets is an increase of selectivity.  This is because the RF load resistance presented to the tank is raised when the diode saturation current value is reduced. Use an audio transformer between the detector output and the phones.  A smaller step-down transformer impedance transformation ratio will raise the transformed diode source resistance seen by the phones.  A larger ratio will decrease it. If the headphone elements are in series, reconnecting them in parallel will reduce their impedance to 1/4 the previous value.  This has the same effect as increasing the effective source resistance.  If they are in parallel, series connecting them has the effect of decreasing the effective source resistance. Refer to Articles #0, #3,#5 and #14 for more info.  Consider the 'Ulti-Match' by Steve Bringhurst at: http://www.crystalradio.net/  Check out Index>Sound powered>Impedance matching>Impdance matching... If you are interested in DX reception with headphones and do not have normal hearing, you might want to customize the source resistance driving the headphones.  This enables using the 'change in headphone frequency response as a function of headphone driving resistance' to partially compensate for high frequency hearing loss.  Input a voice signal and reduce its volume to a sufficiently low level such that you judge you understand about 50% of the words.  Readjust the switch to see if you can obtain greater intelligibility at another setting.  If you can, this new switch setting indicates the source resistance with which to drive the particular headphones being used to deliver maximum voice intelligibility for your ears.  I call this resistance: Personalized Headphone Impedance (PHI).  For magnetic headphones, this resistance is higher than the average impedance of the earphones, for piezoelectric ceramic earpieces, the resistance is lower. Two FILVORA units enable one to compare the actual power sensitivity of two headphones, even if the effective impedance the two headphones are very different.  A dual unit to do this (DFILVORA) is described in Article #3.  

Section 2. The effective impedance of hi-fi stereo headphones may be checked with the FILVORA.  The effective impedance of  the two earpiece elements can be checked by determining the switch position for maximum volume with one of these connections:  (1) The sleeve, to the ring and tip in parallel or (2) the ring to the tip.  Measurement (1) will show one half the effective impedance of one earpiece and measurement (2) will give a reading of two times the effective impedance of one element.   

Section 3. To help define the equations used to calculate the the resistor values for the asymmetrical attenuator 'FILVORA' the following requirements were set up: 1. Output resistance range: 10 to 100k ohms, with 12 switch positions.  This range covers the span of impedances found in headphones used in transistor radios, up to that found in piezo earpieces.  A

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Measure effective impedance of headphones or a speaker>

12 position rotary switch was used because it is readily available. 2. The FILVORA must exhibit the minimum possible constant insertion loss and input resistance, independent of switch position or load impedance selected.  The maximum and minimum output resistances are 100,000 and 10 ohms.  For a constant, and minimum insertion loss at all switch positions, this requires the input resistance be: sqrt(100,000*10)=1,000 ohms at each switch position.  The requirement for a constant input resistance is closely met by an equation equating the sum of the 12 resistors in the vertical string equal to 1000 ohms. 3. The ratio of the output resistance from one switch point to the next shall be constant.  The output resistance ratio between adjacent switch positions is (100,000/10)^(1/11)=2.3101.  12 simultaneous equations are necessary to meet this requirement on each switch position. 4. The same insertion loss shall exist on each switch position.  The voltage ratio (loaded output to input) required at each switch point, for constant insertion loss (26 dB), requires another 12 simultaneous equations. A system of 25 simultaneous was written and solved in MathCad for the values of the 24 resistors.  Those are the values (5% resistor series) shown in the schematic.  To minimize power loss, the attenuator becomes an inverted L minimum-loss pad at the two extreme switch positions. It is a nonminimum loss T pad at the intermediate positions. The output resistance range of the FILVORA is 10,000 to 1. This establishes the minimum loss. If the output resistance range were 100,000 to 1, the insertion loss would have to be 31 dB. Insertion power loss = 5*log(resistance ratio)+6dB. #2 Published: 07/15/99;  Last revision: 06/21/2003 060410

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Compare the sensitivity and impedance of headphones or speakers even if their parameters differ greatly. No lab test equipment is needed http://www.bentongue.com/xtalset/3cmp_hph/3cmp_hph.html Go

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Compare impedance and sensitivity of headphones, and/or speakers even if they differ greatly in impedance by Ben H. Tongue

  The purpose of this article is to show how to compare the sensitivity of two pair of speakers or mono headphones even if they differ greatly in effective impedance.  See Article #2 on how to measure impedance.  The Dual Fixed Insertion Loss Variable Output Resistance Attenuator (DFILVORA) will be described and directions for its use will be given in Section 1.  It is essentially a combination of two FILVORA units along with some extra attenuators.   Section 2 will describe how to modify the DFILVORA for use with Hi-Fi stereo headphones.  Note: The use of resistors that difer by +/- 10% from the values shown in the schematic should not have an appreciable impact on performance of this unit.

Section 1.

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Compare the sensitivity and impedance of headphones or speakers even if their parameters differ greatly. No lab test equipment is needed

Connect an audio source to jack J3. (I use the output jack of a transistor radio for my source.)  Connect the plug of one of the two mono headphone sets or speakers to jack J1 and the other to jack J2.  Set attenuators A1, A2, A3, and A4 to 0 dB.  Switch S1 should be set to the position providing the loudest sound in the headphone set or speaker connected to J1.  Switch S2 should be set to the position providing the loudest sound in the unit connected to J2. (Read Article #2 to see the recommended procedure for doing this.)  If the unit connected to J2 is louder than the unit connected to J1, reverse the units.  Now add attenuation in the path to the unit connected to J1 in 3 dB steps by using A1, A2 and A3 in the proper combinations (the dB's add), until the volume from the unit connected to J1 equals the volume in the unit connected to J2 as closely as possible.  If the sound cannot be reduced to a low enough level because of volume control limitations in the INPUT source, use A4 to reduce the volume by 20 dB.  The sum of the dB settings of A1, A2 and A3 equals the difference in power sensitivity between the two headphones or speakers, independent of the effective impedance of the units.  The settings of S1 and S2 indicate the average impedance of the two units.  See Article #2 for more details on this subject.  The power insertion loss from jack J3 to either jack J1 or jack J2, with the attenuators set to zero, is 29dB.  

Section 2. To compare the power sensitivity of two stereo headphones, I recommend that several modifications be made to the DIFLVORA.  Jack J1 should be changed to a stereo jack and the ring and tip connections tied together.  The same change should be made to J2.  this will cause each stereo headphone to be tested in mono mode with its elements connected in parallel.  The value of all resistors should be halved.  The setting of switches S1 and S2 indicate the average impedance over the audio frequency range of two earphone elements in parallel, and that figure will be onehalf the value of each element by itself.  Also, the measurable range of individual element impedances will be changed from 10 to 100k Ohms to 20 to 200k. The range of impedance measurable for the parallel combo of two elements is still 10 to 100k Ohms.  To correct this condition and have the DFILVORA switches S1 and S2 indicate the value of the impedance of one element (and not two in parallel), halve the value of all resistors in the schematic.  If this modified DFILVORA is now  used to measure a mono headset, the resistance readings of switches S1 and S2 will be twice the actual value. These modifications change the input resistance of the DLVORA to https://web.archive.org/web/20131030052237/http://www.bentongue.com/xtalset/3cmp_hph/3cmp_hph.html[06.08.2019 19:51:35]

Compare the sensitivity and impedance of headphones or speakers even if their parameters differ greatly. No lab test equipment is needed

250 Ohms.  #3  Published: 07/15/99;  Last revision: 11/04/00 060410

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    The best diode and audio transformer for a crystal set, and a way to measure diode saturation current by Ben H. Tongue

Here is a practical way to determine the diode and audio output transformer impedance matching characteristics needed to maximize sensitivity and selectivity for weak signals and to reduce strongsignal audio distortion in a Crystal Radio Set.  Unfortunately, this may be an iterative process. 1. Determine the RF output resistance at resonance of the tuned circuit driving the diode while the Crystal Radio Set is connected to its antenna. 2. Calculate the Saturation current (Is) that the diode should have. The ideality factor of the diode should be as low as possible.  Get an appropriate diode. 3. Know the effective impedance of the headphones to be used. 4. Calculate the impedance transformation ratio needed to transform the diode audio output impedance to that of the headphones. 5. Connect it all up.

1. Connect the Crystal Radio Set as presently configured to antenna, ground and headphones.  Select a frequency for optimization. About 1 MHz is suggested.  Tune the Crystal Radio Set and adjust the antenna coupling and diode tap (if there is one) for the desired compromise between sensitivity and selectivity on a signal near 1 MHz.  Replace the headphones with a 10 Meg resistor load bypassed with about 0.002 uF capacitor (no transformer yet).  We will now use the diode as a voltage detector.  Measure the detected DC voltage with a high impedance (10 Megohm) DVM.  If the diode can be tapped down lower on the RF tuned circuit, do so until the detected voltage is as low as can easily be read.  Trim the tuned circuit tuning if necessary.  Find the value of a 0.125 or 0.25 watt carbon or metal film resistor which when connected across the RF tuned circuit reduces the detected voltage to about 0.35 of its previous value (retune as needed).  Use short leads on the resistor.  The value of the resistor (lets call it Rr) approximates the resonant resistance of the tuned circuit with antenna connected. See Part 11 of Article #0 for more info on resistor types. What we have done here is to minimize loading on the tuned circuit from the diode detector.  If this diode loading is made negligible, using a resistor of value equal to that of the resonant resistance of the tuned circuit will reduce the RF voltage to 0.5 of what it was before the resistor was placed.  Here, the diode has been given a high resistance DC load to further reduce its loading effect on the tuned circuit (the 10 Meg resistor connected in place of the headset).  The detector is used as an indicator of the RF voltage across the tank circuit.  The diode will be operating somewhere between linear and square law. That is where the 0.35 comes from (geometric mean of 0.5 and 0.25). A Better approach, if one has a high sensitivity scope good to above 1.0 MHz, is to disconnect the diode from the tuned circuit. Then very lightly capacitively couple the scope to the tuned circuit and use it as a measuring tool when placing the resistor across the tuned circuit. Then of course, one would use the 0.5 figure for voltage reduction since the measurement is linear. Bear with the problem of the measured voltages jiggling up https://web.archive.org/web/20131030052242/http://www.bentongue.com/xtalset/4opd_xfr/4opd_xfr.html[06.08.2019 19:52:23]

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The best diode and audio transformer for a crystal set, and a simple way to approximate diode saturation current

and down due to modulation.  Just estimate an average.  (See Article #0 for information on diode Saturation Current and Ideality Factor.)

2.  A good diode to use in the crystal radio set above, for weak signal reception, is one with an axiscrossing resistance equal to Rr.  A diode that has an axis-crossing resistance of Rr is one having a Saturation Current of Is = (25,700,000*n)/Rr nanoAmps.  The ideality factor of the diode (n) is an important parameter in determining very weak signal sensitivity.  If all other diode parameters are kept the same, the weak signal input and output resistances of a diode detector are directly proportional to the value of n.  Assume a diode with a value of n equal to oldn is replaced with an identical diode, except that it has an n of newn; and the input and output impedances are re-matched.  The result will be a detector insertion loss change of: 10*log(oldn/newn) dB.  That is, a doubling of n will result in a 3 dB drop in power output, assuming the input power is kept the same and impedances are re-matched.  This illustration shows the importance of a low value for n.  Back leakage resistance should be low and the diode series resistance (Rs) should also be fairly low.  Diode barrier capacitance should be fairly low (6 pF or less) . Schottky barrier diodes usually have low series resistance, barrier capacitance, Ideality Factor and very low back leakage.  The challenge is to get a diode reasonably close to the correct Is.  (If it's within 0.3 and 3 times the calculated value, you won't notice much difference.)  A simple way to check for back-leakage is to measure the back resistance of the diode with a non-electronic VOM such as the Triplett 630 or Weston 980. Use the 1000X resistance switch position.  If no deflection of the meter can be seen, the diode back leakage is probably OK.  Another way is to place a DC blocking capacitor in series with the diode.  If the audio becomes very distorted, the diode leakage is low (this is the desired result).  A value of 1000 pF or so is OK for this test. Here is an easy way to determine the approximate Is of a diode.  Forward bias the diode at about 1.0 uA.  A series combination of a 1.5 volt battery and a 1.5 Meg resistor, connected across the diode will do this.  Measure the voltage developed across the diode with a DVM having a 10 Meg input resistance.  Calculate Is=667*(Vb-Vd)/(e^(Vd/(0.0257*n))-1) nA. e = base of the natural logarithms = approx. 2.718,  ^ = "raise the preceding number to the power of the following number",  Vb = voltage of the battery, Vd = voltage across diode and n = diode Ideality Factor (Emission Coefficient).  I suggest using an estimate of 1.12 for n.  Most good detector diodes seem to have a n between 1.05 and 1.2  A method for measuring both n and Is is shown in Article #16.  Measurements on 1N34A germanium diodes at various currents show that the values for Is and n are not really constant, but vary as a function of diode current.  Is can increase up to five times its value at low currents when currents as high as 400 times Is are applied.  However, germanium diodes I have tested exhibit a fairly constant n and Is when measured at currents below about six times their Is.  A rectified current of about 6 times Is corresponds to a fairly weak signal.  The following chart shows some results from measuring several diodes at a current of 1.0 uA.  The calculated low-signal-level value of the diode junction resistance Rj= 0.0257*n/Is is is also given.  Note the wide variation among the various diodes sold as 1N34A.  Schottky diodes, as a rule are fairly consistent from unit-to-unit.  The Agilent '2835 measured 11 nA, and many others test close to this value.  I think that many years ago early production '2835 diodes probably matched the Spec. sheet value of 22 nA for Is.  Over the years, I would guess that the average value was allowed to drift in order to optimize other more important parameters (for most applications) such as reverse breakdown voltage.  BTW, Is is not a guaranteed 100% tested production spec.

Caution:  If one uses a DVM to measure the forward voltage of a diode operating at a low current, a problem may occur.   If the internal resistance of the DC source supplying the current is too high, a version of the sampling voltage waveform used in the DVM may appear at its terminals and be rectified by the diode, thus causing a false reading.  One can easily check for this condition by reducing the DC source voltage to zero, leaving only the diode in parallel with the internal resistance of the source connected to the terminals of the DVM.  If the DVM reads more than a tenth or so of a millivolt, the problem may be said to exist.  It can usually be corrected by bypassing the diode with a ceramic capacitor of between 1 and 5 nF.  Connect the capacitor across the diode with very short leads, or this fix may not work.  If one wishes to screen a group of diodes to find one having a specific Is, use the setup described above.  Substitute the desired value of Is into the following equation:  Vd=0.0282*ln(667*(VbVd)/Is+1) volts.  'ln' means natural base logarithm and Is is in nA.   A diode having a Vd equal to the

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The best diode and audio transformer for a crystal set, and a simple way to approximate diode saturation current

calculated value will have approximately the desired Is. Here are some tips to consider when measuring diodes:  Keep all leads short and away from 60 Hz power wires to minimize AC and electrostatic DC pickup.  Place a grounded aluminum sheet on the workbench, and under the DVM and other components to further reduce spurious pickup by the wiring.  A piece of grounded kitchen aluminum foil will do nicely for the aluminum sheet.  You may find that the reading of Vd slowly drifts upwards.  Wait it out. What you are observing is the temperature sensitivity of Vd to heat picked up from handling the diode with your fingers.  Let the diode return to room temperature before taking data. Many glass diodes exhibit a photoelectric effect that can cause measurement error.  Guard against it by checking to see if a diode current reading changes when the light falling on the diode is changed.

Saturation Current (Is) and the related Junction Resistance (Axis Crossing Resistance), Rj, of some Diodes, Measured at 1.0 uA. (*=Mfg's data) Type of Diode

Is in nA

Junction Resistance in ohms

Agilent 5082-2835 Agilent HBAT-5400 Agilent HSMS-2870

11 100* 140*

(Axis-crossing resistance) 2.5 Meg 282k* 191k*

Radio Shack 1N34A (marked 12101) Radio Shack 1N34A (blue body marked BKC) Radio Shack 1N34A (brown, orange and white bands) Radio Shack 1N34A (labeled BKC 2000) Radio Shack 1N34A (clear glass) 2N404A connected as a diode (collector and base tied together)

160 180 200 400 600

170k 150k 130k 65k 45k

1700

16k

 

Published SPICE Parameters for some Agilent (formerly Hewlett-Packard) Schottky Barrier diodes: HSMS-2800 This is a SMD (Surface Mount Diode) HSMS-2810 This is an SMD type HSMS-2820 This is an SMD type HSMS-2860 This is an SMD type HBAT-5400 This is an SMD type HSMS-2870 This is an SMD type 5082-2835 This is a glass type, but expensive now

n=1.08 n=1.08 n=1.08 n=1.10 n=1.0 n=1.04 n=1.08

Is=30 nA Rs=30 Ohms Is=4.8 Rs=10 Is=22 Rs=6 Is=38 Rs=5.5 Is=100 Rs=2.4 Is=140 Rs=0.65 Is=22 Rs=5

Note that these values for Is and n are not cast in stone.  Is can easily vary by 2:1 or more from diode to diode of the same type. Multiple similar diodes may be paralleled to increase Is.  Is is increased proportionally to the number of diodes in parallel. Four identical diodes in parallel will give a saturation current four times the Is of one alone.  For purposes of Crystal Set design, diodes should not be placed in series.  SPICE simulation shows that if two identical diodes are connected in series, the combination will perform the same as one of the diodes alone, but having a doubled value for n.  This increased value of n will reduce weak signal sensitivity. In a particular crystal radio set Is can vary quite a bit without a great effect on performance. One can be

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The best diode and audio transformer for a crystal set, and a simple way to approximate diode saturation current

in error by several times and still get good results.  Too high an Is reduces selectivity on weak signals.  Too low a value reduces sensitivity to weak signals and causes excessive audio distortion. Many times the question is asked,  "What is the best diode to use?"  The answer depends on the specific RF source resistance and audio load impedance of the Crystal Set in question.  At low signal levels the RF input resistance and audio output resistance of a detector diode are equal to 25,700,000*n/Is Ohms (current in nA).  For minimum detector power loss at very low signal levels with a particular diode, all one has to do is impedance match the RF source resistance to the diode and impedance match the diodes' audio output resistance to the headphones by using an appropriate audio transformer. The lower the Is of the diode, the higher will be the weak signal sensitivity (volume) from the Crystal Set, provided it is properly impedance matched to it's circuit (see article #1).  This does not affect strong signal volume.  There is one caveat to this, however.  It is assumed that the RF tuned circuits and audio transformer losses don't change.  This can be hard to accomplish.  It is assumed that the Rs, diode junction capacitance, n and reverse leakage are reasonable.  If the diode you want to use has a higher Is than the optimum value, tap it down on the tuned circuit.  If the diode you want to use has a lower Is than the optimum value, change the tank circuit to one with a higher L and lower C so that the antenna impedance can be transformed to a higher value and repeat step #1. If you don't have a diode of the proper calculated Is, you can simulate what the result would be if you did have one by doing the following:  Put a small voltage in series with the DC load resistor ground return (see point #4 below).  If your diode has too low an Is, biasing the diode in the forward direction will improve sensitivity.  If your diode has too high an Is, biasing the diode in the reverse direction will improve sensitivity.  See Article #9 on the home page on how to build and use a "Diode Detector Bias Box". . 3. Estimate the audio effective impedance of magnetic phones as 6 times the DC resistance.  Alternatively, build the "Headphone Effective Impedance" measuring device described in Article #2 and use it to determine the headphone impedance. Call this impedance Zh.

4. The average audio impedance of the headphones should be transformed up to the value Rr by an appropriate audio transformer. The step-down impedance transformation ratio needed in the transformer is Rr/Zh.  When connecting the transformer high impedance winding to the diode, put a parallel RC (a benny) in series with the ground connection .  This will insure that the DC load on the diode can be made the same as the audio AC load.  A good value for the R should be about equal to Rr.  It's best to use a pot so that the value can be optimized at different signal levels.  For minimum audio distortion at medium and high signal levels, the DC load on the diode should be the same as the AC audio load. The value of the C should be large enough to fully bypass the R for audio.  A good value is C=5/(pi*2*300*Rr).  The parallel RC will have less effect on reducing distortion or affecting selectivity when receiving loud signals if the transformed headphone load on the diode is lower than the diode output resistance, than if it is higher.  For info on the impedance transformation ratios of various transformers see Article #5.  The audio transformer should have a low insertion loss. Try to obtain one with less than 2 dB loss from 300-3300 Hz when measured at low Crystal Set signal levels.  See Article #5 for info on how to measure transformer Insertion Loss.

5.  Connect up the new diode and transformer and the parallel RC.  Trim up the value of the R in the parallel RC for the least audio distortion on a loud signal.  There should be an improvement in low signal volume and high signal audio distortion as well as better selectivity. #4  Published: 10/02/99;  Last revision: 08/22/2002 060410

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Low-loss impedance matching for magnetic and piezoelectric headphones, measurements on many audio transformers, and a transformer loss measurement method By Ben H. Tongue

Quick Summary:  This Article discusses the use of audio transformers with crystal radio sets and gives the results of loss measurements on several of them.  A method for measuring insertion power loss is also described. Many crystal radio set designs provide impedance step down taps on the final RF tuned circuit.  If the diode is connected to one of these taps, its loading on the tuned circuit is reduced and selectivity is improved. Too much of a step down also reduces sensitivity.  RF tuned circuit loading by the diode is affected by the diodes' Saturation Current, the headphone effective impedance and the signal level. One can reduce the loading effect of headphone effective impedance and of high signal level by transforming the headphone impedance up to a value that matches the audio output resistance of the diode detector itself.  This approach can keep the selectivity high and also increase the sensitivity of the crystal radio set.  For info on measuring headphone effective impedance see article # 2. It is important that the diode sees a DC load equal to its AC audio load. This will permit connecting the diode to a higher tap or maybe to the top of the tuned circuit.  The result will be to maintain selectivity and reduce audio distortion for medium and especially for strong signals.  Diodes of lower Saturation Current can be tapped up higher on the tuned circuit than those of higher Saturation Current and, all else being equal, will give higher receiver sensitivity. See articles #0, #1, #4 and #15.

Table of Contents 1. Setup for switchable Transformation Ratios using the A.E.S. P-T157 or equivalent transformers 2. Practical Fixed Transformation Ratio Setups using the A.E.S. P-T157, PT-156, Stancor A-53 or similar Audio inter-stage Transformer "3:1 AIT" 3. Transformer configurations for use mainly with Sound Powered Headphones 4. The BT-UltiMatch, a modified version of Steve Bringhurst's UltiMatch. Insertion power loss and input resistance measurements when using a selection of various 'Stanley-type' transformers or an UTC O-15 for the input transformer 5. How to Measure the approximate Insertion Power Loss of any Audio Transformer or Compare its Performance to that of an Ideal no-loss Transformer 6. Some practical suggestions on where to get and how to identify transformers that may perform well with sound powered headphones

Part 1 - Setup for switchable Transformation Ratios using the A.E.S. P-T157 or equivalent transformers https://web.archive.org/web/20131030052247/http://www.bentongue.com/xtalset/5hpXform/5hpXform.html[06.08.2019 19:54:18]

Audio transformer power loss and optimal impedance matching

The sensitivity improvement mentioned above will only be attained if the audio transformation is performed with a low insertion loss audio transformer. For experimental purposes one of the best transformers I have found is the P-T157 from Antique Electronic Supply.  What immediately follows is the description of two switchable circuits that can supply various transformation ratios for driving a 12k Ohm load.  This is the nominal AC impedance of most 2,000 DC Ohm headphones, as well as many piezoelectric ceramic earpieces.  Later on, specific nonswitched configurations are shown for several different transformers.  Since this Article was written, A.E.S. has stopped selling the P-T157.  Results close to those shown below can be obtained using the A.E.S. P-T156, Stancor A-53 or most any 3:1 turns ratio tube-type inter-stage audio coupling transformer.  A good description of this type of transformer is:  A transformer designed for plate-to-grid inter-stage coupling, having a 3:1 turns ratio, and specified for a 90k to 10k ohm impedance transformation.  Henceforth, in this Article, this type of transformer will be referred to as a "3:1 AIT". Note that the switched transformation ratios shown below vary by a factor of about four from one to another.  Note also that an impedance mismatch of 2:1 gives an insertion loss of only 0.5 dB.  This means that all values of diode output resistance from 12k Ohms up to 750k can be utilized, with a mismatch insertion loss of no more than a maximum value of 0.5 dB, plus the transformer loss.  Measured transformer loss is about 1.0 +/- 0.5 dB from 300- 3300 Hz at the 63 times ratio and about 0.5 +/- 0.2 dB at the 16 and 4 ratios.  Note: The transformation ratio on the H switch position is shown as 63 instead of 72 because of shunt resistive losses in the transformers.  On this switch position the diode sees the 12k headphones transformed to 750k, not 860k.  T1 and T2 are preferably Antique Electronic Supply P-T157 transformers.  Alternatively, one can use most any generic "3:1 AIT". One will get a small amount more loss with the alternatives, mainly at 300 Hz and when the signal is weak.  C2 can be used to peak up response at 300 Hz if a generic "3:1 AIT" transformer is used.  C2 can be omitted if the P-T157 transformers are used.  Experiment with values around 0.02 uF.  Sw1 and Sw2 are DPDT slide or toggle switches.  R can be a 1 Meg pot.  It is used to set the diode DC load resistance to be equal the transformed AC load impedance.*  A log taper is preferred.  Set R for the lowest audio distortion and best selectivity on strong signals.  The diode load at DC must be the same as for AC audio signals for best results. This setting has little effect with weak signals, however.  C1 should be about 0.05 uF.  See the later part of Article #1 for info on determining transformer winding polarity and how to reduce the effect of inter-winding capacitance. * The first time anyone has suggested placing a parallel RC in series with the diode to enable adjusting its DC load resistance equal its average AC load may have been in Article #1.  Some people call it a "benny".   

Fig. 1

There is no need to transform headphone effective impedance up to as high as 750k unless the RF tuned circuit, when loaded with the antenna, has a resonant resistance of around 750k Ohms.  It is very difficult to attain an impedance this high.  The diode also would have to have the appropriate Saturation Current of about 38 nA.  For experimental purposes, if a transformed impedance of no higher than 380k is desired, a one transformer circuit should be used as shown below. This will prove more practical in real world applications.  R may be a 250k or 500k Ohm pot, preferably with a log taper. The transformer insertion loss remains below 1.0 dB from 0.3-3.3 kHz with output loads between from 6k to 24k Ohms when using the A.E.S. P-T157.  Keep in mind that the saturation Current (Is) of the diode should be such that the diode's (Weak signal) RF input resistance is about equal to the (Antenna loaded) RF tuned circuit resonant resistance and also to the transformed headphone effective impedance.

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Audio transformer power loss and optimal impedance matching

This diode resistance is equal to (0.0257*n)/Is.  Is is in Amps. For more information on this, see article #4 listed on the home page.

Fig. 2

Part 2 - Practical Fixed Transformation Ratio Setups using the A.E.S. P-T157, PT-156, Stancor A-53 or similar Audio inter-stage Transformer "3:1 AIT" The following schematics show various connections for the transformers mentioned above. The connections are arranged to provide various diode audio frequency load impedances from headphone loads of either 12,000 or 1,200 Ohms AC impedance. The 12,000 Ohm connection is appropriate for most magnetic headphones of 2,000 Ohms DC resistance and many piezo earpieces. The 1,200 Ohm connection is used when driving a series connected set of typical sound powered elements. As stated before, it is important that the diode have a DC load of the same value as its average AC load.  This can easily be accomplished by placing the parallel combination of a pot with an audio bypass capacitor (a "benny") in series with the lead marked 'RC' between the points marked "x--x" (see below).  The pot should have an audio taper and be connected as a rheostat.  0.5 to 1 Meg is usually a good value.  The value of the capacitor depends upon the impedance reflected into the transformer primary from the headphones.  A value of 0.05 uF or more is usually OK.  The pot should be adjusted to minimize distortion and improve selectivity when receiving strong signals.  Its setting has no effect when receiving weak signals.

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Audio transformer power loss and optimal impedance matching

Fig. 3

First, some help. In schematics A-F it is important to properly phase the windings.  For best performance at the high end of the audio band, one should minimize the effect of transformer inter-winding capacitance.  This is most important to do when using circuits D or E, but has little effect when using circuits A, B, C, or F.  To do this, the start and finish leads of the transformer coils must be properly connected.  In the schematics shown above, the start and finish of the transformer windings are indicated by "s" and "f".  The start of the low impedance winding of a PT-156 or P-T157 transformer is the blue lead. The finish is the red lead. The green lead next to the red lead is the start of the center tapped high impedance winding. The green lead next to the blue lead is the finish.  If Stancor A53-C transformers are (is) being used, the color coding is different. The start of the low impedance winding is the red lead, the finish is the blue lead.  The green lead of the center tapped winding next to the blue lead is the start, and the green lead next to the red lead is the finish. The insertion loss values shown below are were measured using A.E.S. P-T157 transformers.  Stancor A53-C or generic "3:1 AIT" units will perform somewhat worse, as mentioned above.  If you are going to use a generic "3:1 AIT", keep in mind that all or most of the extra insertion loss at 0.3 kHz can be eliminated by using the correct capacitor in series between the transformer and headphones.   Table 1 - Insertion Loss for Various Impedance Transformations when Driving Magnetic Headphones (2k ohms DC resistance) or Piezoelectric Earpieces of about 12k Ohms AC Impedance.  For A.E.S. P-T157 and generic "3:1 AIT" transformers .  Frequency Range is from 0.3-3.3 kHz.  SOURCE IMPEDANCE RANGE LOAD IMPEDANCE CIRCUIT INSERTION LOSS 25k-70k Ohms 12,000 Ohms A 0.6-1.0 dB 70k-150k 12,000 B 0.3-0.8 150k-250k 12,000 C  0.2-0.6 250k-500k 12,000 D 0.3-1.2 500k-700k 12,000 E 0.5-1.5 A very low loss transformer that can be used to transform a 1 Megohm source down to closely impedance match a 12k AC ohm load is the small UTC O-15 'Ouncer' transformer. Its insertion power loss is less than 1 dB from 0.3-3.3 kHz. Table 2 - Insertion Loss for Various Impedance Transformations Driving Sound Powered Headphones of 1.2k Ohms AC impedance.  For A.E.S. P-T157 and

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Audio transformer power loss and optimal impedance matching

generic "3:1 AIT"s.  Frequency Range is from 0.3-3.3 kHz. SOURCE IMPEDANCE RANGE LOAD IMPEDANCE CIRCUIT INSERTION LOSS 16k-54k Ohms

1,200 Ohms

C

1.1-1.3 dB

43k-130k

1,200

F

1.3-1.9

Here are general specifications for the A.E.S. P-T157, Stancor A-53C and generic "3:1 AIT" Inter-stage transformers:  Single Plate (10,000 Ohms) to push-pull grids (90,000 Ohms).  Overall turns ratio: 1 to 3 Primary to Secondary.  Max. Primary DC: 10 mA.  These transformers are still relatively cheap and usually available at Hamfests, personal junk boxes and Used Component Vendors.

Part 3 - Transformer configurations for use mainly with Sound Powered Headphones Now we will talk about some other transformer configurations that are suited for use with Sound Powered phones: UTC LS-10, UTC A-10, UTC A-12, Amertran 923A and UTC C-2080, as well as many others.  The UTC A-10 and A-12 have the same terminal impedance specifications as the LS-10 and will probably perform similarly.  Some of these transformers are currently quite expensive.  For some lower cost options, see Part 5 of this article for some generic transformer specs., or consider the last two connections shown in the chart above.  Shown below are loss measurements using a physically very small, but very low cost transformer, the MOUSER TM-117 as well as two excellent small low loss transformers from the CALRAD line. At the end of this Section (#3), measurements on a combination of two transformers are be shown that enable 900k to 1200 ohm and 470k to 1200 ohm impedance transformation. Six measurements on the TM-117 are shown.  The first test of the transformer is with the input and output resistance values specified by the Manufacturer, but at a low output signal level.  The second is for a TM-117 driven and loaded by the resistances of 24k ohms primary and 300 ohms secondary instead of 50k ohms primary and 1k ohms secondary.  The 24k ohm level is close to that delivered by a generic 1N34A diode when detecting a weak signal.  The next three measurements are for four TM-117 transformers interconnected to give a transformation ratio four times greater than one gets from one transformer alone.  The primaries are connected in series and the secondaries are connected in series/parallel.  The resultant primary and secondary are connected as an autotransformer.  Results are given from measurements made at three output power levels. The last measurement is with the transformers connected for a 1,200 Ohm output instead for a 300 Ohm output.  Most Sound Powered elements I have seen have an AC impedance of about 600 Ohms when averaged over the frequency range of 0.3-3.3 kHz.  When used as a 1,200 Ohm transformer load, the two elements should be connected in series. When used as a 300 Ohm load, the elements should be connected in parallel.  Remember that the insertion loss near 0.3 kHz can usually be reduced by placing a proper capacitor in series with the connection from the transformer to the sound powered headphones.   Table 3 - Insertion Loss Values for Various Transformers driving Sound Powered Headphones or elements of 300, 600 or 1,200 Ohms effective Impedance.  Frequency Range is from 0.3 - 3.3 kHz. Source Impedance Transformer  Load Impedance  Insertion Loss Connections Model # (Secondary) in Ohms Range in dB (Primary) in Ohms UTC LS-10  UTC LS-10  UTC LS-10  UTC LS-10  UTC C-2080* UTC C-2080* UTC C-2080* AMERTRAN 923A

120,000 270,000 270,000 430,000 330,000 540,000 820,000 680,000

300 300 1,200 1,200 300 600 1200 300

G H I G J J J K

0.4 0.7-1.0 0.7-1.0 0.8-1.6 0.8-1.2 1.3-1.9 2.1-3.2 1.0-1.8

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Audio transformer power loss and optimal impedance matching

AMERTRAN 923A

680,000

1200

L

1.0-1.8

* The UTC-2080 is rated by the manufacturer for transforming between source/loads of 100 and 100k Ohms.  A similar transformer made by the Stanley Company (TF-1A-10-YY) is (or was) offered by the Fair Radio Sales Co. as #T3/AM20, for about $7.95.  They are recommended as good all around choices for driving 300 ohm soundpowered phones (SP elements in parallel) in good quality crystal radio sets. Table 4 - AC parameter values of the UTC 2080 and Stanley TF-1A-10-YY transformers, measured at the 100 ohm terminals (#1 & 2). Magnetizing Resistance at Resonant Distributed Inter-winding Inductance resonance frequency capacitance capacitance UTC 2080 395 mH 2.25k ohms 0.98 kHz 69.6 nF 39 pF Stanley TF-1A-10-YY 595 3.15k 1.65 15.7 66 Transformer name

To obtain the approximate magnetizing inductance, resonant resistance and distributed capacitance for the UTC and Stanley units that appears at terminals 3 and 4 (other winding open-circuited), multiply the values of the first two parameters above by 1000 and divide the distributed capacitance by 1000. This is because of the 1:1000 impedance transformation ratio. Note: Terminals 1 and 2 are marked as the "100" ohm terminals, 3 and 4 are marked "100k".  Bear in mind that the magnetizing inductance of these transformers can vary appreciably from sample to sample because of the low (or no) air-gap design used in the laminations. Table 5 - Insertion Loss of MOUSER TM-117 Transformer(s) using various  Interconnections and Load Resistances Source Impedance Load Impedance Output Power Transformer Model  Insertion Loss in dB: Connections # 0.3*, 1.0, 3.3 kHz  in Ohms in Ohms Level Mouser TM-117 Mouser TM-117 4 Mouser TM-117 4 Mouser TM-117 4 Mouser TM-117 4 Mouser TM-117

50,000 24,000 100,000 100,000 100,000 100,000

1000 300 300 300 300 1,200

M M N N N O

-60 dBm -48 dBm -72 dBm -42 dBm -12 dBm -52 dBm

11.1, 1.8, 5.7 4.9, 1.2, 2.6 5.3, 1.5, 4.6 4.9, 1.1, 4.6 1.7, 1.7, 4.6 4.7, 1.2, 4.3 

*Some or all of the loss at 0.3 kHz can be eliminated by coupling the transformer to the headphone load through a series capacitor.  This makes a high pass filter with a cutoff frequency at or somewhat below 0.3 kHz out of the components, instead of having a just a plain old shunt parallel RL 6 dB/octave roll-off response.  The components of the filter are the shunt inductance of the transformer, the series capacitor and the shunt inductance of the headphone impedance.  A value around 2 uF is usually good if the headphone effective impedance is 300 Ohms (elements connected in parallel).  A value around 0.5 uF is good if the headphone effective impedance is 1,200 Ohms. (Elements connected in series)  One must experiment with different values because the inductance and effective impedance of different elements varies from Mfg. to Mfg.  Of course, this principle may be employed at other impedance levels such as the 12k ohms in a Brandes Superior headset, when used with an appropriate transformer (see the paragraph above Fig. 1).   Table 6 - Terminal Connections for UTC, AMERTRAN and MOUSER TM-117 Transformers G. Join 1 & 3, 4 & 6, 8 & 9.  Input is 7. Output is 1. Ground is 4 and 10. H. Join 2 & 3, 4 & 5. 8 & 9.  Input is 7. Output is 2. Ground is 4 and 10.  I. Join 3 & 4.  8 & 9. Input is 7.  Output is 2.  Ground is 5 and 10. J. Input is 3.  Output is 2.  Ground is 1 and 4.  K. Join 1 & 3, 2 & 4, 6 & 7.  Input is 8.  Output is 1.  Ground is 4 and 5.

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Audio transformer power loss and optimal impedance matching

L. Join 2 & 3,  6 & 7.  Input is 8.  Output is 1.  Ground is 4 and 5.  M. Input is 4. Output is 1.  Ground is 3 and 6  N. Take four TM-117s and label them W, X, Y and Z.  They will be connected in an      autotransformer configuration.  Join W6 to X4, X6 to Y4, Y6 to Z4.  Join W1 to       Y1. Join X3 to Z3,  Join W3 to X1. Join Y3 to Z1.  Connect a parallel  RC from      Z6 to W1.  Input is W4.  Output is Y1.  Ground for input and output  is Z3.  For an      explanation of why to use the RC, see the second paragraph after the first graph in       article  #1. O. Take four TM-117s and label them W, X, Y and Z.  They will be connected in an       autotransformer configuration.  Join W6 to X4, X6 to Y4, Y6 to Z4.  Join W3 to       X1, X3 to Y1, Y3 to Z1,  Connect a parallel RC from Z6 to W1.  Input is W4.        Output is W1. Ground for input and output is Z3.  For an explanation of why to       use the RC, see the second paragraph after the first graph in article #1.  Desirable       but optional:  Connect  X1 to the center of the 1,200 Ohm load (junction of two       600 Ohm sound-powered elements connected in series).  This eliminates a narrow       spurious 1 dB dip in the frequency response at about 1.2 kHz. The transformer loss figures for the UTC and AMERTRAN transformers were measured at an output power of about -60 dBm.  Performance is retained at output power levels much less than -60 dBm.  A voice signal at this power level will be quite soft, but understandable through most sound powered headphones. The MOUSER transformer deserves special discussion since it is so low in cost (available at Mouser Electronics (http://www.mouser.com ).  Frequency response and distortion:  The loss figures at two different power levels for a TM117 purchased in March of '00 are as follows: Output power level of +15 dBm:  2.8 dB @ 0.3 kHz,  1.9 dB @ 1.0 kHz and 6.4 dB @ 3.3 kHz.  Output power level of  -60 dBm:  11.1 dB @ 0.3 kHz,  1.8 dB @ 1.0 kHz,  5.7 dB @ 3.3 kHz and 5.4 dB @ 0.6 kHz.  The 0.3 kHz loss is greater at a power level of -60 dBm than at +15 dBm.  Why?  The core laminations of the TM-117 (and many other very small transformers) have low permeability at the low magnetic flux levels generated by the -60 dBm signal.  This low permeability is called initial permeability. The initial permeability, in combination with other factors, results in the transformer having a specific shunt inductance (at low signal levels).  This shunt inductance controls the low frequency roll-off of the transformer.  At higher flux levels (signal levels), but before saturation occurs, the permeability increases to an "effective permeability" value which can be several times greater than the initial permeability.  This means that the transformer shunt inductance is higher at the higher signal level and the low frequency roll-off is much reduced.  There may be some production unit-to-unit variation in the low frequency response of the TM117.  One that I bought about a year ago showed 2.5 dB less loss at 0.3 kHz than the one tested above. Some low frequency harmonic distortion is generated in the changeover region from initial to effective permeability.  This can easily be seen on a 'scope, especially at 300 Hz sine wave.  I doubt that it would be very noticeable in actual crystal radio set use. One can see from lines three, four and five of data in the TM-117 Insertion Loss Chart above, that  the loss at 0.3 kHz, relative to that at 1.0 kHz, gets less as the output power level is increased.  The loss at 1.0 kHz is minimum at the -42 dBm output power level.  The greater 1.0 kHz loss at the -72 dBm power level is caused by the reduced shunt inductance as explained above.  The increase in 1.0 kHz loss at -42 dBm occurs because the core is getting closer to saturation.  The loss at 3.3 kHz in the four-transformer configuration is greater than that for one transformer shown on line 2 because the primary-to-secondary capacitance of transformers A and B is effectively connected from high impedance points and ground, thus rolling off the high end response.  The single transformer in line 2 is wired so that the primary-to-secondary capacitance is not in shunt across the primary to ground. The CALRAD line of small transformers offers two types that are suitable for use in transforming a high diode detector output resistance down to 300 or 1200 Ohms to drive SP phones.  Their insertion loss is quite low and within a fraction of a dB of that of the UTC LS-10.  One distributor of CALRAD transformers is Ocean State Electronics, 6 Industrial Drive, P.O. Box 1458, Westerly, RI. http://www.oselectronics.com/ (they call these transformers (Mini Audio Transformers).  The two transformers are #45-700, spec'd to transform 100k to 1000 Ohms and #45-703, spec'd to transform 200k to 1000 Ohms.  They sell for about $5.95 ea.  The following chart shows the measured performance of a single transformer and of combinations of two.  Lines #1 and 2:  Primaries are in series, secondaries in parallel.  Line #3:  Primaries are in parallel, secondaries in series.  Performance is very good, especially so, considering the price.   https://web.archive.org/web/20131030052247/http://www.bentongue.com/xtalset/5hpXform/5hpXform.html[06.08.2019 19:54:18]

Audio transformer power loss and optimal impedance matching

Table 7 - Insertion Loss of certain CALRAD transformer(s) as single units, and with two connected together. Line #

Transformer Model # (s)

Source Impedance in Ohms

1 2 3 4 5 6

Two 45-700 Two 45-703 Two 45-703 One 45-700 One 45-703 Two 45-700

110k 270k 51k 91k 220k 350k

Load Impedance Output Power in Ohms Level in dBW 300 300 1200 1200 1200 1200

-54 -54 -54 -54 -54 -54

One 45-703+ 510k 1200 -54 one 45-700              * See asterisk just below the preceding Mouser transformer table.  7

Insertion Loss in dB: 0.3*, 1.0, 3.3 kHz 1.2, 0.9, 0.9 1.9, 0.9, 1.3 1.6, 1.0, 1.0  1.8, 1.0, 0.9 3.7, 1.4, 1.3 3.0, 1.1, 1.8 4.8, 1.5, 2.5

Note: The hot lead of the high impedance winding should always be the red lead.  The hot lead of the low impedance winding should be the white lead.  The high impedance windings are connected in series in lines 1, 2, 6 and 7.  They are in parallel in line 3. The low impedance windings are connected in parallel in lines 1, 2, 6 and 7 with leads of like color connected together.  The hot low impedance output connection is to the white leads.  The other two joined leads go to ground.  The low impedance windings are connected in series in line 3. One must properly phase the windings when two transformers are used.  The lead from the hot end of the high impedance winding of transformer #1 should be connected to the diode.  Its cold lead should go to the hot lead on transformer #2.  The cold lead of transformer #2 should go to a parallel RC, the other end of which should either go to ground in lines 1, 2, 3,  and 7 or to the hot low impedance output in line 6 (autotransformer connection).  In line 7, transformer #1 should be the 45-703. A UTC O-15 'Ouncer' transformer can be combined with a Bogen T-725** to make an excellent low loss transformer assembly for matching a wide range of headphone impedances, as well as an 8 ohm speaker, to a 1.35 Meg source resistance. See Fig. 4a.  Insertion Power Loss is 2.6 dB @ 0.3 kHz*, 1.2 dB at 1 kHz and 1.7 dB @ 3.3 kHz.  Note, that for these measurements, the housing of the O-15 was left ungrounded to eliminate the approximately 20 pF stray capacity from terminal #4 to the case.  This reduces loss at 3.3 kHz, but might introduce hum in some applications. An alternative connection that matches to a 1 Meg source is shown in Fig.4b.  This lowers the transformation ratio to reduce the effect of external stray capacitance-to-ground from crystal set components connected to the high impedance point.  It also reduces sensitivity to hum pickup if the case of the O15 is left ungrounded.  The result is a small 0.5 dB loss reduction loss at 3.3 kHz when that stray capacitance is 16 pF.  The Bogen T-725 transformer is available from Dave Schmarder's "Hobby Electronic Parts" at:  http://www.1n34a.com/catalog/parts.htm . The UTC Ouncer O-15 transformer is hard to find, but sometimes shows up on e-Bay. *See the asterisk at the end of the Mouser insertion loss table above. The R1 C1 combination is sometimes called a "benny".  It is used to reduce audio distortion sometimes encountered on strong stations. A good value for the pot, R1, is 1-3 Megs, preferable with an audio taper.  C1 is not critical.  A value of 0.1 uF is suggested. A typical diode for use with this transformer assembly is a one having a saturation current of about 22 nA, such as the Agilent 5082-2835 or HSMS-2820.  The weak signal audio output resistance of such a diode, as well as the input audio resistance of this transformer assembly shown in Fig. 4a are each about 1.35 Megs, making their parallel combination about 675k ohms. If the total shunt capacitance at this point is about 70 pF, audio frequencies above 3.3kHz will be attenuated by more than 3 dB.  This capacitance consists of the sum of the windings capacitance of the transformer assembly referred to its input, wiring capacity to the diode and the https://web.archive.org/web/20131030052247/http://www.bentongue.com/xtalset/5hpXform/5hpXform.html[06.08.2019 19:54:18]

Audio transformer power loss and optimal impedance matching

junction capacity of the diode, etc, all in parallel with the RF bypass capacitor of the detector (C9 in Fig. 5 in Article #26).  When using this transformer assembly, if the audio high frequencies seem deficient, try reducing that capacitor (C9), or maybe eliminating it and depending upon the other capacitive elements for RF bypassing.  If one possesses good high frequency hearing, a higher impedance tap than normal may strengthen the highs. This is because the impedance of magnetic headphones is not constant.  It rises as frequency increases, therefore, a better impedance match will exist for high frequencies when a higher impedance tap than normal is used.  See "The effect of source impedance on tone quality" in Article #2.

 

**Note re the Impedance Table for the Bogen T725 transformer, above: The Bogen Speaker Matching transformer is designed to be used when one wishes to drive multiple 8-ohm speakers, distributed over a wide area, from a single audio source, e.g., a public-address system. In order to limit I-R losses in the distribution line, the system is operated at a higher than normal impedance and voltage. For example, a 100-watt amplifier, with a 49-ohm output impedance, will deliver 70 volts to the line. At each speaker, a transformer is used to connect the 70-volt line to the speaker voice-coil. The line-to-voice-coil transformer has multiple primary taps to allow the power delivered to each speaker to be individually adjusted to suit system requirements. The taps on such transformers are often labeled with the power they will draw from a 70-volt, or sometimes a 25 volt line. When adding an 8 ohm speaker to a system with a Bogen T725, it is first connected to the pink wires of the T725. One then selects a tap to connect to the audio source, depending upon how loud one wants the speaker to be (taps white through brown), with black as common. The step-down turns ratio between [(white through red)-to-black] and [pink-to-pink] sets the volume. Basically, to accomplish its objective, the T725 was designed to transform an 8 ohm speaker load to one of various other impedances between 150 to 40k ohms as shown in the Table in Fig 4, above. Now let us get out of the context of sound distribution and into crystal set audio impedance matching. Consider the tapped black through white winding of the Bogen T-725 as just a conventional autotransformer designed for maximum efficiency (low loss) when used at the impedances shown. There is no "magic" in the "nominal" values of 150 through 40k ohms assigned to the various colored taps. The autotransformer can just as well be used at impedances a multiple higher or lower than those shown, although with some extra insertion power loss. It seems that the convention of assigning impedance values to the taps has fostered some confusion. For instance, one should not think that the "right" impedance to connect to the green wire is 2.5k ohms. In the BTUltimatch (see Part 4, below), the settings of the input and output switches connected to T725 should be set for minimum insertion power loss. Probably the 'nominal" impedance of the output tap used will be close to that of the load but not necessarily the same.

Part 4 - The BT-UltiMatch, a modified version of Steve Bringhurst's UltiMatch.  Insertion power loss and input resistance measurements when using a selection of various 'Stanley-type' transformers or an UTC O-15 for T1 for the input transformer are displayed Steve Bringhurst's UltiMatch (see http://www.crystalradio.net/soundpowered/matching/index.shtml#UltiMatch) on Darryl Boyd's Site provides a convenient low-loss way to provide audio impedance matching between the output resistance of a diode detector and the average impedance of headphones or a speaker. The BT-UltiMatch is somewhat different from Steve's, the differences being the replacement of Steve's SW5 with a single-pole 10 point rotary switch and provision for switching in an UTC O-15 in place of the "Stanley-type" transformer used for T1. https://web.archive.org/web/20131030052247/http://www.bentongue.com/xtalset/5hpXform/5hpXform.html[06.08.2019 19:54:18]

Audio transformer power loss and optimal impedance matching

The two10-point rotary switches enable one to connect any of the taps of T2 to the secondary terminals of either T1 or T3, as well as to the output capacitors C2-C6. This provides for a greater range of impedance transformation and a further reduction in power loss (especially at high source resistances) than when one is limited to using only the brown or red wires of T2. Provision is also made for switching in a UTC O-15 Ouncer transformer in place of the Stanley-type unit. Two sets of measurements were made using 300 and 1200 ohm resistive loads (typical average impedance of SP headphones having both elements connected in parallel is 300 ohms, in series, 1200). The input voltage at 1 kHz was series-connected through a selection of source resistors to the input of the BT-UltiMatch.  The level of this voltage was adjusted to produce about 10 mV RMS across the output load of 1200 ohms (5 mV when measuring with a 300 ohm load). See Part 5 of this Article for info on how the BT-UltiMatch loss measurements were made.

Parts list T1 - "Stanley-type" 100k-100 ohm transformer, available from Fair Radio Sales as # T3/AM-20 T3 - UTC Ouncer O-15 1 meg-10k ohm transformer R1 - 2 or 3 Meg log taper pot or, a 1 Meg log taper pot with provision for switching in a series resistor to increase the total resistance to 2 Megs if low saturation current diodes (having a high axis-crossing resistance) are to be used C1 - 0.22 uF capacitor C2 - 4.7 uF non-polar capacitor C3 - 2.2 uF non-polar capacitor C4- -1.0 uF non-polar capacitor C5 - 0.47 uF non polar capacitor C6 - 0.22 uF non polar capacitor SW1, SW2 - Single pole 12 position (only 10 used) rotary switches. Designate SW1 and SW2 switch positions with the nominal impedance values given in the Table in Fig 5 SW3 - One pole, 6 position rotary switch SW4 - Two pole, 4 position rotary switch Operation of the BT-UltiMatch Four modes of operation are provided by SW4:

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Audio transformer power loss and optimal impedance matching

1. This most common mode uses a "Stanley type" transformer as the input transformer, T1. For use with a wide range of diodes having moderate axis-crossing resistances, such as the ITT FO-215 germanium diode (Is~100 nA). 2. Uses UTC O-15 Ouncer transformer for T1. Use with diodes having high axis-crossing resistances such as the Agilent 5082-5235 Schottky diode (measured Is~15 nA, not the spec sheet value of 22 nA), or 2-3 in parallel. 3. Does not use input transformer T1. Use with diodes having low axis-crossing resistances such as the 1N34A germanium diode (Is~600 nA). 4. Does not use input transformer T1. Use for general purpose impedance transformation, working with T2 only (SW1 and the "benny" - R1,C1 are out of the circuit). J1 should be connected with a very short cable (when using very low Is diodes) to the diode output of a crystal set, the usual audio source. J2 is connected to headphones or a low impedance speaker. The "nominal" impedance designations on SW1 and SW2 are for reference and do not always represent the settings for the least insertion power loss. When starting out to match real world headphones or a speaker to the diode output of a crystal set, do the following: 1. Select a setting for SW4, depending upon the estimated Is of the diode being used (see Tables 1 and 2 in Article #27 for some help on this). 2. Set the "nominal impedance" of SW2 to the expected average impedance of the output load (see Article #2 for info on how to obtain this info). 3. Set SW3 to the "thru" position. 4. Adjust SW1 for loudest volume. 5. Adjust R1 for minimum distortion. 6. The optimum settings for SW1 and SW2 are interactive. Try higher and lower settings for SW1 , then tweak SW2 to see if greater volume is available, then iterate. 7. Try different settings for SW3 to see if bass response improves. Table 8 - Insertion power loss in a BT-UltiMatch @ 1 kHz using a selected Stanley

transformer TF-1A-10-YY "D" or an UTC Ouncer O-15 transformer for T1. Measurements are made with different series-connected source resistances and with load resistances of 300 or 1.2k ohms. SW1 and SW2 were adjusted for maximum output Transformer

Source and load resistances in ohms, insertion power loss in dB

Stanley "D"

2.2 Meg, 300; -2.59

1.0 Meg, 300; -1.41

470k, 300; -0.70

220k, 300; -0.69

100k#, 300; -0.94

UTC O-15

2.2 Meg, 300; -1.61

-

-

-

-

Stanley "D"

2.2 Meg, 1.2k; -2.50

1.0 Meg, 1.2k, -1.37

470k, 1.2k; -0.94

220k, 1.2k; -0.95

100k#, 1.2k; -0.84

UTC O-15

2.2 Meg, 1.2k; 1.54

-

-

-

-

Table 8A - Nominal** settings for SW1 and SW2 taps in ohms for minimum insertion power loss, using a UTC or selected Stanley transformer for T1 Transformer

Source resistance, load resistance of 300 and [T1 and T2 nominal tap settings] in ohms

Stanley "D"

2.2 Meg; 600, 300

UTC O-15

2.2 Meg;, 10k, 150

Transformer

1.0 Meg; 300, 300 -

470k; 1.2k, 1.2k -

220k; 600, 1.2k -

100k#; 40k, 150 -

Source resistance, load resistance of 1.2k and [T1 and T2 nominal tap settings] in ohms

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Audio transformer power loss and optimal impedance matching

Stanley "D" 2.2 Meg; 1.2k, 1.2k UTC O-15

2.2 Meg; 10k, 600

1.0 Meg; 600,1.2k

470k; 300, 1.2k

220k; 300, 2.4k,

100k#; 40k, 600

-

-

-

-

** See Table of Impedance taps in Fig 5 showing nominal impedances for the various taps on the Bogen T-725 transformer # SW4 set to position 3

Table 9 - Insertion power loss (dB) in a BT-UltiMatch @ 1 kHz using various transformers for the input transformer with various series-connected source resistances. Load resistance of 1.2k ohms. SW1 and SW2 were adjusted for maximum output Transformers

Series-connected source resistance in ohms; insertion power loss in dB

Stanley "C"

-

1.5 Meg: -1.95 

1.0 Meg: -1.51

470k: -0.98

220k: -0.97

-

Stanley "Z"

-

1.5 Meg: -2.26

1.0 Meg: -1.75

470k: -1.03

220k: -1.00

-

Stanley "D"

2.2 Meg: -2.50

1.5 Meg: -1.81

1.0 Meg: -1.37

470k: -0.94

220k: -0.95 100k#, -0.84

UTC C-2080 "A"*

-

1.5 Meg: -1.73

1.0 Meg: -1.36

470k: -0.99

220k: -0.96

-

UTC C-2080 "B"

-

1.5 Meg: -1.90

1.0 Meg: -1.46

470k: -0.93

220k: -0.96

-

No name TA18.071*

-

1.5 Meg: -1.81

1.0 Meg: -1.42

470k: -0.92

220k: -0.97

-

UTC O-15 Ouncer 2.2 Meg: Tx -1.54 * The polarity of one winding in each of these transformers was reversed during its manufacture. Measurements were made with terminals 1 and 2 interchanged to correct the condition. The polarity assumption used in the BTUltiMatch for a Stanley-type T1 is as follows: If an AC voltage is applied from terminals 3 to 4, a voltage of the same polarity will appear from terminals 1 to 2.  It is recommended that anyone building a BT-UltiMatch check the polarity of the internal terminal connections of the T1 transformer with a 'scope.

Table 10 - Input resistance of a BT-UltiMatch driven from various series-connected source resistances, terminated by a 1200 ohm load and adjusted for minimum loss Transformer used for T1

Series-connected source resistance

Stanley TF-1A-!0-YY  "D" Stanley TF-1A-!0-YY  "D" Stanley TF-1A-!0-YY  "D" Stanley TF-1A-!0-YY  "D" Stanley TF-1A-!0-YY  "D"

100k 220k 470k 1 Meg 2.2 Meg

BT-UltiMatch input resistance 171k# 286k 517k 751k 1.10 Meg

UTC O-15 Ouncer

2.2 Meg

1.68 Meg

# SW4 set to position 3 Notice, since the transformers are mostly not used at their design-center impedances, settings for minimum insertion power loss do not always coincide with an impedance matched condition.

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Audio transformer power loss and optimal impedance matching

Part 5 - How to Measure the approximate Insertion Power Loss of any Audio Transformer or Compare its Performance to that of an Ideal no-loss Transformer The equipment needed are an audio sine wave generator, an assortment of resistors (preferably not a resistance box), and a high sensitivity scope or DVM.  The use of a vertically calibrated scope is preferable to a DVM, as one can see that the waveform is clean and without appreciable hum or noise.  A difficulty with this approach is that one must make sure that the scope decade attenuator as well as the 10X switch on the probe are accurate.  I use the scope probe switched to 1X when reading the low voltage secondary voltage and to 10X setting when measuring at the higher voltage primary.  The high input impedance of the probe prevents excessive loading of the high impedance primary, thus reducing the voltage there and causing an incorrect reading. When a DVM and a 'scope of adequate sensitivity are available, the best approach, and the one I now use, is to connect them in parallel. This provides the relatively high precision of a reading with the DVM along with the ability to monitor the voltages for purity (low distortion of the sine wave measuring wave form and low noise). Connect the hot lead of the generator to the high impedance primary of the transformer through a resistor of value equal to Rs.  Rs should be equal to the expected output resistance of the diode detector.  Connect a load resistor of value Zh (expected effective impedance of the headphones) to the secondary.  Connect all grounds to a common point. Tune the generator to the first frequency of measurement, say 1000 Hz.  Connect the scope or DVM to the low impedance secondary.  Adjust the audio generator to as low a level as possible while still being able to get an accurate reading of the voltage without error from hum and noise. Read this voltage and call it E3.  Now connect the scope probe to the hot end of the primary.  Read that voltage and call it E2.  Connect the scope probe or meter to the actual generator output (not the transformer hot lead).  Read this voltage and call it E1.  Calculate insertion loss:  Loss=10*log{4*RS*[(E3/E1)^2]/Rl} dB.  Also take measurements at 300 and 3300 Hz.  If the 300 Hz loss is much greater than the 1000 Hz loss, a transformer with a higher primary inductance is needed.  If the 3300 Hz loss is much higher than the 1000 Hz loss, the transformer has too high a winding capacitance for the primary source resistance (RS) selected.  If the loss at 1000 Hz is above about 2 dB, a better transformer probably exists.  Hopefully all readings will be better than -2 dB.   If the transformer is doing a good job of impedance matching RS to Rl, E2 will be about 1/2 the value of E1 and the transformer insertion loss will be at about its minimum.  If E2 is much lower than 1/2 of E1, a greater impedance transformation (turns ratio squared) is needed.  If the transformer has taps on the secondary, using a lower impedance tap might improve results.  If E2 is higher than 1/2 of E1, the impedance transformation ratio is too large and a higher impedance secondary tap should be tried (if available).  It is assumed here that reactive mismatch from transformer shunt inductance and distributed capacitance is negligible.  It's usually best to make the 1/2 voltage measurement at the frequency of minimum loss (usually about 1 kHz for audio transformers. In this series of Articles the statement is often made or implied that power loss in an audio transformer is at a minimum when the input is impedance matched.  This is not strictly true.  If a transformer has internal resistive power loss and is matched at its input, the output will, in general, be mismatched.  A simultaneous matched condition at both input and output is usually impossible unless the transformer has no internal losses, or its series and shunt losses are in the correct proportion.  A real world transformer delivers its minimum loss when the input and output mismatches (S-Parameter return losses) are equal.  Verification of this condition is both difficult and unnecessary because the two loss values (matched input vs equal mismatch at input and output) normally differ very little.  This being the case, one can say, for practical purposes, that the minimum insertion power loss occurs when the input is impedance matched. An easy way to compare the performance (loss) of a particular transformer with that of an ideal no-loss transformer of just the right transformation ratio is to build and use the 'Unilateral Ideal Transformer Simulator' described in Article #14. Tip:  If hum and noise are a problem, place the scope (or DVM), signal generator transformer and all leads on a metal ground plane connected to the scope ground.  Ordinary kitchen aluminum foil is suitable for the ground plane. Note:  If one has some sort of audio impedance measuring device and desires to measure the shunt inductance of an audio transformer, make sure the measurement frequency is low enough so that the transformer winding https://web.archive.org/web/20131030052247/http://www.bentongue.com/xtalset/5hpXform/5hpXform.html[06.08.2019 19:54:18]

Audio transformer power loss and optimal impedance matching

capacitance does not interfere with accuracy.  A transformer, tested above, that is very good for many crystal radio sets when driving 300 ohm headphones is sold by Fair Radio Sales Co. http://www.fairradio.com/ as #T3/AM20 (similar to UTC #2080).  Its winding capacitance is at approximate resonance with its shunt inductance at 1 kHz.  This is good design practice since it minimizes insertion power loss at the (approximate) geometric center of the audio band.  A measurement of its unloaded (high impedance winding) Z at 1 kHz yields a result of "infinite" shunt inductance in parallel with a resistance of more than a Megohm.  A measurement at 300 Hz gives a result of several hundred Henrys.  A measurement at 3300 Hz would show a capacitive, not inductive impedance.

Part 6 - Some practical suggestions on where to get and how to identify transformers that may perform well with sound powered headphones Here are some generic transformer specifications, which when met, probably indicate that the transformer will exhibit low insertion loss when used to drive sound powered phones in a crystal radio set.  A transformer obtained at a Hamfest, junk box or Surplus Dealer that meets these specs. will probably cost substantially less that the UTC and Amertran transformers. Fair Radio Sales Co. at http://www.fairradio.com/often has suitable transformers available at reasonable prices. Wide frequency response specification such as +/- 1 dB, 20-20,000 Hz:  A transformer having a Manufacturer's specified operating frequency range from, say, 200-5,000 Hz will probably have several dB more loss than a wide band unit when both are sourced and loaded with resistances that reduce their bandwidth to covering only the 0.3-3.3 kHz range.  The reason for this is that we usually want to operate the transformer with primary source and secondary load resistances several times higher than that which the manufacturer specifies.  This always narrows the transformer pass-band.  We should shoot for a final passband of 0.3 - 3.3 kHz, or so.  High impedance winding specification:  Single grid, preferably push pull grids, single plate or preferably push pull plates. The impedance level, if specified, will usually be between 20,000 and 80,000 Ohms.  The high impedance winding is the one to connect to the diode detector output. Low impedance winding specification:  Low impedance mike, pickup, multiple-line or simply a number between 100 and 1000 (Ohms).  Several taps may be supplied to enable various  impedance levels.  The specification might be: 50, 125/150, 200/250, and 333, 500/600 Ohms.  This winding is the one to which the sound powered phones are to be connected. The correct low impedance tap to use for connecting the sound powered phones may be calculated as follows: Decide the audio load resistance to be presented to the detector.  Let's select 200,000 Ohms.  (See Articles #1 and #4 for info on how to determine this value).  Assume that the sound powered elements are connected in series. This will typically result a headphone average impedance of 1,200 Ohms.  Calculate the needed impedance transformation ratio as:  200,000/1,200 = 167.  Note the Manufacturer's specification for the high impedance winding of the transformer. (If you don't know what it is, estimate 80,000 Ohms.), and divide it by 167.  Select the Manufacturer's low impedance winding tap specification (if you have that info) that most closely equals the value calculated above. If you are using the 80,000 Ohm estimate, the desired tap impedance would be 80,000/167 = 479 Ohms.  Call this number A.  Now check what the result would be if the sound powered elements were connected in parallel.  They will now present an effective impedance of 300 Ohms and require an impedance transformation ratio of 200,000/300=667.  The desired Manufacturer's tap marking will now be 80,000/667 = 120 Ohms.  Call this number B.  Pick the number A or B, whichever is closest to an available transformer tap marking.  Connect the phone elements appropriately.  Note that we are using the transformer at a higher impedance level than that for which it was designed.  What we lose is by doing this is audio bandwidth and a small increase of insertion loss.  We don't need the 20-20,000 Hz range anyway, do we?  What we gain is an ability to transform headphone impedance to a higher value than if we used the manufacturer's ratings. If you have a transformer on which you have no specs. except that it is designed to couple from a low impedance to push-pull grids, a grid, push-pull plates of a plate or just "high impedance",  connect that winding to the crystal diode and experiment with connecting the https://web.archive.org/web/20131030052247/http://www.bentongue.com/xtalset/5hpXform/5hpXform.html[06.08.2019 19:54:18]

Audio transformer power loss and optimal impedance matching

headphones to the various taps provided on the low impedance winding.  Do this experimentation using a weak signal and pick the connection that gives the greatest volume. #5  Published: 10/22/99;  Last revision: 03/30/2008 060410

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A Crystal Radio Diode Detector Simulation using SPICE by Ben H. Tongue

A crystal radio set detector may be simulated in Spice by using a voltage source V1 feeding a parallel tuned circuit L1|C1 through a source resistance R1.  The parallel tuned circuit may be made to have any Q by placing a parallel resistor across the tuned circuit.  In the simulation circuit files enclosed, an infinite Q is assumed (no RF tuned circuit losses).  The actual source loaded Q of the tuned circuit is R1/(Reactance of C1 at resonance).  The voltage at the hot end of the tuned circuit is connected through a diode D1 to a parallel RC load R2|C2.  The detected output voltage is developed across this load. The purpose of doing this is to enable experimentation to determine how the detection sensitivity changes if the diode type, diode source resistance, and/or load resistance are changed.  This program enabled me to develop the graphs shown in Article #1 on my home page that show how detector power loss varies as a function of rectified diode current for a HP 5082-2835 diode and also, more importantly, as a function of diode saturation current Is.  The input voltage is modeled as an un-modulated 1.0 MHz sine wave consisting of 4002 individual cycles, sampled at eight points per cycle. If one wants to evaluate the result of using an AM modulated wave, three simulations can be made using min., carrier, and max. Voltage levels of the desired modulated wave.  Note: Graphs of diode current and voltage waveshapes, as a function of signal power, may be viewed in Article #8. One of the simulations in the enclosed Zip archive 'Crystal Set SPICE Simulations' (click here) uses a Spice model of a Schottky diode similar to the HP 5082-2835.  This is called simulation XtlSetSim1 and its files are contained in the directory XtlSetSim1.  The other simulation uses a Spice model of the 1N34A.  This is called simulation XtlSetSim2 and its files are in the directory called XtlSetSim2.  Each of these directories contains all the files that were generated by my SPICE simulator when I ran each simulation.  The diodes used in each of these models have the value of CJO set to 0.0 pF.  This does not effect the simulation and makes it easier to experiment with various values of C2 without the detuning effect of CJO.  The input source and output load resistance values are equal and match the diode RF input impedance and audio output impedance values.  One would expect this condition to give the lowest loss (highest Xtal Set sensitivity) at very low signal power levels.  This is not so because at very low input power levels, the diode detector exhibits a square law relation, not linear relation between output and input power.  See Article #15 for an explanation of how a theoretical 2 dB increase in detector output can be obtained by a deliberate RF mismatch. In XtlSetSim1 the input sine wave voltage is set to a peak value of 0.1 volts.  Since the source resistance is set to 700,000 ohms, the power incident on the detector is -57dBm.  The output power delivered to R2 is -68dBm at 10.5 mV.  The scale is not shown for the green output curves in the graphs below.  That scale is 0.002 mV per division with the zero depressed two divisions below the zero centerline used by the other graphs.  A broadcast AM voice signal, if it developed a peak instantaneous power in the detector load of -68dBm, would be just sufficient to enable me to understand about one half the words.  This assumes that I am using headphones of an equivalent 700,000 Ohms AC impedance having the power sensitivity of a good real world Sound-Powered Headset.  (The 700,000 Ohm impedance, of course would be obtained with the aid of an audio transformer.)  The RMS audio power would be about 18dB less or -86dBm.  Of course, the impedance values used here are quite high, but they are the values I achieve in my loop crystal radio set.  To find out where the -18 dB came from, see Article #1, end of

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Diode detector Simulation using SPICE

part 1, from the home page. In XtlSetSim2 the input sine wave is set to a peak value of 0.045 volts.  Since the source resistance is set to 16,000 ohms, the power incident on the detector is -47dBm. The output power delivered to R2 is -68dBm, the same as in the XtlSetSim1 example.  The audio load used is 16k ohms. Note that the insertion loss in XtlSetSim1 is 68-57=11 dB.  The loss in XtlSetSim2 is 68-47=21 dB.  XtlSetSim1 requires 10 dB less input than XtlSetSim2 for the same output!  XtlSetSim1 uses a diode with a saturation current Is=40 nA and n=1.08. XtlSetSim2 uses a diode of Is=2600 and n=1.6.  The second graph in article #1 on this site predicts that the loss difference would be 8dB.  This experiment illustrates that a detector using a of a lower Is, if it is matched at the input and output, will have a lower loss than one using a diode of a higher Is. I have found, since this article was written, that in a 1N34A germanium diode, the values of Is and n change at low currents.  Is may go down as much as 5 times and n may drop 25% from the values used in simulation XtlSetSim2. (Those values were obtained at an unrealistically high diode current of about 320 uA.)  This was not expected. The result is that the germanium diode is unfortunately shown incorrectly and in a very unfavorable light (for crystal radio set use).  The simulation in XtlSetSim2 probably should have used an Is of about 700 nA and n should have been about 1.15.  I used the SPICE program from Intusoft called ICAP4WINDOWS demo version.  It can be downloaded for free from their Website at http://www.intusoft.com.  The netlists: XtlSetSim1.cir and XtlSetSim2.cir can be edited and used in any other SPICE simulator. Keep the following things in mind:

1. Simulations are only as good as the SPICE simulator, its device models and the circuit topology used.  The Shockley diode equation agrees well with the results from the Schottky diodes I have checked, even at low currents.  With the one germanium 1N34A I have checked, the Shockley diode equation equation works well above about 40 micro-amps but not very well below that. (for a specific voltage, the equation specifies a higher current than the diode delivers.) 2. The tuned circuit L1|C1 must be tuned to resonance.  When this is the case, the voltage across the tuned circuit will be in phase with the source voltage V1.  If the Intusoft simulator is used, the probe point for V1 is Y1 and the probe point for the tuned circuit voltage is Y2.  If one views Y1 and Y2 on the same graph one can check the relative phases of the two voltages. Y3 gives the output voltage.

3. The carrier ripple shown at the output has negligible effect on the average output.  A larger value for the filter bypass C2 can reduce the ripple, but at the expense of rise time of the output voltage.

4. When considering the practical application of simulation ideas, keep in mind the advice in articles # 1, 4 & 5 on this Website, especially as regards audio impedance matching.

5. Shown below are the schematic diagram from the schematic editor Spicenet, the simulation of all 4002 cycles of the 1.0 MHz signal at Y1, Y2 and Y3, and the last four cycles of the 1.0 MHz signal. Note that this simulation uses a Schottky diode, not a 1N34A diode.  

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Diode detector Simulation using SPICE

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Diode detector Simulation using SPICE

#6  Published: 01/02/00;  Last revision: 11/23/01 060410

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Do diodes have a specific knee voltage or is it just a matter of scale? http://www.bentongue.com/xtalset/7diodeCv/7diodeCv.html Go

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    Diode Voltage/Current Curves: Does a Specific "Knee" Voltage really Exist? by Ben H. Tongue

I think that there is validity to the notion of the existence of a diode "knee" when clamping circuits are considered, and maybe with other circuits.  I do not think that there is any validity to the notion of a "knee Voltage" in the forward conduction portion of a diode curve when low signal level detection is considered.  The reason is that the apparent Voltage of the knee is an artifact of the Current Scale used in plotting the diode V/I curve.  In fact, the shapes of the forward conduction curves of all normal diodes are quite similar, and with no "knee", if the Current scale is logarithmic, not linear.  To illustrate this, take a look at the charts below.  The first four use a linear scale for the Current axis.  The full-scale Current values are: 4000 uA, 600uA, 4uA and 1.25uA.  The 1N34A diode is one purchased at Radio Shack with measured Is =2.57uA, n=1.6, and Rs=6.55 ohms.  The values of Is and n were calculated from measurements made at an effective diode current of 320 uA.  The fifth chart shows the 1N34A and a 1N914 using a linear current scale.  The sixth chart shows the two diodes using a log Current scale.  The 1N914 has n1.85, Is=2.3nA and Rs=6.0 Ohms. Graph #1 seems to show a knee at about 0.2+ Volts.  A knee at about 0.2 Volts seems a little ambiguous in graph #2.  In graph #3 the knee has vanished.  Graph #4 seems to show a knee on the current scale in the reverse bias region!  The fifth and sixth graphs show a comparison of the 1N34A and 1N914 in the forward conduction region with a linear and then a log Current scale.  Note the apparent knees on the linear plot and the total absence of any knee on the logarithmic plot. For RF diode detectors to work, one needs a device that has a non-linear V/I curve.  In other words, the slope of the V/I curve must change as a function of applied Voltage.  The slope must be steeper (or shallower) at higher voltages and shallower (or steeper) at lower voltages than at the quiescent operating point.  To clarify this, look at curve #3.  As a low-level signal detector, this diode will rectify if biased at -0.025, 0.0 or +0.025 volts.  The difference is that the diode resistance at the -0.025 Volt operating point is higher than that at 0.0 Volts. It is lower at +0.025 than at 0.0 Volts.  If one places a straightedge on the screen of one's PC monitor, tangent to the curve at -0.025, 0, and then +0.025 Volts, one can measure a slope of about 80k Ohms at -0.25 Volts, 40k Ohms at 0.0 Volts, and 20k ohms at +0.25 Volts.  The rate-of-change of slope as a function of voltage (second derivative) is less at -0.025 Volts than at +0.025 Volts. This means that the detection sensitivity when biased at -0.025 Volts will be less that when biased at +0.025 Volts, even it the input and output are properly impedance matched.

 

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Do diodes have a specific knee voltage or is it just a matter of scale?

#7 Published: 01/08/00;  Last revision: 05/25/00 060510

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Do diodes have a specific knee voltage or is it just a matter of scale?

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Current and voltage weveforms in a half-wave AM peak detector, at several input-power levels http://www.bentongue.com/xtalset/8DetVIWG/8DetVIWG.html Go

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Crystal radio diode detector power loss with current and voltage waveforms, as determined from a SPICE Simulation By Ben H. Tongue

Quick summary:  This Article shows diode detector voltage and current waveforms and how they change as a function of signal strength. In this article I am going to show an analysis of the operation of a crystal radio set detector using a SPICE simulator.  The detector voltage and current waveforms will be shown for three different input "available power" sources.  These sources will supply either  -85.54, -65.54 or -45.54 dBW (number of dB's below one Watt) power to a matched load.  Each power source is made up of a pure voltage source combined with a resistance.  (The combo could also be referred to as a "voltage source with an internal resistance").  In each case the available input power, the output power and detector insertion loss will be shown. Conformance to or deviation from the usually assumed peak-detector model will be investigated.  The change in input resistance with change in input power will also be examined. Here is a derivation one needs to know in order to understand the rest of this article.  The concept of "available power":  If one has a voltage source V with an internal resistance R, then the load resistance to which the maximum amount of power (Pa) can be delivered is itself equal to R.  Pa will be called the "maximum available power".  Any load resistance other than one equal to the source resistance R will absorb less power from the source.  This applies whether the voltage is DC or AC (RMS).  An equation for power absorbed in a resistance is voltage squared divided by resistance.  In the impedance matched condition, because of the 2 to 1 voltage division from the source resistance and load resistance, one-half of the internal voltage V will appear across the load resistance.  The actual power absorbed by the load will be, as indicated in the preceding relation: P = ((V/2)^2)/R = (V^2)/(4R).  Half of the power delivered to the series combination of the source resistance and the load resistance will be delivered to the load.  The other half is dissipated and lost in the source resistance.  In the crystal radio set case the input voltage is AC RF voltage.  If the input voltage is referred to by its peak value (Vp) as it is in SPICE, instead of by its RMS value, the equation changes.  The RMS voltage of a sine wave is equal to the peak value of that wave divided by the square root of 2.  Since the power equation squares the voltage, the equation for the "available input power" changes to P = (Vp^2)/(8R).  This is the equation that will be used to calculate available input power to the detector, from the source. Here are some definitions, assumptions and explanations: 1. The internal resistance of the antenna is transformed up to the equivalent parallel resistance R that is used in the simulation.  The tuned circuitry used to do this is not shown. 2. The single tuned circuit used is assumed to have an infinite Q.  A finite Q will cause an increase in insertion loss. 3. "Diode Detector Power Loss" is defined as the ratio of DC output power dissipated in the output load resistance to the RF input "available power". (Expressed in dB) 4. The L/C ratio of the tuned circuit L1, C1 is sufficiently low so that no appreciable harmonic https://web.archive.org/web/20141130232014/http://www.bentongue.com/xtalset/8DetVIWG/8DetVIWG.html[06.08.2019 19:58:11]

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Current and voltage weveforms in a half-wave AM peak detector, at several input-power levels

voltages will be developed across it by the detection action of the diode. 5. The RF bypass capacitor C2 is sufficiently large so that the RF ripple voltage across it is small compared to the voltage across the tank circuit. (Appreciably all to the tank circuit voltage, therefore, appears across the diode). 6. The output load resistance may seem to be a high value for headphones.  It is assumed that in practice, the headphone impedance will be transformed up to that value by a low loss audio transformer.  It is also assumed that the transformer primary has an appropriate capacitor bypassed resistor in series with it.  The purpose of this is to insure that the audio load on the diode has the same DC as AC value. 7. The RF and AF load resistances used in the simulation will seem quite high.  This is because the average unloaded shunt resistance of the loop in my single tuned loop receiver is 700k Ohms, and I am using it in the simulation that follows. 8. The diode junction capacitance is set to zero in the netlist.  This has no effect on the operation of the detector if C1 is retuned to take account of this fact.  Experimentation is now more convenient since a change of C2 will have no effect on tuning. 9. The diode parameters are specified so as to produce an RF input resistance of 700k Ohms when operated in a detector circuit and driven by a low available power source of, say, -85 dBW. A basic crystal radio set diode detector schematic is shown below.  An Intusoft SPICE simulator will be used in three separate simulations to measure circuit currents and voltages.  The calculations from the simulations will show that the detector insertion loss approaches zero at high input power levels and that it goes up sharply as the input power goes down below a certain point.  This loss will be minimized if the input and output resistances of the detector are impedance matched.  The following discussion assumes that the RF source and both the DC and Audio AC load are matched to the diode at a low signal input power level.  Two modes of operation for a detector have been defined:  Linear and square law.  Linear operation is said to occur when a change of input power (in dB) causes an equal change in output power.  Square law operation is said to occur when a given small change in input power (in dB) causes double that change in output power.  Where is the breakpoint between linear and square law operation?  SPICE simulation gives the answer, to the extent that SPICE and the diode models are accurate (See Note 1. after SPICE netlist).  An input power sufficient to cause the rectified DC current to equal to the saturation current (Is) of the diode is an indication of operation half way between linear and square law.  The detector power loss at this level is 7.1 dB.

 

 

The Intusoft ISpice netlist shown below is automatically generated by the SpiceNet program after the

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Current and voltage weveforms in a half-wave AM peak detector, at several input-power levels

schematic and parts values are entered into the program. C:\spice8d\Circuits\XSchottky.cir Setup1

*#save V(1) V(2) @R1[i] @R1[p] @C1[i] @L1[i] V(3) @D1[id]

*#save @D1[p] @C2[i] @R2[i] @R2[p]

*#viewtran iy3

*#alias iy3 @d1[id]

*#alias y1v(1)

*#viewtran y1

*#alias y2v(2)

*#viewtran y2

*#alias y3xv(3)

*#viewtran y3x

.TRAN 31.25n 502u

*#save all

.OPTIONS reltol=0.00001

.OPTIONS vscale=0.25

.PRINTTRAN IY3

.PRINTTRAN Y1

.PRINTTRAN Y2

.PRINTTRAN Y3x

V1 1 0 SIN 0 0.125 1meg 0 0 0

R1 1 2 700k

C1 2 0 50.52p

L1 2 0 500u

D1 2 3 _HP2835

.MODEL _HP2835 D BV=15 CJO=0 EG=0.69 IBV=2.5e-5 IS=38nA

+ N=1.03 RS=6.4 VJ=0.56

C2 3 0 100p

R2 3 0 700k

END Note 1:  In regard to the accuracy of the SPICE diode model, some diodes, notably the 1N34A are unusual.  The values of Is and n are not constant and do vary with diode current.  Measurements made on one 1N34A shows Is and n values of 2.7E-6 and 1.64 at 320 uA which drop to 1.21E-6 and 1.34 at 32 uA, then down to 6.6E-7 and 1.05 at 1.8 uA.  Schottky diodes seem to have constant values for n and Is. The SPICE netlist above shows, as the input, a 1.0 MHz sine wave of peak amplitude 0.125 volts for V1. (This Input signal level is 2.74 dB less one that would operate the detector half way between the linear and square law modes. At this lower input signal power level the insertion power loss of the detector is 7.12 dB).  The first of the three simulations will be done with an input sine wave of 0.125 volts peak for V1 as shown in the netlist.  The second simulation will use a 1.25-volt peak sine wave. The third will use a 12.5-volt peak sine wave.  The respective available input powers are: -85.54 dBW, -65.54 dBW and -45.54 dBW (dB below one Watt).

 

 

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Current and voltage weveforms in a half-wave AM peak detector, at several input-power levels

The black curve shows the diode current.  The other three curves all use the same scale on the vertical axis.  The blue curve shows the voltage at the test point Y2.  This is the voltage across the tuned circuit.  It has a peak value of 61.9 millivolts, about 1/2 that at test point V1.  This shows that the detector has an input resistance of about 700k Ohms.  There is a good input impedance match here.  The red curve shows the voltage across the diode.  Note that where it is positive, a forward diode current flows for about 42% of the time for one cycle of the 1.0 MHz wave.  Note that where it is negative, a reverse diode current flows. This reverse current flattens out and if a higher input signal was used, it would flatten out at about 38 nanoAmps, the saturation current of the diode.  Finally, note that there is no peak detection going on.  The diode output voltage, measured at test point Y3x is only 15.7 millivolts even though the peak forward voltage applied to the detector is 61.9 millivolts.  Input power as stated above is -85.54 dBW. The output power is ((0.0157)^2)/700k = -94.53 dBW.  Insertion loss = 94.53 - 85.54 = 8.99 dB.

 

 

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Current and voltage weveforms in a half-wave AM peak detector, at several input-power levels

Here, the input voltage at test point Y1 is 1.25 volts, but the voltage across the LC tank circuit, as measured at test point Y2 is only 494 millivolts, not 625 which would be the case if we had a perfect impedance match.  This shows that the detector input resistance is now lower than 700k Ohms.  Diode operation is getting closer to peak detection. The green output voltage at test point Y3x is 361 millivolts.  Forward current is now drawn over about 24% of one cycle time.  The input available power, as stated

Before, is -65.54 dBW.  The output power is ((0.361)^2)/700k = -67.30 dBW.  Detector power loss is: 67.30 - 65.54 = 1.76 dB.

 

 

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Current and voltage weveforms in a half-wave AM peak detector, at several input-power levels

Now it looks as if we are getting much closer to peak detection.  The peak positive voltage applied to the diode at test point Y2 is 4.30 volts.  The detected DC voltage at test point Y3x is 4.08 volts (only about 5% less than the 4.30 volt peak).  The diode forward conducts only during about  12% of the cycle time of the 1.0 MHz wave.  As stated before, the input available power is -45.54 dBW.  The output power calculates as: ((4.08)^2)/700k = -46.23 dBW.  Detector power loss goes down to: 46.23 45.54 = 0.69 dB.  The input resistance is now even lower than before. The green output voltage at test point Y3x is 4.08 volts, kind of low compared with the 6.25 volts we would get with a perfect input impedance match.  Why is this?  The input and output resistances of a diode detector both approach the value (0.026*n)/Is Ohms at low signal power levels. (n and Is are diode parameters used in SPICE.  n is called the diode Ideality Factor, or Emission Coefficient.  Is is called diode saturation current.)  Is is defined as the current that is asymptotically approached in the diode back bias direction before extraneous leakage factors or reverse breakdown comes into play.  It also has a major effect at an on the amount of current a diode will pass in the forward direction at any specific applied Voltage. As we have seen, as signal input power increases, the quality of the RF impedance match starts to degrade.  The AC input resistance to the diode detector decreases from the value obtained in the first well matched low power level simulation.  Interestingly, the output resistance increases. The reason for this change is that a new law now governs input and output resistance when a diode detector is operated at a high enough power level to result in a very low power loss.  The rule here is that the DC input resistance of an ideal diode peak detector is one-half the value of the output load resistance.  Also, the output resistance is equal to two times the value of the input source resistance.  Further, since in this example the detector now approaches being a true peak detector, the DC output voltage approaches the square root of 2 times the value of the RMS input voltage.  This relationship is necessary in an ideal peak detector so that the AC input power can equal the DC output power with no power lost in the diode (No free lunch).  If we were to restore an optimum impedance matched condition by adjusting the input source resistance to 495k ohms and the output load resistance to 990k ohms (by changing the input and output impedance transformation ratios), the power loss would be further reduced to 0.22 dB.  See Part 5 of Article #0 for further discussion on the subject of input and output resistance of diode detectors operated in their peak-detection mode.

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Current and voltage weveforms in a half-wave AM peak detector, at several input-power levels

#8  Published: 02/13/00;  Last revision: 11/25/01 060510

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Optimum diode for any crystal set http://www.bentongue.com/xtalset/9DiDBBox/9DiDBBox.html Go

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Build the Crystal Set Diode Detector Bias Box: a simple and easy way to determine if one's diode is optimum for weak signal reception, or it should have a higher or lower axis-crossing resistance (0.026*n/Is ohms) By Ben H. Tongue

Quick Summary:  The 'Diode Detector Bias Box' enables one to check whether the diode being used in a crystal radio set has optimum characteristics for that set.  The optimum detector will deliver the greatest low-signal sensitivity. A detector diode, in order to deliver the highest sensitivity and lowest audio distortion, must be properly impedance matched to its RF source.  It must also be matched to the correct (for that diode) audio and DC load resistances.  See Articles # 0, 1, 5 and 15a for more info on this subject.  How can one know for sure that the diode used in one's own crystal radio set is the best one for it?  Another way of putting it is:  Does my diode have the Saturation Current (Isopt) that the optimum diode, for my set, would have?   An easy way to find the answer is to build and use the diode Detector Bias Box.  

 

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Optimum diode for any crystal set

A detector diode having particular saturation current (Is) can be biased to perform almost exactly the same as a diode having a different Is.  This statement assumes that the diode conforms to the classic Shockley diode voltage/current relationship:  Id = Is*{exp[(Vd-Id*Rs)/(0.0257*n)]-1)}, at room temperature.  Id is the diode current in Amps.  Is is the diode Saturation Current.  "exp" means:  raise the base of the natural logarithms (2.718...) to the power of the expression following.  Vd is the voltage applied to the diode in volts.  Rs is the fixed series parasitic resistance of the diode in ohms.  n is the Diode Ideality Factor (Emission coefficient) and is dimensionless.  It is usually between 1.05 and 1.2.  The lower the value of n, the higher will be the very weak signal sensitivity.  At low signal levels, the Id*Rs expression is small and can be neglected. To change the detector performance of a diode of Is = Isor (original) to the performance of a diode of Is = Isop (optimum), a DC bias voltage must be inserted in series with the diode.  The required bias voltage is:  Vbias = 0.0257*n*[ln (Isop/Isor)].  ln represents the natural logarithm of the expression following it.  This equation is accurate if the values of Is and n do not change as a function of diode current.  This assumption is correct for the Schottky diodes I have checked. Some germanium ones I have checked do not accurately follow the Shockley equation.  They tend to have high values of Is such as 500 nA or more.  Germaniums having Is values in the 100-200 nA range do seem to follow the Schockley equation well.  At high currents, Is increases from its value at low currents.  The Vbias equation is given for information only and is not used in the following experimental procedures.  Whether a Schottky, germanium or other diode is used, a convenient way to 'tune' the Is of a diode is to use the "Diode Bias Box".  It effectively enables one to change a diodes' effective Is (and therefore its operating impedance) by merely turning a knob on a box.  The Diode Bias Box also enables one to determine the best diode DC and AC load impedance. Here is an interesting relationship that applies to most Schottky diodes: A Schottky diode detector having a saturation current of (Is1) that has no external DC current bled into it will perform, as a diode detector, identically to that of another diode having a saturation current of (Is2) if a DC current (Ib) equal to (Is1-Is2) is bled into it. To use the Bias Box, connect the terminals labeled T1 to the crystal radio set ground and the cold end of the audio transformer primary, if one is used. If no transformer is used, connect the terminals of T1 to the crystal radio set ground and the cold end of the headphone headset.  Also make sure that the connection where the Bias Box is inserted is well bypassed for RF and audio. To operate the box, snap the switch to OFF, disconnect the Hot T1 connection from the crystal radio set and adjust the DIODE DC LOAD pot to the DC load desired (See articles #1 & 4 or pick 100k Ohms to get started).  The DC load resistance can be measured across the terminal strip labeled T1 when its hot lead is disconnected from the crystal radio set.  Reconnect the Hot T1 connection to the crystal radio set

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Optimum diode for any crystal set

DC return.  Tune in the weakest station you can copy. Snap the switch to ON.  Adjust the BIAS pot for the the greatest volume.  Tune in the strongest station you can get.  Adjust the DIODE DC LOAD pot for the least audio distortion. Disconnect the antenna. Connect a DVM to terminal strip T2.  If you find a voltage there, that is an indication that your diode is not optimum.  A diode having a different Is could work the same, but without the need for any bias.  If your diode is biased in the forward direction, the optimum diode would have a higher Is than your present diode.  A reverse bias indicates that the optimum diode would have a lower Is.  As stated before, the relationship between the required bias (Vbias), the Saturation Current of the original diode (Isor) and the Saturation Current for the optimum diode (Isop) is:  Vbias = 0.026*n*ln(Isop/Isor) volts.  Some illustrations:  To change Is by five times, the bias Voltage required is about 0.044 Volts.  To change it by 25 times, the Voltage is about  0.088 Volts.  Note:  When adjusting the BIAS pot from the optimum position, moving toward forward bias reduces volume, sensitivity and selectivity.  Moving toward reverse bias increases selectivity, reduces volume and sensitivity and adds audio distortion. What to do now?  If the optimum diode has a higher Is than your present one, several identical diodes can be paralleled to create the equivalent of one of higher Is.  For instance, five in parallel will have an Is five times that of one alone.  If you have several different diodes, experiment with them.  Maybe you can find one that does not need a bias for best results.  In recent years many different types of diodes called 1N34A have been sold.  Their Is values vary all over the lot. Some final comments:  Using the Bias Box to reduce the effective Is of a diode that has a high Is does not work very well if a large reduction is needed.  The reason is that diodes of high Is naturally have higher back leakage and a lower reverse breakdown voltage.  This causes losses and audio distortion when the RF voltage across the diode swings to reverse polarity every RF cycle.  Less sensitivity and selectivity is the result.  When one increases the effective Is of a diode that has a low Is by applying a forward voltage bias, this problem does not occur.  Some other things that will cause some optimized diodes to work worse than others are:  High series resistance (Rs), high diode barrier capacitance (this reduces high frequency performance compared to that at lower frequencies) and high reverse leakage current. #9  Published: 03/30/00;  Last revision:01/24/07 060510

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Detector Linear-to-Square-Law Crossover Point (LSLCP), and a new diode detector equivalent circuit http://www.bentongue.com/xtalset/10npddec/10npddec.html Go

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A New Diode Detector Equivalent Circuit, with a Discussion of the Linear-to-Square-Law Crossover Point: the signal level at which the detector is functioning midway between linear and square-law operation by Ben H. Tongue

Quick Summary:  The purpose of this article is to describe and and then compare a new diode detector equivalent circuit (DDEC) to a real world detector circuit (RWDDC), such as might be used in a crystal radio set.  This equivalent circuit uses an ideal diode. Comparisons are made using SPICE simulations of the two circuits.  Calculations using equations given in Article #15A are also supplied for comparison.  The concept of the Linear-to-square-law crossover point (LSLCP) in the relation between output DC and input AC power is introduced (not to be confused with the exponential relationship of DC current to DC voltage in a diode).

Part 1:  General Description of a Diode Detector. The new diode detector equivalent circuit (DTEC) is based on the idea that a detector diode imbedded in a proper circuit can be thought of as a 'black box' device that converts RF power into DC power.  Some power is lost in the process and that is called Diode detector insertion power loss (DDIPL).  This approach completely avoids such concepts as duty cycle, pulse current, bypass capacitor charging and non-linear instantaneous voltage/current relationships.  It is also consistent with the material given in Article #1.  The peak-detector, capacitor-charging-current line of thought is good when signal levels are high enough to assure that true peak detection occurs.  It is not very useful when signal levels are low.  However, when all is said and done, the more different valid ways one can use in thinking about how a circuit works, the better becomes one's understanding of that circuit. This analysis applies to an AM detector fed by a CW RF sine wave voltage of frequency fo:  It has a peak (not RMS) value equal to V1 and an internal source resistance of R1.  The "maximum available RF input power" is called P1 (see section 2 in Article #0 for info on "maximum available power").  The DC output power delivered to the load resistor R2 is called P2.  The DDIPL (in dB) is equal to ten times the log of the ratio between the two powers P2 and P1.  This approach can also be used to model how a diode detector behaves with an AM modulated input signal by performing a SPICE simulation three times.  Once with the RF signal equal to the value of the desired modulated wave's envelope minimum value, once with the signal equal to the carrier value and once with the signal equal to the crest value.  The three DC output voltages give the minimum, carrier equivalent and peak value of the demodulated output audio wave. ***** Please do not skip this next paragraph! ***** To understand the new diode detector equivalent circuit, one must abandon the usual way of thinking

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Detector Linear-to-Square-Law Crossover Point (LSLCP), and a new diode detector equivalent circuit

the about the diode in a detector.  Instead, one must think about the "diode detector circuit".  This circuit includes a tank circuit T, the output capacitor C, as well as the diode.  The shunt input reactance of the circuit is assumed to be zero at all frequencies except fo, the frequency to which the tank is tuned.  The input resistance at fo will be discussed later.  The output reactance of the circuit is assumed to be zero at all RF frequencies.  The output resistance will be discussed later. A real world diode is a two terminal device. The "real world diode detector circuit" will be modeled as a "two port,  four terminal device" having a pair of  terminals for the input and another for the output. One of the input terminals is the "hot" input terminal; the other is "low".  One output terminal is the "hot" one, the other is "low".  The two "low" terminals are connected together and usually to ground.  Please note, that in the topology of the two schematics shown below, the "Diode Detector Circuit" and the "Diode Detector Equivalent Circuit" both include the tank T and the bypass capacitor C2 as an integral part of the detector.  Also, look at the circuits in this way:  The tank circuit, looking towards the output, sees the diode as a one-end-grounded shunt load since the output bypass cap is a short at RF.  The output load resistor, looking back towards the input, sees the diode as a one-end-grounded shunt DC resistive source since the input side of the diode is shorted to ground by the tank. See Fig 1. The detector tank circuit T is modeled as lossless and resonant to the input frequency fo.  Losses in a real world tank can be accounted for by using Thevenin's Theorem to calculate the appropriate changes in V1 and R1.  This leaves the circuit topology unchanged.  See Article #1 for more on this subject.  The value of the tuning capacitor in T is sufficiently large so that essentially no harmonics of fo can appear across T.  This assures that the "pendulum-like resonator effect" of a high Q circuit will be available to supply the narrow, high-current pulses the diode requires every cycle when strong signals are handled.  Another advantage is that tank-voltage-waveform peak clipping by diode conduction is essentially prevented when the current pulses are drawn.  All this assures that the input impedance to the detector will be linear over one cycle of RF and the input current to, and voltage across the tank T will always be sinusoidal, no matter how weak or strong the input signal.  See Article #8 for an illustration of typical waveforms.  A reactance value for the tank capacitor equal to less than one hundredth of the value of R1 will be sufficient.  The DC resistance of the tank inductor should be small enough so that no appreciable DC voltage will appear across it.  A value less than one hundredth of the value of R2 will be sufficiently small.  This assures that all of the output DC power goes into R2.  The bypass capacitor C2 has a very low reactance compared to the load resistor R2 at the frequency fo. Since C2 acts as a short circuit across R2 at the frequency fo, all of the RF voltage across T will appear across the Diode. The time constant, R2*C2 should be long compared to the time for one cycle of fo.

Part 2a:  Discussion of the new Diode Detector Equivalent Circuit.

RWDDC to be Simulated in Spice.

Fig 1. To gain an understanding of the Diode Detector Equivalent Circuit (DDEC), first consider the following line of thought:  See Fig. 1.  Let  the input RF voltage V1 become very low.  V1, at a frequency fo, looking toward the load resistance R2, will see an RF resistance (at fo) equal to the junction resistance

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Detector Linear-to-Square-Law Crossover Point (LSLCP), and a new diode detector equivalent circuit

of the diode at zero bias.  At this very low signal condition the detector input resistance is not affected by any changes made to R2.  The value of this junction resistance is the slope of the diode V/I curve at the origin. From a differentiation of the ideal diode equation, the numerical value of this resistance is: (0.0256789*n)/Is ohms at a temperature of 25 degrees C.  Let's call this Ro.  Is and n are parameters in the ideal diode equation. (For a discussion of Is, n, etc., see the text after the schematics in Part #1 of Article #1).  From the load resistance R2, looking back toward the input, one sees the same resistance value Ro, and it is independent of any changes at the source.  Now look at Fig. 2.  Here, the real world diode has been changed to a theoretical ideal diode and two attenuators, A1 and A2, of characteristic resistance Ro have been are added.  If V1 becomes zero, the attenuators A1 and A2 must be set to infinite attenuation to enable the model to duplicate the behavior of the circuit in Fig.1.  When an input signal is applied, the values of A1 and A2 must become finite.  The DDIPL is equal to the sum of the loss of each attenuator plus the impedance interface loss between the ideal diode Di and each attenuator, as well as any mismatch loss between R1 and the detector as well as between R2 and the detector (See ** after Table 2).  SPICE simulation shows that the diode detector equivalent circuit does a pretty good job modeling the operation of a real world diode detector.  To verify this, one can perform a SPICE simulation of Fig.1 and Fig. 2 with V1, R1 and R2 the same in each case.  The attenuation value of A1=A2 dB must be set to a value that causes the output, V2, in Fig. 2 to be the same as in Fig.1.  The input impedance match of the two simulations differ from each other by less than 14% over an input power range of 48 dB, centered at the Linear-Square-Law Transition (LSLCP) point.  This is the main area where the results from the DDEC simulation differ from those of the RWDD. The input resistance of the DDEC is always higher than that of the REDD.  This equivalent circuit seems to work for signals from well below the LSLTP point up to levels just before "Diode Reverse Breakdown Current" comes into the picture.

DDEC to be Simulated in SPICE.

Fig. 2 Some definitions and conditions that apply to Fig. 2 follow: Di is an ideal diode.  It has zero forward resistance and infinite reverse resistance.  That is, it can pass any amount of current in the forward direction with no voltage drop, and it will conduct no current in the reverse direction, no matter how much voltage is applied.  Rs represents the series parasitic resistance of the real world diode (Dr) being modeled.  It is shown for completeness, but has negligible effect on the results at the values encountered in crystal radio set operation (5 to 50 Ohms) and will be ignored. A1 and A2 are "constant resistance" attenuators of equal attenuation, X dB.  Their loss is dependent on the strength of the received signal power.  The attenuators each have a characteristic resistance Ro.  Is is the saturation current of the real world diode Dr in Fig.1.  n is its ideality factor.  Note: When a "constant resistance" attenuator is driven by and loaded by a resistance value called its "characteristic resistance", its own input resistance and output resistance remain constant no matter what value the attenuation it is set to. The source and load resistances of the detector are set equal to the characteristic resistance of the attenuators. Table 1 shows three groups of data:  SPICE simulations of the RWDDC and the DDEC, and a set of

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Detector Linear-to-Square-Law Crossover Point (LSLCP), and a new diode detector equivalent circuit

calculated values from equations appearing in Article #15A.  Data is shown for three input power levels for each data group  The levels are: 1) The input power that will operate the RWDDC at its LSLCP [Plsc(i)],  2) 1/128 the value of Plsc(i), and 3) 128 times the value of Plsc(i).  These power levels are believed to be correct if the input and output impedances of the detectors are impedance matched, using appropriate values for R1 and R2.  Actually, in the simulations, R1=R2=Ro=0.0256789*n/Is.  This causes the required input power for the desired output to be somewhat greater than if input and output were perfectly matched.  The attenuators A1 and A2 in the DTEC are set equal to each other, and to a value that causes the output power of the DDEC to closely equal that of the RWDDC.  SPICE parameters for the diode in the RWDDC and "Calculated values" are: (Is)=38 nA and n=1.0*.  The "calculated values" assume impedance matched conditions.  The SPICE circuit simulation program "ICAP/4" from Intusoft was used in all simulations.

Data for three different data groups, including loss in attenuators A1 and A2 and the 'excess' loss.  RF DC Input Output Type of Voltage Voltage analysis V1, in V2, in mV peak mV

DC Output Current I2, in nA

RF DC DDIPL, Sum of the 'Excess Input Output Attenuation, loss', above Power Power |S21|, A1+A2, in A1+A2 P1, in P2, in dB dB dBW in dBW

RWDD simu.

1.0126

0.001231 0.0018208 -127.22 -176.50 49.28*

---

---

RWDD simu.

16.165

0.3149

0.4660

-103.16 -128.33 25.17*

---

---

RWdd simu.

64.923

4.849

7.176

-91.08

-104.59 13.54*

---

---

RWDD simu.

258.97

51.34

75.97

-79.06

-84.09

5.03*

---

---

RWDD simu.

4142

1312.4

1942.1

-54.98

-55.97

0.99*

---

---

DDEC simu.

1.0123

0.001231 0.0018209 -127.22 -176.50 49.28

42.36

6.92**

DDEC simu.

16.198

0.3162

0.4679

-103.14 -128.30 25.16

18.67

6.49**

DDEC simu.

64.942

4.867

72.02

-91.08

-104.59 13.54

9.20

4.34**

DDEC simu.

259.12

51.79

76.64

-79.06

-84.01

4.95

2.80

2.15**

DDEC simu.

4143

1309.4

1937.7

-54.98

-55.96

0.98

0.20

0.78**

Calculated 1.0120 values***

0.001231 0.0018210 -127.22 -176.49 49.27

---

---

Calculated 16.123 values***

0.31500

0.4662

-103.18 -128.33 25.15

---

---

Calculated 64.72 values***

4.867

7.176

-91.11

-104.59 13.48

---

---

Calculated 257.3 values***

51.22

75.80

-79.32

-84.09

4.77

---

---

Calculated 3841 values***

1307.4

1934.7

-55.64

-55.97

0.33

---

---

Table 1

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Detector Linear-to-Square-Law Crossover Point (LSLCP), and a new diode detector equivalent circuit

* The n of real world diodes is never 1.0.  Actual values of good detector diodes are usually between 1.03 and 1.10.  The input and output power values given in the data group for the RWDD can be corrected if n is over 1.0 by adding 10*log (n) dB to the P1 and P2 figures.  Keep in mind that n and (Is) are most always independent of current for Schottky diodes.  This is not the case for silicon pn junction or germanium point contact diodes. A New diode detector equivalent circuit, with a discure law crossover point. *** Calculations for a RWDDC using equations #6 and *2an given in Article #15A.  These equations assume perfect impedance matching at the input and output.

Part 2b:  An alternative DDEC. An alternative 'diode detector equivalent circuit' (DDEC2) can be formed by moving the tank circuit T from its position shown in Fig. 2 to the left hand terminal of diode Di and moving the bypass capacitor C2 to the right hand end of resistor Rs.  This equivalent circuit always operates as a peak detector, so no 'excess loss' need be accounted for.  The loss for attenuators A1=A2, at any input signal level may be calculated from equations #3n and #6 in Article #15A.  Loss for A1=A2=5*log(DIPL from equation #3n) dB.  The input impedance (S11) of the DDEC2 approaches that of the RWDD at high and low input power levels.  Its input resistance at intermediate power levels is always lower than that of the RWDD.

Part 3:  Further Discussion of the Linear-to-Square-law Crossover Point. The RF input resistances in the simulations of the DDEC (Fig.2) are within 17%, 17% and 8% at the low, medium and high power inputs respectively, of the simulated resistances of the RWDC (Fig 1).  The DDIPL values at each input power level for the circuits in Figs. 1 and 2 were set to within 0.1 dB of each other by adjustment of the loss in A1 and A2. Operation at the LSLCP:  Operation at the LSLCP can be said to occur when the detector is operating half way between its linear and square law response mode, the point where the two areas overlap equally.  At this point there is a sqrt(2) dB change in output power for every 1.0 dB change in input power. Operation at power levels below the LSLCP point:  As input power levels are lowered, the DDIPL approaches 10*log{[I2/(I2 + Is)]}-6 dB. Operation at power levels above the LSLCT point:  Here, the DDIPL tends to approach zero, but the detector input and output impedance match starts to deteriorate.  This is the regime where the mode of detection changes from "averaging" to "peak".  (See Article #0, Section 5 for an explanation of this effect.)  Re-matching the input and output circuits at these higher input RF power levels recovers the excess loss caused by the mismatch, and results in the performance given by the equations in Article #15A. Input/Output impedance interaction:  When an input signal is present, interaction between the input and output circuit occurs.  That is because the attenuation of the attenuators A1 and A2 must become finite and that lets the interaction come through.  If the output load R2 is reduced, the input resistance to the detector will be reduced.  If the input source resistance R1 is reduced, the output resistance of the detector will be reduced.  This interaction is dependent on the strength of the input signal.  For greater input signals, there will be less DDIPL (Lower values for attenuators A1 and A2) and greater interaction.  If DDIPL approaches zero, the output resistance will approach two times the source resistance R1.  Similarly, the input resistance will approach 1/2 the load resistance R2.  If the input signal power is reduced, detector input and output resistance values become decoupled from each other and both approach Ro.  See the paragraph below Fig. 1. Overview:  One can think of a diode detector circuit as a device to change input RF power to an almost equal amount of DC output power, provided the input power level itself is high enough.  In this instance the attenuators A1 and A2 in Fig. 2 have very low values.  If the input power is reduced, A1 and A2

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Detector Linear-to-Square-Law Crossover Point (LSLCP), and a new diode detector equivalent circuit

increase in loss, thus reducing the output power.  At low input power levels, square law operation occurs.  In this region, if the input power is reduced by, say, 1 dB, the loss in attenuators A1 and A2 are each increased resulting in an output reduced by 0.5 dB. Voila, square law operation!  There is an extra loss besides that of A1 and A2.  It is the interface mismatch loss between each attenuator and the diode Di as well as input and output mismatch losses.  This interface loss varies as a function of input power.  It is about zero when the values of A1 and A2 are very low (large signal power condition) and approaches 3 dB for each attenuator at low signal power levels (total of about 6 dB).  See the Table 1 above and the ** comment below it. #10  Published: 04/04/00;  Revised: 10/27/2002 060510

Return to the Index Page of this Section (A)

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A Procedure for Measuring the Sensitivity (Insertion Power Loss), Selectivity and Input/Output Impedance of a Crystal Radio By Ben H. Tongue

Quick Summary:  This Article describes a device and procedure for quantifying several characteristics of crystal radio sets.  They are: (1) Insertion power loss, (2) Selectivity, (3) RF input impedance match and (4) Audio output resistance.  First, an acknowledgement:  This article was inspired by a paper written on 9/15/99 by Charlie Lauter at: [email protected] .  It can be accessed at:  http://home.t-online.de/home/gollum/testing.htm .  He led the way with a good procedure for sensitivity and selectivity measurement, but I wanted a more general approach.  Here is mine:

 

Definitions and Acronyms used in this Article abs AMCS CSUT D DUT Eo_pp FLVORA ILCS IM IPL Is MAP MASP n p-p Po sqrt RL

Absolute value (sets the next expression to a positive value). Apparatus for use when Measuring crystal radio set Insertion Power Loss and Selectivity. crystal radio set under Test. Difference between RF envelope peak-to-peak and valley-to-valley voltage. Device Under Test. Peak to peak demodulated output voltage Fixed Loss, Variable Output Resistance, Attenuator. Ideal Lossless crystal radio set. Impedance Match. Insertion Power Loss in dB. Saturation Current of a diode.  See Article #1 for an explanation of this term. Maximum Available Power, in Watts. Maximum Available Sideband Power, in Watts. Ideality factor of a diode.  See Article #1 for an explanation of this term. Peak to peak. Detector Output Power, in Watts. Square root of the expression that follows. Detector load resistor.

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Measurent of sensitivity, selectivity and input/output impedance of Crystal Radios

Ro S-3 S_20 S11

Detector Internal Output Resistance. Frequency difference between two points 3 dB down on the selectivity curve. Frequency difference between two points 20 dB down on the selectivity curve. Voltage Reflection Coefficient.

SF

See the paragraph above Fig. 3 for the suffix labeling conventions used when measuring IPL. Shape factor, the ratio of the 20 dB down bandwidth to the 3 dB down bandwidth.

SG SPHP SPICE Vs VSWR

Signal Generator. Sound Powered Headphones. A computer program used to simulate the physical operation of circuits. RF Voltage source Voltage Standing Wave Ratio.

Suffix

This article is divided into six sections. The first describes the IPL (Insertion Power Loss) measurement method.  The second gives a theoretical derivation.  The third shows a method for the measurement of selectivity.  The fourth shows how to measure the input impedance match of a CSUT (crystal radio set Under Test).  The fifth shows a method for measuring the output resistance of a crystal radio set.  The sixth gives some comments and suggestions on how to improve crystal radio set performance. A quick definition:  The IPL of a crystal radio set may be loosely defined as 10 times the log of the ratio of the audio power delivered to the output load divided by the maximum RF sideband power available from the antenna. Here comes a more rigorous definition of IPL:  The function of a crystal radio set is to convert (demodulate) the modulated RF signal sideband power received by the antenna-ground system and deliver as much of that power as possible to the output load as audio output power.  Understand that all of the signal information modulated on a carrier and picked up by an antenna-ground system resides in the power carried in the sidebands of that signal.  No signal information is contained in the RF carrier.   The Insertion Loss Method assumes that a voltage source with a specific internal impedance is connected through a "device under test" (DUT) to a load resistor.  We can say that the DUT is "inserted" between the source and the load. First, consider what happens when an Ideal Lossless crystal radio set (ILCS) is inserted as the DUT, tuned to the source signal and adjusted for maximum output.  It is connected between the signal source and a Load Resistor (Rl) representing the average impedance of the headphones to be used later.  This ILCS presents a perfect impedance match to the signal source and also to the output load.  It has no internal power losses.  The ILCS will convert all of the Maximum Available Sideband Power  (MASP) in the modulated signal source into useful audio power in the output load.  Power loss is zero when the ILCS is inserted as the DUT. Second, consider what happens when a real world crystal radio set is inserted as the DUT.  It probably will not present a perfect impedance match to the signal source nor perfectly match the output audio load, thus incurring mismatch losses.  It will have some internal power losses.  Its output audio power will be less than that of the ILCS.  The IPL of the CSUT is:  IPL = 10*log ((Output power of CSUT)/(Output power of ILCS)) dB. Now, a brief detour to explain the concept of MAP (Maximum Available Power) and a more detailed look at Insertion Power Loss (IPL) as used in this Article. Maximum Available Power (MAP) Assume that any electrical source of power can be represented as a voltage source (Vs) that has an inaccessible internal impedance Zs = Rs + jXs.  See Fig. 1.  Assume that the reactance component (Xs) of this impedance is tuned out.  The crystal radio set tuner should do this by generating a series reactance whose value is the negative of Xs.  There is a maximum amount of power that Vs, with its internal series resistance Rs, can deliver to any load.  The value of the load (Rl) for maximum power transfer is Rs itself. 

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Measurent of sensitivity, selectivity and input/output impedance of Crystal Radios

This is called an impedance matched condition.  Any other value for Rl will absorb less power from the source than a value of Rs.  

Here is how to calculate MAP from the Vs and Rs combination.  As mentioned before, the maximum power output occurs if Rl = Rs.  This means that the total load on Vs is the series combination Rs + Rl = 2*Rs.  Since power in a resistor can be calculated as (V^2)/R, the total power dissipated in the two resistors is (Vs^2)/(2*Rs).  Since one half of the power is dissipated in Rs (and lost) and one half in Rl, the maximum power deliverable to Rl is: (Vs^2)/(2*Rs)/2 = (Vs^2)/(4*Rs).  We will use this relationship later on.  Note that Vs^2 means Vs squared and 4*Rs means 4 times Rs. Vs is in RMS volts.  If Vs is given  in peak or peak-to-peak units, a correction factor must be applied. Definition of IPL when the input signal is an RF carrier, modulated by a sine wave.

Input Power:  Audio information that is amplitude modulated on an RF carrier is contained solely in what are called sidebands.  Sidebands are better called side frequencies if the audio modulation waveform is a single sine wave, as will be the case here.  In sine wave AM, two side frequencies are generated in the modulator.  One is at a frequency above the carrier and one is below it.  They are each spaced away from the carrier by an amount equal to the modulation frequency.  These two side frequencies carry all the information that is in the signal.  The RF carrier carries none.  When we receive a signal on our crystal radio set it is this sideband power that we want of capture and convert to audio power in our headphones.  The carrier acts only as a "carrier" for the sidebands and generates the DC diode current and DC voltage across the DC resistance component of the load.  Output power and IPL:  Assume that an RF source with a MASP of Pa Watts is connected to a CSUT and that the CSUT feeds a load resistor.  The source has an internal RF impedance of Za Ohms and the load has an impedance of Rl.  The SCUT is tuned and adjusted to deliver maximum audio power to the load, with the desired selectivity.  Define the output power as Po.  Now imagine the replacement of the CSUT with an ILCS.  It provides a perfect impedance match to the source and perfectly matches the load.  Its output power will equal Pa because there are no losses.  This ideal crystal radio set will function as a device to convert all of the MASP into audio power.  The ratio of the output power of the CSUT to that of the ICS set is Po/Pa.  This ratio, expressed in dB is the IPL of the CSUT.  IPL = 10*log (Po/Pa) dB.  The load resistor should have a value equal to the average impedance of the headphones to be later used with the CSUT. (See Article #2 on how to measure headphone impedance.) Section 1.  IPL Measurement Method. The test equipment required is: 1. An RF signal generator (SG) covering 530 -1700 kHz and capable of linear amplitude modulation up to 50%.  The generator can be a modern function generator or a conventional RF signal generator, provided that the RF waveform has a reasonably low harmonic content.  It should have a 50 Ohm output resistance. 2. A scope with a flat response to at least 1.7 MHz and an accurate calibrated vertical sensitivity of 0.002 V per division or better.  Input resistance is assumed to be 1 Megohm.  Input capacitance (including that of the connection cable) is assumed to be about 175 pF. 3. A special attenuator set up and impedance adjuster unit called AMCS. The signal source is modeled as a voltage source Ea with series internal impedance elements of Ra, La and Ca.  See Fig. 3  The components Ra, La and Ca are intended to have the same impedance as the average antenna that used to be used for AM reception in the USA.  These components are termed a "dummy

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Measurent of sensitivity, selectivity and input/output impedance of Crystal Radios

antenna" and are specified for use in standardized testing of AM receivers.  The standard is described in "Standards on Radio Receivers", Institute of Radio Engineers (predecessor of the IEEE), New York, 1938. It is assumed that by tuning the CSUT for maximum output volume, that the best conjugate impedance match possible is presented to the antenna.  In simpler terms, tuning for maximum volume adjusts the resistance component of Zi to as close to 25 Ohms as possible and the reactive component of Zi to as close a value as possible to the negative of the reactance of La and Ca in series.  This set of circumstances transfers the most signal power possible from the antenna to the CSUT.  The test procedure that follows involves applying a modulated RF Voltage (Ea) through a dummy antenna to the input of the CSUT and then measuring the Audio Output Power (Po) delivered to the output load.  The IPL of the CSUT is calculated as: IPL = 10*log (Po/(MAP in the sidebands of Ea)). Measurement of IPL

 

We will use use a special attenuator box between the SG and the CSUT and call it the AMCS.  Refer to the schematic in Fig. 2.  The AMCS has one 3 dB and one 20 dB attenuator that are used in measuring selectivity.  It has an additional 10 dB attenuator in the event some extra attenuation is needed.  The 20 dB attenuator can also be used to determine the voltage Ea at test point P1 when it is so low that it is hard to read.  The series 45.0 and two parallel 11.1 Ohm resistors form a "minimum-loss impedance transforming attenuator".  Its input design resistance is 50 Ohms.  Its attenuation is set so that the ratio of the voltage at test point Pi to that at P1 is 10:1 when Sw1, Sw2 and Sw3 are set to zero dB.  The source resistance feeding the Dummy Antenna and crystal radio set series combination is 5.25 Ohms.  Two 11.1 Ohm resistors are used in place of one of 5.55 Ohm resistor because resistors under 10 Ohms may be hard to find.  This also minimizes lead inductance.  If the 45.0 and 11.1 Ohm resistors are held to within +/- 4%, the attenuation accuracy will be within +/- 0.33 dB. of nominal.  Resistor accuracy tolerances for the other attenuators, to hold a +/- 0.33 dB accuracy are:  3 dB-10%, 10 dB-4% and 20 dB- 2.5%. The load on the CSUT must be a resistor (R1) of value equal to the effective impedance of the headphones used with the crystal radio set.  One can determine the impedance of the headphones by building and using the FLVORA described in Article # 2.  Alternatively, it may be estimated as 5 or 6 times the DC resistance of the phones. To measure the IPL of a crystal radio set, connect the SG**** to the AMCS and set it to a test frequency of, say, 1.0 MHz.  Turn on the sine wave modulation function and adjust the frequency to 1000 Hz**** and the modulation percentage to 50%****.  (50% modulation exists when Ea_pp is three times Ea_vv.)  Connect the AMCS to the antenna and ground terminals of the CSUT.  Connect the scope to Rl and set it to a

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Measurent of sensitivity, selectivity and input/output impedance of Crystal Radios

sensitivity of 2 mV/div.  Set the SG to a high RF output and tune the CSUT to maximize the 1000 Hz trace on the scope****.  Reduce the SG output as necessary to keep the scope trace on scale****.  Reset the SG to deliver a 4 mV p-p trace on the scope.  Connect the scope to point P1 and measure and record Ea_pp and Ea_vv at Point P1. **** Some RF signal generators have too much harmonic waveform distortion in their output to give accurate results with this procedure and will need a simple harmonic filter to clean up the output.  If the RF waveform looks like a fairly good sine wave it's OK. 1000 Hz is chosen instead of the usually specified 400 Hz because most high performance crystal radio sets use an audio transformer to drive the headphones.  At 400 Hz, the impedance of most transformers is well below the average value between 300 and 3,300 Hz.  Also, transformer loss and distortion is usually greater at 400 Hz than at 1000 Hz. The usually specified modulation percentage is 30 %.  I suggest using 50 %.  This gives a greater output voltage and makes low signal level measurements easier. This test procedure uses one scope at several input attenuator settings as well as at 1000 Hz and 1.0 kHz.  It depends upon calibration accuracy from one switch position to another as well as from 1.0 kHz to 1.0 Mhz.  I got caught on this.  My scope is 21 yeas old and the frequency response flattening trimmers in the vertical attenuator had drifted.  This didn't affect the accuracy at low frequencies, but produced error at 1.0 Mhz.  The best way to check for this problem is to use a quality, fast rise-time Square Wave Generator and check for a good clean corner at the leading edge of a 100 kHz square wave.  Another option is to use a sine wave Function Generator, the output of which is known to be flat vs. frequency.  If it has an output up to over 10 Mhz, the output is probably flat from 1.0 kHz through 1.0 Mhz.  One probably will find an undue amount of noise, hash and carrier RF on the scope screen when measuring the output waveform.  This can be caused by capacity coupling in the transformer between the hot end of the primary winding and the hot end of the secondary.  I eliminate this hash by using a very simple low-pass filter.  To do this, connect a 100k Ohm resistor in series with the scope input cable, very close to where it connects to the transformer output terminal.  Assume that the scope has a one Megohm (check it!) input resistance, in parallel with a 175 pF input capacity when using the probe at the X1 setting. (These are the values for my Tektronix model T922 scope.)  At 1000 Hz the voltage divider from the series 100k Ohm resistor and the input impedance of the probe causes the scope to read 0.87 dB less than the actual output of the CSUT.  At 1.0 MHz the attenuation will be will be 41 dB.  Keep the leads short to minimize 60 Hz hum pick-up.  Only use the 100k resistor when measuring the output at 1000 Hz.  Don't use it when measuring RF at the input.  When calculating IPL, correct your results for the 0.87 dB loss (Use 0.9 dB). The output sine wave may look distorted.  This can come from modulation distortion in the signal generator or distortion generated in the CSUT.  Generator distortion is not very important here.  Distortion generated in the CSUT can be caused by an incorrect resistance in the parallel RC used in series with the audio transformer primary (if one is used).  To check, replace the resistor with a pot and adjust it for minimum distortion.  BTW, this is the best way to find the correct value for the resistor.  See Article #1 of this series. Here are the labeling conventions that will be used.  Voltages on the input side of the CSUT always start with Ea.  Voltages on the output side start with Eo.  The underscore is a separator from the description suffix  that follows.  fo = carrier frequency,  fmod = modulation frequency,  pp = peak-to-peak,  vv = valley-to-valley,  car = carrier, dc = direct current,  sf = side-frequency, carpp = carrier peak-to-peak,  1sfpp = one side-frequency peak-to-peak, 1sf = one side-frequency,  2sf = two side-frequencies.

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Measurent of sensitivity, selectivity and input/output impedance of Crystal Radios

The IPL of any crystal radio set depends upon the output power level at which it is operating.  At very low output levels (signal barely readable with sensitive headphones), the IPL increases about 6 dB for every 6 dB reduction in input power.  This results in a 12 dB reduction in output power.  When this happens, the diode detector is said to be operating in its "square law region".  Because of this effect, it is suggested that the IPL be measured at several audio output power levels when characterizing a crystal radio set, maybe -80 and -110 dBw. Section 2.  Derivation of IPL. Figure 3 shows of the envelope of an AM carrier of frequency fo, modulated at 50% by a sine wave of frequency fmod.  This modulation produces two side frequencies separated from the carrier by fmod.  One is above fo and one is below it.  If no side frequencies were present, Ea_pp would equal Ea_vv and the modulation envelope would be straight lines. With some modulation is present, one half of the total envelope fluctuation is caused by one side-frequency and one half by the other. Two side frequencies, each of amplitude Ea_sfpp, when added to a carrier of amplitude Ea_carpp, will cause the modulation envelope to have a maximum value of Ea_pp = Ea_carpp+2*(Ea_1sfpp).  The minimum value of the envelope will be Ea_vv = Ea_carpp-(2*(Ea_1sfpp)). Define: D = (Ea_pp)-(Ea_vv) = 4*(Ea_1sfpp).  Rearranging terms, we get:  Ea_1sfpp = D/4.  We can calculate the MAP of one side-frequency as: MAP_1sf = ((Ea_1sfpp/(2*sqrt2))^2)/(4*Ra).  The first "2" changes the value of Ea_1sfpp to a peak value.  The "sqrt2" changes the resultant peak value to RMS.  The equation, restated, is MAP_1sf = ((Ea_1sfpp)^2) / (32* Ra).  The total power in the two side frequencies is twice that in one side-frequency and is:  MAP_2sf = ((Ea_ 1sfpp)^2)/(16*Ra).   Now, substituting Ea_1sfpp = D/4, we get:  MAP_2sf = (D^2)/(256*Ra). The output waveform shown in Fig.3 is a sine wave Eo_pp, having a DC value of Eo_dc.  The audio power it supplies to the output load Rl is: Po = ((Eo_pp/(2*sqrt2))^2)/Rl.  The "2" and the "sqrt2" are needed as before to change Eo_pp from a peak to peak to an RMS value.  Simplifying, Po = ((Eo_pp)^2)/8*Rl.  Since IPL = 10*log (Po/MAP_2sf), and we can state the Final Result we've all been waiting for, and it is:                              INSERTION POWER LOSS = IPL = 10*log {32*Ra*[(Eo_pp/D)^2]/Rl}. There is one caveat to using this method:  It is assumed that the audio bandwidth through the audio transformer, as well as one half the -3 dB bandwidth of the RF tank is 3 or more times as large as the recommended 1000 Hz modulation frequency.  If both are 3000 Hz, the error will be about 0.6 dB.  I either of these bandwidths is too small, a lower modulation frequency such as 400 Hz can be used.

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Measurent of sensitivity, selectivity and input/output impedance of Crystal Radios

The MAP of the RF carrier only from the AMCS to the CSUT is: ((Ea_pp + Ea_vv)^2)/(3200) Watts. Section 3.  Measurement of Selectivity Shape Factor: Here is a method for measuring selectivity using the instrumentation used for measuring IPL.  It is adapted from Terman's Radio Engineer's Handbook:  Using a CW source, measure the frequency difference between two points that lie 3 dB down on the selectivity curve.  Let us call this value S_3 kHz.  Measure the frequency difference between two points that lie 20 dB down.   We'll call this S_20.  The input is measured at test point P1. Depending upon the input signal level chosen for this measurement, the detector may not be operated in the linear part of its operating region, but partly into its square law region.  This non linearity will cause an erroneous result if the measurements are made using a constant input signal level and then measuring the output at each of the four frequencies.  The correct method is to measure the input required at test point P1 to attain the specified fixed output level at each of the four frequencies.  The non linearity will now be the same for all measurements and cancel out.  The Shape Factor (SF), of the selectivity curve of a CSUT, at a particular RF frequency and output audio power is defined as SF = ((S_20)/(S_3)). The lower the number, the better. Things to remember:  The selectivity of a CSUT varies, depending on coupling, tap settings and frequency of measurement.  It is suggested that measurements be taken at 520, 943 and 1710 kHz and any other ones where you think there might be a large variation from the average.  With fixed coupling settings, the SF of a CSUT can change if the input signal power is changed.  This effect can be minimized if the correct an audio transformer is used with a correct parallel RC in series with the cold lead of the primary of the transformer.  See Article #1. Section 4.  Measurement of Input Impedance Match Impedance Match (IM) refers to how closely the input impedance of a device equals the conjugate of the impedance of the source driving it.  We will define the IM of a CSUT only at the frequency to which it is tuned.  It's assumed that the input impedance is resistive at this frequency.  Impedance match may be defined in terms of "Voltage Reflection Coefficient" (S11) or Voltage Standing Wave Ratio (VSWR).  Either can be calculated from the voltages appearing at test points P1 and P2.  Turn off the modulation of the SG.  Define: RF voltage at P1=EP1_pp and voltage at P2 = EP2_pp.  S11 = 20*log abs(1 - 2* (EP2_pp/EP1_pp)).  VSWR =  (1 + abs(1 - 2*(EP2_pp)/(EP1_pp)))/(1 - abs(1 - 2*(EP2_pp)/(EP1_pp)))  These calculations define how closely the input impedance of the crystal radio set matches that of the IEEE standard dummy antenna. Section 5.  Measurement of the Output Resistance (Ro) of a Diode Detector. The addition of a variable resistor and an ohmmeter are needed to measure the output resistance of the CSUT.  Connect the SG, AMCS and scope as before.  Set the fo of the SG to 1 MHz and the AM modultaion to about 50% at 1 kHz.  Connect the variable resistor to the output of the CSUT and set it to the nominal audio load resistance for which the SCUT is designed.  Call this value RL.  Pick a moderate input power, say one that delivers an audio output power (Po) of -75 dBW to RL.  An output power of -75 dBW is indicated when the 1 kHz p-p output voltage Eo_pp is:  sqrt(RL*(31.6*(10^-9))).  Increase the load resistor to a value 1.3*RL and call the resulting demodulated output voltage Eohi_pp.  Reduce the resistor to 0.7*RL and call the new output voltage Eolo_pp. Ro = 1.3*RL*((Eohi_pp - Eolo_pp)/((13/7)*Eolo_pp Eohi_pp)).   Ro varies with change of input power.  At low input power levels, Ro, measured at the diode detector output (before any step-down from an audio transformer), will equal about 0.026*n/Is.  At high input power levels, in the region of peak detection, Ro will approach twice the antenna-loaded RF tank resistance.  Section 6.  Comments. 1. Remember that output transformer loss is included in the measurement of IPL.  The usual audio transformer loss is in the range of 0.5-2 dB, but some are higher.  It's a good idea to to check the loss of the one being used.  A method is given in Article #5.  Don't forget to reduce the calculated IPL by the 0.9 correction factor if you are using the 100k resistor in series with the scope.  The MAP of the RF carrier only from the AMCS to the CSUT is: ((Ea_pp + Ea_vv)^2)/(3200) Watts. 2. It's possible for two different CSUT to have the same IPL at moderate input signal powers, but differ when receiving weak stations or strong ones. Very low input signal performance is enhanced (better DX) if the RF tank resonant resistance and transformed audio load can be made a high value.  This enables the optimum diode to be one of a lower Saturation Current.  The result is less IPL at low https://web.archive.org/web/20131030052102/http://www.bentongue.com/xtalset/11IPLmXs/11IPLmXs.html[06.08.2019 20:01:50]

Measurent of sensitivity, selectivity and input/output impedance of Crystal Radios

3.

4.

5. 6. 7. 8.

9.

10.

signal levels.  See Article #1. Very high input signal performance is enhanced (louder maximum volume) if diode reverse leakage is kept low.  This point is often overlooked.  Diodes vary greatly in reverse conduction current.  There are two kinds of reverse current effects:  One is a gradually increasing reverse leakage current that loads the circuits more and more if the input signal increases, maybe by tuning to a stronger station.  It acts as sort of an automatic volume control.  Unfortunately, this effect reduces the maximum volume one can get from the crystal radio set. The other is normal reverse current that increases rapidly above a certain input signal power and causes audio distortion as well as reduced volume.  This effect can be observed when performing the IPL tests.  For instance, in my single tuned loop set, several Agilent 5082-2835 in parallel, while very good with low signals, distort when the input carrier power at 50 % modulation gets above about -35 dBW.  Several Agilent 5082-2800 or HSMS-2800 work fairly well at low signal levels but do not distort at the highest signal level I can supply.  This improvement comes about because the HSMS-2800 has much less back leakage current than does the HSMS-2820 or 5082-2835 at high reverse voltages.  This effect is more noticeable if the diode load resistance is above the optimum value than if below it.  If you use an audio transformer, don't forget to replace the R in the parallel RC with a pot and adjust it for the least audio distortion. Actually, I keep a pot in there all the time because the optimum value is usually zero for weak signals and about 1/2 the loaded RF source resistance driving the diode for strong signals. For a given amount of output audio power, the output voltage is proportional to the square root of the output load resistance.  This may cause a problem for those who use 300 Ohm Sound Powered Headphones (SPHP) and those who may want to make measurements at low output power levels.  With the suggested starting output of 0.002 V p-p, the output power to a 1200 Ohm load (SPHP elements in series) is -94 dBW.  It would be -88 dBW @ 0.002 V p-p if the SPHP elements were wired in parallel.  To take readings at a lower power level, there are several options to consider: Use a more sensitive scope. Use a low noise 10X gain audio amplifier.  An an improvement on this would be a single tuned bandpass amplifier tuned to 1,000 Hz.  It will filter out some of the noise and hum that will probably be present. Temporarily, for the tests, use an output audio transformer that transforms to a higher output resistance, along with its corresponding load resistor.  Going from a 300 Ohm to a 12,000 Ohm output resistance will boost the output voltage by sqrt (12,000/3,00) = 6.3 times.  I use two A.E.S. P-T157 transformers connected as shown in the first schematic in Article #5 as a variable-impedance-ratio transformer to boost the audio signal voltage.  I also use it to experimentally determine if the load on the diode equals the output resistance of the diode.  The switch position that gives the most output voltage is the one that provides the best match: (4, 16, 63 times ratio, or near the mean of two of the adjacent values).  Here are some test results with my single tuned crystal radio set that uses a 14 " square loop wound with #12 ga. solid wire for the resonator.  The average parallel shunt loss resistance of the tank is 700k Ohms over the frequency range of 550-1650 kHz..  I use three Agilent 5082-2835 diodes (Is = 38 nA) in parallel for the detector and an audio transformer to convert the 700k Ohm (low signal) AC output resistance of the diode detector down to a 12,000 Ohm load resistor.  I have not yet set up to measure a loop set directly, but have coupled in an external antenna connection to a tap on the tank 6 turns from ground.  This, of course, loads the tank and results in a lower tank resistance than 700k Ohms.  The input impedance match is very good  The measured IPL at 1.0 MHz using the external antenna-ground connection is 9.65 dB at an input carrier power of -84 dBW, giving an  audio output power of -102.9 dBW.  The noise and hash on the scope prevented the measurement of selectivity.  Measurements were then made at a carrier input power of -69.4 dBW.  The output audio power became -82.9 dBW,  IPL =  4.5 dB, -3 dB RF bandwidth = 30 kHz and SF = 9.0.  Tapping the antenna 2 turns from ground increased the -3 dB selectivity to 8 kHz, kept the SF at 9.0 and increased the IPL by about 4.9 dB.  Note: The IPL figures use the 0.9 dB correction for the 100k resistor feeding the scope cable and also include the estimated transformer loss of 0.4 dB.  A SPICE simulation of this setup with no loss in the tank gives, for the 6-turns-from-ground tap condition, an IPL of of 6.1 + 0.4 (for the output transformer) = 6.5 dB instead of the 9.6 dB and 1.7 + 0.4 (for the transformer) = 2.1 dB instead of the 4.4 dB.   This suggests a tank loss of about 2.7 dB. The lower the IPL crystal radio set, the more noticeable will some of the effects noted above become..  The use of a parallel RC in the transformer primary for reducing distortion when receiving

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Measurent of sensitivity, selectivity and input/output impedance of Crystal Radios

strong signals is important if the audio load resistance is higher than the output resistance of the CSUT.  If the audio load resistance is lower than the output resistance of the SCUT, it becomes less important.  This effect shows up in simple Xtal Sets that do not use an audio transformer.  Here, the headphone impedance is usually lower than the output resistance of the Xtal Set.  Also, the headphones' DC resistance, as a fraction of its AC impedance, is generally 2 or more times larger than the corresponding fraction looking into the primary of a headphone-loaded transformer.  This goes part way towards equalizing the AC and DC impedance of the diode output load. 11. Here is an interesting point of information:  The exact frequency to which the CSUT is tuned is a function of the input level.  Reason?  For small signals, the voltage across the diode is rather small, it is reverse biased for about 1/2 the RF cycle, and the average junction capacitance is close to the zero bias capacitance.  When a large signal is present, the diode tends toward peak detection and is reverse biased for more than 1/2 the RF cycle.  The average back voltage during this period is higher than when small signals are applied.  Since the junction capacitance reduces when reverse bias increased, the average bias over one RF cycle is less than it is for small signals.  Thus, when the signal level applied to a CSUT is increased, the frequency to which it is tuned also increases.  All semiconductor diodes exhibit some of this varactor-type behaviour. 12. If the receiving antenna has a different internal resistance than the 25 Ohms used in the AMCS dummy antenna, the calculated values of S11 and VSWR and IPL will be in error.  I may develop a simple way to measure the input resistance of a CSUT and will add it to this article if I do. #11  Published: 07/21/00;  Last revision: 04/10/2003 060510

 Return to the Index Page of this Section (A)

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Directivity of the inverted L antenna and how one might enhance it http://www.bentongue.com/xtalset/12ILAnt/12ILAnt.html Go

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Directivity of the "Inverted" L Antenna, with Speculation as to why it Occurs and How one might enhance it by Ben H. Tongue

Computer modeling of the inverted L antenna shows a small directivity with the greatest signal pickup from the direction opposite that to which the open end points.  I have given some thought as to why the inverted L might exhibit directional characteristics for the reception of ground (vertically polarized) waves, and present some ideas here.  

First off, understand that I am not an antenna engineer and present these speculations to suggest a way to increase the directive gain of a small (compared to a 1/4 wavelength) antenna.  For simplicity of discussion, wave propagation issues will not be delved into.  We will consider that the operation of an inverted L antenna results from the sum (superposition) of two modes of operation. The first mode is that of a capacitively loaded vertical antenna. See Fig. 1. Co represents the "top hat" loading capacity.  Visualize the horizontal wire BCD shifted to the left so as to be symmetrical relative to the downlead AB (with point C of ABC directly above vertical downlead BA).  The total capacitance, Co, of wire BD to ground acts as the top hat capacitance for the "vertical antenna" downlead BA (the additional capacitance between the upper and lower parts of down-lead BA can be ignored because the antenna is assumed to be short compared to 1/4 wavelength).  The second mode is as single turn 'virtual loop' antenna.

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Directivity of the inverted L antenna and how one might enhance it

Let X represent a crystal radio set with antenna and ground connections, a and g.  Fig. 2 shows Co as a lumped capacitor C1, connected to ground at the center of the BCD horizontal element.  The rectangular loop circuit ABCFG, consisting of the four sides AB, BC, CF and FG can be looked at as a single turn loop antenna of area A, oriented to pickup signals from the BD direction.  Note that the path for the 'displacement current' through C1 makes up one side of the loop.  The current flowing from the induced EMF in the loop will combine to current from the EMF picked up in the down lead BA.  These two EMFs add when a signal comes from the direction opposite to that to which the open end points and tend to cancel when coming from the opposite direction.  This gives a plausible explanation of the mild directivity of the inverted L antenna.  This directivity has  been theoretically demonstrated by using computer simulation.  For clarity, Fig. 3 shows a top view of the antenna. The following changes to the configuration may serve to increase the directional gain of the antenna (I haven't tried them out.).  The induced voltage in a loop antenna (small compared to a wavelength) is proportional to its area, among other things.  If the effective location of capacitor C1 could be moved to point D, and its value kept the same, the area of the loop would be doubled to 2*A (ABDEG), thus doubling the current from its induced EMF and further increasing the directive antenna gain.  Let us change the lumped representation of Co as one capacitor C1 into two capacitors, one from point B to ground and the other from point D to ground.  They will each be equal to one-half of Co and both still will act as a top-tat capacitor for the vertical antenna BA, otherwise known as the lead-in.  The one from D to ground will be called C2.  See Fig. 4.  One way to add more capacitance to ground at point D is to construct two lateral arms on the antenna.  See Fig. 5.  If each arm is the same length as one half the horizontal element BD (They can be of some other length.), the effective capacitance they add at point D is 2*Co/2=Cadded.  The sum of the two capacitors C2 and Cadded is 1.5*Co = C4.  The loop area is doubled and the current from the induced EMF is tripled (because C3 is one and one half times C1).  The antenna directivity may thus be increased giving more gain in the direction in which the two effects add, and less in the opposite direction.  If the directive effect can be made strong enough, a cardioid pattern should result, with a good null in the "opposite" direction.  A more practical approach might be to have the two side arms droop down at an angle and be secured  to ground  with insulated guy wires.  A single vertical wire, similar to the lead-in, might work as a substitute for the two arms if its bottom end does not get too near the ground (inverted U antenna). Note there is no "free lunch" here. To the extent that the signal pickup is increased in the direction opposite to that to which the open end points, it is reduced in the other direction. #12  Published: 07/29/00;  Last revision: 11/20/05 060510

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Sensitivity measurements of headphone and earphone receiver elements http://www.bentongue.com/xtalset/13MHpLs/13MHpLs.html Go

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How to measure the electric-to-acoustic transduction power loss of magnetic and ceramic earphone elements, with measurements of some headphone receiver elements By Ben H. Tongue

Quick Summary:  This Article describes a device and procedure for measuring the sensitivity of earphone elements.  Its purpose is to provide a quantitative method for comparing elements.  Elements may be easily sorted for application to listening to weak signals, as in crystal radio sets.  Actual measurements of an assortment of elements is provided.

1. Measurements The Transduction power loss of a headphone element can be defined as the ratio of its output acoustical power to input electrical power.  We will call it HPEL and express it in dB.  A convenient way to measure HPEL is to use one element of a pair of identical headphone elements as a speaker and the other as a microphone, acoustically couple them together and then measure the input electrical power to the speaker element and the output electrical power from other element.  Ten times the ratio of the log of the ratio of output to input power is the transduction power loss of the combination of the two elements, in dB.  If the two elements are identical, the power loss of each is one-half that figure. Here is a step by step procedure: 1. Know the average impedance, Zh of the headphone elements.  If you don't know it, measure it by means of a FILVORA (See Article #2 of this series), or estimate it as 6 times the DC resistance of the element, assuming it is a magnetic element. 2. Couple two identical elements A and B together with an appropriate acoustic coupler and hold everything in place with several heavy rubber bands. 3. See Fig. 1.  Connect a white noise generator through a 0.3-3.3 kHz bandpass filter and a source resistor Rh of value Zh to element A. Connect element B to an output load resistor Rh of value equal to Zh.  The filter is necessary to limit the bandwidth of the white noise signal to the audible range of interest.  If this were not done, the reading of e1 would be too high, since the noise at that point covers a wider band than that at the output.  4. We will measure the HPEL by the insertion loss method.  See the section on "Maximum Available Power" in Article #0 and the Part 4 of Article #5 for information on this method.  Measure the input voltage e1 at point P1 and output voltage e2 at point P2.  The HPEL  = 5*log (4*((e2/e1)^2)) dB.  The 5 is there instead of the usual 10 because only half the measured loss can be attributed to one element, and we are actually measuring the sum of the two losses.  Note: It is usually recommended that elements A and B be pressed together with a force of 1 to 2 pounds so that no air leak occurs between the elements and the coupler.  Actually, if squeezing elements A and B together more tightly than the rubber bands do does not increase the value of voltage e2,

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Sensitivity measurements of headphone and earphone receiver elements

the rubber bands are OK to use by themselves.

Figure 2 shows the circuit of a bandpass filter having -3 dB points of 0.3 and 3.36 kHz with a loss of 0.4 dB at 1.0 kHz.  It's powered by a common 9 V. battery.  Since the typical 1000 DC Ohms magnetic earphone element has an impedance of 6000 Ohms and the typical balanced armature sound powered magnetic element has an impedance of 600 Ohms, approximations of these two resistance values are included in the switched resistive output controlled by S1.  An IC suitable for the circuit is an LF353 or an MC34002.

 

A convenient source for white noise is the headphone output of a small FM/AM transistor receiver, switched to FM and tuned to a point on the dial where it receives no signal, just noise.  The noise density is rolled off at 6 dB per octave above 2.1 kHz by the de-emphasis filter in the receiver, but this should make little difference in the results.  The acoustic coupler used to couple the two elements under test is based on the ANSI 9-A earphone coupler. See "Acoustic Measurements by Leo Beranek, pages 743 and 744".  An approximation to the ANSI 9-A coupler can be made of a piece of 1" nominal diameter, medium weight copper tubing having a #120 O-ring glued on each end.  The length of the copper tube used is 0.26 inches.  The I..D. of the O rings is specified as 0.987" and thickness as 0.103".  1" copper tubing is specified to have an I.D. of 1.025 and an O.D. of 1.125".  The total enclosed volume is about 6 cubic cm.  An alternative coupler that may give similar results is a stack of eight or nine 1/8 inch thick garden hose washers having an ID of about 5/8 inches.  The ANSI 9-A coupler is (was?) the standard coupler used in Audiometry when calibrating an earphone element with a standard microphone.  It is a greatly simplified version of a model of the human ear canal with an earphone cushion pressing on it.   Comments: The DVM should preferably be an RMS responding instrument.  The typical DVM responds to the full wave rectified average signal and will probably be satisfactory.  Don't use a meter that responds to the peak or peak-to-peak value of the AC signal.  1. A pink-noise generator can be substituted for the white-noise generator, but it is hard to use.  It has a larger low-frequency output than does the white-noise generator and therefore will show a greater fluctuation in the output as read on the DVM. 2. The noise output voltage of the white noise generator will probably have to be amplified (or increased with an audio transformer) when measuring headphone elements having a high HPEL, https://web.archive.org/web/20131030052112/http://www.bentongue.com/xtalset/13MHpLs/13MHpLs.html[06.08.2019 20:03:07]

Sensitivity measurements of headphone and earphone receiver elements

in order to overcome ambient noise and hum pickup. 3. The measurement method described here does not include the effect of the usual air leak between the ear pinna and the headphone element cap.  This leak rolls off the low frequency response below 500 Hz and results in a somewhat greater actual power power loss than is shown below. 4. It's a good idea to make sure that the two elements used have about the same sensitivity, otherwise the result will be the average of the good and not-so-good elements. The result will be a higher loss than if two good elements were used. Table 1 - HPEL of some Representative Headphone elements (average of two elements). Optimum HPEL HPEL: Acoustic Output e1 e2

Source/Load

Power  Device under Test (DUT) in in Resistance for the in dB vs. Available Input Power mV mV DUT Western Electric D173011 Sound

105 12 600 Ohms 6.4 23% Powered Transmitter Elements Western Electric D173012 Sound

Powered Receiver Elements RCA/GE Sound Powered

(Receiver?) Elements* Brandes Superior ''Matched Tone" Earphone Elements** 

94

13.3

600

5.5

28

94

11.4

600

6.2

24

685

5.6

6000

18

1.6

* One of the RCA/GE units was about 6 dB less sensitive than the other. Thanks to Dieter Billinger (sky_wave_99), I knew that some RCA/GE elements having low sensitivity could be improved by sticking a small neodymium magnet to the outside of the case.  It worked in this case, increasing sensitivity of the weak element by 6 dB, so it was somewhat more sensitive than the other element.  BTW, a magnet could not increase the sensitivity of the other originally more sensitive element. These two units appear to be of somewhat different construction.  To easily compare the power sensitivity of any two elements, even if they differ widely in impedance, see Article #3.

** Ttwo individual elements were selected for having strong magnets and their air gaps were optimized.  Run-of-the-mill Brandes elements may not be as sensitive. To help in understanding these charts, consider that an eight dB (6.3 times) change of power is usually perceived as a two times subjective change in loudness.

2. Comparisons In order to compare the sensitivity of headphone elements that are used flat against the ear, as well as those that are not, (but are inserted into the ear canal (tips) or outer ear (buds)), I decided to make one of my best elements a "standard" and compare the others to it using a DFLVORA (see Article #3).  That "standard" is a Western Electric Sound Powered receiver element # D173012 held flat against one ear.  In the results shown below, two Mouser elements were tested and found to be of equal sensitivity.  (That was after I found one Mouser to be weak until I whacked it several times.)   The two Radio Shack units also tested equal.   Note that the DFLVORA can be used to easily compare the power sensitivity of any two earphone elements even if they differ greatly in impedance.  For more information, see the next-to-last paragraph in Section 1 of Article #2.   Table 2 - Comparison of the Sensitivity of Selected Headphones, and Headphone Elements to a "Standard". Acoustic Power Output Sensitivity of the DUT  Optimum Source  Device under Test (DUT) Compared to the Resistance for the of the DUT, compared

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Sensitivity measurements of headphone and earphone receiver elements

Mouser #25CR035 Piezo-  Electric Ceramic Earpiece. Internal capacitance=13 nF Radio Shack #273-091B Piezo Speaker Element held flat against the ear. Internal Capacitance=46nF One element of a stereo  magnetic earbud that came 

with a small Grundig radio One element of a No-name  stereo magnetic earbud Western Electric Model  #509W Headphones (element 

pair connected in series)* Baldwin type C Headphones  with mica Diaphragms (element 

pair connected in series)* Brandes Superior Matched  Tone Headphones (element 

pair connected in series)*

"Standard"

DUT

-20 dB

12k-18k Ohms

1

-12

5k

6

-32

120 (One element)

0.06

-26

26 (One element)

0.25

to the "Standard" in %

19k (Two elements -6

connected in series)

25

-9

12k (Two elements 

connected in series)

13

-12

12k (Two Elements 

connected in Series)

6

These comparisons were made using a voice signal from a small transistor radio fed into a DFLVORA with the radio volume set to a level at which I estimated I could understand about 50% of the words.  Results may differ for people who are not old and do not have poor high frequency hearing, such as myself.  The differences in tone quality between the standard element and a DUT will have a different effect on intelligibility for different people. The sensitivity values for the piezo electric elements can only be attained if the elements do not have a resistor placed across them to supply a DC path for diode detector current.  The resistor adds loss (although this is a low cost approach to provide a DC path for the diode current).  Also, if the resistor is made large in order to reduce its loss contribution, audio distortion will oftentimes take its place.  The best way to drive the elements is to use an audio transformer to impedance match the diode detector output resistance to the average impedance of the element. The transformer supplies supply a DC return path for the diode.  A further advantage of using a transformer is that no DC voltage can get across the piezo element.  Sometimes, if a strong signal is tuned in and it produces a large rectified DC voltage on the element, the element will "freeze" and its sensitivity will drop.  See Article #5 for info on transformer coupling and diode DC resistance loading. (The value of the DC load resistance on the diode should equal the average value of the AC audio load impedance.) *  The comparison of the sensitivity of an element in a series connected element pair DUT with the "standard element" was made in the following manner:  The full (two element) headphones DUT was connected to the J1 output of the DFLVORA. The DFLVORA was fed by a weak voice signal and the source resistance switch adjusted for the greatest volume and intelligibility.  The "standard element" was then connected to the J2 output and the 3, 6, and/or 12 dB attenuators were adjusted so that the intelligibility of the voice in the "standard element" was equal to that in one element of the headphones DUT .(The other element was left dangling.)  The amount of attenuation placed in the circuit feeding the standard element is a measure of the difference in sensitivity between the standard and the DUT.  Since 1/2 the power going into the full headphones DUT goes into each element, one element of the DUT headphones being listened to receives 1/2 the power (3 dB less power) than that delivered to the https://web.archive.org/web/20131030052112/http://www.bentongue.com/xtalset/13MHpLs/13MHpLs.html[06.08.2019 20:03:07]

Sensitivity measurements of headphone and earphone receiver elements

full headphones, giving the reading for a single element a 3 dB handicap.  Thus, the sensitivity of one element of the headphones DUT is 3 dB better than the sum of the readings of the attenuators.  This 3 dB correction is made in the figures for the DUT in the table above. When doing a comparison of this type (comparing one element of the pair in a  full headphones, to a single "standard element"), first check the volume in each of the two elements of the pair.  If they are not equal, error will result.  If the volumes are not too far apart, perform the measurement for each element of the pair and average the result.  There is some error introduced by the procedure given above because the acoustic loading on each earphone of the pair is not the same. Summary:

The Western Electric #509W headphones tested 6 dB less sensitive than the "standard". The Baldwin type C headphones tested 9 dB less sensitive than the "standard".

The Brandes Superior Matched Tone headphones and the two Radio Shack Piezoelectric speakers tested 12 dB less sensitive than the "standard". The each of two Mouser Ceramic Earpieces tested 20 dB less sensitive than the "standard". The sound powered elements turned out to be the most sensitive and are therefore to be prefered for use when listening to weak signals, as is the case when trying for DX with a crystal radio set. In all cases it is assumed that the source resistance driving an element is equal to the average impedance of the element over the audio frequency range of interest.  This is the closest that we can get to an impedance matched condition. Last item:  Remember that headphone sensitivity can vary from unit to unit.  The figures given above are not gospel for all units of a particular model.  Diaphragms warp, magnets weaken and air gaps may get changed.  All affect the sensitivity. #13  Published: 08/30/00;  Last revision: 10/28/2004 Return to the Index page of this Section (A) 060510

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No-loss audio transformer simulator with independently adjustable input and output impedances http://www.bentongue.com/xtalset/14UITSp/14UITSp.htmlGo

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A Zero Loss, Unilateral 'Ideal' Audio Transformer Simulator, plus...  This device makes is very easy to determine the optimum audio transformer source and load resistances for any crystal set diode/headphone combination. No test equipment necessary By Ben H. Tongue

Quick Summary:  This device works as an audio transformer when connected between the output of a diode detector and headphones, but with several differences.  (1) No insertion power loss.  (2) Input and output resistances can be independently  varied over a wide range by selector switches.  This provides for the simulation of a wide range of "transformer turns ratios". The main purpose of this device is to enable oneself, by twisting two dials, to find out the optimum audio impedance transformation needed in a 'real world transformer', while experimentally trying different diodes or headphones in a crystal radio set.  The effect the transformer has on selectivity and volume may be evaluated.  Another purpose is to enable one to check how closely the performance of one's audio transformer conforms to that of an ideal one, both having the same input and output impedances. It also has a switchable 20 dB amplifier to enable better reading of very weak signals. The first version of this device, shown in Figs. 1, 2 and 3 is designed for driving typical sound-powered balanced-armature, magnetic diaphragm or piezo electric earphones.  The schematic for Version B, shown in Fig.4 is designed for feeding a wider range of loads, down to an impedance of 8 ohms.  This unit can match the impedance of the earphones mentioned above as well as that of typical dynamic earphones.  

1. What's it good for? Consider a crystal radio set that uses an audio transformer to drive headphones. One can determine what its performance would be if the transformer had no loss and provided an optimum impedance match between the output resistance of the diode detector and the headphone load. One can determine if the optimum diode load resistance changes as a function of signal level by adjusting SW3 for the loudest volume on a weak signal and then readjusting it for a strong one. One can determine the optimum turns ratio for a real-world transformer. To do this, set SW3 and SW4 for maximum volume.  Calculate the output-to-input winding turns ratio as the square root of the ratio of the port resistances of SW4 to SW3 (the numbers in parentheses in Fig. 3). One can determine if the optimum diode load resistance changes from one end of the BC band to

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No-loss audio transformer simulator with independently adjustable input and output impedances

the other by adjusting SW3.  It usually does change, when receiving strong signals. Some of the mystery can be taken out of evaluating diodes.  A diode will exhibit its best weaksignal sensitivity when the RF source resistance driving it, and the audio load resistance are set to the optimum values for that diode.  When comparing various diodes in a crystal radio set that is using a Unilateral 'Ideal Transformer' Simulator (UITS), the optimum audio load resistance required for that diode can be easily dialed up just by setting SW3 for the loudest volume.  The diode is then not penalized for being used in a poor impedance environment (for that diode). The sensitivity of various headphones may be compared without the problem of needing an optimum audio transformer for each.  Just adjust SW4 for maximum volume on each headphone and read the approximate optimum source resistance from the calibration. One can determine, in a particular crystal radio set, how closely a particular real-world transformer emulates an ideal one. One can easily demonstrate how the frequency response (tone quality) of a particular headphone changes as a function of the source resistance driving it by changing the setting of SW4.  One can also find out out if one's real-world audio transformer alters tone quality.  This can happen if its shunt inductance is too low or if its distributed winding capacitance is too high. The average audio impedance of headphones can be determined.  For more info on this, see Articles #2 and 3. An added feature of the device as implemented is the capability of adding a 20 dB boost to the audio signal (this is where the plus... comes from).  This feature does not affect the input and output resistances.  It can be used to just add volume to weak signals, or as an aid in centering tuning on a very weak signal. In normal operation (20dB boost turned off), the UITS is calibrated to provide no power gain of loss.  It has a flat frequency response +/- 0.3 dB over the audio band of DC - 3.3 kHz.

2. What is it? The UITS, unlike a real world transformer, can pass a signal from the input port (J1) to the output port (J2), but not from J2 back to J1.  The 'unilateral' in the name comes from this property.  See Fig. 3.  A real world transformer is bilateral.  That is, it can pass a signal in either direction. A good transformer has very little loss.  The UITS can be set to have no power loss (or gain), no matter what the effective turns ratio setting is.  The effective turns ratio is controlled by the settings of SW3 and SW4.  A real world transformer has a turns ratio of, say 'n'.  This gives it an impedance transformation ratio of n^2.  That is, a resistor of value R, connected to one winding will be reflected as a value R*(n^2) or R/(n^2) at the other.  'n' is a fixed parameter of the real world transformer unless it has taps, then several various values of 'n' can be obtained.  The UITS can be adjusted with SW3 and SW4 to a very wide range of transformation ratios.  It has the advantage of independent control of input and output resistance by means of switches, with no power loss for any combination of input and output resistance.

3. A Short tutorial on some aspects of audio transformer utilization in crystal sets. One of the issues one encounters when designing a high performance crystal radio set is determining the optimum parameters for the detector-to-headphone audio coupling transformer.  Its impedance transformation ratio is the main factor to be considered, though the inherent loss and reactance parameters are  also important.  Another factor is the primary and secondary impedance levels for which the transformer was designed, compared with the levels to be used in a crystal radio set application. Consider the performance of two transformers having the same transformation ratio, but originally designed to operate at different impedance levels.  They will not perform the same.  To illustrate this point we will consider a transformer designed to transform a 10,000 Ohm source to a 90,000 Ohm load.  This could be an AES  PT-156, Stancor A-53C or similar transformer originally designed to couple the output of a first (tube) audio stage to push-pull grids.  If the designer did a good job, this transformer will have the lowest possible loss consistent with its specified frequency range, power handling capability and cost goals.  If it were to be driven from a 40,000 Ohm source and loaded with a 360,000 Ohm load (still a 1:9 impedance ratio), its center-band power insertion loss will be increased and the low frequency end of the band will be rolled off.  The reason for the increase of center-band loss is that the shunt resistance https://web.archive.org/web/20150104013144/http://www.bentongue.com/xtalset/14UITSp/14UITSp.html[06.08.2019 20:04:05]

No-loss audio transformer simulator with independently adjustable input and output impedances

caused by losses in the iron core load down the now higher source resistance (40,000 Ohms) thus increasing loss.  The shunt inductive reactance of the primary winding, at the low end of the band loads down the now higher source resistance (40,000 Ohms) more than before, thus increasing the roll-off at the low frequency end of the audio band.  The high end of the audio band will also probably be rolled off because the reactance of the shunt capacitance of the primary winding will cause more loss when being driven by a 40,000 Ohm source than one of 10,000 Ohms.  On the other hand, if the transformer was driven from a 2,500 Ohm source and fed a 22,500 Ohm load, center-band power insertion loss again still be increased.  The reason is the ratio of the source resistance to the series resistance of the primary winding is not as high as when the source was 10,000 Ohms.  More of the input power will be dissipated in this series resistance and less transferred to the secondary.  A similar loss effect from the winding resistance occurs in the secondary.  The low frequency end of the band will reach to lower frequencies than before, but the high end may get some roll-off due to leakage inductance in the primary and secondary windings.  One can think of this effect by visualizing a parasitic inductor in series with the primary and secondary windings. It is important to understand that the impedance numbers a transformer manufacturer specifies for various terminals are the source and load resistances they used to specify the performance of the transformer. In most instances when one uses a transformer originally designed for use between tubes (plate-to-grid) or to match a low impedance line to a plate or grid in a high-performance crystal set application, the following statement applies:  Optimal results usually occur when the actual crystal set source and load resistances are higher than the values for which the transformer was designed, but are of the desired ratio. For instance, if a Stancor A-27 transformer is connected with terminals 8 and 9 joined together and 3 and 4 joined together (diode input to pin 7, diode return to pin 10), it is specified by the manufacturer for use between a 100k source and 600 ohm load connected to pins 1 and 6. Using it between approximately 200k and 1.2k ohms will result with a very slight increase of midband transformer power loss, but a greater offsetting increase of detector sensitivity from the higher detector load of 200k. This assumes a diode having a relatively low saturation current such as a Schottky, FO-215 or other high axis-crossing-resistance diode is used. The audio bandwidth will also be reduced but probably by a non-perceivable amount. Some illustrations of these effects can be viewed in Article #5, Tables 5, 7 and 8. To go further in this direction to present the diode with an even higher transformed resistance from a 1200 ohm load, connect the load to terminals 1 and 5 instead of 1 and 6. Volume may diminish from increased transformer loss and reduced audio bandwidth.

4. The Unilateral 'Ideal Transformer' Simulator. How should one proceed in determining the specifications for a transformer that will provide optimum performance in the crystal radio set?  One may not know the audio source resistance of the diode detector, or even the average impedance of the headphones load.  The UITS can be used to find these two values.  It also has a 20 dB gain switch option that can be used to enable reception of very weak signals as well as a switch to block DC from the phones, if desired.  There are two operating adjustments. One sets the input resistance Ri, the other the output resistance Ro.  These two settings don't interact. The equivalent real-world transformer turns ratio is the square root of the ratio of the two resistance settings.  Here are some ways that the UITS can be used: Compare the performance of a candidate transformer to that of an ideal transformer to see how much signal is lost in the candidate.  There is no point in looking for a better transformer if the difference between the two is small. Use it to find the impedance transformation ratio that would be optimum for the crystal radio set/headphone combination being used. Use it in place of an actual transformer. Enhance reception of very weak signals. See bullets in the "What's it good for?" section, above. To use the UITS, connect it between the detector output and headphones.  Insure that the diode has an appropriate RF bypass capacitor.  Set the amplification to 0 dB.  Adjust each rotary switch independently for the loudest volume.  Calculate the impedance transformation ratio from the settings of S3 and S4.  A transformer specified with this ratio is optimum for the detector and headphone impedances being used, all other things being equal.  Its specifications should include primary and secondary source and load https://web.archive.org/web/20150104013144/http://www.bentongue.com/xtalset/14UITSp/14UITSp.html[06.08.2019 20:04:05]

No-loss audio transformer simulator with independently adjustable input and output impedances

resistances about equal to the values determined with the UITS.  A transformer that has factory specified impedance levels as much as four times lower than desired, but with the correct transformation ratio, and a frequency response range much wider than 0.3-3.3 kHz will probably work well. Note. The parallel RC (a 'benny') (see Article #5), needed in series with the primary of a real world transformer, is not needed with the UITS because its input resistance is the same for DC as for AC.  

Fig. 1

Fig. 2  

Some component specifics: B: 9 Volt batteries. IC: JFET input op-amp such as one section of an LF353, TL081 or M34002.  Basically, it should have a JFET input and a gain-bandwidth product of 3 MHz or more. The 22 uF caps, electrolytic or tantalum, should have a voltage rating between 10 to 25 Volts. https://web.archive.org/web/20150104013144/http://www.bentongue.com/xtalset/14UITSp/14UITSp.html[06.08.2019 20:04:05]

No-loss audio transformer simulator with independently adjustable input and output impedances

The resistor values shown in the schematic are those in the standard 5% series of values.  The use of resistors that difer by +/- 10% from the values shown should not have an appreciable impact on performance of this unit.

5. Setup. Calibration is simple. With SW2 in its 0 dB position and SW3 and SW4 at their 10k Ohm settings, set potentiometer P for zero gain.  To do this, load J2 with a 10k Ohm resistor and feed a 1 kHz signal from an audio generator into J1.  Adjust P so that the output voltage at J2 equals the input voltage at J1.  If no audio generator is available, connect the output of the crystal radio set diode detector to J1 (no audio transformer to be used), and a headphone set of about 10k ohm impedance (2k ohm DC resistance) to J2.  Tune in a station and adjust potentiometer P so that the volume is the same as when the detector output feeds the headphones directly.  This setting does not have to be changed in the future.  Note: Connect the output of the crystal radio set detector to the UITS with as short a length of cable as possible in order to minimize added shunt capacity.  If the tone quality of the signal changes from one resistance setting of SW3 to another, the shunt capacity in the detector output circuit is too high.  This can be caused by using a diode RF bypass capacitor or an interconnecting cable of too high a shunt capacitance for the resistance setting of SW3 being used.  I use an eighteen inch length of RG-59 type coax for my cable.  It has a capacitance of about 20 pF per foot. The performance of magnetic diaphragm type headphones can be affected by the DC current passing through them when no coupling transformer is used.  SW5 is provided for those who choose to block the DC.

6. Schematic for version B (Added 05/25/2003).  The differences between this version and that shown in Fig. 3 are: 1. The output resistance range is changed from 40k-150 ohms to 20k-8 ohms.  This allows the use of the UITS with typical dynamic headphones. 2. The DC blocking is made fixed (SW5 is eliminated). 3. The schematic shows only provision for input impedances up to 640k. The extra switch position for 1.28M shown in Fig. 3 may be added if desired.

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No-loss audio transformer simulator with independently adjustable input and output impedances

#14  Published: 01/05/01;  Last revision: 01/17/10 Return to the Index Page of this Section 011910

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AM diode detector equations relating diode parameters to the LSLCP and sensitivity http://www.bentongue.com/xtalset/15adi_eq/15adi_eq.htmlGo

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Quantitative insights into Diode Detector Operation derived from Simulation in SPICE, and some Interesting new Equations relating diode parameters to weak signal sensitivity By Ben H. Tongue

Quick Summary:  Several new equations are presented showing various relations between diode detector rectified current, input AC and output DC power, insertion power loss and the 'Linear-toSquare-Law Crossover Point' (LSLCP).  The LSLCP is an operating point where the diode detector is operating half way between its linear and square law modes.  It can also be thought of as a dividing point between weak and strong signal reception.  Bear in mind that the LSLCP is a point (see Fig. 3) on a graph of output DC power vs input RF power of a diode detector system.  It is not a point on a graph of DC current Vs voltage of a diode.  Article #27 shows actual measurements on a crystal radio set using eleven different diodes, that tends to experimentally back up the validity of equation #5 and those following it. This Article, #15A, used to be Part 1 of the old Article #17. Definitions of terms to be used: Class A    Impedance matching condition in which  R1=R2=Rx Class B    Impedance matching condition in which R2=2*R1 and sqrt(R1*R2)=Rx LSLCP    A point on the curve of output power vs input power of a diode detector where it                 operates half way between its linear and square law mode Plsc(i)      Input power at the linear-to-square-law crossover point Plsc(o)     Output power at the linear-to-square-law crossover point Is             Saturation current of the diode n              Ideality factor of the detector DIPL       Detector insertion power loss in dB DIPLR    Detector insertion power loss ratio (ratio of output to input power) DIR         Detector input resistance (AC) Pi            Available input power Po           Output power sqrt         Take the square root of the expression following Kt           Temperature in degrees Kelvin C.           Temperature in degrees Celsius Ri            Detector input resistance Ro           Detector output resistance  R1           Source resistance R2           Load resistance I2            Rectified current Rx           Slope of voltage/current curve of a diode at the origin.   Rx=0.0256789*n/Is, at

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AM diode detector equations relating diode parameters to the LSLCP and sensitivity

25° C. S11         A measure of input impedance match.  S11=20*log|[(|Ri-R1)/(Ri+R1)]|.  S11 is always                a negative number, and the greater its absolute value, the better the impedance match. V2lsc(o) Detector DC output voltage when it is operating at its LSLCP SPICE   A computer circuit simulation program.  ICAP/4 from Intusoft was used in all simulations.   The diode detector circuit to which we will refer is shown in Fig. 1.

Fig. 1 Assumptions used in the following discussion: The Q and L/C ratio of tuned circuit T are assumed to be high and low enough, respectively, so that the 'stored energy effect' of  T prevents any appreciable clipping of the positive voltage wave form peak by diode D1. The value of C2 is assumed to be high enough so that a negligible amount of RF voltage appears across it. The diode parameters Is and n are known from measurement or a Data Sheet.  A simplified method of estimating Is is given in Section 2, Article #4, but the parameter n has to be estimated.  A method for measuring both Is and n is given in Article #16.  The effect of the series parasitic resistance of the diode is assumed to be negligible - as it is at low signal levels for most all detector diodes.  Diode back leakage current from either 'parasitic leakage' or operation with voltage swings reaching into the 'reverse breakdown current' region is assumed to be negligible.  The diode temperature will be assumed to be 25 degrees C. Approach: The RF signal input power range is divided into two regions and one point; impedance and power relationships are determined.  Refer to Figs. 2 and 3.  Two Cases will be considered.  In Case A, R1=R2=Rx=0.0256789*n/Is.  In Case B, R1=Rx/sqrt2 and R2=Rx*sqrt2. 1. The low power region:  Here, the relation between output power and input power approaches 'square-law'.  That is, for every one dB change in input power there is about a two dB change in output power. The detector input and output resistances approximate Rx. 2. The high power region:  Here, the relation between output power and input power approaches 'linear'.  That is, for every one dB change in input power there is about a one dB change in output power.  The detector input and output resistances are no longer equal.  The detector input resistance is equal to about half of R2.  The detector output resistance is about twice R1. 3. The point where the two areas overlap equally:  This is the 'linear-to-square-law crossover point' (LSLCP).  At this point there is a 10*log(sqrt2) dB change in output power for every 1.0 dB change in input power (slope of about 1.5).  If R1 and R2 are both equal to Rx, in Case A the detector input resistance is about 12% less than Rx and its output resistance is about 12 % greater than Rx. Transition from the linear to the square law region:  All good diode detectors, at high input power levels, if well impedance matched at input and output, have a low insertion power loss (a fraction of a https://web.archive.org/web/20131030052117/http://www.bentongue.com/xtalset/15adi_eq/15adi_eq.html[06.08.2019 20:04:44]

AM diode detector equations relating diode parameters to the LSLCP and sensitivity

dB).  If the input power is reduced, at first the output will drop approximately dB for dB in step with the input.  If the input is further reduced, the output will start to drop faster (in dB).  This can be thought of as the onset of noticeable 'detector insertion power loss'.  The insertion power loss at the LSLCP, in two SPICE simulations (see Cases A and B below), is about 5 dB.  Put another way, at the LSLCP the output power is about 0.3 times the available input power.  This power loss figure changes by less than 0.1 dB between Cases A and B. Most crystal radio sets can deliver a readable signal at an input of Plsc(i) Watts. It would obviously be desirable to lower the input power at which the LSLCP occurs so that more of the weak signals would be closer to the linear mode of operation, experience less insertion power loss and therefore be louder. Example SPICE simulation of a diode detector at 25° C.:  Figs. 2 and 3 show power relations at various power levels.  The LSLCP is shown by a red arrow.  In the SPICE simulations for these graphs, the source and load resistances, R1 and R2, are equal to Rx (Case A).  The DIPL values for Case B (Fig.3) are within 0.4 dB of those of Case A.  The main difference is the lower DIPL values in Case B at high input powers.  For instance, the insertion power loss at an input of -48.912 dBW is 0.76 dB for Case A and 0.30 for Case B.  The loss figures from the equations that follow are quite close to those that occur in a SPICE simulation of both Case A and Case B. At input power levels several times or more below the LSLCP, the impedances of the input and output ports of the detector both approach Rx for both Cases, A and B.  At input power levels several times or more above the LSLCP, the detector approaches operation as a peak detector having a low insertion power loss.  In this condition the input RF resistance of the detector approaches half the output load resistance and the output resistance of the detector approaches twice the RF source resistance.  Summary:  In Case A, the detector input and output ports both approach an impedance matched condition when the signal power is several times lower than that at the LSLCP.  At signal power inputs several times greater than that at the LSLCP, a moderate impedance mismatch exists at both the input and output ports.  In Case B, conversely, the detector input and output ports are both are moderately impedance mismatched when the signal power is several times lower than that at the LSLCP.  At signal power inputs several times greater than that at the LSLCP, both input and output ports approach an impedance matched condition.     Simulated diode detector output power and insertion loss vs input power, Case A.

This diode has a low saturation current, compared to that used in the average crystal set, Is=38 nA, n=1.03 The LSLCP is shown by the red arrow.

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AM diode detector equations relating diode parameters to the LSLCP and sensitivity

Fig. 2 - A SPICE simulation of the relation between output and available input power.

Fig. 3 - Data from a SPICE simulation showing  detector insertion power loss vs. input power.

Note the following in Fig. 2:  At input power levels well above the LSLCP, the relationship between input and output power (see the data points, not the Least Squares Line) approaches linearity.  That is, the output changes about one dB for every one dB change in input.  At input power levels well below the LSLCP, the relationship between input and output power (see the data points, not the Least Squares Line) approaches a square law relationship.  That is, the output power changes about two dB for every one dB change in input power.  This has bad implications for weak signal reception.  If a weak signal fades, the detected signal will drop twice as many dB as the reduction in input signal strength.  For best weak signal sensitivity, one should push the LSLCP to as low a power level as possible.  This moves weak signals closer to the LSLCP and linear operation (less detector power loss), and thus increases volume.  Lowering of the LSLCP power is associated with using a diode having low values for n and Is, and impedance matching the antenna-ground system impedance and headphone impedance to the now higher values of detector input and output impedances.  For good results, one must make sure the impedance transforming means does not introduce other losses.  A high Q tank inductor, tuning capacitor, and low loss audio transformer are important.  It may be difficult to achieve the required greater impedance transformations in a low loss manner. Example:  Assume that Is=38 nA and n=1.03, as was used in the graphs and chart above.  Rx becomes approximately 696009 ohms.  R1 and R2 are each fixed at 696009 ohms for all simulation points in Case A.  This establishes a very good input and output impedance match at low signal levels and a moderate match at higher levels.  The input return loss (S11) is better than -14 dB at signal levels up to 12 dB above Plsc(i).  S11 approaches about -9.5 dB at very high input power levels.  The input impedance match conditions are reversed in Case B.  Rx is still 696009 ohms but R1 is set to 492153 and R2 to 984305 ohms.  Now, at low input power levels, the input and output are somewhat mismatched (S11=-15.3 dB), but at high signal power levels, a very good impedance match is approached.  The bottom row shows these two conditions.   Unpublished information from Xavier Le Polozec indicates that the optimum practical compromise values for R1 and R2, for input powers well below the LSLCP to well above it is:  R1=Rx and R2=Rx*sqrt2.

The diode detector equations: The following equations are developed for the Class A termination condition of R1=R2=Rx.  They give insertion power loss values to within a fraction of a dB of those provided by SPICE simulation for both Cases A and B. The output current, I2, is different for Class A and B.   Observation of a curve of output vs. input power (in dB), from SPICE simulation of a Class A terminated detector reveals a slope of 1.5 at an input power value of -78.91 dBW, for the particular diode used.  This is the LSLCP for input power.  Another observation is that the rectified diode current I2 at the LSLCP point appears to be very closely two times the Is of the diode.  This two times figure appears to be apply to all diodes.  Note: The Plsc(i) of -78.91 dBW occurs when the detector parameters are R1=R2=Rx and the diode parameters are: Is=38 nA, n=1.03 and temperature is 25° C.  In general, the 'two times' figure does not hold for termination conditions other than R1=R2=Rx.

Calculation of diode detector output power when it is operating at its LSLCP: Differentiating the Shockley diode equation with respect to the diode junction voltage yields: Diode junction resistance=Rx=0.0256789*n/Is ohms.                      (0) At the LSLCP, I2=2*Is.  (From the paragraph above)                         (1) Some obvious relations:  Output power=Po=(I2^2)*R2 Watts.  The output load R2 has been specified as equal to Rx, Rx is defined in equation (0). I2 is 2 times Is at the LSLCP (See equation 1).

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AM diode detector equations relating diode parameters to the LSLCP and sensitivity

 Substituting into the equation for Output power Po, we get, for the output power at the LSLCP: Plsc(o)=0.102716*Is*n.         (2)

Calculation of the diode detector DC output voltage [V2lsc(o)] when it is operating at its LSLCP: Some simple manipulation of equations (0) and (2) results in the relation:  V2lsc(o)=0.051*n Volts       (2a)

Calculation of the ratio of output power to input power (DIPLR) at any power level: A proper relation between Po, Pi and I2 obviously requires that I2 approach zero as Po/Pi approaches zero, that Po/Pi approach proportionality to I2 as I2 becomes low (the square law relation) and that Po approach Pi as I2 becomes very high.  Also, at an output power of Plsc(o), I2 must equal 2*Is, as stated earlier.  Curve fitting suggests this relationship:  Po/Pi=(I2/(I2+4*Is)=DIPLR               (3) Interesting note: Since, at the LSLCP, I2=2*Is (eq. 1),  Plsc(i)=Plsc(o)*3.         (4)

Calculation of the diode detector input power when it is operating at its LSLCP: Substituting the value of Plsc(o) from equation 2 into equation 4 results in:  Plsc(i)=0.308148*Is*n for the input power at the LSLCP      (4a)

Various relationships between input power, output power and diode parameters: A lot of mathematical manipulation of the relations given above results an equation that fits the simulation data quite well over the whole range of the graph in Fig. 2. Po=[sqrt(0.102716*n*Is+Pi)-sqrt(0.102716*n*Is)]^2 Watts.        (5) Po={sqrt[Plsc(o)+Pi]-sqrt[Plsc(o)]}^2 Watts.        Normalized to Plsc(o).  (5n) A rearrangement of the terms in equation (5) yields: Pi=Po+sqrt(0.41104*n*Is*Po)  Watts.       (5r) Pi=Po+2*sqrt(Plsc(o)*Po)  Watts.        Equation (5r) normalized to Plsc(o), by using equation (2).  (5rn) From equation (5r), at low output power power levels, the input power required to produce a given output approaches: Pi=sqrt(0.41104*n*Is*Po)               (5Li) Prearranging terms of equation 5Li: Po=(Pi^2)/(0.41104*n*Is)                 (5Lo) An equation that fits the detector Insertion Power Loss Ratio (DIPLR) is obtained by dividing equation (5) by Pi: DIPLR=[sqrt(1+0.102716*n*Is/Pi)-sqrt(0.102716*n*Is/Pi)]^2          (6) DIPLR={sqrt[1+Plsc(o)/Pi]-sqrt[Plsc(o)/Pi]}^2      Normalized to Plsc(o) by dividing right side of eq. (5n) by Pi    (6n)

The Insertion power loss (DIPLR) at which a diode detector is operating can be determined by noting the DC rectified output voltage: https://web.archive.org/web/20131030052117/http://www.bentongue.com/xtalset/15adi_eq/15adi_eq.html[06.08.2019 20:04:44]

AM diode detector equations relating diode parameters to the LSLCP and sensitivity

Adjust the DC component of the diode load to equal its axis-crossing resistance (0.0256789*n/Is ohms).**  Measure the DC voltage V2 developed across the DC load. Some simple manipulation of equation (3) above results in equation (7). DIPLR=V2/(V2+0.1027156*n)      (7) **  See articles #16 and #27 for info on determining the Is and n of diodes as well as measurements on some diodes. Equation (5r) seems important.  It shows that the input power required for a specific output power is reduced if n and/or Is is reduced.  At low input powers, the required input power for a specific output power approaches direct proportionality to the square root of n and/or Is, as shown in equation (5Li).  The product n*Is can be considered to be a 'figure of merit' for diodes as weak signal detectors, provided input and output impedance matching exist and losses from passive components remain unchanged.  The ideality factor (n) and saturation current (Is) of the diode are important parameters in determining ultimate very weak signal sensitivity.  If all other diode parameters are kept the same, the weak signal input and output resistances of a diode detector are directly proportional to n and inversely proportional to Is.  Assume a diode with a value of n equal to oldn is replaced with an identical diode, except that it has an n of newn, and the input and output impedances are re-matched (the new impedances are doubled).  The result will be a detector insertion power loss change of: 10*log(oldn/newn) dB.  That is, a doubling of n will result in a 3 dB increase in insertion power loss, assuming the input power is kept the same and input and output impedances are re-matched.  The result is a 3 dB reduction of output power (volume).  A similar effect occurs if Is of the diode is increased except that this change reduces the impedances that must be re-matched instead of increasing them.

Interesting note:  A simple manipulation of Equations #0, 2 and 4 shows that, at the LSLCP, the RMS value of the AC signal at the input to the diode is: (0.08895*n) Volts, and it is independent of Is. One final equation: One can combine two equations: Rx=0.0256789*n/Is, as given in the "Definition of Terms" at the beginning of this Article and equation (5Lo) to come out with a very useful result relative to actual crystal set design. For a given input power, equation (8) gives the output power as a function of the diode axis-crossing resistance and ideality factor (for weak signals and matched conditions).  Po={(Pi/n)^2}*(Rx/0.010554)       (8) Let us review the conditions that apply to equation (8) before discussing it.  1) The signal power to the detector diode is well below the LSLCP (weak-signal reception).  2) Detector source and load impedances are well matched to Rx, the axis-crossing resistance of the diode (see "Definition of Terms").  Equation (8) indicates that the maximization of output power, when receiving weak signals, requires using a diode of low n because output power is shown to be inversely proportional to the square of n. Also, with other factors being fixed, higher source and load impedances increase output power in direct proportion to their increase in value (remember they are both kept equal to Rx).  A real-world problem occurs when one manipulates the RF input and audio output impedance transformations when attempting to optimize them to get greater weak-signal volume. Their internal power losses can change and this is not accounted for in equation (8). The RF input impedance transformation loss probably won't change a lot if the ratio of unloaded to loaded Q of the tank doesn't change, and will not be treated here. Audio transformer loss is worth investigating. An audio transformer usually has a Manufacturer-stated loss that applies when it is used between the Manufacturer-stated impedances.  When used between other impedances (higher, in the usual case with crystal sets), transformer loss will most always be greater.  Equation 8 shows that the transformer winding connected to the audio output side of the diode detector should present the highest impedance possible but, then that is done, transformer power loss usually increases. A compromise is needed. Warning: Don't use two diodes in series if you want the best weak signal sensitivity.  The result of using two identical diodes in series is the emulation of an equivalent single diode having the same Is but an n of twice that of one original diode.

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AM diode detector equations relating diode parameters to the LSLCP and sensitivity

Experimental measurements on eleven different diodes used as detectors is shown in Article #27.  Close correlation between these equations and actual measurements is demonstrated. #15A  Published:  04/10/2001;   Revised:  12/07/2008 060510

Return to the Index Page of this Section (A)

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Diode saturation current and ideality factor measurement, with measured values for various diode types http://www.bentongue.com/xtalset/16MeaDio/16MeaDio.html Go

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20 Sep 2007 - 8 Dec 2018

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A Procedure for Measuring the Saturation Current and Ideality Factor of a Diode, along with Measurements on various diodes By Ben H. Tongue

Quick Summary:  A schematic and operational instructions are given for a device for use in measuring Saturation Current and Ideality Factor of a diode.  Measurements of various detector diodes are included. The Saturation Current and Ideality Coefficient of a diode can be determined by measuring an applied junction voltage along with the associated current flow at two different voltages.  These two data pairs are then substituted into the Shockley diode equation to create two simultaneous equations in Is and n, and then solved for Is and n.  Since the equations include exponential functions, they can not be solved by ordinary algebra.  Numerical methods must be used.  The Shockley diode equation at 25 degrees C. is:  Id = Is*(exp(Vd/(0.0256789*n))-1) Amps.  Id = Diode Current (amps),  Is=Saturation Current (amps),  Vd = Diode Voltage,  n = Ideality Coefficient.  The series resistance Rs of the diode is ignored because the measurement currents are so low that the voltage drop across Rs is negligible.  Measurements have shown that Is and n of point contact germanium diodes can vary with current, but are relatively constant, down to very low currents, when the current is under six times Is.  Silicon p-n junction diodes exhibit values of Is and n that vary with current.  The values for Is and n of Schottky diodes are quite constant over the range of currents used in ordinary crystal radio set reception. A convenient set of measuring currents is about 6*Is and 3*Is.  Substituting Id = 6*Is, then Id = 3*Is into the Shockley and solving for Vd yields:  For Id = 6*Is, Vd = 0.05000*n volts.  For Id = 3*Is, Vd =  0.03561*n volts.  The value of n will probably be between 1.0 and 1.2 for the type of diodes used in crystal radio sets, so use 1.1 in determining the applied voltage to use.  Suggested voltages to use are about 0.055 and 0.039 volts, although other values may be used.

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Diode saturation current and ideality factor measurement, with measured values for various diode types

S1 is a triple pole double throw switch, S2 is a push button momentary-contact SPST switch.  DVM is a digital voltmeter with 10 Meg input resistance having a 200 mV range setting.  S3 is a range switch that enables greater precision when using a conventional 3 1/2 digit DVM.  It is also used when measuring diodes having a high Is.  R2 is used for coarse setting of the diode voltage.  R1 is a ten turn precision 20k pot such as part # 594-53611203 from Mouser.  It is used for fine setting of the diode voltage.  

Procedure for Measuring Is and n: 1. Set S3 for 300k for diodes expected to have a low to medium Is.  Set S3 to 100k if the diode is expected to have a high Is.  S4 to HC and R1 to 1 about turn from point B. 2. Take Data Set #1:  Set S1 to V.  Push S2 and adjust R2 to obtain a reading of about 0.055 volts.  Use R1 to set the voltage to the voltage desired (0.055 volts is suggested).  Call this voltage V1.  Set S2 to I, read the DVM and call that voltage V2. 3. Take Data set #2:  Set S1 to V.  Push S2 and adjust R2 to obtain a reading of about 0.039 volts.  Use R1 to set the voltage to the voltage desired (0.039 is suggested).  Call this voltage V3.  Set S2 to I, read the DVM and call that voltage V4. 4. The diode voltage (Vd1) from Data Set #1 is V1.  The diode current from Data Set #1 (Id1) is (V2/300,000)-(V1/10,000,000) or (V2/100,000)-(V1/10,000,000) Amps, depending on the setting of S3.  The diode voltage (Vd2) from Data Set #2 is V3. The diode current (Id2) is (V4/300,000)(V3/10,000,000) or (V4/100,000)-(V3/10,000,000) Amps, depending on the setting of S3. 5. The two data sets Vd1, Id1 and Vd2, Id2 must now be entered into two Shockley diode equations (shown above) in order to make two simultaneous equations in Is and n.  Solving them will yield values for Is and n, measured at an average current of about 4.25 times Is. A numerical equation solver can be used to solve the two simultaneous equations for Is and n.  One is available in MathCad.  If you have MathCad 5.0 or higher, go to http://www.agilent.com/.  Click your way through Communications, Communications Designer Solutions, RF and Microwave, Schottky Diodes, Library, MathCad worksheets and download the file: sch_char.mcd.  Execute it in MathCad, then enter your Current and Voltage values: Id1, Vd1 and Id2, Vd2 as I2, V2, I1 and V1.  Pull down 'Math' and click 'Calculate Worksheet" .  The program calculates Is and n.  Since most crystal set operation occurs at currents so low that there is negligible voltage drop across the diodes' parasitic series resistance, there is no need to enter any new numbers for I3, 4, 5 and V3, 4, 5 on the worksheet.  The program sch_char.mcd does not work in versions of MathCad earlier than 6.  If you have an earlier version of MathCad, and it has a non-linear equation solver, actual entry of the Data Set will have to take place without the convenience of the sch_char program.  Those who do not have MathCad but do

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Diode saturation current and ideality factor measurement, with measured values for various diode types

have Microsoft Windows Word can get an unformatted view of the default data and text provided in the MathCad program by clicking here. There is currently available on the Web, a program from Polymath Software at: http://www.polymathsoftware.com/.  This program has many capabilities, and among them is a nonlinear equation solving capability.  A free demo copy of the latest program is available for download, but is limited to 20 uses.  After that, for more usage, you have to buy it. Some programmable pocket calculators include a nonlinear equation solver.  One calculator that has one is the HP 32S Scientific Calculator.  A program to solve for n and Is takes only 28 steps of program memory and is here.  Mike Tuggle posted on 'The Crystal Set Radio Club' the following simple procedure for determining Is and n by using a spreadsheet.  "In lieu of an equation solver package, the Schottky parameters can be solved for by simple trial-and-error. This is easily done with an ordinary spreadsheet, like Excel or Lotus. For the two measurement points, (Id1, Vd1) and (Id2, Vd2), set up the spreadsheet to calculate:  Id2[exp(Vd1/0.0257n) - 1] and, Id1[exp(Vd2/0.0257n) - 1].  Then experimentally plug in different trial values of n, until the two expressions become equal.  This gives the correct value of n.  Now, plug this value of n into:  Is = Id1 / [exp(Vd1/0.0257n) - 1] or, Is = Id2 / [exp(Vd2/0.0257n) - 1] to get the correct value of Is."  An Excel spreadsheet constructed as Mike suggested is here.  An example from data taken on an Agilent HBAT-5400 is entered, for reference, on line 2.  Line 3 may be used for calculations using data from other diodes.  Column H automatically calculates a value for Is each time n is changed.  All one has to do is enter the values as described above in columns A through E and hit enter. 

Caution:  If one uses a DVM to measure the forward voltage of a diode having a high saturation current, a problem may occur.  If the internal resistance of the DC source supplying the current is too high, a version of the sampling voltage waveform used in the DVM may appear at its terminals and be rectified by the diode, thus causing a false reading.  One can easily check for this condition by reducing the DC source voltage to zero, thus leaving only the internal resistance of the source in parallel with the diode, connected across the terminals of the DVM.  If the DVM reads more than a tenth of a millivolt or so, the problem may be said to exist.  It can usually be corrected by bypassing the diode with a ceramic capacitor of between 1 and 5 nF, preferably, an NPO type.  I use a 0.047 uF NPO multi-layer ceramic cap from Mouser Electronics.  Connect the capacitor across the diode with very short leads, or this fix may not work.  

Tips If the Is of the diode under test is too high, 0.055 volts will not be attainable for V1 in step 1.  The solution is to set switch S3 to 100k.  The calculations for diode current then become: Id1= (V2/100,000)-(V1/10,000,000) Amps and (Id2=V4/100,000)-(V3/10,000,000) Amps. If the voltage readings seem to unstable, try placing the measuring setup on a ground plane and connect the common lead of the DVM to it.  A sheet of household aluminum can be used for the ground plane.  Use shielded cable from the lead from the DVM to the test setup. The voltage readings are very sensitive to diode temperature.  You can see this easily by grasping the diode body with thumb and forefinger and noting the change in the voltage reading when measuring V1 or V3.  Don't take data until the readings stabilize.  Saturation current is a strong function of junction temperature. For germanium and the usual (n-doped) Schottky diodes, a temperature increase of 10° Celsius results in a saturation current increase of about two times.  A simple rule is: For each 1° C. increase in temperature, Is increases by 7.2%.  The figures are different for zero-bias-type Schottkys.  Here, a 14 degree C. (25 degree F.) change in temperature will result in approximately a two times change in Is. Shield glass enclosed diodes from ambient light by placing a cardboard box over the unit.  Many diodes have a photo-diode response and will give an output voltage when exposed to light even if no current is applied. Note: A simplified method of determining the Saturation Current of a diode, if the Ideality Factor is estimated in advance is shown in Section #2 of Article #4. https://web.archive.org/web/20141029205315/http://www.bentongue.com/xtalset/16MeaDio/16MeaDio.html[06.08.2019 20:06:18]

Diode saturation current and ideality factor measurement, with measured values for various diode types

Summary of measurements on some diodes: The following charts show typical values for Is and n for diodes that might be used in crystal radio sets.  One can see, for any particular diode, that Is and n do not vary by much over a moderate current range.  Therefore, they may be considered to be dynamically constant when receiving a signal.  Each value of n and Is is calculated from two voltage/current pairs as described above.  The diode current (Id) given for each of the n, Is pairs is the geometric mean of the two currents used in the measurement.  A Fluke model '89 IV' 4-1/2 digit DVM was used to enable measurements down to as low as 15 nA on some diodes.  Noise problems cause some measurement error at low currents.  That is the reason for the fluctuations in some of the readings.  Values of n very close to 1.0 or below are obvious measurement errors.  Those low values for n should have come out somewhat higher and the associated values of Is, also higher. Note that the germanium diodes show an unexpected tendency to increased values for Is and n at the higher currents.  The 1N4148 silicon p-n junction shows the expected increase of Is and n at lower currents.  The Schottky diodes seem to have pretty constant values of Is and n across the current ranges measured.  Experiments described in Article #27 indicate that the measured values of Is and n for silicon Schottky diodes tested here, when used as detectors, remain at the measured values at rectified currents so low that a voice signal is barely readable.  This is not necessarily true for all germanium diodes.

Table 1 - Measured n and Is values for various diodes, over a range of currents (Id), in nA. Base-emitter junction of 1N404A Ge transistor

1N4148 silicon p-n junction diode Id 710k   350k 177k 88k 44k 22k 11k 5500 2760 1380 690 343 170      

n 1.73   1.75 1.87 1.82 1.80 1.88 1.89 1.93 1.94 2.02 1.98 2.06 2.18      

Is 1.23   1.45 2.19 2.26 1.98 3.00 3.10 3.80 3.90 4.90 4.40 5.30 6.70      

Id  

n  

570k  

1.04  

179k   56k 18.9k   5700 1790   620          

1.03   1.01 1.01   1.04 0.98   0.99          

Blue Radio Shack Agilent HBAT1N34A Ge diode 5400 Schottky, having no high Is version nomenclature

Is   1800   1670   1540 1580   1660 1730   1740          

Id 710k  

n 1.71  

350k 177k 88k 44k 22k 11k 5500 2760 1380 690 343 170      

1.69 1.61 1.51 1.39 1.28 1.22 1.14 1.10 1.05 1.20 1.01 1.08      

Is 3500   3200 2550 1980 1470 1100 950 800 750 680 830 670 720      

Id                

n                

8100     990 360 160 76   40

1.15     1.15 1.15 1.15 1.15   1.15

Infineon BAT62-03W Schottky diode

Is

Id

n

Is

265

                  2600*   970 341 133 87 59 39

                  1.06   1.04 1.04 1.04 1.04 1.01 1.06

                  248   240 236 236 236 228 233

                    248 265 255 254   261

* This Infineon diode has an unusually high series resistance of 130 ohms.  The voltage drop across this resistance is low enough in all the measurements to be ignored, except for the highest current one.

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Diode saturation current and ideality factor measurement, with measured values for various diode types

 There, a correction for the voltage drop was made.

Table 2 - Measured n and Is values for various diodes, over a range of currents (Id), in nA. Agilent HSMSAgilent HBAT- Agilent HSMS286L triple 5400 Schottky 282M quad Schottky, all diode (low Is Schottky, all four three diodes in version) diodes in parallel parallel

Radio Shack Ge 1N34A diode marked 12101-3PT Id 47k 17k 9.5k

n Is Id 1.28 230   1.18 188   1.16 174         6.7k 2.8k 1.13 160           630 1.15 162 510         205 1.15 166         151 81 1.14 161         59 37 1.13 160         26.4       13                  

 

 

 

n      

Is

Id

     

   

      102         1140 104 470       203 103 108     102 59   36 100 23.1 102 15.3   10.2   6.3

 

 

1.03     1.03     1.03   1.01   1.02 1.03

4.4

n          

Is          

Id          

1.03 1.02

47 1750 41       360 1.02 41   0.98 40 117       0.99 39   1.00 39 53 0.98 39 24.5 1.02 40   1.00 39 12.6 1.08 42   1.04

42  

n          

One diode of Infineon BAT62-08S triple diode Schottky

Is          

Id

 

 

      4650     700   222   99 47   23.6      

 

 

 

1.04  

76  

1.04  

76  

1.02    

72    

1.03 1.02  

73 72  

1.06

76

n

Is

     

     

     

     

 

 

1.03    

143    

1.02  

142  

1.02  

136  

1.01 1.02  

134 138  

1.01

135

A rare germanium diode that seems to be ideal for many crystal radio set designs is the FO 215, branded ITT.  A search of the Internet has not turned up a manufacturer's datasheet.  ITT is not in the germanium diode business anymore, but from the Internet search it appears that the original company was a German company named ITT Intermetall.  Some of their semiconductor business became ITT Semiconductors.  This was later sold, around 1997 to General Semiconductor Industries.  That business was later sold to Vishay.  One source indicated that General Instruments was also one of the intermediate owners.  Averages of measurements on three samples of the FO 215 are:  Is=109 nA and n=1.02.  These measurements were made at an average current of about 250 nA.  Interesting note: The average Is of the FO 215 diodes is about equal to the geometric mean of that of the Agilent 5082-2835 and a typical 1N34A.  I obtained my FO 215 diodes from Mike Peebles at: http://www.peeblesoriginals.com/ .   Article #27 shows detector measurements of how diodes having different values of Is and n perform as weak signal detectors when impedance matched at both input and out put. #16  Published: 03/28/01;  Revised: 02/10/2004  Return to the Index Page of this Section (A) 060610

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Increase diode detector weak-signal performance; determine if it is functioning above or below its linear-to-square-law crossover point http://www.bentongue.com/xtalset/17Is_n/17Is_n.html

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New ways to Increase Diode Detector Sensitivity to Weak Signals, and a way to determine if a diode detector is operating above or below its Linear-to-Square-Law Crossover Point By Ben H. Tongue

Quick Summary:  The very low signal sensitivity of a crystal radio set can be improved by cooling the diode. This possibility arises when the rectified DC current is below about twice the Saturation Current of the diode. Also see Article #28 for more info on increasing weak-signal sensitivity. Definitions of terms to be used:   Plsc(i)    Input power at the linear-to-square-law crossover point Plsc(o)   Output power at the linear-to-square-law crossover point Is           Saturation current of the diode n            Ideality factor of the detector DIPL     Detector insertion power loss Pi          Available input power Po         Output power sqrt       Take the square root of the expression following C          Temperature in degrees Celsius Ri          Detector input resistance Ro         Detector output resistance R1         Source resistance R2         Load resistance I2          Rectified current Rxc       Slope of voltage/current curve of a diode at the origin (axis-crossing resistance).   Rxc=0.02568*n/Is, at 25° C. Kt         Temperature in ° Kelvin S11       A measure of input impedance match.  S11=20*log|[(|Ri-R1)/(Ri+R1)]|  SPICE  A circuit simulation computer program.  ICAP/4 from Intusoft was used in all simulations.  The old Article #17 has been separated into two Articles.  This new Article #17A is a revision of Part 2 of the old #17.  Part 1 has been broken out and renamed "Quantitative Insights into Diode Detector Operation Derived from Simulation in SPICE, and some Interesting new Equations.".  It is numbered15A. Assume that a station one can barely read has a power sufficient only to operate the detector at or below the "Linear-to-square law crossover point" (LSLCP).  This is the point where the rectified diode DC current is about twice Is.  Volume can be increased if the Plsc(i) point could be shifted to a lower RF power level.  This will result in less insertion power loss since operation will now be closer to the linear

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Increase diode detector weak-signal performance; determine if it is functioning above or below its linear-to-square-law crossover point

region.  The RF power required to operate a diode detector at its Plsc(i) point (at 25° C.) is shown as equation (4a) in Article #15A.  It can be rewritten as: Plsc(i)=0.0010341*Kt*Is*n  Watts    (1) When referring to the schematic of a diode detector, Figure 1 will be used.

Fig. 1

Diode Detector Output and Insertion Loss vs. Input Power.  The LSLCP is shown by the black arrow.

Fig. 2 - A SPICE simulation of the relation between output and input power.

Fig. 3 - Data from a SPICE simulation showing  detector insertion power loss vs. input power.

It is assumed that input and output are impedance matched.  One can see from equation (1) that if Is, Kt

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Increase diode detector weak-signal performance; determine if it is functioning above or below its linear-to-square-law crossover point

or n can be lowered, the Plsc(i) point is lowered and therefore, the volume from weak signals can be increased.  The reciprocal of the product of Is, n and Kt can be seen to be a sort of "weak signal diode figure of merit" (WSDFM).  It has been shown that in all semiconductor diodes, a small % drop in Kt will result in a much larger % drop in Is from its initial value.  It must be remembered that the reduction of Is or Kt increases Ri and Ro.  If n is reduced, Ri and Ro are reduced.  Re-matching of impedances (Ri and Ro) is required to gain the benefits being sought. Reduction of Is:  The main limit to using a diode of a lower Is has to do with the resultant increase in RF input (Ri) and audio output (Ro) resistances of the detector.  Practical low loss RF and AF impedance matching will be a problem.  At input signal levels at or below the Plsc(i) point, those values are about: Ri = Ro = 0.00008614*n*Kt/Is ohms.  The example in Figs. 2 and 3 are for a case where Ri and Ro are both about 700k ohms, using a diode with an Is of 38 nA and an n of 1.03.  This is close to the limit of practicality and applicable mainly to crystal radio sets using a single tuned, high inductance, high Q loop antenna with a high quality, high transformation ratio audio transformer.  A practical maximum value for R2 for most high performance crystal radio sets designed for use with an external antenna is about 330k ohms.  This requires a diode with an Is of about 80 nA instead of 38 nA, for a good impedance match.  The higher Is of the diode increases Plsc(i)  by about 3 dB and that reduces the output of signals that are well into the square law region by about 3 dB.  Signals well above the LSLCP are hardly affected at all.  Note that "production process variation" of Is is usually rather great.  This approach is practical and just requires selecting a diode type having the optimum Is.  Simple as that, no mumbo-jumbo. See Table 1 in Article #27 for measured Is values of several diode types.  Keep in mind that some diode types can be damaged by static electricity. If the diode is not destroyed, it's reverse leakage current gets elevated, ruining weak signal sensitivity.  Usually, diodes that have low values of Is also have a low reverse breakdown voltage, increasing their susceptibility to static electricity damage. Reduction of n:  The value of n does not vary as much as does Is among diodes of the same type.  Schottky diodes designed for detector use usually have a low value for n.  N can range between 1.0 and 2.0.  Probably so called 'super diodes' have a low n and their values of Is and n are such that a good impedance match is realized in the particular crystal radio set used.  The use of a diode with a reduced n not only reduces Plsc(i), but also reduces Ri and Ro, a reverse effect than that from reducing (Is).  Most diode types rated for use as detectors or mixers usually have a low n. Reduction of Kt:  The temperature of any diode can be lowered by spraying it with a component cooler spray (221 degrees K.) every so often.  A longer lasting, but lesser cooling effect can be had if the diode is placed crosswise through two diametrically opposite small holes in a small housing (such as a 1'' dia. by 2.5 inch long plastic pill container) with a stack of old style copper pennies in the bottom to act as a thermal mass.  This assembly is used after being cooled in a home freezer to about 0 degrees F. (255 degrees K.).  It is then taken out and connected in the crystal radio set.  An even lower temperature can be attained if some pieces of dry ice (195 degrees K.) are substituted for the pennies.  The problem with reducing Kt is that (Is) is very temperature sensitive, so it also changes.  Agilent states in App. note #1090 that the junction resistance of HSMS-2850 Schottky diode increases 100 times for a 70 degree K. reduction in temperature.  That indicates a much greater % change in (Is) than in degrees Kelvin temperature.  A 70 degree K. temperature drop may reduce the Is by 100 times, raising Ri and Ro by 100 times.  That ruins impedance matching and increases loss greatly (the signal goes away).  The answer is to experimentally try diodes that have a high Is at room temperature (298 degrees K.), that will drop to the correct value at the reduced temperature.  One candidate is the Agilent HSMS-2850 (room temperature Is = 3000 nA).  Another is a 2N404A Ge transistor with the base and collector leads tied together (room temperature Is = 1500 nA).  Most modern diodes sold as 1N34A have (Is) values ranging from about 200 to above 600 nA.  Measurements show that for germanium or non-zero-bias type silicon Schottkys, a 10 degree C (18 degree F.) change in temperature will result in an approximately two times change in Is.  Other measurements show that with zero-bias-type Schottkys, a 14 degree C. (25 degree F.) change in temperature will result in approximately a two times change in Is.  This approach is not practical since the desired results can be attained by selecting a diode type having the required Is at room temperature. The ideality factor (n) of the diode is an important parameter in determining very weak signal https://web.archive.org/web/20131030052127/http://www.bentongue.com/xtalset/17Is_n/17Is_n.html[06.08.2019 20:07:10]

Increase diode detector weak-signal performance; determine if it is functioning above or below its linear-to-square-law crossover point

sensitivity.  If all other diode parameters are kept the same, the weak signal input and output resistances of a diode detector are directly proportional to the value of n.  Assume a diode with a value of n equal to oldn is replaced with an identical diode, except that it has an n of newn, and the input and output impedances are re-matched.  The result will be a detector insertion power loss change (weak signals only) of: 10*log(oldn/newn) dB.  That is, a doubling of n will result in a 3 dB increase in insertion power loss, assuming the input power is kept the same.  This illustration shows the importance of a low value for n. Warning: Don't use two diodes in series if you want the best weak signal sensitivity.  The result of using two identical diodes in series is the simulation of an equivalent single diode having the same Is but an n of twice that of one original diode. A diode detector is operating at its LSLCP (usually with about a 5 dB insertion power loss), if the average rectified DC voltage across the resistive component of its load is (n*51) mV (See Article #15 for a discussion of this).  When checking this, use a large enough bypass capacitor across the DC load to maximize the voltage.  If one doesn't know the n of one's diode detector, it can usually be assumed to be about 1.07.  A requirement for the (n*51) mV relation to be correct is that the detector be approximately impedance matched at its input for RF and accurately matched at its output for DC and audio.  Specifically, the DC load resistance must be set to 0.026*n/Is ohms (see Part 4 of Article #0 for info on n and Is).  See Fig. 5 in Article #26 for a typical method of adjusting the DC resistance of the diode load and monitoring the rectified voltage.  Typical values for n and Is for many diodes may be found in Articles #16 and 27.  The audio load AC impedance matching requirement is not very important if one is interested only in hearing the volume delivered from ones headphones when the diode is operating at its LSLCP.  The reason is that volume is a slow and gradual function of audio mismatch, for moderate mismatches.  A two-to-one audio mismatch causes a loss in audio output of only 0.5 dB.  A four-to-one mismatch causes a loss of 1.9 dB (hardly audible). #17A  Published:  04/10/01;  Revised 11/29/2006 060610

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3 dB more audio output from a crystal radio without using an external power source http://www.bentongue.com/xtalset/18Fre3dB/18Fre3dB.html Go

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Get 3 dB more Output for Greater Volume on Strong Stations plus... By Ben H. Tongue

Quick summary:   Over the years many experimenters have realized that one could get "free" power from a crystal radio set and operate an amplifier with it.  This has been successfully done by coupling an additional tuned circuit and detector to the antenna and tuning it to a strong station.  The rectified DC from the station was then used to power an amplifier for boosting the audio output of the crystal radio set without appreciably affecting its normal operation, when tuned to a different station far enough removed in frequency.  This Article describes, possibly for the first time, a method of using the carrier power of the station being received to power an amplifier.  One third the total power in a 100% modulated AM signal is in the sidebands that carry the audio modulation.  An ideal, 100% efficient Crystal radio set will convert all of the received sideband power to audio output power.  Call it audio power output #1.  What about the other two thirds of the power?  That is the power in the AM carrier that carries no audio information but has twice the power of the sidebands (at 100% modulation).  This Article shows the circuit of a device that can be used to extract that carrier power and use it to operate a micro-power op-amp. The op-amp uses the detected audio voltage from the diode detector for its input and provides an additional source of audio power. Call it audio power output #2.  These two audio power sources, #1 and #2 can be added together to create a final output at least 3 dB more than the normally available audio power output #1. 

 

1. Background Within the last  year or so, Burr-Brown (now owned by Texas Instruments) came out with a micropower op-amp (OPA349) specified to work with as little as a 1.8 volt DC power source.  It draws a minuscule 1 uA quiescent supply current.  This op-amp opens the possibility of building a device I call a "Free 3 dB Detector Load" (F3dBDL).  I have found that the F3dBDL will actually operate with an input signal low enough to generate a rectified voltage as low as 1.2 volts DC.  Maybe all the OPA349s will work in this circuit at 1.2 volts.  My F3dBDL requires a minimum input carrier power of  -53 dBW and a rectified DC voltage of at least 1.2 volts. 

 

2. A conventional diode detector with standard output loads (DC and audio)  Any crystal radio set that uses an audio output transformer can be represented by the simple circuit shown in Fig. 1.  V1, R1 represent the antenna-ground power source, impedance transformed to the tank circuit.  The detected carrier power is dissipated in the resistive load R2.  The detected side-band power is delivered to the audio load R3. 

 

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3 dB more audio output from a crystal radio without using an external power source

3.  Conventional crystal radio set detector with the F3dBDL The F3dBDL is intended to be used with signals strong enough to cause the detector to operate in its peak-detection mode.  In this case, the DC load R2, seen by the diode D1 should equal to two times the RF source resistance R1.  D1 should also see an AC load resistance of two times R1, at the primary of transformer T1.  (See Article #0 , Section 4, for more info on this.)  The power dissipated in the DC load R2 in the circuit in Fig. 1 will be used, in Fig. 2, to power the op-amp U1.  In Fig, 1 the audio output power is delivered to the output load R3.  In Fig. 2 audio output power is delivered to two loads of value R3 and k*(R3).  With proper selection of the relative impedance transformation ratios of T1 and T2, the value of k may be made equal to about 1.  In addition, the output currents of T1 and T2 become about equal.  In this case, no current will flow in connection X, and it can be eliminated.  This gives us one 600 ohm instead of two 300 ohm outputs.  The resultant load resistance of twice R3 will absorb twice the audio power than did R3 in Fig. 1, although at twice the impedance (600 ohms).   The resistive network R4, R5, R6 and R7 biases + input terminal of U1 at 1/2 the DC supply voltage appearing across C2 and attenuates the detected audio voltage appearing across C1 so that it will not overload U1.  The value of capacitor C2 is made quite large to enable it to hold steady the voltage it supplies U1, between bursts of speech.

 

 

Parts List C1 47 pF - RF bypass.  Physically, it will probably be supplied by the winding capacitance of T1. C2 10 uF low leakage electrolytic - voltage holding storage capacitor for the supply voltage of U1 C3 1nF - audio coupling capacitor 

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3 dB more audio output from a crystal radio without using an external power source

C4 D1 k R1 R2 R3 R4 R5 R6 R7 R9

10nF - DC blocking capacitor 1N34A or several Agilent 5082-2835 or HSMS2820 in parallel A constant, which when multiplied by R3 gives the value of the load on T2 Transformed source resistance of antenna across tank T - assumed to be 150k ohms DC diode load resistance in Fig. 1 - Assumed to be 300k ohms Audio load resistance in Fig. 1 and 2 - Assumed to be 300 ohms 2.2 Meg resistor 5.1 Meg resistor 5.1 Meg resistor 10 Meg resistor AC resistance seen looking into the primary of T2 when connection X is present

T1

Transformer with 1000:1 transformation ratio - such as Stanley 100k to 100 ohm

unit, available from Fair Radio Sales as part # T3/AM20, or UTC C-2080

T2

Transformer with 100:1 transformation ratio - such as Calrad 45-700, available  from Ocean State Electronics.

Burr-Brown Opamp #PA349 - available from a Texas Instruments distributor.  A convenient way to connect to the tiny leads of IC1 is to first solder it to a surfboard such as one manufactured by U1 Capital Advanced Technologies (http://www.capitaladvanced.com).  Their models 9081 or 9082 are suitable and are available from various distributors such as Alltronics, Digi-Key, etc. V1

Internal voltage of RF power source (antenna induced voltage after impedance transformation to the tank circuit "T")

4. Comments If all the power in the carrier could be changed to audio power and added to the main detector audio output, the total audio power would be tripled, a 4.8 dB increase.  It would be nice if the op-amp had 100% efficiency in converting its input DC power to output audio power, but it doesn't.  An ideal class B amplifier has a theoretical efficiency of 78.5%.  Therefore, we lose at least 21.5% (1.05 dB) right off the bat.  Other losses in the op-amp, the 1 uA quiescent current of the U1 and the bias network R5, R6 and R7 use up some more of the 4.8 dB.  The transformer T1 has losses and uses up some more of the 4.3 dB.  We are left with an output power from the U1, T2 combination about equal to that of a conventional crystal radio set.  The two added together gives the 3 dB increase. There are some limitations in using the F3dBDL.  The IC is specified to operate over a supply voltage range of 1.8 to 5.5 volts.  In this circuit it seems to work well over a supply voltage range of 1.2 to greater than 5.5 volts.  This corresponds to an input carrier power range of -53 to >-40 dBW.  I have found, that for me, the volume to be too great for headphone use but barely adequate for high efficiency horn speaker use.  If more than -40 dBW of AM signal carrier power is available, the F3dBDL can be made to handle it (and give a greater sound volume) if the F3dBDL is operated at a lower output impedance level.  In this case, transformers T1 and T2 might have to be changed to ones with a lower transformation ratio. The impedance at the + signal input terminal of U1 is very high.  Use care to minimize stray capacitance to ground at this point.  Too much will roll off the highs.  The high audio frequency output capability of U1 falls as signal strength and, as a result, supply voltage increases.  This can cause audio distortion. The F3dBDL can also be used to increase the volume on weak stations.  This is done by connecting a ceramic electric double layer high capacitance capacitor across C2, charging it up overnight on a strong station and then switching it to power the opamp for weak station listening later on.  A 0.047 Farad capacitor will hold its charge for many hours in this application.  One manufacturer of this type capacitor is Panasonic, and one of their distributors is Digi-Key Corp.

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3 dB more audio output from a crystal radio without using an external power source

If the load on the F3dBDL is a SP headphone set with the elements wired in series, bass response can be improved with a small subjective increase in volume. Consider the two headphone elements as the two impedance equal loads R3 and k*(R3), in Fig. 2.  Restore the connection X.  The element k*(R3) will have a much better bass response than the other one because it is driven by the low output resistance of the opamp.  See "It is interesting to note" at the end of Section 1 in Article #2 for more info on this. Last, but not least, one should not expect too much from the F3dBDL.  After all, a 3 dB or so increase in volume will not be perceived as a lot.  The challenge of this project was to devise a way to use all of the power in an AM modulated signal, I believe that has been accomplished. #18  Published: 07/09/01; Revised: 04/06/2007 0060610

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Mystery Crystal Radio circuit analysis http://www.bentongue.com/xtalset/19mstry/19mstry.html Go

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An Explanation of how the "Mystery Crystal Radio" Works By Ben H. Tongue

Quick summary:  Plans for a crystal radio called the "Mystery Crystal Set" were published  in the newspaper "The Sunday Mail" of Brisbane, Australian in 1932.  The "Mystery" in the name comes from the fact that, in the schematic, there seems to be no ground return to which the antenna currents can flow.  The design was used by entrant Ray Creighton in the "Crystal Set Competition" held on March 19 2000 by the Southeast Queensland Group of the Historical Radio Society of Australia in Malaney, Australia .  His entry won first prize in one category and third prize in another.  see it here  The design has recently  become popular in the US as shown by the many messages posted on the Yahoo! Groups site "thecrystalsetradioclub".  On 6/6/2000, in messages 2172 and 2173, I posted the following explanation (edited here) of how I believe the Mystery Set works:   

Two assumptions made in the analysis:  They are that the distributed capacity between the two coil windings https://web.archive.org/web/20141222194851/http://www.bentongue.com/xtalset/19mstry/19mstry.html[06.08.2019 20:08:47]

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Mystery Crystal Radio circuit analysis

may be represented by one lumped capacitor, Cc, connected between the center of one winding to the center of the other.  See Fig. B.  The other is that the magnetic coupling between the primary and secondary windings is very high.  This assumption is close to reality for the bifilar wound portion of the transformer, provided the capacity coupling is not too high.  The magnetic coupling between the bifilar-ed parts and the end windings is not as close as that between the bifilar-ed parts.  This does not affect the validity of the analysis.  Keep in mind that in transformers with unity coupling, the ratio of the voltage on any winding to any other is directly proportional to the number of turns on each winding.  This also applies to a portion of one winding.  (Just use the number of turns in that portion.)  Figures A through E show the inductive circuit through various changes as the following reduction and simplification proceeds.    Simplification and reduction of the circuit of the Mystery crystal set using the "Broad" non-earthy antenna connection: The physical circuit of the Mystery set is shown in Fig. 1 with the antenna connected to the non-earthy side of the primary.  The black dots on the windings show the start of each winding, assuming that they are both wound in the same direction. Figure 2 shows a coupling capacitor Cc, between the two windings.  It represents the parallel combination of two distributed capacitances:  One is formed of the dielectric of the wire insulation between the bifilar-ed primary and secondary coil turns.  The other is also between the primary and secondary coil turns, but in this case, there are three dielectrics in series.  They are:  (1) The dielectric of the insulation on, say, the primary winding that is in contact with the coil form.  (2) The dielectric of the coil form between the primary and secondary windings.  (3) The dielectric of the insulation on the secondary winding that is in contact with the coil form.  Cc is in a series circuit with the antenna and ground. Fig. 3 shows Cc shifted up to the antenna and out of the way.  No change in performance will result. The top and bottom leads of the secondary are connected (each 12.5 turns from the center), to the corresponding points on the primary (12.5 turns up and down from the center).  This is shown in Fig. 4.  Since the points that are connected together have the same AC voltage on them, no current will flow through their connection and the circuit operation will be undisturbed. Figure 5 shows the resulting equivalent circuit from the connections made in #4.  Since all portions of the winding are assumed to be unity-coupled to each other, performance will not change if the tuning capacitor C1 is connected as shown in Fig. 6, as long as its value is changed appropriately.  C1 is connected across 50 turns of the inductor.  C2 is connected across 37.5 turns.  The inductances of a unity coupled 1:1 transformer are directly proportional to the square of the number of turns.  The number of turns across which C2 is connected is 3/4 of the number of turns turns across which C1 is connected, therefore, the inductance across which C2 is connected will be 9/16 the inductance across which C1 is connected.  C2 must be increased from the the value of C1 to 16/9 of C1 for the circuit to work the same as before the transformation.   The bottom portion of the coil in Fig. 6 can be eliminated since nothing is connected to it. The final result is the equivalent circuit shown in Fig. 7.  Here we see a conventional crystal set circuit with the antenna-ground components connected directly across the full tank, with isolation from full antenna resistive loading supplied by the capacitor Cc.  The detector load is tapped in at 2/3 of the tank voltage to reduce its resistive loading effect on the tuned circuit.  That's it for the non-earthy "Broad" antenna connection. Simplification and reduction of the circuit of the Mystery crystal set using the "Selective" earthy connection.  Figures 8 through 14 show the simplification and reduction of this circuit.  It proceeds in an manner similar to the one for the "Broad" connection.  Now look at Fig. 14.  The value of Cc is unchanged from that in Fig. 7.   C3 will have to be somewhat larger than C2 was for the circuit to work the same. The antenna-ground components and Cc are now connected across only 1/3 of the tank instead of the full tank.  The detector load is still tapped in at 2/3 of the tank voltage.  That's it for the earthy "Selective" antenna connection. What might the value of the magnetic coupling coefficient between the bifilar-ed portion of the

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Mystery Crystal Radio circuit analysis

windings be? To think about this, consider:  Mentally unwind the bifilar portion of the coil from the coil form, but imagine the two wires are still in the same relative positions to each other.  Stretch them out.  The ends of one wire are the terminals of one winding of a transformer and the ends of the other winding, the terminals of the other.  Now you have two parallel wires closely spaced and several tens of feet long.  The spacing (from the wire insulation) between them is maybe 0.005".  It should seem obvious that the magnetic coupling between them could not get much greater (without ferrite cores), no matter what one does with the wires.  It can, however become greater when the bifilar wire is wound on a form.  The reason is that places a primary wire on each side of every secondary wire and vice-versa, providing more magnetic coupling between the windings than when the wires are stretched out. Here is an approach for determining the coupling coefficient of a bifilar winding:  Construct a bifilar wound coil that has about the same inductance as the bifilar-ed wires in a standard Mystery" set.  This inductance calculates out to be 57 uH. No wire of the gage originally used was available, so the largest bonded bifilar wire I had available was used.  It was made by MWS Wire and consisted of two #30 ga. film insulated wires bonded together.  Its cross section measures 0.012x0.024".  Twenty turns were wound on an available 3 1/2" styrene coil form since a 3" diameter coil form, as used in the original Mystery set was not available.  The winding length came out to be a very small 0.475" because of the small wire size.  This is much less than that in the original Mystery set but, tough, that wire is all that was available.  The leads from the coil were still bifilar-ed, 10" long ends. Several resonance measurements were then taken using a Q meter.  The first was with one winding connected to the inductance terminals of the Q meter, the other winding being open circuited (Loc), at several frequencies from 0.515 to 2.36 MHz.  The indicated capacitance readings on the Q meter were noted.  The other was with the same winding still connected to the inductance terminals of the Q meter but with the other winding shorted (Lsc), at frequencies from 3.0 to 11.0 MHz.  Again, the indicated Q meter capacitance readings were noted.  At frequency extremes these readings will be distorted by the presence of distributed capacitance between the two windings, 1020 pF in this case.  The conventional Mystery set would have considerably less capacitance between the windings because of the much thicker insulation on the wires.  Note: The capacitance between the windings cannot be determined at RF by the use of a Q meter.  It can be measured by the use of an RLC bridge operating at 1 kHz or a DVM having a capacitance measuring function (if it operates at about 1 kHz). Over the frequency range of 0.515 to 1.71 MHz, Loc was calculated to be: 66.5 +/- 2.5 uH.  Over the frequency range of 3 to 7 MHz, Lsc was calculated at: 2.01 +/- 0.06 uH.  A derivation results in the following relation for the coupling coefficient between two identical magnetically coupled inductors: k=sqrt(1Lsc/Loc).  The calculated coupling coefficient between the two bifilar-ed windings is 0.984, which I consider very close to unity. The bifilar wire was re-wound on the same form, but spaced to cover a 1" length.  The coupling coefficient came out at 0.966 and the distributed capacitance: 895 pF.  Another coil was then wound from the same piece of wire on a 1.5" diameter polypropylene form.  The winding was slightly space wound and had a length of 1.5 ".  Coupling coefficient: 0.983 and distributed capacity coupling: 945 pF. Of course, manufactured, bonded, bifilar wire is not recommended for use in a Mystery set.  Usually two independent, insulated wires are wound close spaced.  This practical case results in substantially less distributed capacitance than when using bonded wires. Conclusion: The beauty if the Mystery set is that it provides an antenna decoupling capacitor (Cc) (made from the distributed capacity between the bifilar-ed windings), along with the effect of two different points for its connection to the tank; all without any specific physical capacitor or taps on the inductor.  Further, the diode is effectively tapped 1/3 down on the tank for improved selectivity.  The only downside to this arrangement is some loss caused by the probable relatively low Q of Cc. When using the "Broad" antenna connection, the antenna-ground components are connected through Cc

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Mystery Crystal Radio circuit analysis

across the full tank.  This arrangement puts a relatively large amount of antenna resistive loading on the tank.  The loading results in as reduced selectivity, but stronger signal strength than one gets in the "Selective position.  See Fig. 7. When using the "Selective" antenna connection, the antenna-ground components are connected through Cc across only 1/3 of the tank coil turns.  This results in a reduction to about 1/9 of the resistive loading by the antenna on the tank, compared to the loading in the "Broad" connection.  See Fig. 14.  This reduced loading increases the loaded circuit Q, and hence selectivity.  The ratio of unloaded to loaded Q is reduced, thus reducing sensitivity. For practical purposes the 'leakage inductance' between that part of the primary that is bifilar wound with the secondary is very low.  To the extent that it is not zero, it and the leakage inductance between the outer turns of the primary and the inner bifilar-ed 25 turns can be considered to be an added  "leakage inductance" in series with C2 in Fig. 7; and in series with C3 in Fig. 14.  The main effect of this leakage inductance, compared to having none, is to somewhat lower the highest frequency than can be tuned.  The low end of the tuning range will be extended a small amount. #19  Published 08/11/01;  Revised 12/29/2002 060610

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Measure the impedance of an AM-band antenna-ground system http://www.bentongue.com/xtalset/20MeaAGs/20MeaAGs.html Go

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How to measure the impedance of an AM-band antenna-ground system, what one can do with the results, along with some measurements By Ben H. Tongue

Quick Summary:  This Article describes a method to measure the series capacitive and resistive parameters of the impedance of an antenna-ground system vs frequency.  Results from measurements on an attic antenna are given.   

  The circuit in Fig. 1 was inspired by an Article in The Crystal Set Society Newsletter of Jan 1, 1995.  It was written by Edward Richley.  He used a 1 MHz crystal oscillator for his source, so had no problem with using a 200 uA meter.  I use a sine wave function generator for my RF source, but a radio Service man's oscillator may also be used if it has enough output.  Either of these sources cannot supply as much signal as the xtal oscillator, so I had to increase sensitivity.  That's what the 2.5 mH chokes and 5 nF caps are for.  The 2.5 mH chokes eliminate RF loading by any resistive component of the meter or phones on the diode detector.  The 5 nF caps eliminate resistive DC loading on the detector from the two 680 ohm resistors.  I lay out the components breadboard style on a nonconductive table to minimize stray capacity, keep connections short, and especially keep the signal source lead of J1 away from the connections to each end of D1.  In my setup D1 is a 1N34A, M1 is a 0-20 uA DC meter, R1 is a 75 ohm non-inductive carbon pot and C1 is a two gang variable cap of 365 pF per section.  I parallel the two

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Measure the impedance of an AM-band antenna-ground system

sections when the antenna capacitance is above 365 pF.  A lower sensitivity meter can be used than the one used here, at the cost of a requiring a higher applied signal to J1. If a sensitive enough meter is not available, a pair of high impedance phones (2000 ohms DC resistance) or preferably, a sound powered pair with the elements wired in series can be used.  In this case, the generator must have its AM audio modulation turned on at its highest level.  A modulation frequency of about 1 kHz is recommended.  If the meter is used, do not connect the phones.  If phones are used, do not connect a meter. To use the bridge, tune the generator to a frequency of interest.  Adjust C1 and R1 for minimum deflection on M1 or a null of the modulation tone in the phones.  Increase the RF signal to J1 as much as possible in order to get the sharpest and most precise null.  Measure the resistance of R1 with an ohmmeter.  Use any desired method to measure C1.  I use the cap. measurement range of my Fluke DVM.  I'm sure the reader does not need to be reminded that this test involves radiating a weak RF signal from the antenna when making the measurements, so the length of time the generator is on should be kept as short as possible.

Possible issues:  More sensitivity is needed or interference from antenna pickup of local stations obscures the bridge null. If insufficient signal is available from the RF generator to provide satisfactory meter readings, one can use the more sensitive broadband circuit shown in Fig. 2.  The values of L1 and L2 are 2.5 mH and C2 is set to zero in the broadband version.  A full wave rectifier is used instead of the half wave one used in Fig.1 and it gives about twice the output.  One can also change from using 1N34A diodes and try Schottky Zero Bias detector diodes such as the Agilent HSMS-2850 in either circuit.  The HSMS-2855 Zero Bias diode is especially suitable for use in the circuit shown in Fig. 2 since it is a package having two independent diodes, one for D1 and the other for D2.  One must be cautious when using the HSMS-2855 because the diodes can be damaged by the application of too strong a signal to J1.  This can happen if the signal generator signal is very strong when the bridge is greatly unbalanced.  It's best to start with a weak signal, balance the bridge, then increase the signal if necessary. If the signal from the RF generator is not strong enough to override local pickup, thus obscuring the meter null, selectivity may be added to the bridge shown in Fig. 2 by making use of C2 and changing L1 and L2.  If L1 and L2 are changed to, say, 10 uH inductors and C2 is made equal to 1200 pF, the bridge will be tuned to about 1 MHz.  These changes will reduce the influence of local pickup upon measurement of antenna-ground impedance at 1 MHz.  One suitable 10 uH inductor is Mouser's "Fastron" #434-23-100. If one uses headphones instead of a meter as the null indicator, even greater sensitivity can be achieved by AF modulating the bridge signal generator and connecting a parallel L/C tuned to the modulating frequency of the generator across the phones.  This will filter out much of the interfering cross talk from local pickup and pass the modulation tone with little loss.  Suggested values are L=47 mH and C=0.5 uF if the modulating frequency used is about 1 kHz.  A low cost coil having an inductance of 47 mH and a Q of about 9 at 1 kHz is available from Mouser as a Fastron Plugable Shielded coil, #434-02-473J ($1.20 each).  Greater selectivity against cross-talk can be obtained by decreasing the inductance and increasing the capacitor. I live about 9 miles from WOR and 12 from WABC, both 50 kW stations.  10 volts peak-to peak applied to the bridge overrides the local radio station pickup sufficiently to provide a clear null on the meter when using the circuit shown in Fig. 1 when using a 1N34A diode.  A useable null with an applied signal of only 1.5 volts p-p can be obtained when using the circuit in Fig. 2 with zero bias detector diodes, sound-powered phones instead of a meter and the parallel LC filter.

Notes: If the RF source has too great a harmonic content, the bridge balance null will become less deep and sharp.  That's why I used a sine wave function generator to assure a low harmonic content.  If one uses a function generator for pure sine waves, make sure the symmetry control is set for best symmetry (minimum reading on the bridge microampmeter).  In April 2004 Tom Polk published a description and schematic for a low distortion medium wave home brew signal generator.  It looks very good, and can be found at:  http://www.beecavewoods.com/testequipment/sinewave.html . If the resistance of a specific antenna-ground system is greater than 100 ohms, use a pot of a higher value than 100 ohms.

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Measure the impedance of an AM-band antenna-ground system

A typical antenna-ground system will show a capacitance of a few hundred pF at the low end of the BC band.  Because of the series inductance in the system, the measured capacitance will rise at higher frequencies.  At a high enough frequency the system will go into series resonance and the bridge will not be able to be balanced.  To measure the system series resistance at or above this resonance, place a hi Q capacitor of, say 100 to 220 pF in series with the antenna.  That will raise the resonant frequency sufficiently so that the capacitor-antenna-ground circuit will be capacitive, a null can be obtained and the resistive component determined.  An NPO ceramic or mica cap should be OK. At my location, detected signals from local strong stations show up as fluctuations at about 15% of full scale on the meter, but are not strong enough to obscure the bridge nulls from of the signal generator's signal. Unless the signal generator connected to J1 is battery powered (most aren't), it is important to put a commonmode radio frequency choke in the power line to the generator.  I made mine by bundling a length of 18 ga. lamp cord into an 18 turn coil having a 9 inch diameter, and then fitting a male AC plug on one end and a female socket on the other.  The turns were kept together using twist ties.

What can one do with the measurement results? The main practical thing one can do with the bridge is to Measure and Monitor antenna-ground circuit resistance.  This resistance comes primarily from the physical ground, not the antenna and ground connecting leads or radiation resistance of the antenna.  Any increase in the antenna-ground resistance serves to reduce the signal power available from the antenna.  Any decrease, of course increases it.  A halving of the antenna-ground system resistance provides a 3 dB increase in available signal power, if one properly rematches to the crystal radio set input circuit. Measure:  One can experiment with different grounds and various ground paralleling schemes to come up with the one that has the lowest resistance.  Use of this one will result in maximizing the available signal power (more volume).  Experiments using a counterpoise ground can be made. Monitor:  As has been recently been posted on the Yahoo Club: thecrystalsetradioclub, earth ground resistance deteriorates (increases) over time.  This results in a gradual decrease in available signal power (less volume).  Periodic measurement can alert one if this is happening so steps can be taken to correct the problem. The other thing one can do, if one is mathematically engineering a crystal radio set, is to use the R and C values as parameters in the design.  See Article #22.  

Measurement results on an indoor attic antenna system: My present external (as opposed to loop) antenna is in the attic.  The horizontal element used to be made  up of 7 twisted strands of #26 copper wire (17 ga.), suspended by strings about 1 1/2 feet below the peak of an asphalt shingled roof.  It runs along under the peak and parallel to it for 53 feet.  The wire is about 24 feet above ground level.  The lead-in, connected to the center of the horizontal wire, runs horizontally, at a right angles for about 9 feet and then drops down vertically to the crystal radio set location, about four feet above ground level.  The ground system consists of a connection to the cold water supply in parallel with a connection to the hot water baseboard heating system.  To achieve a low inductance ground connection I use 300 ohm TV twinlead, both conductors soldered in parallel, for each lead. The addition of a connection to the AC neutral does not seem to reduce the inductance or resistance of this antenna-ground system.  I always suggest trying the addition of a connection to the AC neutral.  Sometimes it helps.  The measured antenna-ground system capacitance was 295 pF at 0.5 MHz, 325 at 1.0 MHz, 410 at 1.5 MHz and and 660 at 2.0 MHz initially.  The respective series resistances measured: 17, 12, 10 and 14 ohms.  The equivalent reactance elements of this antenna are a capacitance of 285 pF in series with an inductance of 12.5 uH.  Since my ground is composed of the house cold water supply pipes in parallel with the the hot water baseboard heating system pipes,  much of the capacitance from the horizontal attic antenna wire is to them and the roof, not a real resistive earth ground.  That, I think explains the low resistance and high capacitance readings.  Probably the ground system is acting as a sort of counterpoise. I decided to see if I could get greater signal pickup by changing to a very crude simulation of a flattop antenna.  To do this, I paralleled the antenna wire with a piece of TV twinlead connected to it at each end and at the point of down-lead takeoff.  The twinlead was separated from the 7/26 wire by about 2 1/2 feet.  The new measured antenna-ground system parameters became: Capacitance: 430 pF at 0.5 MHz, 510 at 1.0 MHz and 860 at 1.5 MHz.  https://web.archive.org/web/20131030052147/http://www.bentongue.com/xtalset/20MeaAGs/20MeaAGs.html[06.08.2019 20:09:27]

Measure the impedance of an AM-band antenna-ground system

The respective series resistance values became: 15, 12 and 11 ohms.  The equivalent reactance elements became a capacitance of 405 pF in series with an inductance of 14.2 uH.  Signal pickup increased by a negligible 0.8 dB at 710 kHz, and even that was, I'm sure, within experimental error. One may want to compare these equivalent impedance components with the 'Standard Dummy Antenna', as specified in 1938 by the IRE (Institute of Radio Engineers) in 'Standards on Radio Receivers'.  My reference for this is Terman's Radio Engineer's Handbook, first edition, 1943, pp 973 and 974.  A rather complex equivalent circuit for the antenna is shown on page 974.  It is stated that a simpler alternative network, given in footnote #2 on page 973, can be used when only the BC band is of interest.  It consists of the series combination of a 200 pF capacitor, 25 ohm resistor and 20 uH inductor.  Terman states that the two antenna equivalent circuits have closely the same impedance characteristics in the BC band.  The impedance graph on page 974 and the impedance from the series combination of 200 pF, 25 ohm resistor and 20 uH differ, particularly in the resistive curve in the complex equivalent circuit.  The 25 ohm resistance in the simplified circuit is probably taken from the resistance in the complex circuit, at the geometric center of the BC band.  This resistance is shown as constant in the simplified circuit, and as a strong function of frequency in the more complex circuit.  It is suggested that the complex equivalent circuit is theoretically derived, assuming a perfect ground and therefore does not include the resistance of the ground return path.  The ground circuit can easily add 15-50 or more ohms to the circuit. #20  Published: 11/24/01;  Revised 04/16/2004 © 2001-2008 Ben H. Tongue,  All rights reserved 060610

Return to the Index Page of Section (A) 

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Single-tuned four-band crystal radio set using a two-value tank inductor http://www.bentongue.com/xtalset/22St4bXS/22St4bXS.html Go

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Design, construction and measurement of a singletuned crystal radio set using a two-value inductor, along with a discussion of the cause of 'hash', shortwave ghost-signal and spurious FM reception. A way is presented for determining if the signal is operating a detector above or below its linear-tosquare-law crossover point By Ben H. Tongue

 

Summary:  This article describes Version 'b' of a single-tuned four-band crystal radio set, sometimes called a "Benodyne" (constant bandwidth with maximum weak-signal sensitivity across the whole BC band).  It is an attempt to achieve the following two objectives at a -3 dB RF bandwidth of about 6 kHz (relatively independent of signal strength), and constant, high efficiency across the entire AM broadcast band by using two values of inductance in the tank:  1) Best possible sensitivity on weak signals;  2) Loudest possible volume on strong signals.  Version 'c' of this crystal radio set uses Litz wire, introduces a contra-wound coil and has a "narrow selectivity" setting.  It may be viewed in Article #26. Means are provided for increasing selectivity at a small sacrifice in sensitivity.  This crystal radio set is not designed to have strong immunity to local pick-up from local "blowtorch" stations.  Selectivity and insertion power loss figures from a computer simulation are given and compared with those of the actual physical crystal radio set.  A way to tell if the detector is operating below, at or above its 'Linear-to-Square Law Crossover point' (LSLCP) is described.  No external antenna tuner is necessary.  An explanation of 'short wave ghost signals' and 'hash' is provided along with some suggestions on how to combat them.  This version 'b' uses only one diode and audio transformer configuration, as compared to the two used in the original obsolete version (now called Version 'a').  Also a new way to make a higher Q, low inductance coil using all the wire and coil form of the high inductance coil is described.  Finally, the small performance sacrifice at the high end of the band that occurs when more readily available and lower cost parts are used is discussed. Additional benefits of the "Benodyne" type of tank circuit are: (1) Reduction of the the sharp drop in tank Q or sensitivity at the high frequency end of the BC band often experienced when only one value of tank inductance is used for the whole BC band.  (2) Reduction of the tank Q from loss in the variable cap when using lower cost units that use phenolic insulation, such as the common 365 pF cap (see Figs. 2, 3, 4, and 5 in Article #24).  The "two inductance value benodyne* circuit is used in the crystal radio sets in Articles #22 and #26. We assume here that the two "Benodyne" component inductors (see "The Tank Inductor" in Article #26) provide a tank inductance of 250 uH in the low frequency half of the BC band (520-943 kHz) and 62.5 uH in the high half (0.943-1.71 MHz).  If the large 250 uH inductance setting were used all the way up to the top end of the BC band (as in the usual case), a total tuning capacity of 34.7 pF would be required at 1.71 MHz (Condition A).  In the "Benodyne" circuit, with the 62.5 uH inductance setting used for the high frequency half of the BC band, a total tuning capacitance of 139 pF is required at 1.71 MHz (Condition B).  Benefit (1) https://web.archive.org/web/20150402013709/http://www.bentongue.com/xtalset/22St4bXS/22St4bXS.html[06.08.2019 20:10:27]

Single-tuned four-band crystal radio set using a two-value tank inductor

occurs because in condition A, a larger fraction of the total tuning capacitance comes from the typically low Q distributed capacity of the inductor than in condition B.  This results in a higher Q total capacitance in condition B than in condition A.  Benefit (2) occurs because The effective Q of a typical 365 pF variable cap, when used with a 250 uH tank, is about 500 at 1.71 MHz (see Fig. 3 in Article #24).  The Q of the 365 pF variable cap, when set to 139 pF, is greater than 1500 (see Fig.5 in Article #24).  This higher Q results in less loss and greater selectivity at the high end of the BC band in condition 2.  A further benefit of the Benodyne circuit at the high end of the BC band is greater immunity from the Q reducing effects of surrounding high loss dielectric materials such as baseboard etc.  The lossy stray capacity introduced is better swamped out by the high shunt tuning capacity used.  

The Crystal Radio Set Design, in a (large) Nutshell: The design approach is to divide the AM band into several sub-bands in an attempt to keep the selectivity constant and the insertion power loss low.  Many concepts described in various Articles on my Web Index Page, as well as some new ones, are used in the design.  The first step is to divide the band into two halves: Lo (520-943 kHz) and Hi (943-1710 kHz).  Twostep shunt inductive tuning is employed to switch between bands.  A tank inductance of 250 uH is used in the Lo band and of 62.5 in the high band.  The Lo band is further subdivided into two sub-ands: LoLo (520-700 kHz) and HiLo (700-943 kHz).  The Hi band is also subdivided into two sub-ands: LoHi (943-1270 kHz) and HiHi (1270-1710 kHz). Two different operational resistance levels at resonance, measured at the top of the tuned circuit (point 'A' in Fig. 5), are used at the center of the sub-bands.  This impedance level is 125k ohms for the LoLo and LoHi bands and 250k for the HiLo and HiHi bands (excluding the resistive losses of the components used).  These resistance values are made up of the parallel combination of the transformed RF antenna resistance and diode input RF resistance (at point A).  These two resistances should be equal to each other to achieve a minimum insertion power loss, at the design bandwidth.  This means that the transformed antenna and diode RF resistances are each 250k in the LoLo and LoHi bands and 500k in the HiLo and HiHi bands at point 'A'.  The two different transformed RF antenna resistance values (at point 'A'), at the top of the tank are achieved by proper adjustment of a variable capacitor in series with the antenna (C7 in Fig. 5).  The two different diode RF tank loading resistance values (at point 'A') are achieved by tapping the diode onto the tank at a point that is 70% of the turns up from ground for bands HiLo and HiHi.  The tank is not tapped for the LoLo and LoHi bands, and connection is to the top of the tank. The weak-signal audio output and RF input resistances of a diode detector are approximately the same and equal to 0.026*n/Is.  The strong-signal audio output resistance of a diode detector approximately equals 2 times the RF resistance of its source.  Compromise audio impedance transformation ratios are used to optimize performance on both weak and strong signals, thus maximizing sensitivity and volume. The design is scalable.  Less expensive parts that may have somewhat greater losses may be used with some penalty in sensitivity and selectivity at the at the high end of the band.  See the Parts List for a listing of  more easily available and lower cost parts than the ones used in the original de sign.  A tradeoff between sensitivity and selectivity can be achieved by changing the ratio of C7 and C8.  Less capacitance in C7 increases selectivity and reduces sensitivity, and vice versa.

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Single-tuned four-band crystal radio set using a two-value tank inductor

Fig. 1 - Single-Tuned Four-Band Crystal Radio Set, Version 'B'.

The design objectives for the crystal radio set are: 1. To achieve a relatively constant  -3 dB bandwidth of  6 to 8 kHz across the full range of 520 to 1710 kHz, with a relatively constant RF power loss in the RF tuned circuits of less than 4 dB. 2. To to provide adjustment capability for greater selectivity, or less RF loss when needed. 3. To provide optimal performance with external antenna-ground systems having a fairly wide range of impedance. 4. To provide a simple-to-use switching setup for comparison of a 'test' diode with a 'standard one'. 5.  To provide a volume control that has a minimal possible effect on tuning, having a range of 45 dB in 15 dB steps.  This was incorporated in the design because the two local 50 kW blowtorch stations ABC and WOR (about 10 miles away) deliver a very uncomfortably loud output from SP headphones from my attic antenna.  A means of volume reduction was needed.  This method of volume reduction actually increases selectivity by isolating antenna-ground resistance from the tank circuit. 6.  Introduce a new (to me) method for constructing high Q low inductance value inductors.

1. Theory

The frequency response shape of the circuit shown in Fig. 2 is that of a simple single tuned circuit and can be thought of as representative of the nominal response of a single tuned crystal radio set.  Consider these facts: 1. If Lt and Ct have no loss (infinite Q), zero insertion power loss occurs at resonance when Rs equals Rl. This is called the 'impedance matched' case.  The power source (Vs, RS) sees a resistance value equal to itself (Rl).  Also, the load (Rl), looking towards the input sees a resistance (RS), equal to itself.  In the practical case there is a finite loss in Lt and CT  This can be represented by an additional resistance Rt (not shown), shunted across the tuned circuit.  The input resistance seen by (Vs, RS) is now the parallel combo of Rt and Rl and it is less than RS  The impedance match seen by (Vs, RS) when the tank Q (Qt) was infinite is now destroyed.  The impedance matched condition can be restored by placing an impedance transformation device between the source, (Vs, RS) and the tank. In the crystal radio set to be described, the Q of the highest Q practical inductor thought suitable for the design was found to be sufficient to enable about a 6 kHz loaded bandwidth to be obtained with about a 4 dB insertion power loss over the tuning range of 520-1710 kHz. 2. In Fig. 2, if tuning could be done with Lt alone, leaving CT fixed, the bandwidth would be constant.  The problem here is that high Q variable inductors that can be varied over an approximately 11:1 range, as would be needed to tune from 520 to 1710 kHz do not exist.  On the other hand, tuning by varying the value of CT by 11:1 will cover the range, but have two disadvantages.  (1) Bandwidth will vary by 1:11 from 520 to 1740 kHz.  (2) In the practical case, if the bandwidth is set to 6 kHz at the low end of the band, and an attempt is made to narrow the bandwidth at 1710 kHz by placing a capacitor in series with the antenna, the insertion power loss will become great. 3. The compromise used here is a coil design that can be switched between two inductance values differing by 4:1.  The high inductance setting is used for the low half of the band and the low inductance setting for the high half.  Capacitive tuning is used to tune across each band.  The technique used here, in creating the two inductances, enables the Q of the low value inductance to to be much higher than would be the case if a single coil of the same diameter but with fewer turns was used.  This technique uses two coils, closely coupled, and on the same axis.  They are connected in series for the large inductance and in parallel for the small one.  The small inductance has a value 1/4 that of the large one and about the same Q at 1 MHz.  The innovation, so far as I know, is to use the full length of wire used in the high inductance coil, occupy the same cubic volume, but get 1/4 the inductance and keep the same Q as the high inductance co il. 4. The high and low bands are each further subdivided giving a total of four bands (LoLo, HiLo, LoHi and https://web.archive.org/web/20150402013709/http://www.bentongue.com/xtalset/22St4bXS/22St4bXS.html[06.08.2019 20:10:27]

Single-tuned four-band crystal radio set using a two-value tank inductor

HiHi).  If this was not done, we would be faced with a bandwidth variation of about 1:3.3 in each band.  The bands are geometrically divided and are: 520-700 (LoLo), 700-943 (HiLo), 943-1270 (LoHi) and 1270-1710 (HiHi) kHz.  The bandwidth should vary 1:1.8 across each sub-band.  The same relation should hold between the HiHi and LoHi band.  The bandwidth at the center of each of the four bands are made approximately equal to each other by raising the loading resistance of the antenna and diode on the tank by a factor of two in band HiLo compared to the value used in band LoLo.  The same adjustment is used for bands HiHi and LoHi.

2. Design Approach for the Center of each of the four Bands.

Fig. 3a shows the simplified Standard Dummy Antenna circuit, described in Terman's Radio Engineer's Handbook, for simulating a typical open-wire outdoor antenna-ground system in the AM band.  R1=25 ohms, C1=200 pF and L1=20 uH.  See Article #20 for info on how to measure the resistance and capacitance of an antenna-ground system.  The values shown for Fig. 3a are used in the design of the crystal radio set.  R1 represents primarily the ground system resistance.  C1 represents the capacitance of the horizontal wire and lead-in to ground and L1 represents the series inductance of the antenna-ground system. The values of R1, C1 and L1 in Fig. 3a will be considered to be independent of frequency.  To the extent that they do vary with frequency, C7 and C8 in Fig. 5 can be adjusted to compensate.  The current-source equivalent circuit of the antenna-ground circuit is shown in Fig. 3b. To a first degree of approximation, in the practical case, C2 in Fig. 3b is independent of frequency.  R2 will vary approximately inversely with frequency.  We will ignore the effect of L2, since its value is large, except when approaching the first resonance of the antenna-ground system. The design approach is to place a variable capacitor C3 in series with the antenna circuit (Fig. 3a) to enable impedance transformation of the antenna-ground circuit to an equivalent parallel RC (Fig. 3b), the R component of which can be adjusted by changing the value of the C3 to follow a desired relationship vs frequency.  One of the objectives of the design is to enable as constant a bandwidth as possible vs. frequency.  This requires the aforementioned equivalent parallel R2 component to vary proportionally with the square of the frequency if capacitive tuning is used as it is here, in each sub-band (Q must be proportional to frequency for a constant bandwidth).  This design attempts to accomplish this in the center of each frequency band.  Performance is close at band edges.

3. The single tuned crystal radio set The topology of the single tuned circuit is changed from band to band as shown in Fig. 4 below.

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Single-tuned four-band crystal radio set using a two-value tank inductor

The resonant RF resistance values at the top of C8 (Fig. 4), from the transformed antenna resistance, (at the center of each sub-band) are designed to be: 250k ohms for bands LoLo and LoHi, and 500k ohms for bands HiLo and HiHi.  Since the diode is tapped at the 0.7 voltage point for bands HiLo and HiHi, it sees a source resistance at resonance of: 125k for bands LoLo and LoHi and of 250k ohms for bands HiLo and HiHi.  These figures apply for the theoretical case of zero loss in the tuned circuits (infinite Q).  In a shunt capacitively tuned crystal radio set, loaded with a constant resistive load, the bandwidth will vary as the square of the frequency.  To understand why, consider this: When the resonant frequency of a tuned circuit loaded by fixed parallel resistance is increased (from reducing the total circuit tuning capacitance), the shunt reactance rises proportionally, giving rise to a proportionally lower circuit Q.  But, a proportionally higher Q is needed if the bandwidth is to be kept constant.  There for, the square relation. In the practical case, we are faced with two problems.  (1) How should we deal with the fact we work with finite Q components?  (2) At high signal levels (above the LSLCP), the RF load presented by the diode to the tuned circuit is about 1/2 the audio load resistance, and at low signal levels (below the LSLCP) the RF load presented to the diode is about 0.026*n/Is ohms.  Compromises are called for.

Parts List - All components are chosen for the best possible sensitivity at a -3 dB RF bandwidth of 6 kHz (except for not using litz wire in the inductor). C1, C3:  200 pF NPO ceramic caps. C2: 100 pF NPO ceramic cap. C4, C6:  270 pF ceramic caps. C5:  18 pF NPO ceramic cap. ** C7, C8:  12-475 pF single section variable capacitors, such as those that were mfg. by Radio Condenser Corp.  They use ceramic stator insulators and the plates are silver plated.  Purchased from Fair Radio Sales Co. as part # C123/URM25.  Other capacitors may be used, but some of those with phenolic stator insulators probably will cause some reduction of tank Q.  The variable capacitors are

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Single-tuned four-band crystal radio set using a two-value tank inductor

fitted with 8:1 ratio vernier dials calibrated 0-100.  These are available from Ocean State Electronics as well as others.  An insulating shaft coupler is used on C7 to eliminate hand-capacity effects.  It is essential, for maximum sensitivity, to mount C7 in such a way that stray capacity from its stator to ground is minimized.  See Part 9 for info on mounting C7.  The variable capacitors used in this design may not be available now.  Most any other capacitor with silver plated plates and ceramic insulation should do well. C9:  47 pF ceramic cap. C10:  0.1 to 0.22 uF cap. C11:  Approx. 1.0 uF non-polarized cap.  This is a good value when using RCA, Western Electric or U. S. Instruments sound powered phones, with their 600 ohm elements connected in series.  The best value should be determined by experiment.  If 300 ohm sound powered phones having their 600 ohm elements connected in parallel are used, C11 should be about 4 uF and a different transformer configuration should be used. ** L1, L2, L3 and L4:  Close coupled inductors wound with uniformly spaced Teflon insulated 18 ga. silver plated solid wire.  This wire is used only to gain the benefit of the 0.010" thick low-loss insulation that assures no wandering turns can become 'close-spaced'.  L1 has 12 turns, L2 has 8 turns, L3 has 6 turns and L4 has 14 turns.  The coil form is made of high-impact styrene. I used part #S40160 from Genova Products (http://genovaproducts.com/factory.htm).  See Fig. 6 for hole drilling dimensions. ** SW1, 2:  DPDT general purpose slide switches. **SW3, 4, 5 and 6:  Switchcraft #56206L1 DPDT mini Slide switches.  This switch has unusually low contact resistance and dielectric loss, but is expensive.  Other slide switches can be used, but may cause some small reduction of tank Q.  SW6 is used as a SPDP switch.  Don't wire the two halves in parallel. T1, T2:  Calrad #45-700 audio transformer.  Available from Ocean State Electronics, as well as others.  If 300 ohm phones are to be used, see the third paragraph after Table 1. R3:  1 Meg Pot. (preferably having a log taper). Baseboard:  12'' wide x 11 1/8 '' deep x 3/4" thick. Front panel is made of 0.1" high-impact styrene.  Other materials can be used.  I was looking for the lowest loss, practical material I could obtain. **  For lower cost, the following component substitutions may be made:  Together they cause a small reduction in performance at the high end of the band (about 1.75 dB greater insertion power loss and 1.5 kHz greater -3 dB bandwidth).  The performance reduction is less at lower frequencies. Mini air-variable 365 pF caps sold by many distributors such as The Crystal Set Society and Antique Electronic Supply may be used in place of the ones specified for C7 and C8. 18 ga. (0.040" diameter) "bell wire" supplied by many distributors such as Home Depot, Lowe's and Sears may be used in place of the teflon insulated wire specified.  This  vinyl insulated bare copper wire is sold in New Jersey in double or triple twisted strand form for 8 and 10 cents per foot, respectively.  The cost comes out as low as 3 1/3 cents per foot for one strand.  The main catch is that one has to untangle and straighten the wires before using them.  I have used only the white colored wire but I suppose the colored strands will work the same (re dielectric loss).  The measured outside diameter of the wire from various dealers varied from 0.065 to 0.079".  The high dielectric loss factor of the vinyl, compared to the teflon specified above will cause some reduction of sensitivity and selectivity, more at the high end of the band than the low end.  I don't think the difference would be noticeable to a listener.   Radio Shack mini DPDT switches from the 275-327B assortment or standard sized Switchcraft  46206LR switches work fine in place of the specified Switchcraft 56206L1 and cost much less.  See Article #24 for comparison with other switches.  Any switch with over 4 Megohms Rp shown in Part 2 of Article #24 should work well as far as loss is concerned.  Overall, losses in the switches have only a very small effect on overall performance.

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Single-tuned four-band crystal radio set using a two-value tank inductor

The coil should be mounted with its axis at a 30 degree angle to the front panel as shown in Fig.1.  The center of the coil form is 2 7/8" back from the rear edge of the baseboard and 5 5/8" to the left of its right edge.  These dimensions are important, as is the actual size of the breadboard, if one wishes to construct a doubletuned four band crystal radio set out of two Version 'b' single-tuned four band crystal radio sets as described in Article #23.  

Table 1 - Switch Functions for Version 'b': SW1

15 dB volume control "capacitive" attenuator.  'Down' places a 15 dB loss in the input.

30 dB volume control "capacitive" attenuator.  "Down' places a 30 dB loss in the input. 'Up' position for operation in the LoLo (520-700) and HiLo (700-943 kHz) band. SW3: 'Down' position for operation in the LoHi (943-1270) and HiHi (1270-1710 kHz) band. SW4: Same as SW3. SW2

'Up' position for operation in the LoLo and LoHi band. 'Down' position for operation in the HiLo and HiHi band. 'Up' position for normal crystal radio set operation, using a diode having an Is of SW6: about 100 nA. 'Down' position for increased selectivity, using a diode having an Is of about 15 nA in the #2 position, or for comparison testing of diodes. SW5:

SW7:

'Down' position for normal operation.  'Up' position to bypass the onboard audio transformers, if one wishes to use an external one.

The diode:  This design is optimized for use with a diode having an n of 1.03 and a Saturation Current (Is) of about 82 nA, although this is not critical and other diodes can be used with good results.  See Articles  #0, #4 and #16 for info on n and saturation current (Is) of diodes, and how to measure them.  If desired, and one has a favorite diode, its effective (Is) can be changed by applying a DC bias voltage, using perhaps, the 'Diode Bias Box' described in Article #9. One suitable diode, the published parameters of which show an (Is) of 100 nA is a Schottky diode, the Agilent HBAT-5400.  It is a surface-mount unit that was originally designed for transient suppression purposes.  Measurements of many HBAT-5400 diodes seems to show that there are two varieties.  One type measures approximately: n=1.03 and (Is)=80 nA.  The other type seems to have an n of about 1.16 and an (Is) of about 150 nA.  Both work well but the former works the best.  This part, available in an SOT-23 package is easily connected into a circuit when soldered onto a "Surfboard" such as manufactured by Capital Advanced Technologies (http://www.capitaladvanced.com/), distributed by Alltronics, Digi-Key and others.  Surfboard #6103 is suitable.  The HBAT-5400 is also available in the tiny SO-323 package that can be soldered to a 330003 Surfboard. The Agilent HSMS-2860 microwave diode (Specified Is=50 nA) is available as a single or triple with three https://web.archive.org/web/20150402013709/http://www.bentongue.com/xtalset/22St4bXS/22St4bXS.html[06.08.2019 20:10:27]

Single-tuned four-band crystal radio set using a two-value tank inductor

independent diodes in the SO-323 and SO-363 packages, respectively.  The Agilent number for the triple diode is HSMS-286L.  I find it to be particularly good for DX in this crystal radio set.  It is a convenient part since one can connect it using only one section (shorting the unused ones) or with two or three in parallel.  This gives one a choice of nominal saturation currents of 50, 100 or 150 nA.  Samples of this part I have tested measured about 35 nA per diode, not 50.  I don't know the normal production variations.  The only disadvantage of this diode, as far as I know, is its low reverse breakdown voltage which may cause distortion and low volume on very loud stations.  It has the advantage, as do most Schottkys, of having much less excess reverse leakage current than do germanium diodes.  This helps with volume and selectivity on very weak stations. Infineon makes a BAT62 Schottky diode in several different quite small surface mount packages.  The single BAT62 is physically the largest.  It has a specified (Is) of about 100 nA and performs quite well.  Be forewarned that the diode parasitic series resistance is a high 100 ohms in this diode.   A resistance even this high should not have a noticeable effect on the performance of a crystal radio set. Most germanium diodes have too high a saturation current for the best selectivity and should to be back-biased or cooled for optimum performance.  See Article #17A for more info on this.  Different type diodes may be connected  to the terminals labeled Diode #1 and Diode #2, with either one selectable with SW6. When one diode is selected, the other is shorted.  This feature makes it easy to compare the performance of a 'test' diode with one's 'favorite' diode. Another use is to place one's best DX diode in one position and one having a very low reverse leakage resistance at high reverse voltages in the other.  This will maximize strong signal volume and minimize audio distortion. A good choice for this crystal radio set is a diode having a relatively low saturation current such as 3 or 4 Agilent HSMS-2820 or HSMS-2860 diodes in parallel as Diode #1 for high selectivity and sensitivity on weak signals, and an Agilent HBAT-5400 or one of the lower saturation current germaniums as Diode #2 for low distortion and maximum volume on strong stations.  Don't use two diodes in series if you want the best weak signal sensitivity in any crystal radio set.  The result of using two identical diodes in series is the simulation of an equivalent single diode having the same (Is) but an n of twice that of either one.  This reduces weak signal sensitivity. The inductor for this single tuned crystal radio set is made up of the four closely coupled inductors L1, L2, L3 and L4.  The inductance from point A to ground (Fig. 5) is 250 uH when SW3 is in the 'up' position (used for low band reception) and 62.5 uH in the 'down' position (used for high band reception).  Better performance from a higher tank Q at the high frequency end of band B may be obtained by using the "contra-wound" coil winding technique described in Article #26. This minimizes distributed coil capacitance in band B as opposed to the winding connections used here that minimize coil distributed capacity in band A. Audio impedance transformation from the audio output resistance of the diode detector to 'series connected' 1.2k ohm sound-powered phones is provided by the audio transformers.  If one wishes to use 300 ohm soundpowered phones with two 600 ohm elements connected in parallel instead of series, a very good low loss transformer choice is the 100k-100 ohm transformer from Fair Radio Sales, #T3/AM20.  The configuration of two Calrad transformers shown on line 2 of the Calrad chart in Article #5 is also a good choice.  C11, along with the shunt inductance of the transformer and the inductance of the sound powered phones form a highpass filter, hopefully flat down to to 300 Hz.  R3 is used to adjust the DC resistance of the diode load to the AC impedance of the transformed effective AC headphone impedance.  C10 is an audio bypass. The two variable capacitors C7 and C8 interact substantially when tuning a station.  C7 mainly controls the selectivity and C8 mainly controls the resonant frequency.  If the antenna-ground system being used has a resistance larger than 25 ohms, C7 will have to be set to a smaller capacitance in order to maintain the proper resonant resistance at point A in Fig. 5.  If the capacitance of the antenna-ground system is greater than 200 pF, C7 will also have to be set to a lower value than if it were 200 pF. The "capacitive" attenuators controlled by SW1 and SW2, used for volume and selectivity control, are designed so as to cause minimal tank circuit detuning when the equivalent circuit of the antenna-ground system used has the same values as the old IRE simplified Dummy Antenna recommended for testing Broadcast Band radio receivers.  It consisted of a series combination of a 200 pF cap, 20 uH inductor and a 25 ohm resistance.  The geometric mean of the sum of the reactances of the capacitor and inductor at 520 and

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Single-tuned four-band crystal radio set using a two-value tank inductor

1710 kHz is (-605) ohms. This is the reactance of a 279 pF capacitor (characteristic capacitance of the "capacitive" attenuator) at 943 kHz, the geometric mean of the BC band of 520-1710 kHz.  The "capacitive" attenuators were designed for the specified attenuation values (15 and 30 dB) utilizing the 500 ohm resistive pi attenuator component values table shown in the book "Reference Data for Radio Engineers".  The resistor values for 15 and 30 dB "capacitive" attenuators were normalized to 605 ohms, then the "capacitive" attenuator capacitor values were calculated to have a reactance, at 943 kHz, equal to the value of the corresponding "capacitive" attenuator shunt or series resistance.  Since the "capacitive" attenuators, when switched into the circuit, isolate the antenna-ground system resistance from the tank circuit, selectivity is increased.  This is a convenient feature, since less retuning is required than if selectivity is increased by reducing C7 and increasing C8.  If the series capacitance of the equivalent circuit of one's own antenna-ground system is 200 pF, at 943 kHz, practically no retuning is required. If the equivalent L and C of one's own antenna-ground system differ substantially from those of the simplified IRE dummy antenna used here, one can normalize the values of the capacitors used in the "capacitive" attenuators to match ones's own antenna-ground system.  A method for measuring the parameters of one's own antenna-ground system is shown in Article #20.

4.  'Loop Effect' of the tank inductor, and how it can be used to tame local 'Blowtorch' stations when searching for DX. One can use local signal pickup by the tank (loop effect) to reduce the effect of interference from strong stations by rotating the crystal radio set about a vertical axis.  The correct angle will generally reduce it.

5.  How to improve selectivity with a relatively small loss in sensitivity. Selectivity can always be increased by reducing the value of C7 and re-tuning C8.  If neither "capacitive" attenuator is in-circuit, switching one into the circuit will increase selectivity (and reduce volume). Selectivity can be increased by changing to a diode having a lower Is than the HBAT-5400, such as the Agilent 5082-2835 or HSMS-2820.  A DC bias, applied to the 'Diode Bias' terminals can 'fine-tune' performance.  The diode 'Bias Box' described in Article #9 is useful here.  One can choose less audio distortion and less selectivity by biasing the diode in a more forward direction, or better selectivity, at the cost of more audio distortion  by biasing the diode toward its reverse direction. Selectivity in the LoLo band (520-700 kHz) can be increased somewhat from the performance resulting from using the settings shown in Table 1 by switching SW5 to the 'down' position, and even more by, in addition, switching SW4 to the 'down' position. Selectivity in the HiLo band (700-943 kHz) can be increased from the performance resulting from using the settings shown in Table 1 by switching SW4 to the 'down' position. Selectivity in the LoHi band (943-1270 kHz) can be increased somewhat from the performance resulting from using the settings shown in Table 1 by switching SW5 to the 'down' position. The only way to increase selectivity in the HiHi band is to use a diode having a low Is, reducing C7, or switching in a "capacitive" attenuator such as SW1 or SW2.  See Fig. 5. A large increase in selectivity can be attained by going to a double tuned circuit.  See Article #23. Note:  When altering selectivity by changing switch positions, always re-balance the relative settings of C7 and C8.    

6.  Just how loud is a station that delivers the amount of power necessary to operate the Diode Detector at its 'Crossover Point' between Linear and Square-Law Operation? Many Articles in this series have talked about the 'Linear-to-Square-Law Crossover Point' (LSLCP).  Please bear in mind that the LSLCP point is a point on a graph of output DC power vs input RF power of a diode detector system.  It is not a point on a graph of DC current vs voltage of a diode. Two things can be said about a detector when it is fed a signal that operates it at its LSLCP.  (1) A moderate increase of signal power will move the detector into its region of substantially linear operation.  (2) A similar moderate decrease of input power will move it closer to its region of substantially square law operation, where a 1 dB decrease of input

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Single-tuned four-band crystal radio set using a two-value tank inductor

power results with a 2 dB decrease of output power.  For more info on the LSLCP, see Article #15A. The crystal radio set described in this Article is operating at its LSLCP if the rectified DC voltage at the 'Diode Bias' terminals is 53 mV, a diode having a Saturation Current (Is) of 82 nA and an ideality factor (n) of 1.03 is used (such as a selected Agilent HBAT-5400), and if R3 is set to 325k ohms.  At this point the diode rectified current equals two times its Saturation Current.  The volume obtained is usually a low to medium, easy-to-listen-to level.

7. 'Short Wave ghost Signal', 'background hash' and spurious FM reception. All single tuned crystal radio sets may be, in fact, considered double tuned (except single tuned loop receivers).  The second response peak arises from resonance between the equivalent inductance of the antenna-ground system and the impedance it sees, in this case, the series combination of capacitors C7 and C8.  This peak usually appears at a frequency above the broadcast band and gives rise to the possibility of strong so-called 'short wave ghost' signal interference when a short wave station has a frequency near the peak . The response at this ghost frequency can be made somewhat weaker and moved to a higher frequency if the antenna-ground system inductance is reduced.  One can use multiple spaced conductors for the ground lead to reduce its inductance.  I use a length of TV 300 ohm twin lead, the two wires connected in parallel for this purpose.  Large gauge antenna wire, or spaced, paralleled multiple strands helps to reduce the antenna inductance (flat top antenna).  If the down-lead is long compared to the ground lead, use multiple, paralleled, spaced conductors to reduce its inductance (similar to using a 'cage' conductor). Another possible cause of 'ghost' signal reception resides in the fact that the response of the so-called single tuned circuit does not continuously drop above resonance as frequency rises, but only drops to a relatively flat valley before rising again to the second peak. The frequency response above the main (lower) peak would drop monotonically (true single tuned operation) if the second peak did not exist.  The relatively flat response valley that exists between the two peaks, provides the possibility (probably likelihood) of interference 'hash' if several strong stations are on the air at frequencies in the valley range.  It also is the cause of a strong local station, above the frequency of a desired station "riding through" and appearing relatively constant even if the tuning dial is moved.  The response should drop at a 12 dB per octave rate above the second peak.  A useful side effect of the response behavior of this type of circuit is that the response below the main resonance drops off at an extra fast rate of 12 dB per octave rate instead of an expected 6 dB.  The most effective way to substantially eliminate 'short wave ghost' and hash reception is to go to a doubletuned circuit configuration or to use traps. Spurious FM reception caused by so-called FM 'slope' detection can occur from close by local FM stations if a spurious FM resonance appears somewhere in the circuitry of a crystal radio set.  If ground wiring is not done properly in the crystal radio set, spurious signals can get into the detector. The thing to do here is to run all the RF and audio grounds to one point as shown in Fig.5.  Sometimes a small disc bypass capacitor, 22 pF or so, placed across the diode will help. Another way to try to reduce FM interference is to put a wound ferrite bead 'choke' in series with the antenna and/or ground leads.  In order not to affect normal BC band reception, the resultant ferrite inductor should have a reasonable Q and a low inductance in the BC band.  It should also exhibit a high series resistance at FM frequencies.  Suitable wound ferrite chokes (bead on a lead) are made by the Fair-Rite Corp. as well as others.  Two types available from Mouser are #623-29441666671 and #623-2961666671.  This suggestion may also help reduce "short wave ghost" signal reception.

8.  Some simulated and actual measurements on the crystal radio set.

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Single-tuned four-band crystal radio set using a two-value tank inductor

Fig. 7 - RF frequency response from antenna to diode input, center of  LoLo Band, using the simplified dummy antenna.

Fig .8 - RF frequency response from antenna to diode input, center of HiHi Band, using the simplified dummy antenna.

Fig. 7 shows the simulated frequency response at the center of the LoLo band, from the antenna source to the RF input of the diode.  The red graph and figures in the left panel show an insertion power loss of 2.4 dB with a -3 dB bandwidth of 6 kHz, along with the spurious response peak at 4.4 MHz, caused by the antenna-ground system inductance.  The insertion loss at the spurious peak is 15 dB.  The loss in the valley is 40 dB.  The right graph and figures show the Input Return Loss (impedance match) at resonance to be -12.2 dB.  The output return loss (not shown) is the same.  Fig. 8 shows the simulated frequency response at the center of the HiHi band, from the antenna source to the RF input of the diode.  The red graph and figures in the left panel show an insertion power loss of 4.1 dB with a -3 dB bandwidth of 6 kHz, along with the spurious response peak at 6.9 MHz, caused by the antenna-ground system inductance.  The insertion loss at the spurious peak is 20 dB.  The loss in the valley is 47 dB. The right graph and figures show the Input Return Loss (impedance match) at resonance to be -8.5 dB.  The output return loss is the same.

Table 2 - Expected and Measured Tank Q values (antenna and diode disconnected) Band Frequency in kHz Expected coil Q, according to Medford Measured, unloaded tank circuit Q (includes loss in the tuning caps and all other misc. loss)

LL 603 497

HL 813 577

LH 1094 669

HH 1474 777

431

463

555

620

 

9.  A method for measuring the unloaded Q of an L/C resonator. 1. Connect the 50-ohm output of a precision frequency calibrated RF generator (I used an Agilent digitally synthesized unit.) to a radiating test loop by means of, say, a 5 foot long coax cable.  The loop can be made from 15 turns of solid #22 ga. vinyl insulated wire, bunched up into a ¼ " diameter cross section bundle, wound on a 2" diameter vitamin pill bottle.  The coil is held together by several twist-ties. 2. Make sure that all resistive loads are disconnected from the tank.  Remove all metallic (especially ferrous) material from the vicinity of the coil.  Capacitively couple the probe of a 5 MHz scope to the hot end of the L/C tank.  This coupling must be very weak.  This can be done by clipping the scope probe onto the insulation of a wire connected to the hot end of the coil (or a tap) or placing the probe very close to the hot end. 3. Place the 2" loop on-axis with the coil, about 6" from its cold (grounded) end.  Tune the generator to

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Single-tuned four-band crystal radio set using a two-value tank inductor

4.

5. 6.

7.

say, fo MHz and adjust the generator output, scope sensitivity and L/C tuning to obtain 7 division pattern from fo on the scope.  Note the frequency. Detune the generator below and then above fo to frequencies (fl and fh) at which the scope vertical deflection is 5 divisions.  This represents an approximate 3 dB reduction in signal.  Record those frequencies.  You may encounter some hum and noise pickup problems and will have to respond appropriately to eliminate them.  It is usually beneficial to conduct experiments of this type over a spaced, grounded sheet of aluminum placed on top of the workbench. Calculate approximate unloaded tank Q.  Qa=fo/(fh-fl).  Calculate the actual Q by dividing Qa by 1.02 to reflect the fact that 5/7 does not exactly equal SQRT (0.5). Try reducing the loop and capacitive coupling, and repeat the measurement and calculation.  If the Q comes out about the same, that shows that the 50 output resistance of the generator and the scope loading do not significantly load the tank. Note:  When measuring the Q of an inductor with a Q meter it is common practice to lump all of the losses into the inductor. This includes magnetic losses in the inductor as well as dissipative losses in its distributed capacitance. We generally try to get a grip on tank Q values by measuring the inductor with a Q meter, when one is available. We assume that all the loss that affects the measured Q is magnetic loss. Not so, there is also loss in the dielectric of the distributed capacitance of the inductor. Actually, we are measuring an inductor having a specific Q (at a specific frequency), in parallel with the distributed capacity of the coil. We usually assume that the Q of this distributed capacity is infinite, but it isn't. The dielectric of the coil form material makes up much of the dielectric of the coil's distributed capacity and is the controlling factor in causing different coil Q readings when using coil forms made up of various different materials. This distributed capacity is in parallel with the tuning capacitor and can have an important effect on overall tank Q at the high end of the band because it is paralleled with the small, hopefully high Q, capacitance contribution from the variable cap. At lower frequencies, the dielectric material of the coil form becomes less important since its contribution to the distributed capacity is swamped out by the larger capacitance needed from the tuning capacitor in order to tune to the lower frequencies.

10.  Important information re: unloaded tank Q. Every effort should be made to achieve as high an unloaded tank Q as possible, in order to minimize RF loss at the desired -3 dB bandwidth (selectivity), and especially when using narrower bandwidths.  Somewhat greater insertion power loss and/or broader selectivity may result if components having a greater dielectric loss than those specified are used.  Sensitive areas for loss are: 1. Q of the coil.  See Table 2 for the Q values realized in the tank circuit. 2. Stator insulation in the variable caps C7, C8. 3. Skin-effect resistive loss in the variable capacitor plates.  Silver plated capacitor plates have the least loss, brass or cadmium plated plates cause more loss.  Aluminum plates are in-between.  Rotor contact resistance can be a problem. 4. Contact support plastic used in slide switches SW3, 4, 5 and 6. 5. Front panel material. 6. Coil form material.  Styrene has 1/10 the dielectric loss of PVC.  High impact styrene forms are available from Genova Products at their retail store:  http://genovaproducts.com/factory.htm .  These forms are listed as drain couplers. 7. Capacitive coupling from any hot RF point, through the wood base to ground must be minimized because it tends to be lossy and will reduce performance at the high end of band A and band B.  The steps I took to reduce these losses are:  (1) Mounting C7 to the baseboard using strips of 0.10" thick, 0.5" wide and 1.5" long high-impact styrene as insulators and aluminum angle brackets screwed to the baseboard and (2) and connecting these brackets to ground.  This isolates the lossy  dielectric of the baseboard from the hot end of C7.  See Fig. 1.  Ceramic stand-off insulators can be adapted, in place of the styrene strips for the job.  Another way to mount C7 is to make a mounting plate from a sheet of low loss dielectric material, somewhat larger than C7's footprint, and screw C7 on top of it.  Holes made in the plate can then be used, along with small brackets or standoffs to mount the assembly onto the baseboard.  Don't forget to wire the metal mounting pieces to ground.  These same considerations apply to any metal coil mounting bracket, close to a hot end of the coil, used to mount the coil form to the baseboard.  The bracket should be grounded.

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Single-tuned four-band crystal radio set using a two-value tank inductor

8. The physical size of the coil is important.  A large size coil was chosen to enable a high Q.  Medhurst's work enables one to calculate the Q of a solenoid wound with solid copper wire, provided that:  0.410) can be modeled as a parallel combination of an ideal capacitor of value C1 and a resistor (Rp).  The resistor, Rp in this case, has a value of:: (reactance of C1)*Q1.  Note that since capacitor reactance is a function of frequency, the value of the resistor will, in general, vary with frequency.  In crystal radio set design it is sometimes convenient to model the tuning capacitor loss as a parallel resistor, other times as a series resistor. Credit must go to Bill Hebbert for making the time consuming, difficult, precision measurements required for Figs. 2-5. B2:  Slide switches used in the Crystal Radio Set described in Article #22 have dielectric losses, as do all switches.  To get a handle on this loss, samples of several different types of DPDT switch were measured at 1500 kHz.  Each switch except the last three, below, were wired as a SPDT unit by paralleling the two sections.  The Q of the capacitance appearing across the open contacts was then measured and Rp was calculated.  Rp usually varies approximately inversely with frequency and therefore causes more loss at the high end of the band than at the low end.  Contact resistance of all switches was found to be very low.  It is unknown how well that characteristic will hold up over time.  Note the extremely low loss of the Switchcraft 56206L1.  The loss is so low that this switch is overkill in most crystal radio set applications.  For applications in which the crystal radio set builder wants to use the lowest loss DPDT slide-switch available, this switch is the best I have found.  

Table 3 - Equivalent parallel Loss Resistance (Rp) caused by the loss tangent of the dielectric of some DPDT Slide Switches at 1.5 MHz. Brand name, model number and Size of switch ARK-LES (std. size) Radio Shack 275-403A (std. size) Radio Shack 275-407A (sub mini) Stackpole S7022X (std. size) Switchcraft 46206EE-6 (std. size) Radio Shack 275-327B (mini) CW (mini) Switchcraft 46206LR (std. size) C&K L202-1 (mini) Switchcraft 56206L1 (mini) Radio Shack 275-327B connected as SW3 in Article #22 (HI band)

Rp in Megohms 2.3 3.5 4.1 4.9 5.1 5.7 6.0 6.5 6.8 13.3 4.1

Switchcraft 56206L1 connected as SW6 in Article #22

9.4

Radio Shack 275-327B connected as SW6 in Article #22, See Graph--->>

3.5

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Variable capacitor Q measurement, diode problems, RF loss in slide switches and dielectrics; sensitivity and selectivity in crystal radio sets

Rotary selector switches using ceramic insulation should have very low loss, even lower than the Switchcraft 56206L1.  Quality switches using brown phenolic insulation probably have losses similar to slide switches using similar material.  I would expect that the slope of the Rp vs. frequency graph of the other slide switches to be the similar that shown above.   B3:  The loss tangent of an insulating material is the reciprocal of the Q of a capacitor made of that material.  Some of the insulating materials listed below are used as front panels, detector stand bases, wire insulation and coil forms in crystal radio sets.  A capacitor formed by the use of one of these materials, connected across a high impedance point and ground, will contribute a loss proportional to the loss tangent and capacitance.

Table 4 - Loss Tangent of some Insulating Materials used in Crystal Radio Sets, Measured at 1.5 MHz. Loss tangent

Q of a capacitor using the material

0.017 0.03

59 33

0.0017

590

Polypropylene 1.5" diameter drain pipe from Genova Mfg. Co. High impact styrene sheet, 0.1" thick (opaque white and flexible) Plexiglas 0.115" thick FR-4 PCB material 1/16' thick

0.0022 0.0023 0.016 0.027

452 430 55 37

Black 3/16" Condensite panel, brand name "Celoron" (Bakelite, new old-stock radio panel from the '20's)

0.035 (@ 0.8 MHz)

29

ABS styrene (black)

0.010

100

Garolite (black) ABS styrene (light beige) HDPE (milky white)

0.033 0.020 0.0009

30 50 1120

Polystyrene (light brown opaque)

0.0032

320

Dielectric Material PVC as used in coil form PVC wire insulation High-impact styrene coupler from Genova Mfg. Co. (opaque white)

Note: GE's version of polycarbonate is called Lexan. A review GE's spec. sheets of various grades of Lexan show loss tangent values at 1.0 MHz ranging between 0.006 and 0.026 . Many grades are specified 0.01. B4:  Please see Parts 10 and 11 of Article #26 as well as Table 4. Also see Table 2 of Article #22 and Article #29. B5:  Sometimes, when working with high Q tank circuits, a need pops up for a fixed capacitor with a value between say, 100 and 1000 pF that will not degrade overall circuit Q.  Generic NPO disc capacitors in that range usually have a Q of around 2000-3000 at 1 MHz.  Table 4 shows some caps having higher Q values.  The only downside to the high Q caps is that they are SMD types and require some skill when soldering pigtail leads to them to easy connecting to one's circuit.  The capacitors were measured singly, in parallel or in series, aiming for values approximating 500 pF. This was for convenience in measurement.  I used solid tinned copper wire having a diameter of about 0.010" for my pig-tails. The source for the strands was a piece of stranded hook-up wire.

Table 4 - Q of easily available capacitors in the 100 - 1000 pF range Type

Value in pF

Voltage

Q at about 920 kHz

Mfg

Mfg. part number

1

Polypropylene

Two 1k in series=500

630

2,000

Xicon (Mouser)

1431-6102K

2 3

Polystyrene Generic NPO disc

One 470 One 220

50 500

6,200 2,800

Xicon (Mouser) 3/8" dia.

23PS147 NA

Multilayer, hi Q

Two 1k in

50

8,000

Murata

ERB32Q5C1H102JDX1L

 

4

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Variable capacitor Q measurement, diode problems, RF loss in slide switches and dielectrics; sensitivity and selectivity in crystal radio sets

SMD

series=500

5

Multilayer, hi Q SMD

One 470

100

18,000

Murata

ERB32Q5C2A471JDX1L

6

Multilayer, hi Q SMD

Two 220 in parallel=440

200

20,000

Murata

ERB32Q5C2D221JDX1L

7

Multilayer, hi Q SMD

Two100 in parallel=200

500

40,000

Murata

ERB32Q5C2H101JDX1L

Note:  Solder flux contamination on a dielectric is the enemy of high Q because it usually provides a resistive leakage path.  If one gets solder flux on the insulation of a variable cap or switch, remove it with a commercial flux remover.  This is important when a DX crystal radio set is involved. #24  Published: 03/25/2002;  Revised: 06/10/2008 0060610

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Amplify a crystal radio's output without using batteries or socket power http://www.bentongue.com/xtalset/25AmpXS/25AmpXS.html Go

30

24 captures

2012 2013 2015

20 Sep 2007 - 22 Mar 2017

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JUN OCT DEC

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▾ About this capture

   

A new approach to amplifying the output of a crystal radio, using energy extracted from the RF carrier to power a micro-power IC to drive headphones or a speaker By Ben H. Tongue

 

Quick summary:  This article describes an amplifier that can be used to substantially increase the volume from a crystal radio set when tuned to a weak signal when using headphones.  It can also be used to amplify the output of a crystal radio set, when tuned to medium or strong stations, to drive a speaker.  No battery for powering is required.  The amplifier can be added to most any crystal radio set, provided access to a strong station is available.  As shown here, the amplifier is applied to Version 'B' of the "Benodyne", a single-tuned four-band crystal radio set.  See Article #22.  It has been also applied to version ""C" of the "Benodyne", described in Article #26.  A switch is provided so the crystal radio set can perform as it normally does, or with about 20 dB of audio amplification (+20 dB represents a large increase of volume.).  This amplification is provided by a micropower integrated circuit that does not use battery power.  Power to operate the integrated circuit is stored in an electric double-layer "supercapacitor" that can be charged overnight by leaving the crystal radio set on, tuned to a strong local station.  One charge can last for tens of hours when listening to weak stations.  For loudspeaker operation, a large reentrant horn type PA speaker is best, for the highest volume, although other types may be used.  Depending upon volume, a full charge on the capacitor can last for about 5 hours of low volume loudspeaker listening.

The Amplifier, applied to a crystal radio set: This crystal radio set operates in the same manner as the ones described in Articles #22 (Benodyne version B)and #26 (Benodyne version C) when switches SW7 and SW 8 are in their 'up' positions and SW9 is to the right.  To operate the amplifier, first, supercapacitor C13 must be charged up to at least 1.5 volts.  The manufacturer of the IC specifies a minimum of 1.8 volts, but so far, I have found that 1.5 volts to be sufficient.  To charge C13, set SW7 and SW8 to their 'up' positions, SW9 to the right, and the wiper arm of R3 to the center (see Fig. 1).  Tune in a station that provides between 1.3 and 5 .5 volts DC at the 'Detector bias monitor' terminals.  If the voltage is too low, try changing the antenna impedance matching by optimizing the settings of C7 and C8.  Set SW7 to its down position and C13 will start charging.  If no station exists that is strong enough to supply at least 1.5 volts, C13 may be charged by connecting a series combination of a 4.5 volt battery and a 100 ohm current limiting resistor across it for about 30 minutes.  Make sure the + side of C13 is charged positive.  After C13 is charged, set SW7 to its up position.  The higher the final charged voltage on C13, the higher the maximum volume will be. Non-amplified operation with Sound Powered 1200 ohm headphones:  SW7 and SW8 are up and SW9 is to the right.  R3 is used to optimize DC current in the diode for minimum audio distortion.   Amplified operation with Sound Powered 1200 ohm headphones on very weak signals:  SW7 is up,

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Amplify a crystal radio's output without using batteries or socket power

SW8 down and SW9 is to the right. Amplified operation, driving an 8 of 16 ohm speaker from medium and strong stations:  Operate SW7 to its up position, SW8 down and SW9 to the left.  The speaker will probably give forth with some distorted audio.  To reduce the distortion, try adjusting R3.  If this doesn't help enough, reduce the signal into the amplifier.  The attenuators, controlled by SW1 and/or SW2 can be used to do this (see Fig. 1).  If no SW1 or SW2 is present, reduce the output of the detector by decoupling the antenna (reduce C7 and restore tuning using C8). Switch SW10 provides a tradeoff between maximum volume and current drain.  Switching to the white wire connection gives the, longest listening time, but with a lower maximum volume.  Each listener must make his own choice here.  The current drain from C13 and the life of its charge are directly proportional to the strength of the audio signal and the setting of SW10.  Maximum low-distortion volume is proportional to the voltage charge on C13. For comparison purposes with receiving locations other than mine, there are two 50 kW stations about 10.5 miles from my home. They are WOR and WABC. My attic antenna is described in Article #20.  Either station can deliver about a 5.0 volt charge to C13. This crystal radio set was constructed by modifying a Version 'b' crystal radio set (See Article #22), using the air-mounted, flying joint method of wiring the amplifier components.  A convenient way to connect to the tiny leads of IC1 is to first solder it to a surfboard such as one manufactured by Capital Advanced Technologies (http://www.capitaladvanced.com).  Their models 9081 or 9082 are suitable and are available from various distributors such as Alltronics, Digi-Key, etc.  The amplifier can be built in as an addition to any crystal radio set if proper allowance is made for impedance matching considerations. Charge/discharge considerations for C13:  C13 (0.33 F) will charge close to full capacity after about 24 hours of charging.  The first charge will not last as long as subsequent ones because of a phenomenon known as "dielectric absorption".  If C13 is reduced to 0.1 F, about 8 hours are needed.  Listening time when using headphones should be greater than 24 hours when using 0.33 F, and 10 hours when using a 0.1 F value.  There is a greater current drain on C13 when using a speaker, and the listening time will depend upon the volume setting.  Listening times approximate 10 hours when using a 0.33 F cap and 3 hours when using 0.1 F.

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Amplify a crystal radio's output without using batteries or socket power

Parts List when the crystal radio set used is the that described in Article #22.  The amplifier is easily adapted to the higher performance crystal radio set described in Article #26 as well as others. C1, C3:  200 pF NPO ceramic caps. C2: 100 pF NPO ceramic cap. C4, C6:  270 pF NPO ceramic caps. C5:  18 pF NPO ceramic cap. ** C7, C8:  12-475 pF single section variable capacitors, such as those that were mfg. by Radio Condenser Corp. (later TRW).  They use ceramic stator insulators and the plates are silver plated.  Purchased from Fair Radio Sales Co. as part # C123/URM25.  Other capacitors may be used, but some of those with phenolic stator insulators probably will cause some reduction of tank Q.  The variable capacitors are fitted with 8:1 ratio vernier dials calibrated 0-100.  These are available from Ocean State Electronics as well as others.  An insulating shaft coupler is used on C7 to eliminate hand-capacity effects.  It is essential, for maximum sensitivity, to mount C7 in such a way that stray capacity from its stator to ground is minimized.  See Part 9 of Article #22 for info on mounting C7.  The variable capacitors used in this design may not be available now.  Most any other capacitor with silver plated plates and ceramic insulation should do well. C9:  47 pF ceramic cap. C10:  100 nF cap. C11:  1.0 uF non-polarized cap.  This is a good value when using RCA, Western Electric or U. S. Instruments sound powered phones, with their 600 ohm elements connected in series.  The best value should be determined by experiment.  If 300 ohm sound powered phones having their 600 ohm elements connected in parallel are used, C11 should be about 4 uF, and a different transformer configuration should be used. C12:  0.1 uF cap C13:  0.1 to 0.33 F electric double layer capacitor (supercap).  Elna's 0.33 F "Dynacap", available from Mouser as #555-DX5R5H334 or Panasonic's 0.033 F "Gold" capacitor #EEC-S0HD334H, https://web.archive.org/web/20131030052209/http://www.bentongue.com/xtalset/25AmpXS/25AmpXS.html[06.08.2019 20:14:01]

Amplify a crystal radio's output without using batteries or socket power

available from Digi-Key etc. are suitable.  Do not use an ordinary electrolytic cap in this application.  Its leakage current will probably be so great that C13 can only charge to a low voltage, and it won't be able to hold a charge anywhere near as long as a supercap.  A 0.33 F supercap will charge more slowly, but it will last longer than on a 0.1 F supercap. C14:  1.0 nF ceramic cap C15:  470 nF plastic film cap. (polyester or mylar) C16:  10 nF ceramic cap (Connect with short leads across + and - supply voltage terminals of IC1.) ** L1, L2, L3 and L4:  Close coupled inductors wound with uniformly spaced teflon insulated 18 Gage silver plated solid wire.  This wire is used only to gain the benefit of the 0.010" thick lowloss insulation that assures that no wandering turns can become 'close-spaced'.  L1 has 12 turns, L2 has 8 turns, L3 has 6 turns and L4 has 14 turns.  The coil form is made of high-impact styrene.  I used part #S40160 from Genova Products (http://genovaproducts.com/factory.htm).  A piece of plastic drain pipe of the same OD, made of ABS, can also be used, with the same results.  PVC pipe will result in somewhat less selectivity and sensitivity.  See Fig. 6 for hole drilling dimensions.   IC1:  Texas Instruments micropower opamp OPA349UA (Formerly a Burr-Brown product.)  Here is a link to the data sheet for this IC: http://www-s.ti.com/sc/ds/opa349.pdf   A convenient way to connect to the tiny leads of IC1 is to first solder it to a surfboard such as one manufactured by Capital Advanced Technologies (http://www.capitaladvanced.com).  Their models 9081 or 9082 are suitable and are available from various distributors such as Alltronics, Digi-Key, etc. SW1, 2, 7 and 9:  DPDT general purpose slide switches. **SW3, 4, 5 and 6:  Switchcraft #56206L1 DPDT mini Slide switches.  This switch has unusually low contact resistance and dielectric loss, but is expensive.  Other slide switches can be used, but may cause some small reduction of tank Q. SW8:  3P2T slide or other type switch. SW10:  3 position rotary switch. T1, T2:  Calrad #45-700 audio transformer.  Available from Ocean State Electronics, as well as others.  If 300 ohm phones are to be used, see the third paragraph after Table 1. T3:  Bogen T725 4 watt P/A transformer.  Available from Lashen Electronics, Grainger or other sources (http://www.lashen.com/vendors/bogen/Speaker_Transformers.asp) R3:  1 Meg linear taper pot. R4:  10k resistor R6, R7:  10 Meg resistors.  For minimum waveform clipping in IC1, values of R5 and R7 should be selected to be within 5% of each other. R8, R9:  2.2 Meg resistors.  For minimum waveform clipping in IC!, values of R8 and R9 should be selected to be within 5% of each other. R10:  10 Meg resistor Baseboard:  12'' wide x 11 1/8 '' deep x 3/4" thick. Front panel:  0.125" thick high-impact styrene.  Other materials can be used.  I was looking for the lowest loss, practical material I could obtain. **  For lower cost, the following component substitutions may be made:  Together they cause a small reduction in performance at the high end of the band (1.75 dB greater insertion power loss and 1.5 kHz greater -3 dB bandwidth).  The performance reduction is less at lower frequencies. Mini air-variable 365 pF caps sold by many distributors such as The Crystal Set Society and Antique Electronic Supply may be used in place of the ones specified for C7 and C8. 18 Ga. "bell wire" supplied by many distributors such as Home Depot, Lowes and Sears may be used in place of the teflon insulated wire specified.  This  vinyl insulated non-tinned copper wire is sold in New Jersey in double or triple twisted strand form for 8 and 10 cents per foot, respectively.  The cost comes out as low as 3 1/3 cents per foot for one strand.  The main catch is that one has to untangle and straighten the wires before using them.  I have used only the white colored wire but I suppose the colored strands will work the same (re dielectric loss).  The measured OD of strands from various dealers varied from 0.065 to 0.079".  The extra dielectric loss factor of the vinyl, compared to the teflon will cause some reduction of sensitivity and selectivity, more at the high end of the band than the low end.   Radio Shack mini DPDT switches from the 275-327B assortment or standard sized Switchcraft  https://web.archive.org/web/20131030052209/http://www.bentongue.com/xtalset/25AmpXS/25AmpXS.html[06.08.2019 20:14:01]

Amplify a crystal radio's output without using batteries or socket power

46206LR switches work fine in place of the specified Switchcraft 56206L1 and cost much less.  See Article #24 for comparison with other switches.  Any switch with over 4 Megohms Rp shown in Part 2 of Article #24 should work well as far as loss is concerned.  Overall, losses in the switches have only a very small effect on overall performance. #25  Published: 07/04/2002; Revised and renamed: 02/25/2003 060610

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Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank http://www.bentongue.com/xtalset/26St4bXc/26St4bXS.html Go

DEC OCT JUL

30

40 captures

2010 2013 2015

20 Sep 2007 - 30 Dec 2018

⍰

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▾ About this capture

Highly sensitive and selective single-tuned fourband crystal radio set using a new contra wound dual-value inductor, and having a 'sharp selectivity setting'; along with a way to measure the unloaded Q of an L/C resonator By Ben H. Tongue

Summary:  This article describes Version 'c' of a single-tuned four-band crystal radio set, sometimes called a "Benodyne" (constant bandwidth with maximum weak-signal sensitivity across the whole BC band, achieved by using 2 or more values of inductance in the tank - lower values at higher frequencies).  It is designed for a constant bandwidth across the AM band, two selectivity settings (normal and sharp) and low loss (high sensitivity) especially for weak signals at the high end of the band.  It is an attempt to achieve the two objectives at a -3 dB RF bandwidth of about 5-6 kHz (relatively independent of signal strength), with a constant high efficiency across the entire AM broadcast band (normal selectivity setting):  1) Best possible sensitivity on weak signals,  2) Loudest possible volume on strong signals.  The sharp selectivity setting reduces the -3dB bandwidth to about 2 kHz, but unavoidably introduces some extra insertion power loss. Selectivity and insertion power loss figures from a computer simulation are given and compared with those of the actual physical crystal radio set.  A way to tell if the detector is operating below, at or above its 'Linear-toSquare Law Crossover point' (LSLCP) is described.  See Article #15a for a discussion of LSLCP.  No antenna tuner is necessary for the average outdoor or attic antenna.  An explanation of 'short wave ghost signals' and 'hash' is provided along with some suggestions on how to combat them.  Version C uses a tank coil constructed with litz wire, as compared to the solid teflon insulated wire used on version 'B'.  A new way to make a higher Q, low inductance coil is described. Some additional benefits of the "Benodyne" type of tank circuit are: (1) Reduction of the the sharp drop in tank Q or sensitivity at the high frequency end of the BC band often experienced when only one value of tank inductance is used for the whole BC band. (2) Reduction of the tank Q loss from the variable cap when using lower cost units that use phenolic insulation, such as the common 365 pF cap (see Figs. 2, 3, and 4 in Article #24).  The "two inductance value benodyne* circuit is used in the crystal radio sets in Articles #22 and #26.  We will assume here that the two "benodyne" component inductors (see "The Tank Inductor" in this Article) provide a tank inductance of 250 uH in the low frequency half of the BC band (520-943 kHz) and 62.5 uH in the high half (0.943-1.71 MHz).  If the large 250 uH inductance setting were used all the way up to the top end of the BC band (as in the usual case), a total tuning capacity of 34.7 pF would be required at 1.71 MHz (Condition A). In the "Benodyne" circuit, with the 62.5 uH inductance setting used for the high frequency half of the BC band, a total tuning capacitance of 139 pF is required at 1.71 MHz (Condition B).  Benefit (1) occurs because in condition A, a larger fraction of the total tuning capacitance comes from the typically low Q distributed capacity of the inductor than in condition B.  This results in a higher Q total capacitance in condition B than in condition A.  Benefit (2) occurs because the effective Q of a typical 365 pF variable cap, when used with a 250 uH tank, is about 500 at 1.71 MHz (see Fig. 3 in Article #24).  The Q of the 365 pF variable cap, when set to 139 pF, is greater than 1500 (see Fig.5 in Article #24).  This higher Q results in less loss and greater selectivity at the high end of the BC band in condition 2.  A further benefit of the Benodyne circuit at the high

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Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

end of the BC band is greater immunity from the Q reducing effects of surrounding high loss dielectric materials such as baseboard etc.  The lossy stray capacity introduced is better swamped out by the high shunt tuning capacity used.  

The Crystal Radio Set Design, in a (large) Nutshell: The design approach is to divide the AM band into several sub-bands in an attempt to keep the selectivity relatively constant and the insertion power loss low across the whole band. The first step is to divide the BC band into two halves: band A (520-943 kHz) and band B (943-1710 kHz).  Two-step shunt inductive tuning is employed to switch between bands.  A tank inductance of 250 uH is used in band A and 62.5 in and B.  Band A is further subdivided into two bands: sub-bands 1 (520-700 kHz) and 2 (700-943 kHz).  The band B is also subdivided into two bands: sub-band 3 (943-1270 kHz) and 4 (1270-1710 kHz). In the normal selectivity mode, two different resonant RF resistance levels, measured at the top of the tuned circuit (point 'A' in Fig. 5), are used at the center of the sub-bands.  This impedance level is about 125k ohms at the center of sub-bands 1 and 3.  It is 250k at the center of sub-bands 2 and 4 (excluding the resistive losses of the components used).  These resistance values are made up of a parallel combination of the transformed RF antenna-ground system resistance and the input RF resistance of the diode.  These two resistances should be equal to each other to achieve minimum insertion power loss, at the design bandwidth.  This means that the transformed antenna-ground system and diode RF resistances are each about 250k in sub-bands 1 and 3 and 500k in sub-bands 2 and 4 at point 'A'.  The two different transformed RF antenna-ground system resistance values are achieved by proper adjustment of a variable capacitor in series with the antenna (C7 in Fig. 5).  The higher diode RF tank loading resistance value for sub-bands 2 and 4 are achieved by tapping the diode onto the tank at a point that is 70% of the turns up from ground.  The tank is not tapped for sub-bands 1 and 3 and connection is to the top of the tank.  In the sharp selectivity mode the diode is tapped half of the turns down on the tank from the point used for normal selectivity. The weak-signal RF input and audio output resistances of a diode detector are approximately the same and equal to 0.026*n/Is ohms (Is means diode saturation current, see Article #0-Part 4).  The strongsignal audio output resistance of a diode detector is approximately equal to 2 times the RF resistance of its source.  Compromise audio impedance transformation ratios are used to optimize performance on both weak and strong signals. The design is scalable.  Less expensive parts that may have somewhat greater losses may be used with some penalty in sensitivity and selectivity, especially at the at the high end of the BC band and at the Sharp Selectivity setting.  See the Parts List for a listing of some more easily available and lower cost parts than the ones used in the original design.

Fig. 1 - Single-Tuned Four-Band Crystal Radio Set, Version 'C'.  These are actually pictures of Version B as described in Article #22, converted to version C, as described in this Article, but modified with the addition of the amplifier in Article #25.  This Article does not include the amplifier.

Design objectives: A relatively constant -3 dB bandwidth of  5 to 6 kHz across the full range of 520 to 1710 kHz at normal selectivity, with a relatively constant RF power loss in the RF tuned circuits of less than 3 dB. A switched adjustment to achieve about 3 times sharper selectivity than normal. https://web.archive.org/web/20131030052212/http://www.bentongue.com/xtalset/26St4bXc/26St4bXS.html[06.08.2019 20:15:03]

Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

Optimal performance with external antenna-ground systems having a fairly wide range of impedance. To provide a simple-to-use switching setup for comparing a 'test' diode with a 'standard' one.  To provide a volume control with a range of 45 dB in 15 dB steps that has the minimal possible effect on tuning,   This was incorporated in the design because the two local 50 kW blowtorch stations WABC and WOR (about 10 miles away) deliver a very uncomfortably loud output from SP headphones from my attic antenna.  A means of volume reduction that did not reduce selectivity was needed.  This method of volume reduction actually increases selectivity by isolating antenna-ground resistance from the tank circuit.  Introduction fo a new (to me) method for constructing low inductance high Q coils.

1. Theory

The frequency response shape of the circuit shown in Fig. 2 is that of a simple single tuned circuit and can be thought of as representative of the nominal response of a single tuned crystal radio set.  Consider these facts: 1. If Lt and Ct have no loss (infinite Q), zero insertion power loss occurs at resonance when Rs equals Rl. This is called an 'impedance matched' condition.  The power source (Vs, Rs), looking towards the tank, sees a resistance value equal to itself (Rl).  Also, the load (Rl), looking towards the input sees a resistance (Rs), equal to itself.  In the practical case there is a finite loss in Lt and CT  This loss can be represented by an additional resistance Rt (not shown), shunted across the tuned circuit.  The input resistance seen by (Vs, Rs) is now the parallel combo of Rt and Rl and it is less than Rs  The perfect impedance match seen by (Vs, Rs) when the tank Q (Qt) was infinite is now destroyed.  The impedance matched condition can be restored by placing an impedance transformation device between the source, (Vs, Rs) and the tank. 2. In Fig. 2, if tuning could be done with Lt alone, leaving CT fixed, the bandwidth would be constant.  The problem here is that high Q variable inductors that can be varied over an approximately 11:1 range, as would be needed to tune from 520 to 1710 kHz do not exist.  On the other hand, tuning by varying CT by 11:1 will cover the range, but have two disadvantages.  (1) The -3dB bandwidth will vary by 1:11 from 520 to 1740 kHz.  (2) In the practical case, if the bandwidth is set to 6 kHz at the low end of the BC band, and an attempt is made to narrow the bandwidth at 1710 kHz by placing a capacitor in series with the antenna, the insertion power loss will become great. 3. The compromise used here is a coil design that can be switched between two inductance values differing by 4:1.  The high inductance setting is used for the low half of the BC band and the low inductance for the high half.  Capacitive tuning is used to tune across each half.  The new technique used here, of using a combination of two inductors, enables the Q of the low value inductance (used in the high half of the band) to to be much higher than would be the case if a single coil of the same diameter and wire size, but with fewer turns, were used.  This technique uses two coils, closely coupled, and on the same axis.  They are connected in series to obtain the large inductance and in parallel for realization of the small one.  The small inductance has a value 1/4 that of the large one and about the same Q at 1 MHz. (if coil distributed capacity is disregarded).  The innovation, so far as I know, is to use the full length of wire used in the high inductance coil, occupy the same cubic volume, but get 1/4 the inductance and keep the same Q as the high inductance coil (at the same frequency).  See Table 4. 4. The high and low bands are each further subdivided giving a total of four sub-bands (1, 2, 3 and 4).  If this were not done, we would be faced with a bandwidth variation of about 1:3.3 in each band.  The geometrically subdivided bands are: sub-band 1 (520-700 kHz), 2 (700-943 kHz), 3 (943-1270 kHz) and 4 (1270-1710 kHz).  The bandwidth should vary about 1:1.8 across each of these sub-bands.  The bandwidths at the center of each of the four sub-bands are made approximately equal to each other by raising the loading resistance of the antenna-ground system and the diode on the tank by a factor of two in sub-bands 2 and 4, compared to the value used in sub-bands 1 and 3.

2. Design Approach for the Center of each of the four sub-bands.

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Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

Fig. 3a shows the simplified Standard Dummy Antenna circuit, described in Terman's Radio Engineer's Handbook for simulating a typical open-wire outdoor antenna-ground system in the AM band.  R1=25 ohms, C1=200 pF and L1=20 uH.  See Article #20 for info on how to measure the resistance and capacitance of an antenna-ground system.  These values are used in the design of the crystal radio set.  R1 represents the antennaground system resistance, C1 the capacitance of the horizontal wire and lead-in to ground and L1 represents the series inductance of the antenna-ground system. The values of R1, C1 and L1 in Fig. 3a are considered to be independent of frequency.  To the extent that they may vary with frequency, C7 and C8 in Fig. 4 can be adjusted to compensate.  The current-source equivalent circuit of the antenna-ground circuit is shown in Fig. 3b.  To a first degree of approximation, C2 in Fig. 3b is independent of frequency.  R2 will vary approximately inversely with frequency.  We will ignore the effect of L2, since its value is large, except when approaching the first resonance of the antenna-ground system.  The design approach is to place a variable capacitor C3 in series with the antenna circuit (Fig. 3a) to enable impedance transformation of the antenna-ground circuit to an equivalent parallel RC (Fig. 3b), the R component of which can be adjusted by changing the value of the C3 to follow a desired relationship vs frequency.  One of the objectives of the design is to enable as constant a bandwidth as possible vs. frequency.  This requires the aforementioned equivalent parallel component (R2) to vary proportionally with the square of the frequency if capacitive tuning is used in each sub-band (loaded Q must be proportional to frequency for a constant bandwidth).  The shunt variable capacitor to ground, shown across the tank coil, is used to tune the tank to resonance.  This design attempts to accomplish this in the center of each sub-band.  Performance is close at the band edges.

3. The single tuned crystal radio set The topology of the single tuned circuit is changed from band to band as shown in Fig. 4 below.

Resonant RF resistance values at the top of C8 (Fig. 4) from antenna loading are designed to be: 250k ohms at the center of sub-bands 1 and 3 and 500k ohms for sub-bands 2 and 4.  Since the diode is tapped at the 0.7 voltage point for bands 2 and 4, it sees a source resistance at resonance of: 125k for sub-bands 1 and 3 and of 250k ohms for sub-bands 2 and 4.  These figures apply for the theoretical case of zero loss in the tuned circuit components (infinite Q).  In a shunt capacitively tuned crystal radio set, loaded with a constant resistive load, the bandwidth will vary as the square of the frequency.  To understand why, consider this:  When the resonant

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Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

frequency of a tuned circuit loaded by fixed parallel resistance is increased (from reducing the total circuit tuning capacitance), the shunt reactance rises proportionally, giving rise to a proportionally lower circuit Q.  But, a proportionally higher Q is needed if the bandwidth is to be kept constant.  Therefore, the square relation. In the practical case, we are faced with two problems.  (1) How should we deal with the fact we work with finite Q components?  (2) At high signal levels (above the LSLCP), the RF load presented by the diode to the tuned circuit is about 1/2 the audio load resistance, and at low signal levels (below the LSLCP) the RF load presented by the diode is about 0.026*n/Is ohms.  Compromises are called for.

Parts List - All components are chosen for the best possible sensitivity at a -3 dB RF bandwidth of 5-6 kHz. C1, C3:  200 pF NPO ceramic caps. C2: 100 pF NPO ceramic cap. C4, C6:  270 pF ceramic caps. C5:  18 pF NPO ceramic cap. ** C7 (Antenna cap.), C8 (Tank cap.):  12-475 pF single section variable capacitors, such as those that were mfg. by Radio Condenser Corp. (later acquired by TRW).  They use ceramic stator insulators and the plates are silver plated.  Purchased from Fair Radio Sales Co. as part #C123/URM25.  Other capacitors may be used, but those with phenolic stator insulators will cause some reduction of tank Q, especially at the high end of sub-band 4.  The variable capacitors are fitted with 8:1 ratio vernier dials calibrated 0-100.  These are available from Ocean State Electronics as well as others.  An insulating shaft coupler is used on C7 to eliminate hand-capacity effects.  It is essential, for maximum sensitivity and selectivity, to mount C7 in such a way that stray capacity from its stator to ground is minimized.  See Part 11 for info on mounting C7.  The variable capacitors used in this design may not be available now.  Most any other capacitor with ceramic insulation should do well.  Note: If one has available two capacitors having different losses for use as C7 and C8, the best one should be used for C8 since the sensitivity of this crystal radio set is less affected by a Q reduction of C7 than of C8. C9:  47 pF ceramic cap. C10:  0.1 to 0.22 uF cap. C11:  Approx. 1.0 uF non-polarized cap.  This is a good value when using RCA, Western Electric or U. S. Instruments sound powered phones with their 600 ohm elements connected in series.  The best value should be determined by experiment.  If 300 ohm sound powered phones having their 600 ohm elements connected in parallel are used, C11 should be about 4 uF and a different transformer configuration should be used. **L1, L2, L3, L4, and L5:  See "The tank inductor" below. **SW1, SW2 and SW6:  DPDT general purpose slide switches.  Radio Shack mini DPDT switches from the #275-327B assortment or Switchcraft #46206LR are relatively low loss units. **SW3 (Used to switch between bands A and B):  5 position two pole ceramic insulated with silver plated contacts rotary switch, used as a 2 position 2 pole switch. For low loss, it is essential that the switch use ceramic insulation.

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Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

**SW4 (Used to select a sub-band and switch between normal and sharp selectivity):  5 position single pole ceramic insulated rotary switch.  For low loss, it is essential that the switch use ceramic insulation. **SW5:   Switchcraft #56206L1 DPDT mini Slide switch.  Used as a SPDT switch.  This switch has unusually low contact resistance and dielectric loss, but is expensive.  Other slide switches can be used, but may cause some reduction of tank Q. T1, T2:  Calrad #45-700 audio transformers.  Available from Ocean State Electronics, as well as others.  If 300 ohm phones are to be used, see "Audio impedance transformation", below. R3  (used to adjust the resistive load on the diode): 1 Meg Pot., preferably having a log taper. Baseboard:  12'' wide x 11 1/8 '' deep x 3/4" thick. Front panel is made of 0.1" thick high-impact styrene.  Other materials may be used.  This is the the lowest loss practical material I could obtain. **  For lower cost, the following component substitutions may be made:  They cause a reduction in performance at the high end of the BC band, especially, sub-band 4 when the "narrow selectivity" setting is used.  Performance reduction is much less in the lower sub-bands and in the "normal selectivity setting. Mini air-variable 365 pF caps sold by many distributors such as The Crystal Set Society and Antique Electronic Supply may be used in place of the ceramic insulated ones specified for C7 and C8.  Their maximum capacitance of 365 pF may not be large enough to enable achieving the design bandwidths at the lower end of bands A and B, especially when short antennas are used.  This problem can be solved by making provision for switching a 220 pF NPO (sometimes called COG) disc capacitor across C7 and C8 when tuning to these frequencies. Radio Shack mini DPDT switches from the 275-327B assortment or standard sized Switchcraft 46206LR switches may be used in place of the Switchcraft 56206L1 specified for SW5 and cost much less.  See Article #24 for comparison with other switches. Molded plastic insulated rotary switches may be used for SW3 and SW4, such as those made by Lorin and sold by Mouser and others. Wiring the crystal radio set:  The stator and rotor terminals of C8 are labeled points A and B (see Fig. 5), and all connections to them should be short and direct.  The purpose is to minimize spurious FM and short-wave resonances which might be created otherwise.  This approach eliminates as much wiring inductance associated with C8 as possible, maximizing its ability to shunt out any high frequency spurious responses that might be present.  Some more info on this subject is presented near the end of part 8. The 'contra wound' tank inductor: L1, L2, L3 L4 and L5 are all components of the tank.  It is wound with litz wire having 660 strands of #46 conductor.  L1 has 13 turns, L2 has 3.125 and L3 has 8.875, all close wound (because the form is not long enough to enable spacing and the extra turns that would be required to maintain the inductance) as component inductor #L(1,2,3) with two taps.  L4 has 7.25 turns and L5 has 17.75, both close wound as component inductor #L(4,5) with one tap. The start of L1 of component inductor #L(1,2,3) is spaced 0.06" to the right of the center of the coil form, looking at the crystal radio set from the front and winding continues through L2 and L3 clockwise to about 0.25" of the right end of the form, looking at the crystal radio set from the right.  The start of L4 of component inductor #L(4,5) is spaced 0.06" to the left of the center of the form, looking at the crystal radio set from the front and winding continues through L5 clockwise to about 0.25" of the left end of the form, looking at the crystal radio set from the right.  When one looks at a completed contra wound inductor, one can see that the component inductors #L(1,2,3) and #L(4,5) are wound in opposite directions.  Note: All coil dimensions are measured from turn center to turn center.  See Article #0, Part 12 for a mini-Article about the purpose and use of the 'contra wound' inductor.  Figures 2 and 3 in Article #29 provide more info on the contra wound inductor approach. Here is the reason for this winding scheme:  One can see from Fig. 4 that this crystal radio set design connects component inductors #L(1,2,3) and #L(4,5) in series for the lower half of the BC band and in parallel for the upper half.  If the two coils were wound in the same direction from the hot to the cold end, as was done in the crystal radio set described in Article #22, distributed capacitance would be low in the series connection (about 7.7 pF) and higher in the parallel connection (about 21 pF), mainly because the finish (ground end) of

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Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

component inductor #L(1,2,3) is located close to the start (hot end) of component inductor #L(4,5).  This reduces the Q at the high end of the BC band.  If the coils are contra wound, as I call it, the lower distributed capacitance condition occurs in the parallel, not the series connection, resulting a Q increase of approximately 17% at 943 kHz.  It is increased even more at the high end of the BC band.  The coil form is made of highimpact styrene.  OD=4.5", ID=4.22" and length=3.625".  I used part #S40140 purchased from the Genova Products factory retail store.  (http://genovaproducts.com/factory.htm).  A PVC form can be used, but its dielectric has about 4-5 times the loss of the styrene form and will reduce Q, especially at the high end of the BC band. The start (hot) ends of L1 and L4 are affixed to the form by being lead through two 0.25" diameter holes placed 0.5" apart, measured in the circumferential direction, and held in place by 0.5" wide film tape on the inside of the form.  The finish (cold) ends of L3 and L5 are affixed to the form by being lead through two 0.125" holes placed 0.5" apart, measured in the circumferential direction, and held in place as above.  Three 0.125" diameter holes spaced 0.5" apart are used when pulling a tap.  In Fig. 6, the red line represents the litz wire and the yellow arcs represent a cross-section of the coil form through the center of the 0.125 or 0.25" holes.

Fig.7  Coil mounting hardware. To wind the tank coil, first cut five pieces of 660/46 litz as follows:  For L1: 16' 9",  L2: 4' 3",  L3: 11' 10",  L4: 9' 11" and L5: 22' 5".  These lengths provide about 9" of free length at each end.  The ends of each wire length https://web.archive.org/web/20131030052212/http://www.bentongue.com/xtalset/26St4bXc/26St4bXS.html[06.08.2019 20:15:03]

Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

should be tinned to prevent unraveling of the strands and serving while winding the coils.  Use a small Weller WC-100 adjustable temperature iron (or equivalent), set to maximum temperature (really hot!) for tinning.  The method is to immobilize an end of the wire end by extending it about 2" over the end of a table and placing a weight on top of it.  One can then apply the very hot iron tip to the cut strand ends and feed in a little solder to wet them.  As the heat percolates down the litz and the insulation burns off or melts, more solder can be applied a little further down and around the end to obtain a solid tinning for a lead length of about 0.25".  If one don't want an inch or so of litz beyond the solder to become stiffened from melted insulation, one might do as John Davidson has suggested.  He tightly wraps a length of aluminum foil around the litz, up to 0.375" from the end before soldering to act as a heat sink and keep the insulation cool.  I haven't tried this out. The start leads of L1 and L4 should be spaced 0.06", right and left from the longitudinal center of the coil form.  One can use a bent up plastic soda straw in the 0.25" holes to keep the wires approximately in place).  Gradually taper the wires further apart going through the first turn, then to become close wound for the remainder of the windings.

Table 1 - Longitudinal locations for the taps and start/finish of L1, L2. L3, L4 and L5. Coil name Start - inches to right or left of center Finish - inches to right or left of center L1

0.058 R

0.81 R

L2 L3 L4

0.81 R 0.99 R 0.058 L

0.99 R 1.50 R 0.48 L

L5

0.48 L

1.50 L

After the windings are completed, one should have a coil with ten droopy wires coming from it.  The next step is to tidy up the coils, adjust the 0.12" wire spacing at the start of L1 and L4 and their one-turn taper. Move any excess winding space to slightly space-wind the last several turns of L3 and L5 at their finishes (cold ends).  The turns should then be sprayed with one light application of crystal clear "Krylon" acrylic lacquer, RustOleum Specialty high luster lacquer coating (clear) or equivalent, to hold them in place.  The ends of L1 through L5 that are to be joined to form the taps should be cut to a length of about 0.5", tinned and soldered together as shown in Fig. 6.  Pigtails for wiring to the switches should now be soldered to the taps.  The coil form should be mounted with its axis parallel to the front panel as shown in Fig.1, its center about 6.50" back, and centered horizontally. Tank coil specs. for those who wish to use a different diameter coil form, axial length of total winding, wire size or wire to wire spacing: 1.  The total tank inductance, measured from point A to ground, should be 250 uH with SW3 in position 1 and 62.5 uH in position 2.  Optimum partitioning of turns:  L1 should comprise 26.1% of the sum of the turns of L1, L2, L3, L4, and L5;  L2: 6.15%;  L3: 17.75%;  L4: 14.5% and L5: 35.5%.  To get the highest Q in sub-bands 3 and 4 it is essential that the sum of the turns of L1, L2 and L3 equals the sum of the turns of L4 and L5.  The values for L1 and L2 are compromises when SW3 is set to position 2 (normal selectivity on sub-bands 1 and 3).  They minimize the error caused by using the same number of turns to ground at that setting.  See Table 2. 2. It is desirable that the start and finish ends of the coils on the form (as mounted) should be located on that half of the coil form nearest the front panel.  This will prevent taps from being located on the far side of the coil, as viewed from the front panel, thus preventing excessive lead lengths. 3. Some experimentation in tradeoffs of the requirements in 1.) and 2.) may have to be made, since they may not be fully compatible. The diode:  This design is optimized for use with a diode having an n of 1.03 and a Saturation Current (Is) of about 106 nA at 25° C., although this is not critical and other diodes can be used with very good results.  See Articles  #0, 4 and 16 for info on n and Is of diodes, and how to measure them.  If one has a favorite diode, its effective (Is) can be changed by applying a DC bias voltage, using perhaps, the 'Diode Bias Box' described in Article #9.

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Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

An excellent diode to use in this set is the ITT FO-215 germanium unit that was made 20 or so years ago (see Article #27).  NOS may be available from from Dave Schmarder at http://www.1n34a.com/catalog/index.htm and Mike Pebble at http://www.peeblesoriginals.com Another suitable diode, the published parameters for which show an (Is) of 100 nA is a Schottky diode, the Agilent HBAT-5400.  It is a surface-mount unit that was originally designed for transient suppression purposes.  Measurements of many HBAT5400 diodes seem to show that there are two varieties.  One type measures approximately: n=1.03 and (Is)=80 nA  The other type seems to have an n of about 1.16 and an (Is) of about 150 nA  Both work well but the former works best.  This part, available in an SOT-23 package is easily connected into a circuit when soldered onto a "Surfboard" such as manufactured by Capital Advanced Technologies (http://www.capitaladvanced.com/), distributed by Alltronics, Digi-Key and others.  Surfboard #6103 is suitable.  The HBAT5400 is also available in the tiny SO-323 package that can be soldered to a 330003 Surfboard. The Agilent HSMS-2860 microwave diode (Specified Is=50 nA) is available as a single or triple with three independent diodes in the SO-323 and SO-363 packages, respectively.  The Agilent number for the triple diode is HSMS-286L.  I find it to be particularly good for DX in this crystal radio set.  It is a convenient part since one can connect it using only one section (shorting the unused ones) or with two or all three in parallel.  This gives one a choice of nominal saturation currents of 50, 100 or 150 nA  Samples of this part I have tested measured about 35 nA per diode, not 50.  I don't know the normal production variations.  The only disadvantage of this diode, as far as I know, is its low reverse breakdown voltage which may cause distortion and low volume on very loud stations.  It has the advantage, as do most Schottkys, of having much less excess reverse leakage current than do germanium diodes.  This helps with volume and selectivity on very weak stations. Infineon makes a BAT62 Schottky diode in several different small surface mount packages.  The single BAT62 is physically the largest and easiest to handle.  It has a specified (Is) of about 100 nA and performs quite well. Most germanium diodes have too high a saturation current for the best selectivity when receiving weak signals and should to be back-biased or cooled for optimum performance, although the difference is usually hard to notice.  See Article #17A for more info on this. Different type diodes may be connected  to the terminals labeled Diode #1 and Diode #2, with either one selectable with SW5. When one diode is selected, the other is shorted.  This feature makes it easy to compare the performance of a 'test' diode with one's 'favorite' diode. Another use is to place one's best DX diode in one position and one having a very low reverse leakage current at high reverse voltages in the other.  This will maximize volume and minimize audio distortion on strong signals. A good choice for this crystal radio set is a diode having a relatively low saturation current such as 3 or 4 Agilent HSMS-2820 or HSMS-2860 diodes in parallel as Diode #1 for high selectivity and sensitivity on weak signals, and an Agilent HBAT5400 or one of the lower saturation current germaniums as Diode #2 for low distortion and maximum volume on very strong stations.  Don't use two diodes in series if you want the best weak signal sensitivity in any crystal radio set.  The result of using two identical diodes in series is the simulation of an equivalent single diode having the same (Is) but an n of twice that of either one.  This reduces weak signal sensitivity. Different type diodes may be connected  to the terminals labeled Diode #1 and Diode #2, with either one selectable with SW5. When one diode is selected, the other is shorted.  This feature makes it easy to compare the performance of a 'test' diode with one's 'favorite' diode. Another use is to place one's best DX diode in one position and one having a very low reverse leakage resistance at high reverse voltages in the other.  This will maximize strong signal volume and minimize audio distortion. Audio impedance transformation: from the audio output resistance of the diode detector to 'series connected' 1.2k ohm sound-powered phones is provided by the audio transformers.  If one wishes to use 300 ohm soundpowered phones with two 600 ohm elements connected in parallel instead of series, a very good low loss transformer choice is the 100k-100 ohm transformer from Fair Radio Sales, #T3/AM20.  The configuration of two Calrad transformers shown on line 2 of the Calrad chart in Article #5 is also a good choice.  C11, along with the shunt inductance of the transformer and the inductance of the sound powered phones form a high-pass

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Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

filter, flat (hopefully) down to to 300 Hz.  R3 is used to adjust the DC resistance of the diode load to the AC impedance of the transformed effective AC headphone impedance to minimize audio distortion on very strong signals.  C10 is an audio bypass. The two variable capacitors C7 and C8: interact substantially when tuning a station.  C7 mainly controls the selectivity and C7 and C8 together control the resonant frequency.  Reducing the capacitance of C7 increases selectivity.  If the antenna-ground system has a resistance larger than 25 ohms, C7 will have to be set to a smaller capacitance in order to maintain the proper resonant resistance at point A in Fig. 5.  If the capacitance of the antenna-ground system is greater than 200 pF, C7 will also have to be set to a lower value than if it were 200 pF.  If the maximum capacitance of the capacitor used for C7 used is not large enough to enable a large enough bandwidth at the low end of sub-band 1, provision can be made to switch a 330 pF NPO ceramic cap in parallel with it.  This may be needed if the antenna-ground system has too low a capacitance (small antenna). The "capacitive" attenuators controlled by SW1 and SW2: Used for volume and selectivity control and are are designed so as to cause minimal tank circuit detuning when the equivalent circuit of the antenna-ground system has the same values as the old IRE simplified Dummy Antenna recommended for testing Broadcast Band radio receivers.  It consists of a series combination of a 200 pF cap, 20 uH inductor and a 25 ohm resistance.  The geometric mean of the sum of the reactances of the capacitor and inductor at 520 and 1710 kHz is -605 ohms.  This is the reactance of a 279 pF capacitor (characteristic capacitance of the "capacitive" attenuator) at 943 kHz, the geometric mean of the BC band of 520-1710 kHz.  The "capacitive" attenuators were designed for the specified attenuation values (15 and 30 dB) utilizing the 500 ohm resistive pi attenuator component values table shown in the book "Reference Data for Radio Engineers".  The resistor values for 15 and 30 dB "capacitive" attenuators were normalized to 605 ohms, then the "capacitive" attenuator capacitor values were calculated to have a reactance, at 943 kHz, equal to the value of the corresponding "capacitive" attenuator shunt or series resistance.  Since the "capacitive" attenuators, when switched into the circuit, isolate the antenna-ground system resistance from the tank circuit, selectivity is increased.  If the series capacitance of the equivalent circuit of one's own antenna-ground system is 200 pF, at 943 kHz, practically no retuning is required. If the equivalent L and C of one's own antenna-ground system differ substantially from those of the simplified IRE dummy antenna used in this design, one can normalize the values of the capacitors used in the "capacitive" attenuators to match one's own antenna-ground system.  A method for measuring the parameters of an antennaground system is shown in Article #20.

Table 2 - Switch Functions for Version C SW1 15 dB volume control "capacitive" attenuator.  'Down' places about 15 dB loss in the input. SW2 30 dB volume control "capacitive" attenuator.  "Down' places about 30 dB loss in the input. SW3

520-943 kHz - Band A (sub-bands #1 and #2) - position 1 943-1710 kHz - Band B (sub-bands #3 and #4) - position 2

520-700 kHz - Band A, sub-band 1.  Normal selectivity: position 2,  Sharp selectivity: position 3 700-943 kHz - Band A, sub-band 2.  Normal selectivity: position 5,  Sharp selectivity: position 4 SW4 943-1270 kHz - Band B, sub-band 3.  Normal selectivity: position 2,  Sharp selectivity: position 1 1270-1710 kHz - Band B, sub-band 4.  Normal selectivity: position 4,  Sharp selectivity: position 5 SW5 Used to select diode 1 or diode 2. 'Down' position for normal operation using 1.2k ohm phones.  'Up' position to bypass the onboard SW6 audio transformers if one wishes to use an external transformer to match an impedance other than 1.2k ohms.

4. Tuning the Crystal Radio Set to to a specific frequency. C8 is considered the primary tuning control.  C7 is used, in conjunction with the capacity of the antenna-ground system to adjust selectivity to the designed value.  It also has considerable interaction with the tuning frequency.  There are two methods for tuning in a station of a known frequency that will result in the selectivity https://web.archive.org/web/20131030052212/http://www.bentongue.com/xtalset/26St4bXc/26St4bXS.html[06.08.2019 20:15:03]

Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

being fairly close to specification, as shown in table 5.  One requires a knowledge of the capacitance of C8 vs. its dial setting.  The second requires fitting C8 with a knob having a linear calibration of 0-100 over a 180 degree span and having a dial reading of zero at maximum capacity.  To use this method C8 must be as specified in the parts list or an exact equivalent. 1. To tune to a specific frequency, read the necessary capacity for C8 from Fig. 8 and set C8 to that value.  Adjust C7 to tune in the station. -or2. To tune to a specific frequency, read the necessary dial setting for C8 from Fig. 9 and set C8 to that value.  Adjust C7 to tune in the station. It is assumed that the tank inductor has the required 250 and 62.5 uH inductance values and is contra wound as described.  Of course different inductance values can be used to make a good crystal radio set, but the graphs in Figs. 8 and 9 would have to be changed.  It is also assumed, when using the figs. 8 or 9, that the impedance of the antenna-ground system being used is equal to that of the Standard Dummy Antenna.

Fig. 9 - Dial setting of C8 when using the specific variable capacitor specified in the Parts List.

Fig. 8 - Designed capacitance of C8 vs. Frequency

Another method of tuning is to estimate from Table 3 the dial settings for C7 and C8 required to tune to the desired station.  C7 and C8 can then be tuned together higher or lower to actually tune in the station.  If more selectivity is desired, reduce the capacitance of C7 and retune C8.  If the volume is too low, try increasing C7 and decreasing C8.

Table 3 - Tuned frequency in kHz as a function of dial settings, if C7 and C8 are set to the same dial number and SW1 and SW2 are set to 0 and 30 dB, respectively. Dial settings--> Sub-band 1 switch setup, normal selectivity Sub-band 2 switch setup, normal selectivity Sub-band 3 switch setup, normal selectivity Sub-band 4 switch setup, normal selectivity

0

10

20

30

40

50

60

70

80

90

100

386

423

482

560

650

776

867

994

387

424

484

562

658

765

881

1015 1171 1389 1581

765

835

951

1096 1268 1466

1681 1921 2192 2565 2881

773

839

950

1104 1278 1485

1708 1953 2241 2650 2987

1176 1394 1606

5. How to improve selectivity with a relatively small loss in sensitivity, in addition to using the "Sharp Selectivity" switch positions on SW 4. https://web.archive.org/web/20131030052212/http://www.bentongue.com/xtalset/26St4bXc/26St4bXS.html[06.08.2019 20:15:03]

Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

Selectivity can always be increased by reducing the value of C7 and retuning C8.  If neither "capacitive" attenuator is in-circuit, switching one into the circuit will increase selectivity. Selectivity can be increased by changing to a diode having a lower Is than the HBAT5400, such as the Agilent 5082-2835 or HSMS-2820.  A DC bias, applied to the 'Diode Bias' terminals can 'fine-tune' performance.  The diode 'Bias Box' described in Article #9 is useful here.  One can choose less audio distortion and less selectivity by biasing the diode in a more forward direction, or better selectivity, at the cost of more audio distortion  by biasing the diode toward its reverse direction. Experimentation using a position on SW4 that taps the diode further down on the tank than specified in Table 2.

6. 'Loop Effect' of the tank inductor, and how it can be used to tame local 'Blowtorch' stations when searching for DX. One can use local signal pickup by the tank (loop effect) to reduce the effect of interference from strong stations by rotating the crystal radio set about a vertical axis.  The correct angle will generally reduce it.

7.  Just how loud is a station that delivers the amount of power necessary to operate the Diode Detector at its 'Crossover Point between Linear and Square Law Operation'? Many Articles in this series have talked about the 'Linear to Square-Law Crossover' (LSLCP).  Please bear in mind that the LSLCP is a point on a graph of DC output power vs input RF power of a diode detector system.  It is not a point on a graph of DC current vs voltage of a diode.  Two things can be said about a detector when it is fed a signal that operates it at its LSLCP.  (1) A moderate increase of signal power will move the detector into its region of substantially linear operation.  (2) A similar moderate decrease of input power will move it closer to its region of substantially square law operation where a 1 dB decrease of input power results with a 2 dB decrease of output power. The crystal radio set described in this Article is operating at its LSLCP if the rectified DC voltage at the 'Diode Bias' terminals is about 51 mV.  This assumes a diode having an Is of 106 nA and an ideality factor of 1.03 (such as a selected Agilent HBAT5400 or an Infineon BAT62) is used, with R3 is set to 355k ohms.  The audio volume obtained is usually a low to medium, easy-to-listen-to level when using sound power phones.

8. 'Short Wave ghost Signal', 'background hash' and spurious FM reception All single tuned crystal radio sets may be, in fact, considered double tuned (except single tuned loop receivers).  The second response peak arises from resonance between the equivalent inductance of the antenna-ground system and the impedance it sees, in this case, the series combination of capacitors C7 and C8.  This peak usually appears at a frequency above the broadcast band and gives rise to the possibility of strong so-called 'short wave ghost' signal interference when a short wave station has a frequency near the peak . The response at this "ghost" frequency can be made somewhat weaker and moved to a higher frequency if the antenna-ground system inductance is reduced.  One can use multiple spaced conductors for the ground lead to reduce its inductance.  I use a length of TV 300 ohm twin lead, the two wires connected in parallel for this purpose.  Large gauge antenna wire, or spaced, paralleled multiple strands helps to reduce the antenna-ground system inductance (flat top antenna).  If the down-lead is long compared to the ground lead, use multiple, paralleled, spaced conductors to reduce its inductance (similar to using a 'cage' conductor). Another possible cause of 'ghost' signal reception resides in the fact that the response of the so-called single tuned circuit does not continuously drop above resonance as frequency rises, but only drops to a relatively flat valley before rising again to the second "ghost" peak. The frequency response above the main (lower) peak would drop monotonically (true single tuned operation) if the second peak did not exist.  The relatively flat response valley that exists between the two peaks, provides the possibility (probably likelihood) of interference 'hash' if several strong SW stations picked up at frequencies in the valley range.  This also is the cause of a strong local station, above the frequency of a desired station "riding through" and appearing relatively constant even if the tuning dial is moved.  The response should drop at a 12 dB per octave rate above the second peak.  A useful side effect of the response behavior of this type of circuit is that the response below the main resonance drops off at an extra fast rate of 12 dB per octave rate instead of an expected 6 dB. 

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Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

The most effective way to substantially eliminate 'short wave ghost' and hash reception is to go to a doubletuned circuit configuration. Spurious FM reception caused by so-called FM 'slope' detection can occur from close by local FM stations if a spurious FM resonance appears somewhere in the circuitry of a crystal radio set.  If ground wiring is not done properly in the crystal radio set, spurious signals can get into the detector. The thing to do here is to run all the RF and audio grounds to one point as shown in Fig.5.  Sometimes a small disc bypass capacitor, 22 pF or so, placed across the diode will help. Another way to try to reduce FM interference is to put a wound ferrite bead 'choke' in series with the antenna and/or ground leads, if the FM interference is coming in on those leads.  In order not to affect normal BC band reception, the resultant ferrite inductor should have a reasonable Q and a low inductance in the BC band.  It should also exhibit a high series resistance at FM frequencies.  Suitable wound ferrite chokes (bead on a lead) are made by the Fair-Rite Corp. as well as others.  Two types available from Mouser are #623-29441666671 and #623-2961666671.  This suggestion may also help reduce "short wave ghost" signal reception in some cases. Note: See "Wiring the crystal radio set:", in Part 3, above.

9.  Measurements.

Fig. 10 - RF frequency response from antenna to diode center of  sub-band 1, normal selectivity, using the simplified IRE dummy antenna.

input,

Fig. 11 - RF frequency response from antenna to diode input, center of sub-band 4, normal selectivity, using the simplified IRE dummy antenna.

Fig. 10 shows the simulated frequency response at the center of sub-band 1, from the antenna source to the RF input of the diode.  The red graph and figures in the left panel show an insertion power loss of 2.4 dB with a -3 dB bandwidth of 6 kHz, along with the spurious response peak at 4.4 MHz, caused by the antenna-ground system inductance.  The insertion loss at the spurious peak is 15 dB.  The loss in the valley is 40 dB.  The right graph and figures show the Input Return Loss (impedance match) at resonance to be -12.2 dB.  The output return loss (not shown) is the same.  Fig. 11 shows the simulated frequency response at the center of sub-band 4, from the antenna-ground system source to the RF input of the diode.  The red graph and figures in the left panel show an insertion power loss of 4.1 dB with a -3 dB bandwidth of 6 kHz, along with the spurious response peak at 6.9 MHz, caused by the antenna-ground system inductance.  The insertion loss at the spurious peak is 20 dB.  The loss in the valley is 47 dB. The right graph and figures show the Input Return Loss (impedance match) at resonance to be -8.5 dB.  The output return loss is the same. Fig. 10 and Fig.11 are actually simulations of the RF frequency response of version 'b' as described in Article #22.  The response curves of version 'c', described in this article should be the same, with the exception of halving less loss at the peak response points.  This is because of the higher tank Q in version 'c'. https://web.archive.org/web/20131030052212/http://www.bentongue.com/xtalset/26St4bXc/26St4bXS.html[06.08.2019 20:15:03]

Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

Table 4 - Measured unloaded tank Q values.  Antenna and diode disconnected, SW1 and SW2 set to -15 and -30 dB and C7 set to 50 on the dial Band--> Frequency in kHz.--> Measured unloaded tank circuit Q (includes loss in the tuning caps, switches and all other misc. loss)-->

Sub-band 1 Sub-band 2 520 943 1020

1000

Sub-band 3 Sub-band 4 943 1710 1240

940

 

Table 5 - Measured RF bandwidth and power loss @ resonance, at approx. the LSLCP. Diode parameters: Is=106 nA, n=1.03. Output power=15.8 nW=-78 dBW Center frequency in kHz

Insertion loss in -3 dB bandwidth in Insertion loss in dB, -3 dB bandwidth in dB, kHz, normal selectivity sharp selectivity kHz, sharp selectivity normal selectivity

603

6.5

6.3

9.0

1.9

813

7.3

5.0

10.0

2.2

1094

7.5

4.7

12.0

2.2

1474

8.8

5.8

13.5

2.9

The data in Table 5 show the insertion power loss when the crystal radio set is driven by a CW RF signal, with the diode feeding a resistive load of 355k.  R3 is used for the resistive load and is set to 355k (be sure to disconnect any diode connected to the terminals when setting R3 for 355k).  SW6 is set to the 'down' position.  For greatest measurement accuracy, one should short out the series connected primaries of T1 and T2.  The signal generator used in the measurements is adapted to have a source impedance equal to that of the standard IRE simplified dummy load (see Article #11).  The expected diode detector power loss, at the output power level used, is about 5 dB.  The remainder of the insertion loss shown in Table 5 is caused by losses in the inductive and capacitive parts of the tank.  Weaker signals will result in a higher detector power loss, stronger signals, a lower loss.  Some more info on detector power loss and LSLCP is given in Fig. 2 and its succeeding paragraph in Article #15a. The signal level used was chosen to operate an HBAT5400 diode having an Is of 106 nA and an n of 1.03 near its LSLCP.  The input RF voltage was set to cause a DC output voltage of 0.075 volts* across the R3=355k ohms (measured at the 'Diode DC V.' terminals).  This gives an output power of -78 dBW.  The signal generator output was varied, depending on the insertion power loss of the passive components as measurements were made at the different frequencies.  In practice, one should add about 1.0-2.0 dB to the insertion power loss shown in Table #5 to allow for a typical audio transformer loss.  In actual practice, of course, one uses an audio load (headphones), fed through the audio transformer, instead of a resistor for the diode load. *A diode detector is operating at its LSLCP when its DC load resistance is R=n*0.0257/Is and the detected DC across it is 0.051 volts. This CW method of measuring loss is much easier than the more complicated general method using AM modulation, as shown in Article #11.

10.  A method for measuring the unloaded Q of an L/C resonator 1. Connect the 50-ohm output of a precision frequency calibrated RF generator (I used an Agilent digitally synthesized unit.) to a radiating test loop by means of, say, a 5 foot long coax cable.  The loop can be made from 15 turns of solid #22 ga. vinyl insulated wire, bunched up into a ¼" diameter cross section https://web.archive.org/web/20131030052212/http://www.bentongue.com/xtalset/26St4bXc/26St4bXS.html[06.08.2019 20:15:03]

Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

bundle, wound on a 2" diameter vitamin pill bottle.  The coil is held together by several twist-ties. 2. Make sure that all resistive loads are disconnected from the tank.  Remove all potentially lossy nonmetallic and metallic (especially ferrous) material from the vicinity of the coil.  Capacitively couple the probe of a 5 MHz (or greater) scope to the hot end of the L/C tank and set the probe to its 1:1, not its 10:1 setting.  This coupling must be very weak.  This can be done by clipping the scope probe onto the insulation of a wire connected to the hot end of the coil (or a tap) or placing the probe very close to the hot end. 3. Place the 2'' loop on-axis with the coil, about 6'' from its cold (grounded) end.  Tune the generator to fo MHz and adjust the generator output, scope sensitivity and L/C tuning to obtain, say, a 7 division pattern from fo on the scope.  Note the frequency. 4. Detune the generator below and then above fo to frequencies (fl and fh) at which the scope vertical deflection is 5 divisions.  This closely represents a 3 dB reduction in signal.  Record those frequencies.  You may encounter some hum and noise pickup problems and will have to respond appropriately to eliminate them.  It is usually beneficial to conduct experiments of this type over a spaced, grounded sheet of aluminum placed on top of the workbench. 5. Calculate approximate unloaded tank Q.  Qa=fo/(fh-fl).  Calculate the actual Q by dividing Qa by 1.02 to reflect the fact that 5/7 does not exactly equal SQRT (0.5). 6. Try reducing the loop magnetic and probe capacitive coupling, and repeat the measurement and calculation.  If the Q comes out about the same, that shows that the 50 output resistance of the generator and the scope probe loading do not significantly load the tank. 7. Note:  When measuring the Q of an inductor with a Q meter it is common practice to lump all of the losses into the inductor. This includes magnetic losses in the inductor as well as dissipative losses in its distributed capacitance. We generally try to get a grip on tank Q values by measuring the inductor with a Q meter, when one is available. We assume that all the loss that affects the measured Q is magnetic loss. Not so, there is also loss in the dielectric of the distributed capacitance of the inductor. Actually, we are measuring an inductor having a specific Q (at a specific frequency), in parallel with the distributed capacity of the coil. We usually assume that the Q of this distributed capacity is infinite, but it isn't.  The dielectric of the coil form material makes up much of the dielectric of the coil's distributed capacity and is the controlling factor in causing different coil Q readings when using coil forms made up of various different materials. This distributed capacity is in parallel with the tuning capacitor and can have an important effect on overall tank Q at the high end of the band because there, it is paralleled with the small, hopefully high Q, capacitance contribution from the variable cap. At lower frequencies, the dielectric material of the coil form becomes less important since its contribution to the distributed capacity is swamped out by the larger capacitance needed from the tuning capacitor in order to tune to the lower frequencies.

11.  Important information re: maximizing unloaded tank Q, especially at the high end of the band. Every effort should be made to achieve as high an unloaded tank Q as possible in order to minimize RF loss at the desired -3 dB bandwidth (selectivity), and especially when using narrower bandwidths.  Somewhat greater insertion power loss and/or broader selectivity may result if components having a greater dielectric loss than those specified are used.  Sensitive areas for loss are: 1. Q of the coil.  See Table 3 for the Q values realized in the tank circuit. 2. Stator insulation material used in the variable caps C7, C8.  Very important!  Ceramic is best. 3. Skin-effect resistive loss in the variable capacitor plates.  Silver plated capacitor plates have the least loss, brass or cadmium plated plates cause more loss.  Aluminum plates are in-between.  Rotor contact resistance can be a problem. 4. The type of plastic used in slide switches SW1, 2, and 4. 5. Front panel material. 6. Coil form material.  High impact styrene has less dielectric loss than PVC.  Styrene forms are available from Genova Products:  http://genovaproducts.com/factory.htm .  The forms are listed as drain couplers in their "400" series of products. 7. Capacitive coupling from any hot RF point, through the wood base to ground must be minimized because it tends to be lossy and will reduce performance at the high end of band A and band B.  The steps I took to reduce these losses are:  (1) Mounting C7 to the baseboard using strips of 0.10" thick, 0.5" wide and

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Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

1.5" long high-impact styrene as insulators and aluminum angle brackets screwed to the baseboard and (2), wiring these brackets to ground.  This electrically isolates the capacitor formed from the lossy dielectric of the wooden baseboard from the rotor of C7.  Ceramic stand-off insulators can be adapted, in place of the styrene strips for the job.  Another way to mount C7 is to make a mounting plate from a sheet of low loss dielectric material, somewhat larger than C7's footprint, and screw C7 on top of it.  Other holes made in the plate can then be used, along with small brackets or standoffs to mount the assembly onto the baseboard.  Don't forget to wire the metal mounting pieces screwed to the wood baseboard to ground.  These same considerations apply to any metal coil mounting bracket, close to a hot end of the coil, used to mount the coil form to the baseboard.  The bracket should be grounded to short out its capacitance through the wood baseboard to ground. The contra wound coil configuration used in this crystal radio set is very helpful here since both outside ends of the coil, in band B are at ground potential.

12. Appendix:  Design approach for double and single tuned Benodyne versions, as posted to the Discussion Group Rap 'n Tap (edited). Ben H. Tongue Posted - 25 February 2005 15:53;  The Benodyne approach to a double-tuned crystal radio set is shown in Article #23.   The basic circuit is that of a conventional double-tuned circuit operating with equal loaded-Q values for primary and secondary.  I decided to use equal values of inductance for the primary and secondary coils for convenience.  The reason to use the two varicaps, C7 and C8 (in the primary circuit in unit #1), connected as they were in the crystal radio set in Article #22, is to enable an adjustable impedance transformation (vs. Frequency) between the antenna-ground system source resistance (assumed to be 25 ohms) and the top of the tank (point A).  Since the primary and secondary inductors are of the same value and their loaded Q values are designed to be equal, the transformed antenna-ground resistance at the top of the primary tank should be made the same as that at the top of the secondary tank, including loading from the diode.  These values are approximately (at band center):  LoLo band:250k;  HiLo band:500k;  LoHi band:500k;  HiHi band:1000k.  Since the diode RF load is tapped at the 0.707 voltage point for bands HiLo and HiHi, the RF resistance driving the diode is in these cases is 250k and 500k respectively, the same as in the case of the LoLo and HiLo bands.  If the diode was not tapped at the 0.707 voltage point for bands HiLo and HiHi, their bandcenter -3 dB bandwidths would be twice as wide as those of bands LoLo and LoHi.  This equalizes all four band-center bandwidths to the desired value.  If the tank inductance were the same for the four bands, the -3dB bandwidth at the center of the LoHi and HiHi bands would be four times as great as that at the center of the LoLo and HiLo bands.  To correct this condition, the tank inductance in bands LoHi and HiHi is reduced from the 250 uH used in bands LoLo AND HiLo to 62.5 uH. This reduces the -3dB bandwidths at the center of bands LoHi and HiHi so they are the same as the bandwidths at the center of the LoLo and HiLo bands.  There is some conflict in the design of a crystal radio set for best performance on strong signals (well above the "Linearto-square-law crossover point), and one designed for weak signals (well below the "Linear-to-square-law crossover point), when one uses the same diode and audio transformation in both instances.  This is because for strong signals, the RF input resistance of the diode detector is about half the audio load resistance, and the audio output resistance of the detector diode is about 2 times the RF source resistance driving it. The conditions for weak signal reception are different. Both the input RF and the output audio resistance of the diode detector are equal to the axis-crossing resistance of the diode.  This resistance is Rd=0.026*n/Is (see Article #0 for a discussion on this).  The compromise selected was to make the audio load resistance about 325k ohms.  The design is optimized for a compromise diode having an Is of about 100 nA and an n of about 1.03.  This diode has an axis-crossing resistance of 265k ohms.  Most ITT FO-215 diodes have this characteristic. Many others can be used, with little effect on strong signal performance.  The diode has more effect on weak than on strong signal performance.  A ferrite stick inductor could do well for the coil in the antenna tuner (unit #1) if it has a high enough Q. Bear in mind that the secondary coil should be constructed with the 250/62.5 uH contra wound arrangement and the 0.707 voltage taps.  For this unit, the detector tuner, a 365 pF variable cap would be OK; the extra capacitance of a 485 pF capacitor is not necessary.  The inductor for the antenna tuner should be constructed using the contra wound 250/62.5 uH arrangement, but no 0.707 voltage taps are needed. It is possible to build a double-tuned Benodyne using primary and secondary coils of unequal values.  I chose using equal values.  A higher inductance for the primary might give some impedance matching problems at the low end of the LoLo band.  A lower inductance for the secondary would require a lower RF loading resistance

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Crystal Radio Set using a contra wound dual-value inductor; Measurement of unloaded Q of the resonator tank

from the diode, thus requiring a diode having a higher Is.  Look at Fig. 2 in Article #27 to see how weak signal sensitivity is reduced when using diodes having higher values of Is.  For anyone interested in building a single or double-tuned Benodyne, it is suggested that the design be based on version "c" described in this Article, and not version "b", described in Article #22. #26  Published: 02/10/2003;  Revised: 10/23/2006 060610

Return to Index Page of this Section (A)

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Measurements of weak-signal detection efficiency (below the linear to square-law crossover point) of 15 germanium and Schottky diodes based upon their satur... http://www.bentongue.com/xtalset/27MeaXSD/27MeaXSD.html Go

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Measurement of the Sensitivity of a Crystal Radio Set when tuned to a Weak Fixed Signal, as a function of the Parameters of the Detector Diode; including Output Measurements on 15 diode types By Ben H. Tongue

Summary:  This Article shows how the 'weak signal' power loss, from the resultant operation in the square-law region of the detector, of a crystal radio set, varies as a function of the parameters of the diode.  The measurements clearly shown how 'weak signal' detector loss is reduced when diodes having lower values of the product of saturation current and ideality factor are used. This results in obtaining greater volume from weak signals. See Fig. 2.  Actual measurements compare closely to those predicted from equation #5, developed in Article #15A.  It is assumed that the input and output impedances of the detector are reasonably well matched.

Acronyms and Definitions of Terms Apparatus used when Measuring Crystal Radio Set Insertion Power Loss and Selectivity. CRYSTAL RADIO A crystal radio set, such as that described in Article #26 that has the capability of a SET continuously adjustable input impedance transformation. Is Diode Saturation Current in Amps LSLCP(i) Linear-to-Square Law Crossover Point in dBW (referred to the input power) n Diode Ideality Factor Rxc Axis-crossing resistance of a diode.  Rxc=0.026*n/Is.

AMCS

1.  The Measurements: The measurements of output power are made using a simpler and quicker method than that used in Article #11, since a CW instead of a modulated signal is used.  This method involves measuring DC output voltage into a resistive load when the input of the detector is fed from a fixed source of available RF power. A 3.2nW (-84.95 dBW) un-modulated source of available RF power of is applied to the diode for all measurements.  This power level is about 12 dB below the LSLCP(i) of the average diode used in these tests.  An AM broadcast signal of this power level will result in quite a weak sound in SP phones impedance matched to the output of a crystal radio set.  The RF input power is applied through the AMCS described in Article 11.  If the input to it is monitored by a DVM connected to the "T" connector, the AMCS should be considered to be an attenuator having an input resistance of 50 and an output resistance of 30.244 ohms.  Its attenuation is 22.975 dB.  The crystal radio set used in these measurements is described in Article #26.  It was used because its performance has been well characterized and its input impedance can be changed over a wide range.  The output resistor into which the output power is dissipated is R3.  The primary windings of T1 and T2 are shorted when taking measurements. https://web.archive.org/web/20131030052217/http://www.bentongue.com/xtalset/27MeaXSD/27MeaXSD.html[06.08.2019 20:16:34]

❎

Measurements of weak-signal detection efficiency (below the linear to square-law crossover point) of 15 germanium and Schottky diodes based upon their satur...

The measurement procedure, for each diode, consists of applying an RF power source having an available power of 3.2 nW to the diode detector, adjusting the input impedance transformation (C7 and C8 in the crystal radio set described in Article #27) for maximum output voltage and recording that value.

  The input conditioning device (AMCS), used to aid in measurement of input power is shown in Fig. 2 of Article #11.  There, it was used in a procedure to measure input AM sideband and output audio power.  Here it is used as a convenient way to provide an accurate source voltage having a known internal resistance.  A CW signal generator tuned to, say, 1 MHz is connected to the AMCS as the source of RF power.  If the generator has an AM modulation capability, that can be used with headphones as an aid in initially tuning the crystal radio set to the test signal.  Table 2 and Fig. 2 show the results of the measurements.

Table 1.  Measured values of saturation current and ideality factor for some diodes, normalized to 25° C Diode A B C 1 2 3 4 5 6

Diode type 1N56 germanium marked GE 1N56 germanium marked GE 1N56 germanium marked GE Blue Radio Shack 1N34A germanium, no markings Two high Is Agilent HBAT5400 Schottkys in parallel

Agilent high Is HBAT5400 Schottky Infineon BAT62-03W Schottky Radio Shack 1N34A germanium marked 12010-3PT Infineon BAT62-08S Schottky ITT FO-215 glass germanium (rare, although Mike 6.5 Peebles and Dave Schmarder have them) 7 Agilent low Is HBAT5400 Schottky Agilent HSMS-286L Schottky, all three diodes in 8 parallel 9 Six Agilent 5082-2835 Schottkys in parallel Agilent HSMS-282N Schottky, all four diodes in 10 parallel 11 Four Agilent 5082-2835 Schottkys in parallel

Is* in nA 553 692 1317 678

n* 1.06 1.07 1.17 1.09

438

1.16

236 243 167 143

1.16 1.04 1.16 1.04

109

1.02

104

1.04

78

1.05

77

1.04

45.6

1.02

44.9

1.03

*  Is and n were measured using forward voltages of 39 and 55 mV (average current of between 3.8 to 5 times Is).

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Measurements of weak-signal detection efficiency (below the linear to square-law crossover point) of 15 germanium and Schottky diodes based upon their satur...

Table 2.  CW measurements of output power at 23.5° C.; detector input power: 3.2 nW (-85 dBW) Diode Measured Measured Measured Product Calculated Diode load in DC output output output of n and output # ohms* in mV in nW in dBW Is in nA in dBW

Measured minus calculated output in dB

Detector power loss in dB!

C 1 B A 2 3 4 5 6 7 8 9 10

29.5k 47k 50.5k 63.0k 78k 145k 127k 191k 214k 296k 400k 400k 658k

0.69 1.01 1.25 1.56 2.15 3.62 3.65 4.75 6.11 8.06 10.48 10.48 16.3

0.01614 0.02160 0.03094 0.03875 0.05855 0.09038 0.1049 0.1181 0.1744 0.2195 0.2753 0.2746 0.4038

-108.52 -106.65 -105.70 -104.72 -102.33 -100.44 -99.79 -99.28 -97.58 -96.59 -95.60 -95.61 -93.94

1391 663.3 665.5 529.3 459.3 245.5 228.3 174.0 133.2 97.07 74.0 72.4 41.8

-107.52 -104.50 -104.38 -103.41 -102.80 -100.63 -99.90 -98.80 -97.88 -96.40 -95.90 -95.44 -93.54

-1.00 -2.15 -1.32 -1.31 +0.47 +0.19 +0.11 -0.48 +0.30 -0.19 +0.30 -0.17 -0.40

23.6 21.7 20.8 19.8 17.4 15.5 14.8 14.3 12.6 11.6 10.7 10.7 9.00

11

676k

17.5

0.4530

-93.44

41.6

-93.55

+0.11

8.5

* Diode load is equal to Rx, its axis-crossing resistance Note:  The rectified DC current ranges between 21 and 29 nA, with most diodes close to 25 nA

Fig.2

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Measurements of weak-signal detection efficiency (below the linear to square-law crossover point) of 15 germanium and Schottky diodes based upon their satur...

The red data points indicate actual measurements. The blue values are calculated from equation #5 in Article #15A.  The blue line is a connection of the points calculated from equation #5. Note the close fit.

Discussion:  Fig. 2 shows the close correlation of measured output power with measured diode n*Is, as predicted by equation #5 in Article #15A.  This suggests that n*Is is a valid 'figure of merit' for a diode used to detect weak signals.  Remember:  The detector power loss figures shown in the last column of Table 2 would be even larger if the test signal of 3.2 nW were smaller.  The assumption in all of this is that both the input and output ports of the crystal radio set are reasonably well impedance matched. Note that the input and output resistances of a diode detector using diodes #10 and 11 are very high.  Matched input source and output load resistances this high are hard to achieve in a low loss manner.  A low loss high input resistive source is easier to achieve with a high Q loop driven crystal radio set that uses the loop as the tank than with one driven by an external antenna and ground that uses a separate high Q tank coil.  This is because one of the sources of loaded tank resistive loss, the external antenna-ground system resistance, is eliminated.  The radiation resistance of the loop is usually negligibly small compared to the loss in the loop when considered as a stand alone inductor.  It is assumed in this discussion that the diode is connected to the top of the loop, the point of highest source impedance.  Don't take this as a recommendation to go to a loop antenna for the best weak signal reception.  A good outside antenna-ground system will outperform a loop by picking up more signal power.  Conclusion:  A diode with the lowest n*Is may be theoretically the best, but achieving impedance matching of input and output may not be possible.  In practice, a compromise must be struck between a diode with the lowest n*Is and one having a lower axis-crossing resistance (Rxc).  This means, in general, a higher Is.  It can be achieved by paralleling several diodes or using a different diode type. A good diode array to try in high performance crystal radio sets intended for weak signal reception is an Agilent HSMS-286L, with all three diodes connected in parallel.  This diode array is packaged in a small SOT-363 SMD package but is easy to use even without a surfboard to aid in its connection.  The three anode leads exit from one side of the package with the three cathode leads from the other.  A quick connection solder blobbing all three anodes together and to a thin wire, and a similar connection to the cathodes is easy to do.  Use a low temperature soldering iron and as little heat as possible to avoid injuring the diodes.  This triple diode performs about the same as six Agilent 5082-2835 diodes in parallel, except that audio distortion will come in sooner on strong signals, because of its low reverse breakdown volt age.  It performs best if used in a crystal radio set having RF source and audio load resistances of about 400k ohms, rather high values.  An excellent diode for both weak and strong signal reception is the obsolete ITT FO-215 germanium diode, still available, think from Dave Schmarder at http://www.1n34a.com/catalog/index.htm .  Crystal radio sets having RF source and audio load resistances of about 200k ohms may have better sensitivity with two of the HSMS-286L arrays in parallel.  One section of the Infineon BAT62-08S triple diode should work the same as two HSMS-286L arrays in parallel.  Agilent semiconductors are carried by Newark Electronics and Arrow Electronics, among others.  Agilent or Infineon may sometimes send free samples to experimenters who ask for them.  The apparent error in output power for diode #1 has been checked many times.  The figure appears to be accurate.  I don't know the reason for the anomaly, except that the diode probably has an increased value for n*Is at the 21 Na rectified current, compared to the value of Is*n from the measurements in Table 1 (made at a higher current).  It is known that there are extra causes for conduction in a diode beyond those modeled by the Shockley equation.  Other measurements show that this diode also does not follow the Shockley diode equation at high currents (see Article #16).  Diodes A, B and C are randomly selected 1N56 germanium units.  They also show poorer performance than would be expected from Schottky diodes of the same Is and n.  Note that germanium diodes diodes #1, A, B and C provide less output than would be expected from Equation #5.  The output from germanium diode #5 is close to that expected from Equation #5 as is the output from all the Schottky diodes. Two charts are presented in Article #16 showing measurements of Is and n for 10 different diodes.  The Schottky diodes seem to have fairly constant values of Is and n as a function of current.  The silicon p-n junction and germanium measurements show how Is and n can vary, in other diode types, as a function of current.

Appendix:  The objective of these measurements is to measure the performance of various diodes when https://web.archive.org/web/20131030052217/http://www.bentongue.com/xtalset/27MeaXSD/27MeaXSD.html[06.08.2019 20:16:34]

Measurements of weak-signal detection efficiency (below the linear to square-law crossover point) of 15 germanium and Schottky diodes based upon their satur...

used as detectors; at a signal level well below their LSLCP so that their weak signal performance can be compared.  The measurements described in this Article were made with an 'available RF power' of -84.95 dBW (3.2 nW) applied to the diode.  Here is how that value was chosen: Initial measurements were made using a Tektronix model T922 scope having a maximum sensitivity of 2 mV/cm.  The scope was connected to P1 in Fig. 1; the horizontal sweep rate was set to display about 3 cycles of RF.  The RF voltage that could be read on the scope, with reasonable precision, was considered to be about 2 mV minimum peak-to-peak, providing a vertical display of 1 cm.  The voltage at P1 drives a 25 ohm resistor, the resistance of which is transformed in the crystal radio set up to a value that matches the input resistance of the diode.  The correct input impedance match is attained by interactively adjusting C7 and C8 on the crystal radio set to maximize the rectified DC output voltage.  2 mV pp RF voltage equates to 2/(sqrt8) mV RMS.  Since available power=Pa=(Erms^2)/(4*source resistance), Pa=5 nW.  If one allows for about 2 dB loss between the input to the crystal radio set and that to the diode, the available power that actually reaches the diode becomes about 3.2 nW.  To obtain better measurement precision a Fluke model 8920A true RMS RF digital voltmeter was connected to the "T" connector in Fig. 1 and used in the final measurements.  Since there were internal noise issues with the Fluke, the 20 dB attenuator (SW3) in the AMCS was switched in to enable increasing the signal to the DVM by 20 dB to overcome the noise.  The resistor values in the "inverted L" pad in the AMCS (45.0 and 5.55 ohms), along with the 25 ohm resistor, provide a source resistance of about 30 ohms and an attenuation of 22.98 dB, exclusive of any attenuation introduced by SW1, SW2 or SW3. At first an HP model 3312A function generator was used as the RF source.  Final measurements quoted were made using an HP model 33120A synthesized signal generator. Measurements of the diodes having the lower values of Is were made at 892 kHz (Band A, sub-band 1 of the crystal radio set).  Insufficient impedance transformation range was available to match diodes having the higher values of Is, so those were measured at 1205 kHz (Band B, sub-band 3).  These frequencies were chosen so as to eliminate signal pickup from local stations. The actual insertion power loss in the crystal radio set caused by losses in its L and C components was accounted for in each diode measurement by feeding an RF signal of -84.95+20.98+20+X dBW into the AMCS.  (The raw internal power loss in the AMCS is 22.98 dB, and the 20 dB attenuator (SW3) was activated).  X represents the L/C losses from the tank inductor and C7 and C8 in the crystal radio set used for the tests.  Its value was determined from a computer simulation of the crystal radio set, using a source resistance of 30 ohms and a load resistance equal to the Rxc of the diode to be tested, and noting the insertion power loss as X.  The value of X varied from 0.378 dB for diode #1 up to 1.711 dB for diode #11.  The simulated crystal radio set consisted of two impedance-matching/tuning capacitors (C7 and C8 in Article #26) with a tank inductor having a Q value extrapolated from the values given in Table 4 of Article #26.  The simulation program was 'SuperStar', by Eagleware.  Those uncomfortable with the concept of 'Available Power' may find Part 3 in Article #0 helpful.  Note that the diodes having the lowest n*Is value (and the lowest detector loss) result in the greatest loss from the tuning components in the crystal radio set.  This means that to gain the greatest benefit from using a diode having a low n*Is, the parallel resonant loss resistance of the tank circuit must be made as high as possible(unfortunately reducing selectivity).

Note re diode performance when receiving strong signals:  A high diode reverse-breakdown voltage rating is important in this case to prevent tank resistive loading from diode reverse conduction caused by the high reverse voltage present during the non-forward-conduction half-cycle. When this happens, volume is reduced.  Diodes that have a high reverse breakdown voltage rating usually have a high value for the product of their saturation current and ideality factor and are best for obtaining maximum volume on strong stations.  The diodes that are best for weak signal reception usually have a low n*Is product.  Many of those who use the HP 5082-2835 report inferior volume on strong stations.  I believe the cause is explained above. One solution to this problem is to provide switching means for two diodes as is done in the crystal set described in Article #26.  Another possible approach might be to to use several HP 5082-2800 high-reverse-breakdown-voltage diodes in parallel.  Several diodes would probably be needed because of the low saturation current of one '2800.  One could also use only one '2800 and supply a little forward bias voltage to make it simulate several in parallel.  These approaches have not been experimentally investigated.

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Measurements of weak-signal detection efficiency (below the linear to square-law crossover point) of 15 germanium and Schottky diodes based upon their satur...

#27  Published: 08/14/2003;   Revised: 05/23/2007 092711

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Diode detector weak-signal sensitivity improvement from input-impedance mismatching in crystal radio sets http://www.bentongue.com/xtalset/28SqLDtL/28SqLDtL.html Go

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How to reduce diode detector weak signal insertion-power-loss to less than that possible when the input is impedance matched By Ben H. Tongue

Quick Summary:  Diode detector insertion power loss can be reduced below the value achieved under impedance matched conditions provided it is operating below its LSLC point.  The optimal conditions are:  (1) The output audio load resistance equals twice the RF source resistance.  (2) The Saturation Current and Ideality Factor of the diode are such that the very-low-signal output resistance of the detector (axis-crossing resistance, aka Rd, of the diode) equals the output load resistance.  These conditions insure an impedance match at the audio output and a 1:2 mismatch at the RF input (source resistance = half the RF input resistance of the diode).  Please bear in mind that the LSLC point is a point on a graph of output DC power vs input RF power of a diode detector system.  It is not a point on a graph of DC current vs voltage of a diode.  Info on the LSLC point is available in Article #15a. It has usually been assumed by myself and others that power loss in a two port device (here, a crystal set) is minimized when its input and output ports are impedance matched.  This article will show that this is not true in the case of a diode detector operating at a signal power level well below that of its region of essentially linear operation.  It is true, however, when a strong signal (well above the LSLC point) is being received.  In the linear region, audio output power is proportional to RF input power.  That is, for every dB of change in input power there will be one dB change of output power.  In the lower power region, called the 'square law' region, a change of one dB in input power results in a two dB change in output power.  See Article #15a, Figs. 2 and 3 for info on the LSLC point of a diode detector.   Definition of terms: Rd:               Resistance of a diode at its axis crossing. Rd=0.0257*n/Is at 25 degrees Celsius Ri:                RF input resistance of the detector Ro:               Output resistance of the detector R1:               RF source resistance looking toward the tank R2:               Output load resistor Is:                 Diode Saturation Current n:                  Diode ideality factor T:                 Parallel LC tuned circuit LSLC point: The detector operational point halfway between linear and square law operation Plsc(i)          Max. available input power at the linear-square-law crossover point   

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Diode detector weak-signal sensitivity improvement from input-impedance mismatching in crystal radio sets

It has been asserted in these Articles that the RF input and audio output resistances, Ri and Ro, of a diode detector, approach the same value and equal 0.0257*n/Is = Rd ohms at room temperature when the input signal strength is low enough.  See Article #0, part 4, Article 4, part 2 and Article 16 for information on Is and n, and ways of measuring them. Fig. 1 represents a conventional diode detector.  The tank circuit T is shown with no internal loss.  A real world tank will have loss that can be represented by a shunt resistor connected across it.  For convenience of analysis it is assumed that this loss resistance is absorbed into the source V1, R1  (For a more complete explanation, see Article #1, first paragraph after the third schematic.).  Assume that the impedance of the source (antenna) and load (headphone) are transformed to equal values (R1 = R2) and select a diode that has an Rd equal to them.  This will result in a reasonable impedance match at both the input and output if the signal power level places operation below +10 dB of the linear-to-square law crossover point.  Little of the input power directed towards the detector will be reflected back to the source and most all of the output power from the detector will be absorbed in the load, R2.  If the diode detector were a linear device with linear input and output resistances, this impedance-matched condition would result in the least detector power loss (greatest sensitivity) obtainable.  It would seem clear that the crystal set detector could not be made more sensitive.  Actually, not so!  Very weak signal sensitivity can be improved by about 2 dB by appropriate mismatching at the input.  This provides a rather hard-to-hear increase in volume, but every little bit helps. In the impedance matched condition discussed so far, R1=Ri=Rd and R2= Ro.  Simple math shows that the detector input voltage Vi will equal one half the internal source voltage V1.  If we create an impedance mismatch between the source resistance R1 and the detector input resistance Ri by replacing the diode D with a different one having 1/2 the saturation current, Vi will increase.  The reason is that the detector input resistance Ri is now twice R1.  The voltage divider made up of R1 and Ri will reduce Vi to only two thirds of V1, making the new value of Vi=4/3 the old value.  Since the detector is operating in square law mode, the internal source voltage in the detector that drives its output terminals will be (4/3)^2=1.77... times as much as before. This higher voltage will be divided down by the voltage divider action of the now twice-as-large diode output resistance and R2 to give an output voltage 1.185 as large as before.  This equates to an output power 1.476 dB greater than in the original impedance matched condition.  

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Diode detector weak-signal sensitivity improvement from input-impedance mismatching in crystal radio sets

Fig. 2

Fig. 3

Theoretical calculation and SPICE simulation show that that in a crystal set having equal values for R1 and R2, the diode parameters that give to lowest insertion power loss at low signal power levels fits the equation: R1=R2= 2*(0.0257*n/Is) at room temperature. Now let us look at the effect on Ri and insertion power loss if Ri does not match R1.  Look at Fig. 2. 1. Series 1: The diode has an Is of 38 nA and an n of 1.03.  R1= R2=Rd  The graph shows that Ri is about 700k ohms at low input power levels and that it decreases towards 350k ohms at high input levels, where the detector acts as a peak detector.  Not graphed, Ro, changes from about 700k to 1400k ohms as the input power goes from -95 dBW to -50 dBW.  It is 1190k ohms at the LSLC input power point of -78.9 dBW. 2. Series 2: The Is of the diode is changed to 19 nA.  All else stays the same.  Ri approaches 1400k ohms at low input power levels and decreases towards 350k ohms at high levels.  Not graphed, Ro is approximately 1400k ohms at low input power levels and 1400k ohms at high output levels. 3. Series 3:  The diode Is stays at 19 nA,  the n at 1.03, R1 at 700k ohms and R2 is changed to 1400k ohms.  Ri changes from about 1400k to 700k ohms when going from low to high power levels.  Not graphed, Ro is approximately 1400k ohms at low input power levels and 1400k ohms at high levels. Look at Fig. 3. At the -95 dBW end of the graph, one can see that changing Is from 38 to 19 nA, and keeping R1 and R2 at at 700k ohms reduced the detector insertion power loss by about 1.5 dB  (Series 1 to series 2).  This comes from the increased voltage, Vi, at the detector input.  Raising the output load resistance from 700k to 1400k ohms reduces the mismatch loss at the output to approximate. zero and reduces the overall insertion power loss by another approximate. 0.5 dB for a total improvement of 2.0 dB at low input power levels (Series 3).  The detector insertion power loss at the -50 dBW  input level is is also reduced by 0.5 dB because of the elimination of the output impedance mismatch. Practically speaking, what does all this mean?  Mainly, improved theoretical understanding of diode detectors. (see last bullet point) Compared to the impedance matched condition, an increase in the volume of weak stations can be achieved if the RF source resistance driving the detector is dropped to 1/2 its RF input resistance, leaving the diode and output audio matching unchanged.  Looking at it in another way, again compared to the impedance matched condition, the diode could be be replaced with one having half the Is, and the output load resistance doubled.  Put a third way, the audio load resistance

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Diode detector weak-signal sensitivity improvement from input-impedance mismatching in crystal radio sets

should be twice the RF source resistance and be equal to the axis-crossing resistance, Rd, of the diode. A higher value for the audio load resistance may be created by changing the impedance transformation of the audio transformer.  Be aware that the insertion power loss of an audio transformer tends to increase when one operates it at higher input and output resistances than it was designed for.  It is possible for increased transformer loss to cancel out some of the 2.0 dB improvement.  See Article #5 for info on loss in various audio transformers. Fig.  4 and Part 4 provide info on some ways to audio-impedance match diodes having a high axis-crossing resistance (ones having a low Saturation Current). Changing to a diode having a lower Is will increase selectivity since the RF loading resistance value of the detector, on the tank is increased. This will increase the loaded Q of the detector tank, but will also increase the overall insertion power loss caused by the inherent losses in the tank inductor and tuning capacitor, nullifying some of the 2 dB improvement. By cut-and-try, many crystal set experimenters probably have already converged their designs to include this info. #28 Originally published as Article #15 in Feb. 2001; later withdrawn.  Republished as Article #28: 03/04/05 060610

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets OCT NOV JAN

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About Maximizing the Q of solenoid inductors that use ferrite rod cores, including charts of magnetic flux density and flux lines, with some actual Q and inductance measurements from simulations in FEMM By Ben H. Tongue

Summary:  Many factors interact to affect the Q of ferrite rod cored inductors.  Part one of this Article identifies and comments upon some of them.  A simplified model and an equivalent circuit is also discussed.  The second part describes several ferrite cored inductors, along with measurements of inductance and Q. The third part displays graphs of flux density, flux lines, inductance and Q of several ferrite cored inductors. The fourth part shows how flux density changes when an air gap is inserted in the center of a ferrite rod. It also includes simulations showing the distribution of magnetic flux density and current density in the turns of the solenoid.  The fifth part shows how Q varies when the ratio of the length of the solenoid to the core changes  Also shown is a chart showing the change of Q when the conductor spacing is changed.  The sixth part discusses important info about ferrite 61 and similar materials. Part 1:   Modeling ferrite cored inductors Bulk factors that affect inductor Q: Initial permeability of the ferrite material (µi) and ferrite loss-factor (LF) dielectric constant (ε) and dielectric loss tangent (tan δ) of the ferrite core dielectric constant (ε), dielectric loss tangent (tan δ) and length of the 'former' upon which the solenoid is wound (if one is used) resistivity of the ferrite rod length (lf) and diameter (df) of the rod, and their ratio length (ls) and diameter (ds) of the solenoid, and their ratio Ratio of the length of the solenoid to the length of the ferrite rod size and type of wire (solid or litz) and spacing of the turns A simplified equivalent circuit model for a ferrite cored inductor is shown in Fig. 1.

CLF=ferrite core loss-factor at a specific frequency [(30*10^-6) at 1 MHz for ferrite 61] Co=distributed capacitance. This is made up of mostly capacitance from the hot parts of the solenoid, through the ferrite dielectric, to ground (assuming that one end of the solenoid is grounded).  If a solenoid former is used, its

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

dielectric is in the path and will affect the overall loss. Another part of Co is made up of capacitance from the hot parts of the solenoid through air, to ground. La=inductance of solenoid in air FDF(suffix a or f)=flux density factor. This is a number, greater than 1, that corrects the value of the series DC resistance of the solenoid to its actual AC value. The "a" denotes air surrounding the solenoid, the "f" denotes the inclusion of a ferrite core. LFEF=leakage flux effect factor, the ratio of Lp to µi*La.  (LFEF is always less than 1) when the solenoid conductors are bathed in magnetic flux.  It has a suffix"a" when referring to the solenoid in air, and a suffix"f" when referring to a solenoid having a ferrite core. Lp=parallel inductance representing the increase of inductance caused by the ferrite core. Lp=LFEF*ui*La Henrys Ra=series RF resistance of solenoid in air Ra*(FDF-1)=additional series resistance caused by increased average flux density around the conductors when a ferrite core is placed inside the solenoid Rdc=DC resistance of the wire used in the solenoid Ro=represents resistive power loss in Co.  This loss in Co is contributed by the dielectric loss tangent of the ferrite and that of the solenoid former, if one is used. Rp=parallel RF resistance across Lp, representing magnetic losses in the ferrite core. Rp=LFEF*ω*La/CLF Ω ui=initial permeability of the ferrite. [125 for type 61 ferrite]

Qa=Q of the solenoid in air  Qa=ω*La/(Rdc*FDFa) Qt=Q of the real-word ferrite-cored inductor as represented in Fig. 1 ω=2*pi*frequency The simplified equivalent circuit shown in Fig. 1 provides a convenient way of think about the effect of placing a ferrite core in a solenoid.  Ra and La represent the resistive loss and inductance of the air-cored solenoid without the core (we want to increase the resultant Q and inductance). Adding a core creates the effect of adding a parallel RL in series with the air coil.  When a core is inserted into the air-cored solenoid, the series resistance of the solenoid in air is increased by the factor (FDFa-1) to account for the increased power loss in the copper wire caused by the increased flux density from the core Magnetic flux density surrounding the solenoid turns conductor is not uniform along the length of the solenoid.  It is greater at the ends than along its central part.  Increasing the length/diameter of the solenoid reduces the percentage of total flux that penetrates the copper and thus reduces resistive copper losses (especially at the two ends of the winding).  Increasing the ratio of the length of the ferrite rod to that of the solenoid further reduces the percentage of total flux that penetrates the copper, further reducing resistive losses. The amount of electric field that penetrates the core is important, especially at the high end of the band . The Nickel/Zinc cores such as type 61 have a very high resistivity dielectric as well as a rather low dielectric constant (ε) that has a high dielectric loss tangent (tan δ):  Losses caused by the high (tan δ) may be minimized by using construction methods that keep the parts of the solenoid that are at a high electrical potential spaced away from the core.  For instance a coil former sleeve made of low loss, low dielectric constant material can be used to isolate the high impedance parts of the solenoid from the core. I-squared-R resistive power loss in the conductor caused by the AC current flow:  Increased series resistance of the solenoid reduces Q, especially at the low end of the band compared to the high end, since the inductive reactance is at a minimum there (if the resistance, as a function of frequency is constant).  Proximity and skin effect losses increase the RF resistance of the conductor at the high end of the band more than at the low end. The use of litz wire reduces the loss across the band, but more so at the high end. If solid wire is used, spaced-turns winding will reduce the losses from proximity effects.  An advantage of using Litz wire in a ferrite-rod inductor is that there seems to be little downside to Q from close spaced winding.  This helps with obtaining a larger inductance with a smaller solenoid and ferrite core.  The use of larger diameter wire to reduce one of these losses usually has the effect of requiring a larger solenoid and ferrite core in order to keep the inductance the same, requiring mind-numbing tradeoffs.  Experimentation with 4" long by 1/2" diameter ferrite 61 rods and litz wire of 50/46, 125/46, 270/46 and 420/46 construction with an inductance 250 uH suggest that a winding length of about 1.5" of close-wound 125/46 litz wire is close to optimum, from the standpoint of Q.  I've tried to use 660/46 litz with a 4"x1/2" ferrite 61 rod to attain a high Q inductance of about 250 uH.  It never worked, probably because the length of the rod, being close to that of the solenoid, caused a high flux density condition to occur near the ends of the solenoid, creating extra copper loss. Lesson: For high Q, the rod should be longer than the solenoid, maybe three times as long. Ferrite cores of the same specification often exhibit rather wide variations in their ferrite loss-factor (thus affecting the attainable Q when used as a core).  They also vary, to a lesser degree, in initial permeability (µi).  This affects the https://web.archive.org/web/20141130231602/http://www.bentongue.com/xtalset/29MxQFL/29MxQFL.html[06.08.2019 20:20:37]

Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

inductance. Generally, when selecting cores from a group having identical specifications, the ones with the least initial permeability will have the least hysteresis loss, especially at high frequencies.  This provides a convenient way to select cores that will yield the highest Q coils, without actually measuring Q:  Wind a solenoid on a thin walled, low loss form and measure its inductance after placing each core, in succession, centered in the coil.  Generally the core providing the least inductance will provide the highest Q. Comments:  Consider the schematic in Fig. 1.  La, Ra and Ra*(FDFa-1) define the inductance and Q of the air-cored solenoid (Before a ferrite core is inserted in an air-cored solenoid, FDF=1). Lp and Rp define the inductance and Q of the added inductance produced when a ferrite core is inserted into the solenoid (now FDF becomes FDFf greater than before because of greater flux density in the conductors).  The value of Lp depends upon ui of the ferrite material, La and LFEF.  Some methods of changing LFEF are: 1) Increase the amount the bare rod core extending beyond the solenoid.  This will increase the value of LFEF and consequently the value of Lp.  2) Use a smaller diameter ferrite core than the Id of the solenoid.  This will reduce the value of LFEF and consequently Lp. The L and Q values of the air-cored solenoid are usually quite low**.  The inductance of Lp is usually high and equal to LFEF*ui*La.  The parallel resistance Rp equals (reactance of La)*LFEF/CLF.  If LFEF equals 1 (This can be approached when using a toroid having a high permeability, ui), the Q of a real-world ferrite-cored toroid inductor is about:  Q=1/(ui*CLF).  The Q of a ferrite-cored toroid inductor using ferrite 61 as the core can have a Q of about 330 at 1 MHz, as shown in the 11th Edition of the Fair-Rite catalog. Summary: With no ferrite core present one has a low Q low inductance inductor.  If one could construct a fully fluxcoupled ferrite 61 core (LFEF~1.0), the Q at 1 MHz would be 1/ui*CLF=267.  Highest Q occurs with an optimum value of LFEF, which also provides an intermediate value for real-world inductance.  See Table 6, next to last entry. In my experience with 1/2" diameter ferrite 61 rods aiming for 250 uH and using Litz wire, most of the time LFEF turns out to be greater than the value for maximum Q. An indication of this condition can be obtained by placing two extra cores, each co-axially aligned with the solenoid's core, one at each end of said core, to increase the LFEF.  The Q is usually reduced even though the inductance is increased, showing that LFEF is too high for maximum Q.  Proof of this can be attained by discarding the two extra cores and reducing the number of turns on the rod.  Of course, inductance goes down, but Q will increase. To get the inductance back up and retain the higher Q, a solenoid and ferrite rod of larger diameter are required. ** Note the "no core" entry in Table 6 for inductor BB.  The solenoid (with no core) has a Q of 88 (and an inductance of 17.6 uH). 

Part 2: Measurements Comparison of several conventionally wound Ferrite-cored solenoids having the same winding length and number of turns, but different diameters Ferrite rod length=4", diameter=0.5", material=type 61, µi=125, ferrite loss factor (CLF)=30*10^-6, the "best ferrite core" was used, former=low loss thin wall tubing of various lengths, wire=125 /46 ga. litz, construction=conventional close wound solenoid of 58 turns having a length of about 1.625".

Table 1 - Coil and Former data (uses 'best ferrite core') Coil and Former > Coil former dia. and len. in inches Coil former Material

A

B

C

D

E

0.5

0.625x4.5*

~0.75x4.5**

1.04x2.25

1.50x3.0

Split polyethylene tubing placed over former 'B'

Orange colored polypropylene pill bottle

White Polypropylene drain pipe from Genova Products

No former- wire Polyethylene wound directly sleeve, 1/16" on wall thickness ferrite rod

Ind. of coil in air, in uH

?

19.3

25.9

48

90

Q of coil, air core, 2520 kHz

?

265

320

430

520

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

Inductance of coil in uH with 'best' ferrite rod

237

248

238

240

241

Table 2 - Q of a ferrite-cored conventionally-wound coil of fixed length and number of turns as a function of its diameter (uses 'best ferrite core') Coil and Former >

A

B

C

D

E

\/  Freq. in kHz  \/

Q

Q

Q

Q

Q

520

1060

960

945

820

670

943

1035

1030

1045

995

890

1710

780

855

878

885

845

* Piece of polyethylene tubing having an OD of 0.625" and an ID of 0.50" ** This coil former has a cross section somewhat less than from a full 0.75" piece of tubing. It is constructed by first sliding the 1/2" dia. 4" long ferrite rod into a 5" long piece of 0.625" OD polyethylene tubing. A full longitudinal cut is then made in a second piece of similar tubing, so it can be fitted over the first one. A gap of about 3/8" is left in the second, slit piece of tubing, and that is what causes the cross section to be less than that of a true 3/4" tube. Note 1: Q values are corrected for distributed capacity. Note 2: 'best ferrite core', 'medium ferrite core' and 'worst ferrite core' refer to Q measurements of a large quantity of 4" long, 1/2" diameter ferrite 61 cores purchased from CWS Bytemark over a period of years. The Q measurements were made at 1710 kHz with a test coil wound on a former similar to that used in 'Coil and Former' B, above. The winding had 39 turns, close wound, of 270/46 litz.  The "best ferrite core" was selected from a small batch of cores that were reannealed by a local ferrite manufacturer.  See the third-from-last paragraph. Some observations: 1. Inductance does not change much between a solenoid diameter of 0.5" and 1.5". 2. At low and medium frequencies, Q is the highest when the wire is wound directly on the ferrite.  It drops substantially at the high frequency end. 3. Q at the high frequency end increases as the wire is separated farther from the core, except for coil E. 4. Q at the low frequency end decreases as the coil wire is separated further from the core. Comparison between a conventional and contra wound ferrite-rod cored solenoid using a "best" and a "worst" rod. See Article # 0, Part 12 for a mini-Article about the benefits of the contra-coil construction. Ferrite rod length=4", Diameter=0.5", Material=type 61, µi=125, Ferrite loss factor (CLF)=30*10^-6, Former=polyethylene (not vinyl) tubing, ID=0.5", OD=0.625", length=5", Wire=125 strand/46 ga. litz, Construction=close-wound conventional solenoid of 58 turns having a length of about 1.625" Ferrite rod length=4", Diameter=0.5", Material=type 61, µi=125, Ferrite loss factor (FEF)=30*10^-6, Former=polyethylene (not vinyl) tubing, ID=0.5", OD=0.625", length=5", Wire=125/46 ga. litz, Construction=closewound contra wound solenoid of 58 turns and length of 1.625" (not wound as tightly as the conventional solenoid above).  

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

The winding format for solenoids #1 and #2, below, are shown in Figs. 2 and 3.  For clarity, the windings are shown as space wound, but the actual solenoids #1 and 2 close wound.  Connections for the contra wound inductor shown in Fig. 3: For the series connection, join leads c and e. Lead d is hot and lead f is cold.  For the parallel connection, join leads c and f.  Join leads d and e.  d/e is the hot and c/f is the cold connection. 

Table 3 - Conventional vs contra wound Ferrite-Rod Cored Solenoids #1 Conventional solenoid

 

'Best core'

#2 contra wound solenoid

'Worst core'

'Best core'

'Worst core'

Freq. in kHz

Q

520

960

237

2.8

740

240

2.8

895

231

4.0

700

234

4.0

943 943

~1030 -

237 -

2.8 -

775 -

240 -

2.8 -

990 ~1030

231 57.8

4.0 4.7

765 780

234 58.5

4.0 4.7

1710

855

237

2.8

655

240

2.8

945

57.8

4.7

725

58.5

4.7

Ind. in Co in uH pF

Q

Ind. in Co in uH pF

Q

Ind. in Co in uH pF

Q

Ind. in Co in uH pF

The Q values given above were measured on an HP 4342A Q meter and corrected for the distributed capacity of the inductor (Co).  The ferrite cores were purchased from CWS ByteMark in the third quarter of 2002. They may have changed vendors since then because some rods I purchased in the 3td quarter of 2004 resulted in lower Q coils than the values reported here. These rods also had two small, 180 degree apart, longitudinal flats along their entire length.  CWS gracefully accepted a return of those rods and quickly refunded my money. The 'best' and 'worst' cores used in these measurements were from a group purchased from CWS ByteMark in the 3rd quarter of 2002. Note the better high-band Q values recorded for the contra wound inductor. This is because the low Q distributed capacity from the dielectric of the ferrite (Co and Ro) is connected across an inductor having 1/4 the inductance (and reactance) value of the conventional wound solenoid.  An observation: If the hot/cold connections to the contra wound coil in Fig. 3 are reversed, Q at 1710 kHz drops.  This is because more loss from the low Q dielectric of the ferrite is coupled in to the stray capacitance. Solid wire instead of litz?:  Keep in mind that the work described here used close-wound 125/46 litz wire.  If one duplicates 'Coil and Former B' in Table 2, except using 22 ga. solid copper wire (having the same diameter) as 125/46 litz, the Q values drop to about 1/6 of the values achieved with the litz wire.  The cause is the large proximity effect resistive losses, as well as skin effect, in the solid wire.  The proximity effect, but not the skin effect loss may be much reduced if the wires are space-wound.  New trade-offs now must be considered: Same wire diameter, and therefore a longer solenoid, or a smaller wire diameter and the same overall length?  If one wishes to use solid wire, it should probably be wound directly on the ferrite, not on a former.  The overall Q will still be much less than when using litz, and the loss from the high (tan δ) dielectric of the ferrite will be pretty well swamped out because of the now higher losses from the skin and proximity effect losses.  The Q values, using a close-wound solenoid of 22 ga. solid copper wire on a polyethylene former, as in 'Coil and Former' B in Table 2 are: 520 kHz: 130, 943 kHz: 141 and 1710 kHz: 150 when using the "best core".  The Q drops only 3, 3, and 5 points respectively if the "worst core" is used. Measurements to determine the (tan δ) of the dielectric of a 'medium core':  Two adhesive copper foil coupons, 0.5"x1.75" were affixed to the 4", 0.5" diameter rod made of ferrite material 61 (3M sells rolls of thin copper foil with an adhesive on one side).  The long dimension of each coupon was parallel to the axis of the rod with the two coupons set opposite to each other, 180 degrees apart.  They formed a two plate capacitor having curved plates with the dielectric of the rod between them.  The capacitance of this capacitor came out to be 6.5 pF.  Measurements, using a Q meter and a high Q inductor were made that enabled calculation of the Q of this 6.5 pF capacitor. Q was 25 at 520 kHz, 35 at 943 kHz and 55 at 1710 kHz.  Even though the distributed capacity of a ferrite rod inductor is only made up partially of this poor dielectric, it is, I believe, a previously unrecognized cause of the usual Q drop at the high end of the band.  It is also, I believe, the cause of Q reduction in ferrite toroids when no gap is provided between the start and finish of the winding.

Part 3 - Flux density and flux line simulations, inductance and Q of several ferrite-cored inductors along with some measurements David Meeker's "Finite Element Method Magnetics" program FEMM was used to generate Figs. 4-17.   First a word about the displays:  FEMM, as used here provides a 2-dimensional display of flux density (the colors) and flux lines (the

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

black lines). Only half of the object being simulated is analyzed and displayed since only axisymmetric objects can be analyzed with the program.  This saves simulation time, which can become very great.  FEMM, at this time, cannot simulate using litz wire. That is why the following simulations and measurements use 22 ga. solid copper wire instead of the 125/46 litz used in Part 2. Understanding the images:  Visualize the axis of the ferrite rod as coincident with the y-axis of a conventional 3-D x, y and z coordinate graphing system with the center of the rod at the origin. The FEMM program discards everything to the left of the y, z plane that intersects the origin and displays a view of the other half. The images show field densities that exist in an x, y plane that intersects the origin.  The vertical object at the left in each image is the ferrite rod. Its horizontal width is ½ that of the diameter of the actual round ferrite rod since the parts of the inductor to the left of a vertical y, z plane intersecting the origin have been discarded (see above). The vertical line of little circles to its right show the cross-sections of the turns of the solenoid wires.  Fig. 4 is a plot of magnetic flux density and flux lines on an imaginary plane that cuts longitudinally through the center of ferrite rod inductor AA, shown mostly in purple.  The outline of half the 4"x1/2" rod is shown at the left of the plot.  If one measures, on the computer screen, the height and width of the rectangle, one can see that their ratio is 16.  This is equal to the ratio of the 4" length of the rod to 1/2 of its 1/2" diameter.  The large half-circle defines the area around the inductor that will be included in the simulation.  It's made up mostly of air.  The magnitude of the flux density can be seen from the colors on the display (see the chart).  The range of flux density values for the display was purposely limited to about 20 to help supply flux density detail around the outer turns of the solenoid.  That is why most all the core is colored purple (the flux density is above 4.000e-9 Tesla).  Fig. 5 is a close-up simulation of the area near the upper turns of the solenoid.  If one's browser has a zoom control, one can easily see how the flux density close to the surface of the wires of the end turns of the solenoid (even numbered Figs.) is greater than it is in the more central turns.  High flux density in the copper equals high power loss (Q reduction). Comment:  Look at figs. 6 and 11 in Table 4. Inductors BB and EE are identical except for the length of the ferrite rod.  It appears that about 10% of the end turns of solenoid BB are exposed to a flux density above 2.8e-9 Tesla (3 dB below the maximum plotted value of 4e-9 T).  The corresponding percentage in solenoid EE about 50%.  This shows that a high flux density around a greater percentage of turns results in lower Q.  A parameter listing of the inductors is below Table 4.  Note the Q values for inductors BB and EE.

Table 4 - Simulation of inductors using solid copper wire of OD=0.0253" in Figs. 4, 5, 6, 7, 10 and 11.  Wire OD=0.01765" in Figs. 8 and 9. No litz wire is used. All inductors have 58 turns.

Fig. 4 Simulation of inductor AA

Fig. 5 Close-up view of flux density near upper turns of inductor AA

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

Fig. 6 Simulation of inductor BB

Fig. 7 Close-up view of flux density near the upper turns of inductor BB

Fig. 8 Simulation of inductor DD, same as AA except for using wire of a smaller OD

Fig. 9 Close-up view of flux density near the upper turns of inductor DD

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

Fig. 10 Simulation of inductor EE, short ferrite core

Fig. 11 Close-up of flux density near the upper turns of inductor EE

Parameters of simulated inductors AA through DD, inductance and Q at 1 MHz: Inductor AA: ferrite core length=4", ferrite core diameter'1/2", core type=61, wire type=22 ga. solid copper wire, OD=0.0253", solenoid length=1.624", ID of solenoid=0.5013", Number of turns=58, Inductance=261.66 uH, Q=118.4. Solenoid construction is similar to inductor A in Tables 1 and 2. Inductor BB: ferrite core length=4", core diameter=1/2", core type=61, wire type=22 ga. solid copper wire, OD=0.0253", solenoid length=1.624", ID of solenoid=0.6263", Number of turns=58, Inductance=259.11 uH, Q=130.7. Solenoid construction is similar to inductor B in Tables 1 and 2. Inductor DD: Same as inductor AA except that the wire diameter is reduced to 0.01765".  This creates a spaced winding. Inductance=265.37 uH, Q=267.6. Inductor EE: core length=1.680", core diameter=1/2", core type=61, wire type=22 ga. solid copper, wire, OD=0.0253", solenoid length=1.624", ID of solenoid=0.6263", Number of turns=58, Inductance=121.80 uH, Q=36.2.

Table 5: Measurements at 1 MHz of a physical inductor having the same parameters as simulated inductor BB.  Inductance=~236 uH -Frequency in Hz 540 943 1710

"Best core" Q 130 141 150

"Worst core" Q 127 138 145

Note that the Q difference between the "Best core" and the 'Worst core" is very small. This is because the main loss in this inductor is the high proximity loss in the solid close-spaced copper winding. The much lower ferrite core loss is swamped out and has little effect on Q, showing a Q ratio between the two of about 0.97.  Compare these figures with those in Table 3 for a similar conventionally wound solenoid using close-spaced 125/46 litz wire.  Proximity loss is greatly reduced in close-wound litz wire, compared to close-wound solid copper wire. The Q ratio here is about 0.75. Loss in the ferrite core swamps out the much lower proximity loss in the litz wire, and a much higher Q results.

Part 4 - The effect on impedance parameters of an air gap in the center of a ferrite rod inductor and on magnetic flux/current density in the wire cross-sections. The images and text are based on FEMM simulations of inductor BB, shown in Figs. 6 and 7, the specs of which are shown below Table 4, but with the following difference: Instead of using one 4” long ferrite rod, two 2” co-axially

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

oriented rods are used in each simulation with different air gaps between them (0.0000”, 0.0313”, 0.0625” and 0.1250”). The solenoid is centered on the gap. When the gap is 0.000” the result should be the same as if one solid 4” rod were used.   The inductance and Q values for inductor BB are slightly different than the values in the new simulations, as stated below for a 0.0000” gap between two 2” rods. This is because the “meshing” parameter in the FEMM simulation was changed to reduce the time taken for the simulations. The top half of a full image of a core/solenoid combination is a mirror image of the bottom half.  In figures 12-17 advantage is taken of this characteristic by zooming in and not showing the entire rod so as to be able to get a larger image, thus supplying more detail. The first group of four simulations have central gap widths of 0.0000”, 0.0313”, 0.0625” and 0.1250”. They are named GappedRodA0000, GappedRodB0313, Gapped RodC0625 and GappedRodD0125. They are intended to show magnetic flux density distribution in the ferrite and the air. The simulations are made at a frequency of 1 MHz with an AC current of 1 uA RMS in the solenoid. The actual magnetic flux density values can be estimated by comparing the color display to the color chart to the right of the images. A second group of two simulations shows magnified views of two parameters of the GappedRodB0313 simulation. They are called GappedRodB0313_B (for showing flux density B in Teslas in the cross-sections of the individual wire turns) and GappedRodB0313_j (for showing the current density j in MA/m^2 in the cross-sections of the individual wire turns). If one looks closely at the GappedRodB_B image, one can see how flux density is distributed in the wire cross-sections as a function of distance along the rod.  As the textbooks say, very little flux exists in the interior of the wire. Where the external flux density is great, as it is at the ends of the rod and near the gap, the flux that penetrates the copper is confined near the outer periphery of the wire. The distribution of current density in the turns as a function of position along the length of the rod is shown in image GappedRodB0313_j. This illustrates skin effect. Note the current density is not uniform in the wires because of proximity effect and the fact that the length of the solenoid is not very long, compared to the length of the rod. Some specifications common to the inductors in Figs. 12 through 17: Ferrite rod length: two 2” long rods oriented coaxially, and spaced apart by 0.0000”, 0.0313”, 0.0625” or 0.1250”. Ferrite rod diameter=0.5”, Permeability of ferrite rod=125. Loss factor of ferrite at 1 MHz=30*10^-6, ID of solenoid=0.6263”. Number of turns=58. Wire: solid copper, OD=0.0263”. Length of solenoid=1.624”. Frequency at which the simulations are made=1 MHz. It is interesting to see in Figs. 16 and 17 that the distribution of magnetic flux in the cross-section of the turns has the same shape as that of the current density. Please note in the text accompanying Figs. 12-17 that the copper series loss component corresponds to the sum of Ra and Ra*(FDF-1) as shown in Fig. 1.    Results of the simulations:

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

Fig. 12  GappedRodA0000: Inductance=258.539uH. Series resistive loss components: copper=11.1639 Ω, ferrite magnetic loss=1.32006 Ω, total resistive losses=12.4840 Ω. Inductive reactance=1624.45 Ω.  Q @ 1 MHz =130.122.  

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

Fig. 13  GappedRodB0313: Inductance=193.324uH. Series resistive loss components: copper=6.34439 Ω, ferrite magnetic loss=0.736286 Ω, total resistive losses=7.08067 Ω. Inductive reactance=1214.69 Ω.  Q @ 1 MHz =171.55. Note that this simulation has the highest Q.

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

Fig. 14  GappedRodC0625: Inductance=162.729uH. Series resistive loss components: copper=6.85818 Ω, ferrite magnetic loss=0.52394 Ω, total resistive losses=7.38212 Ω. Inductive reactance=1022.456 Ω.  Q @ 1 MHz =138.5044.

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

Fig. 15  GappedRodD1250: Inductance=130.011uH. Series resistive loss components: copper=8.68753 Ω, ferrite magnetic loss=0.339467 Ω, total resistive losses=9.02699 Ω. Inductive reactance=816.883 Ω.  Q @ 1 MHz =90.4934.

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

Fig. 16  GappedRodB_B: This is a zoomed in view of GappedRodB to more clearly show the magnetic flux distribution in the air and the cross-sections of the wire turns of its solenoid.

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

Fig. 17  GappedRodB_j: This is a zoomed in view of GappedRodB to more clearly show the current density distribution in cross-sections of the wire turns of its solenoid.  

Part 5 - Ferrite-rod inductor simulation experiments; all using centered solenoids 1.624" long and having 58 turns The solenoids used in the simulations in Table 6 all use a conductor having a diameter of 0.0253".  The only parameter varied is the core length.  The simulations in Table 7 all use a 4" long core.  The only parameter varied is the diameter of the conductor.

Table 6: Simulation of solid copper wire inductor BB in FEMM at 1 MHz, with various core lengths (type 61 core material) Core length Inductance Resistive losses Hysteresis Total losses DC in inches in uH in ohms losses in ohms in ohms resistance

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Q

Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

No core

17.58

1.25

-

1.25

0.16

88.4

1.68*

121.8

21.12

0.23

21.35

0.16

35.8

2.5

186.7

13.81

0.58

14.39

0.16

81.51

4.0 8.0

258.5 341.6

11.16 9.80

1.32 3.06

12.48 12.86

0.16 0.16

130.1 166.6

16.0

374.2

9.48

4.39

13.87

0.16

169.6

32.0

378.4

9.44

4.67

14.10

0.16

168.6

* Solenoid winding covers the full length of the core. Table 6 shows that about 77% of the maximum Q is attained with a core about 2.4 times the length of the solenoid with the turns number, solenoid size, core length, etc used here. About 68% of the maximum inductance is attained. Note also that when the length of the core is shortened to approximately the length of the solenoid, Q drops precipitously. Resistive losses are mainly proximity effect losses. Hysteresis losses are magnetic losses in the ferrite core itself.  Total losses are the sum of the two.  There is a good lesson to be learned here:  To maximize Q, do not cover the whole length of the core with the solenoid.

Table 7: Simulation of inductor BB in FEMM at 1 MHz, with various conductor diameters (type 61 core material) Wire dia. Inductance Resistive in inches in uH losses in ohms

Hysteresis losses in ohms

Total losses in ohms

DC resistance

Q

0.02530

258.5

11.16

1.32

12.48

0.16

130.1

0.02320

259.6

8.04

1.33

9.36

0.18

174.2

0.02127 0.01951 0.01789

260.5 261.1 261.6

6.26 5.13 4.37

1.33 1.34 1.34

7.59 6.47 5.71

0.22 0.28 0.36

215.7 253.7 288.0

0.01265

263.4

2.91

1.35

4.26

0.64

388.1

0.008995

264.0

2.48

1.36

3.84

1.25

431.9

0.006300

264.4

3.02

1.36

4.38

2.62

379.7

0.008995*

264.5

2.57

1.40

3.97

1.00

418.6

* Simulates winding the 58 turn solenoid directly on the 4" long ferrite core (solenoid ID=0.5013") instead of on a former having an ID of0.6263". Note that the the two simulations using a conductor diameter of 0.008995" show remarkably similar parameter values. Table 7 shows the benefits of spaced winding when using solid wire. All the inductors in Table 7 use centered solenoids of 58 turns and a length of 1.624".  The only variable is the diameter of the conductor, which controls the spacing of the turns (the winding pitch is held constant).  The lesson here is that, when using solid copper wire, there can be a great Q benefit by space winding the solenoid and using an optimum size wire; in this case a Q of 431.9 vs 130.1 at 1 MHz, with solid wire. One can see that core losses change very little with the various conductor diameters (Hysteresis losses in ohms). Notice how, with a conductor diameter change from 0.02530 to 0.00006300", the AC copper loss decreases from 11.6 to 3.02 ohms overwhelming the increase in DC conductor resistance from 0.16 to 2.62 ohms. See Table 3 for measured inductance and Q values of an inductor similar to inductor BB, but wound with 125/46 litz wire.  Here the Q is even greater than in Table 7 because litz construction is less sensitive to proximity and skin effect losses than is solid wire. Thanks must go to Brian Hawes for making me aware of the FEMM program and showing me how to use it.

Part 6:  Perminvar ferrite, and what the term means

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Q of ferrite-rod inductors & contra wound coils, applied to crystal radio sets

Normal nickel/zinc ferrites (NiZn), the types with less permeability as well as lower loss factors than manganese/zinc (MnZn) ferrites, are often used at RF because of their low loss at the higher frequencies.  They do not suffer appreciably from permanent changes in permeability or loss factor from exposure to strong magnetic fields or mechanical shock such as grinding, or dropping on the floor. Special nickel/zinc ferrites, called perminvar ferrites can achieve a considerably lower loss factor for the same permeability than normal nickel/zinc ferrites, and at higher frequencies. This result is achieved by adding a small amount of cobalt to the ferrite power before firing, but there is a catch. In order to actually achieve the lower loss factor, the ferrite core must be annealed by raising it to a temperature above its Curie temperature (the temperature at which it losses all its permeability), and then cooling it very slowly back down through the Curie temperature, and then to lower temperatures. This process usually takes about 24 hours. The Curie temperature of ferrite type 61 (a perminvar ferrite) is specified in the Fair-Rite catalog as being above 350 degrees C. The annealing process reduces the permeability somewhat, but reduces the loss factor substantially. The low loss-factor property of the annealed perminvar ferrite can be easily degraded by mechanical shock, magnetic shock or just physical stress (as from a tight mounting clamp).  The Fair-Rite catalog sheet for type 61 ferrite cautions "Strong magnetic fields or excessive mechanical stresses may result in irreversible changes in permeability and losses". Actually, the changes are reversible if one goes through the annealing process again. The MMG catalog, issue 1A, in writing about perminvar ferrites, adds: "Mechanical stresses such as grinding and ultrasonic cleaning increase the permeability and lower the Q, especially at the higher frequencies, although the changes in Q at the lower frequencies may be very small. I suspect that there is now much less pressure on ferrite manufacturers to deliver a low loss product than in the past. Since time is money, maybe they now skimp on the annealing process.  Several years ago I took some 4" x 0.5", mix 61 rods I had purchased from CWS ByteMark and had them re-annealed at the plant of a local ferrite manufacturer.  The Q of a litz-wire coil using the re-annealed core, at 2.52 MHz, was increased by 12%. This indicates that the core was not originally properly annealed, or had been subjected to some mechanical or magnetic shock after being annealing by the manufacturer. I was informed, when I asked, that coil Q at high frequencies could be expected to increase by up to100% from the pre-annealed value.  I chose the best of these re-annealed rods to be my "best ferrite core" rod in this Article.  One source informed me that few ferrite manufacturers perform the annealing process anymore.  Toroids made of type 61 material are still made here in the USA. Note: An easy way to use a DVM ohmmeter to check if a ferrite is made of MnZn of NiZn material is to place the leads of the ohmmeter on a bare part of the test ferrite and read the resistance.  The resistance of NiZn will be so high that the ohmmeter will show an open circuit. If the ferrite is of the MnZn type, the ohmmeter will show a reading. The reading was about 100k ohms on the ferrite rods used here. #29 Published: 10/07/2006;  Revised: 01/07/08 060610

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