Surveyor's Guide to Electromagnetic Distance Measurement 9781487583569

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SURVEYOR'S GUIDE TO ELECTROMAGNETIC DISTANCE MEASUREMENT

SURVEYOR'S GUIDE TO ELECTROMAGNETIC DISTANCE MEASUREMENT

edited by

J. J. SAASTAMOINEN

Published for the Canadian Institute of Surveying by UNIVERSITY OF TORONTO PRESS

© University of Toronto Press 1967 Printed in Canada Reprinted in 2018 ISBN 978-1-4875-8222-7 (paper)

"

i_,... .,. ;. ,,,,,,._

. .~: .....6!' A,.•....:.

'

, . . ,.,~

~~

"I""

Electronic distance measuring in the Canadian Arctic.

"-

FOREWORD

THIS TEXT has been produced by the Canadian Institute of Surveying to fill a gap in the existing literature on the subject of electromagnetic distance measurement. There are many excellent texts available on the theory and use of electronic phenomena. There are also very useful pamphlets published by the manufacturers of electromagnetic distance measuring devices describing the use of their instruments. But to our knowledge there is no text that describes the theory of these instruments in a language readily understood by the practising surveyor. We believe that such an understanding is essential to the efficient use of electromagnetic distance measuring equipment. At the time of writing there are only two types of electromagnetic distance measuring device in use in Canada, namely the tellurometer and the geodimeter. We have therefore described these instruments, in their various models, in detail. We are convinced that there is a place for both types of instrument within the profession of surveying, and in certain specific situations we have stated which one can be used with greater efficiency. This text is complete in itself so far as it deals with the basic theory of electromagnetic distance measurement. As to the actual measurement of lines with the geodimeter or the tellurometer, we have presumed that the user has obtained and read the handbook on his instrument as issued by the manufacturer. No purpose would be served in repeating the setting-up and operating procedures outlined in such a handbook. On the other hand the field use of the instruments is covered here by sections which comprise a compendium of experience derived from the field reports and interviews of many experienced users. L. M. SEBERT Past President Canadian Institute of Surveying

CONTENTS

FOREWORD

1

V

ELECTRONIC CONCEPTS AND DEVICES,

L. J. O'Brien

2 THE GEODIMETER, J. Gautheir, L. J. O'Brien APPENDIX I: APPENDIX 11:

Error Location Guide Calibration Procedure L. M. Sebert, L. J. O'Brien, M. Mogg

3

THE TELLUROMETER,

4

HIGH PRECISION TECHNIQUES,

BATTERY POWER SUPPLIES,

48 78 81 101

C. D. McLellan, S. A. Yaskowich,

H. £.Jones 5

3

135

C. Luciani

160

SOME FREQUENTLY USED ABBREVIATIONS AND SYMBOLS

188

INDEX

190

SURVEYOR'S GUIDE TO ELECTROMAGNETIC DISTANCE MEASUREMENT

ELECTRONIC CONCEPTS AND DEVICES 1.

L. J. O'BRIEN

Introduction 1. An electrical conductor can be thought of as a substance possessing a large number of "free" electrons, that is, electrons displaced from their atomic orbits by mutual collision or other excitation. These electrons move about randomly within the molecular structure of the substance but, since each contains a negative electric charge, they can be forced into a directed flow, or current, by the application of electric pressure, or voltage. Associated with the flow of electrons is a resultant "field" of energy comprised of two vector components: an electric component perpendicular to the electron flow and a magnetic component parallel to it. These form an electromagnetic field which, when changing in strength, radiates from the generating source with the velocity oflight. 2. When such a field impinges on another conductor remote from the source, it induces an electron flow within that conductor during the interval of field strength change. It should be apparent, therefore, that to derive energy from an electromagnetic field by induction a steady-state source cannot be used. Instead, a varying, or alternating, source is required. Since the associated field will also vary, it will impress on intercepted conductors a condition of changing influence, and the induced energy will be continuous. Mutual induction is the term used for induction between separate conductors. Self-induction refers to energy induced back to the source by its

4 ELECTROMAGNETIC DISTANCE MEASUREMENT

own field variations. The influence of self-induced energy is such that changes in the originating flow strength are opposed. Alternating Energy 3. Assume a vector of constant amplitude rotating about its point of origin with constant angular velocity. The projection of the head of the vector onto any diameter of the circle traced by its rotation moves with simple harmonic motion, that is, with acceleration toward the centre point proportional to the distance from it. (Refer to Fig. 1.)

FIG.

1

A plot of simple harmonic motion on a time base produces a sine wave. Fig. 2 shows a vector of amplitude A rotating counterclockwise at a rate of w radians per second. If zero time is taken when the vector is on the x-axis,

3

211" FIG .

2

then t seconds later it will have moved through an angle of wt radians to the instantaneous position indicated. The length of its projection on the y-axis will be, by trigonometry, y

= A sin wt

ELECTRONIC CONCEPTS AND DEVICES

5

which is the equation of simple harmonic motion. Plotting a graph of y as t goes through 21r radians produces a sine wave as expected. Note that instantaneous values vary continuously between +A and -A (the sine function changes sign at 1r and 21r radians), and that they are repetitive in cycles of 21r radians. The period of alternation is the time lapse in one complete cycle of rotation, the frequency of alternation refers to the number of cycles completed per second and the amplitude is the maximum positive or negative value reached. 4. Natural vibrations follow simple harmonic motion. Likewise, electrical energy generated by rotary induction or linear oscillation follows a sinusoidal variation. Therefore, the sinusoidal waveform of AC (alternating current) is most generally encountered in studies of energy propagation. If a sinusoidal voltage is applied to a conducting element, the resulting current and electromagnetic field will be sinusoidal. During the positive half of the sine wave, current will flow in a particular direction, and during the negative half, it will flow in an exactly opposite direction. Similarly, the field polarity will vary from positive to negative depending on the direction of flow of the source current. Therefore, the sine wave representation of AC can be considered as a graph of voltage, current or field strength variation with time according to the equation y = A sin wt, where y is the instantaneous strength value, A is the amplitude or maximum strength, w is the angular rate of alternation, and wt is the "phase" angle, that is, the angular change from zero time reference to instant t. Note that in one cycle wt goes through 21r radians and if the frequency is f cycles per second, the angular rate can be taken as 21r/ radians per second, or w

=

21rf.

5. Electromagnetic energy propagated with a sinusoidal waveform goes through 21r radians of phase change in one cycle. It radiates from the source with the velocity of light, a universal constant which is accurately known.* The distance travelled during the time of one cycle is therefore known if the frequency is known. This distance is referred to as a wavelength. Note that although Fig. 3 shows a wavelength between adjacent maxima, it is in fact the distance between any two points on the wave separated by a phase angle of21r radians. The relationship between wavelength A and frequency f is given by the equation A= elf *The retarding effect of medium is not considered here.

6

r

ELECTROMAGNETIC DISTANCE MEASUREMENT

wavelength-----J

FIG,

3

where c is the propagation velocity (appr. 3 x 108 metres per second (m/s) in vacuo). It can be seen that as frequency increases, wavelength decreases since velocity is constant. 6. "Hydro-electric" power, transmitted through linear conductors for industrial and domestic use, is mechanically generated in an alternating form in order to utilize transformation stages. Its frequency, however, is very low, approximately 60 cycles per second (c/s), in order to minimize transmission losses. Radio broadcasting, the "wireless" form of transmission, must use higher frequencies ranging approximately from 100 kilocycles per second (Kc/s; 1 Kc/s = 1000 c/s) to 3 megacycles per second (Mc/s; 1 Mc/s = 1,000,000 c/s) generated by electronic devices. Video broadcasting, radar and the tellurometer are examples of transmission forms using extremely high frequencies in the "microwave" range of the spectrum. The geodimeter uses visible light for transmission. A portion of the electromagnetic spectrum is tabulated below. Nomenclature Long wave radio Standard radio Short wave radio VHF radio Microwaves Visible Light

Frequency 30Kc/s 300Kc/s 3 Mc/s 30 Mc/s 300 Mc/s 100,000 Mc/s

Wavelength (m) 10,000 1000 100 IO

1 0.003 0.000,0007 0.000,0004

Higher frequencies (shorter wavelengths) approach optical characteristics. Reflection becomes more pronounced, thus the energy can be directed into a concentrated beam. This, in part, is the reason that microwaves are

7

ELECTRONIC CONCEPTS AND DEVICES

used in the tellurometer system whereas light is used in the geodimeter system. The MRA I and MRA 2 tellurometer models transmit "S band" microwaves centred on a frequency of 3000 Mc/s, wavelength of 10 cm. The MRA 3 model transmits "X band" microwaves centred on a frequency of 10,250 Mc/s, wavelength of 3 cm. 7. As mentioned previously, the angle traced by a rotating vector generating a sinusoid is referred to as the phase angle. If, for some reason, the vector is caused to move ahead in its rotation relative to the zero time reference we have a "phase advance," and if it is moved backward, we have a "phase retardation." These conditions would appear on the sine wave graph as a displacement of the wave along the time base by a step equivalent to the phase change ,---,.'----+-----',---

~~~ FIG.

\

wt

\

14

The rate of change of Ve, i.e., its instantaneous frequency, is given by the time derivative of its phase angle: d(wet

+ D sin Wmt)/dt =We+ Wm D cos Wmt,

Note that the derivative contains (1) a carrier component and (2) a modulation component which varies within maxima wmD, The factor wmD is known as the "frequency deviation" of the carrier. It is proportional to Vm, the amplitude of the modulation wave. Thus by varying the phase angle of the carrier in step with the modulation voltage, the carrier frequency is modulated but its amplitude Ve is not affected. Figure 15 illustrates this concept.

VVVlJlJ V carrier wave frequency w,

n UV

n

(\ {\ {\ (\ (\ {\

n

modulation wave frequency Wm

nnnnnnn VVU7J VuL modulated carrier wave frequency We

+

Wm

D COS Wmt

FIG.

15

Figure 16 illustrates schematically how frequency modulation is accomplished. The reactance valve is a tube circuit which acts as a variable reactance in parallel with the tank circuit. This reactance varies with the modulation frequency applied to it and thus the total reactance of the tank circuit will vary. The tank resonant frequency, then, changes according to the modulation. In receiving a frequency-modulated signal, the

ELECTRONIC CONCEPTS AND DEVICES

19

fc (carrier) FIG.

16

requirement is to separate the modulation from the carrier. This is referred to as "discrimination" and the circuit element which accomplishes it is a discriminator. A frequency-modulated signal of constant amplitude applied to a discriminator produces a voltage of varying strength according to the frequency deviation of the modulation, as illustrated in Fig. 17. discriminator

FM signal

modulation as varying voltage FIG.

17

18. Frequency modulation (FM) produces higher fidelity than amplitude modulation (AM). A frequency-modulated carrier is less affected by transient "noise" in the atmosphere. However, it does occupy a relatively large band-width of the frequency spectrum, given approximately by B = 2(fa + fm) where fa is the frequency deviation of the carrier. To transmit an FM carrier it is necessary to use a band of frequencies free from other signals, and this band is therefore blocked from other uses. In this respect FM is less efficient than AM which requires a relatively narrow band.

Vacuum Tube Theory 19. When a substance is heated, energy is added to the atomic electrons contained in the lattice structure of the substance. With continued addition of heat, the electrons may attain a sufficiently high energy level to leave

20

ELECTROMAGNETIC DISTANCE MEASUREMENT

the surface of the substance. An electron so emitted loses energy and is attracted back; however, its return is slowed by the repulsion of other newly emitted electrons. Thus an "electron cloud" or "space charge" is built up around the heated element. Tungsten is an example of a material with strong "thermionic emission" characteristics. It has a melting point of 3600° Kelvin and copiously emits electrons at 2800° Kelvin. Mixtures of certain oxides have even stronger characteristics. These are used in making "cathode" elements for vacuum tubes. 20. A diode is a tube consisting of two electrodes fixed in an evacuated container. One electrode is the cathode which is heated to produce a space charge of electrons. The other is the anode, an unheated element to which a positive voltage is applied relative to the cathode. Since the anode contains a positive potential, electrons are drawn to it from the space charge surrounding the cathode. This results in a flow of electrons, or current, from the cathode to the anode. However, if the anode voltage is made negative relative to the cathode there can be no current flow because the anode, being unheated, does not emit electrons and those around the cathode are attracted to a positive charge only. A diode therefore passes current in one direction only (thus the term "valve" is used widely in place of "tube"). Figure 18 shows the elements of a diode in symbolic form . cathode (heated)

evacuated vial anode (positive +/relative to cathode)

~-

electron flow (unidirectional) FIG.

18

If an AC voltage is applied to the anode of a diode, current flows only during the positive half-cycles as shown in Fig. 19.

FIG.

19

ELECTRONIC CONCEPTS AND DEVICES

21

21. A triode is a tube with three elements : the cathode and anode that comprise the diode, and also a grid, or open mesh, located between the cathode and the anode so that the electron flow must pass through the mesh openings. If a negative voltage, or "bias," is put on the grid the effect is to repel some electrons from the stream attracted by the anode. If the grid is located physically nearer the cathode than the anode, a relatively weak grid voltage will have a strong influence on the strength of current drawn to the anode. This is illustrated in Fig. 20.

grid

cathode 20. Relatively weak negative voltage on the grid has a marked effect on the strength of the current flowing from cathode to anode.

FIG.

22. If a resistor (R) is inserted in the path between the anode of a triode and the source of positive voltage, the current (/) drawn by the anode will develop a voltage across the resistor as it passes through (according to Ohm's Law, E = IR) . The magnitude of this voltage will depend upon the current strength, which can be controlled, as already noted, by applying voltage to the triode grid. Grid voltage, or bias, is always kept negative relative to the cathode in order to prevent the grid from actually drawing current, but if this bias is varied, the variations are reproduced in the voltage across the load resistor. Due to the strong influence of the grid potential on current flow, a relatively weak bias variation will produce a large, or amplified, variation of the same form in the load voltage. Thus a weak signal wave superimposed on the grid bias will be reproduced in the anode load as an amplified wave. (See Fig. 21.) The amplified AC voltage can then be applied to the grid of another amplifier stage for further increase or on to a following circuit for further processing. Overall amplification normally involves a number of successive

22

ELECTROMAGNETIC DISTANCE MEASUREMENT R

~-----./\.IV\/'----+

load resistor

signal

'\J'v signal voltage on grid amplified voltage on anode

FIG.

21

stages and if an intermediate frequency is being used these successive stages of amplification are referred to as an "IF Strip." Coupling between the stages is generally made through capacitance or inductance for transferring the AC energy component. One means of coupling makes use of tuned circuits as shown in Fig. 22. Tuned circuits (1) and (2) are each fixed tuned to be resonant at the intermediate frequency. Circuit (1) acts as an impedance load on the first triode and the waveform of oscillations

+ FIG.

22

in (I) is an amplified version of that on the grid of the first triode. This is transferred to (2) by inductance between coils and (2) will oscillate giving an input to the grid of the second triode for further amplification. It can be seen that if the frequency handled was not constant, it would be necessary to tune (I) and (2) to each signal frequency encountered. This indicates one advantage in the superheterodyne approach of converting all signals to a common intermediate value. Before leaving the discussion of tube theory it must be mentioned that the dynamic characteristics of the basic triode can be altered, for specific purposes, by the addition of other grid elements. There are, therefore, a wide variety of vacuum tube types.

ELECTRONIC CONCEPTS AND DEVICES

23

Semiconductor Theory; Junction Diodes 23. Electrons in a solid element can be visualized as arranged in orbits around the nuclei of atoms, these orbits being at discrete levels of energy. The electrons are grouped in the energy levels in definite numbers or "shells," the outermost shell containing the valence electrons. Electrons can also be visualized as arranged in "bands," each band consisting of a definite number of energy levels. All bands have the same number of energy levels, and the separation between the bands is constant for any element. The electrons tend to group in pairs on each level and to fill the bands closest to the nucleus. Therefore, the outermost band of energy levels might not be filled. (See Fig. 23.) outermost band of - - - - - - - - energy levels

--•-·----

-:r-•-•

_L _________

--•-•---- filled band --·-·-----·-·-----•-•---FIG.

23

If an atom is excited by absorption of energy, the electrons in an unfilled band move eaily to a higher energy level in the same band. The separation between the bands, however, is usually too great to permit electrons to move from a filled band to the next higher band. The elements carbon, silicon, germanium and sulphur have filled outer bands but the separation between bands is relatively small, with the result that if a voltage is applied, the electrons can gain sufficient energy to jump to a higher, empty band. These elements are "semiconductors," so called because no movement of electrons can occur until a particular magnitude of energy is applied. Germanium is the most efficient semiconductor because of its very small band separation. When an electron leaves a filled band, a space is left in that band and the atom lacks one negative charge. This space, called a "hole," is then

24

ELECTROMAGNETIC DISTANCE MEASUREMENT

available to be filled by the remaining electrons; the process resembles normal conduction between energy levels within the band. Each time a hole is filled, another occurs so that, in effect, holes are mobile and behave as "positive electrons." For this reason they are also called "positrons." (See Fig. 24.)

t•

-•-·0-----/ ===: __

hole in previously filled band "flows" between energy levels as electrons in that band move up

f ___

--•--•---

--•--•--FIG.

24

Impurities present in any element may possess unfilled bands and these may take up a position which reduces the band separation of the main element, facilitating the movement of electrons between the bands. "P-type" semiconductors contain impurities which accept electrons from the filled bands of the main element (this is called "acceptor impurity"). Since this creates holes in the main element, P-type semiconductors are said to conduct "by holes." "N-type" semiconductors contain impurities which donate electrons to unfilled bands of the main element called ("donor impurity"). Since this adds negative charges to the main element, N-type semiconductors are said to conduct by electrons. 24. Consider a P-type and an N-type semiconductor in contact with each other (see Fig. 25). The excess electrons in the N-type penetrate some distance into the holes of the P-type. This neutralizes the potential of the contact region, but as the electrons depart from the N-type they leave behind positive ions (atoms minus electrons), thus creating an overall imbalance of charge in the N-type, which gains a positive potential. Similarly, the electrons absorbed by the P-type give it a negative potential. A P-N contact produces an element known as a junction diode. Note the voltage gradient across the boundary shown in Fig. 25, the N-type being positive relative to the P-type. This gradient is called the "barrier" because it inhibits any further absorption of electrons into holes across the boundary. By the application of external voltage the barrier can be increased or

ELECTRONIC CONCEPTS AND DEVICES BEFORE CONTACT

AFTER CONTACT electron surplus : . negative

p

(

N

' - - .- - - '

holes due to absorption of acceptor impurity

25

\.

~~~

electron deficiency :. positive

p 0

0

0

0

0

0

0

0

0

I

I I I

I. . .. .. .. N

I

. .. +

I

I•

\_/

electrons due to donation by donor impurity

~

7

~

neutralized zone

/~-+ 0

--~

graph of voltage potential

FIG.

25

decreased, as shown in Fig. 26. Barrier decrease may be sufficient to allow further transfer of electrons, that is, current will flow. Barrier increase will further inhibit current flow. Therefore, if an AC voltage is applied across a junction diode, current will flow only during one half of each cycle, as in the case of a diode tube. They are useful as rectifiers, i.e., converters of AC into pulsating DC current. And since their current-voltage response characteristic is non-linear, junction diodes may also serve as frequency

+N

p /

==7 _ _,,

--

~

-L-~J-~_r -

~

/

barrier increased

barrier decreased FIG.

26

mixers which produce, if impressed with more than one frequency, a complex waveform containing components of the fundamental frequencies, their sidebands and harmonics. The tellurometer employs a junction diode mounted at the tip of the aerial post as a mixer. For microwave mixers of this type a point contact junction diode is used (a small P-N junction will reduce capacitance caused by the dielectric effect of the junction).

26

ELECTROMAGNETIC DISTANCE MEASUREMENT

Transistors 25. Three semiconductors in contact, g1vmg two barriers, form a transistor. Figure 27 illustrates a PNP transistor comprised of an N-type

semiconductor between two P-types. Note the two barriers in the graph of the relative voltage potential of each component.

FIG.

27

If an external voltage is applied to reduce one of the barriers, an "emitter" circuit is formed (see Fig. 28). The reduced barrier permits "emitter current" to flow, that is, absorption of electrons from the N-type by the P-type is enhanced.

=~.___~P~__,__+_N_·_L..-_P___,

FIG.

28

An external voltage applied to increase the other barrier creates a "collector" circuit (see Fig. 29). The increased barrier prevents further absorption of electrons from the N-type by the collector P-type. However, holes created in the N-type by emitter current, being equivalent to positive charges, do move down the collector barrier. Thus "collector current," in the form of holes, does flow.

ELECTRONIC CONCEPTS AND DEVICES

27

p

P,._

(electrons

FIG.

+

29

26. To recapitulate the dynamic characteristics of a transistor, refer to Fig. 30. Collector current, being a flow of holes formed by the emitter circuit absorption of electrons, is directly dependent on emitter current. Thus/, = /, (except for a small flow of holes through the base connection). p

p

~ I.

+

+

base

+

v. FIG.

~

I.

v.

30

A flow of holes in one direction implies a flow of electrons in the opposite direction. Therefore collector current is a "reverse" current (electrons from P to N) and is inherently less mobile than the "forward" current of the emitter. The internal resistance of the collector is, therefore, appreciably greater than that of the emitter (approximately 100,000 ohms and IO ohms, respectively). This allows a relatively large load resistor to be connected in series with the collector without disturbing the overall collector resistance. The collector current flowing through the load resistor develops a voltage across it (E = IR).

28

ELECTROMAGNETIC DISTANCE MEASUREMENT

A small emitter voltage will produce appreciable emitter current because the internal resistance of the emitter is small. But collector current, being due to emitter current, is virtually equal to it. This current flowing through the large load resistor develops a large voltage relative to the emitter voltage. So if a weak AC voltage is superimposed on the emitter, both emitter and collector current will vary accordingly and the voltage developed across the load will vary with the same waveform as the AC input but with amplified magnitude. For example, consider resistors connected as shown in Fig. 3I, with R. = 10 ohms and Re = 1000 ohms. Assume that a 9-volt DC collector voltage is applied and an emitter current p

v.

N

p collector

emitter

'-------------L.--------'-+ FIG. 31

9V

of 2 milliamperes flows. The total emitter resistance is 20 ohms (IO internal + IO external), so from E = IR, the emitter voltage must be v. = 0.002 X 20 = 40 millivolts. But emitter current I, is equal to collector current le, therefore le = 2 milliamperes flows through Re and the voltage across it will be 0.002 x 1000 = 2 volts. Amplification or voltage gain, therefore, will be 2/0.04 = 50 times. This shows that a transistor can be used as a signal amplifier analogous to a triode tube. By rearranging the circuit connections, all functions of a triode can be duplicated by a transistor. A transistor is more compact than a vacuum tube, tends to be more durable and draws less power (there is no cathode to heat). The latest models of the tellurometer and geodimeter have been "transistorized." RF Oscillators

27. An RF oscillator is an electronic circuit which converts DC energy into AC at radio frequencies. The particular configuration illustrated in Fig. 32 is that of a "tuned grid" oscillator. The coil in the anode path and the coil in the grid tank circuit are mutually inductive. The initial surge of anode current produces a rising field around the anode coil which induces EMF in the grid coil. This sets L and C of the tank circuit into oscillation at the resonant frequency l/(21rv(LC)). The oscillations produce a sinusoidal voltage fluctuation on the triode grid, thus causing the anode

ELECTRONIC CONCEPTS AND DEVICES

29

,------~======-=--=-----,---- r----+ resonant output at . frequency

L C

+nc FIG.

32

current to vary at the same frequency. This variation of current passing through the anode coil produces a changing field around that coil which induces further EMF in the tank circuit thus overcoming the "resistive damping" of oscillations in the tank circuit. The whole sequence is regenerative to the extent that energy can be taken off at the anode without attenuating the oscillation. This energy, at the resonant frequency, is passed through a condenser in order to block the DC anode voltage from the output (a condenser of sufficient capacity will "pass" AC but not DC). Note that although the circuit illustrated uses a triode tube, an equivalent transistor could also be used. Also, there are a variety of circuit configurations other than the one illustrated. Each one possesses particular response characteristics but, basically, the object is common-to generate a radio frequency voltage. 28. In an oscillator circuit such as that shown in Fig. 32, the output frequency is directly related to the values of L and C in the tank circuit. In general these values are not constant. The dimensions of a coil, and thus its inductance L, will change with temperature. The same applies to capacitance C of a condenser. Furthermore, condensers tend to "age" with time. The output frequency will therefore be unstable although with good quality L and C components and under controlled conditions, close tolerances can be maintained. In order to "lock" the frequency of oscillation within very narrow limits (a few cycles per megacycle), a quartz crystal can be inserted in the tank circuit (see Fig. 33). Quartz possesses the "piezoelectric" characteristic. That is, if physical pressure is applied to the surfaces of a quartz crystal perpendicular to its optical axis, a voltage occurs between the surfaces. If the stress is reversed, the voltage polarity reverses. The entire process is also reversible: voltage applied to the surfaces produces physical stress in the crystal.

30

ELECTROMAGNETIC DISTANCE MEASUREMENT

C

L

crystal FIG.

33

The resonant vibration frequency of a crystal is a function of its size and shape. If a crystal is manufactured with precise dimensions its vibration frequency can be guaranteed within close limits. A sinusoidal voltage at a frequency nominally equal to the crystal's resonant vibration frequency, if applied across the crystal, will set it vibrating at resonance. The mass of the crystal dampens any tendency of the frequency to wander even though the impressed voltage might do so. This then locks the tank circuit oscillations to the crystal frequency and the result is a "crystal-controlled" oscillator. Because crystal dimensions do change slightly with temperature, and because the resonant vibration frequency is directly related to these dimensions, it is common practice to mount the crystal in a temperaturecontrolled environment in order to stabilize the frequency precisely. In this case the temperature is kept at, or near, the level used for calibrating the crystal frequency. This is done in the tellurometer and geodimeter systems. Microwave Oscillators; Klystron 29. Conventional radio tubes cannot be used to generate microwave frequencies because electron velocity becomes a significant factor compared to the period of such short wavelengths. To show that electron velocity is finite and therefore accountable at sufficiently high frequencies, consider the electrical analogies to the following physical relationships. (1) force= mass x acceleration

(2) kinetic energy =

½x mass x (velocity)2

(3) potential energy = mass x acceleration x distance The electrical analogy to ( 1) above is: force= Exe

ELECTRONIC CONCEPTS AND DEVICES

31

where E is electric field strength (volts/m) and e is electric charge (coulombs). In our particular case e denotes the negative charge of one electron. Note that E = V/d = voltage over distance from the charge (see Fig. 34).

1~

d

E

e

FIG.

= V/d

V 34

The electrical analogy to (3) above is: potential energy= force x distance= Ex e x d = (V/d)ed = Ve. Now the maximum kinetic energy is equal to potential energy, and if the physical and electrical expressions produce identical units Uoules), the two systems can be equated, i.e., ½mv2 = Ve, where m is the mass of an electron and v is its velocity attained due to the attraction of voltage V on charge e. Consequently, electron velocity v = -v(2Ve/m). The values of e and m are both very small and quotient e/m is finite; thus velocity v is also finite. Of course it is very high (say 20 per cent of the velocity of light, under a strong field E) but it is dependent only on the voltage applied, the only variable in the expression (ignoring the trivial loss of mass due to energy). In conventional tubes the intensity of current, i.e., the number of electrons reaching the anode, is varied by the grid voltage. If this variation is to be effective, the time of electron's travel from the cathode to the grid must be appreciably less than the period of half a cycle of grid voltage change. Therefore, at ultra-high frequencies, the intensity of current will not become correctly modulated by the grid. 30. Microwave circuits employ "velocity modulation" devices (as opposed to "intensity modulation"). They are used to vary electron velocity, thereby causing packets or "bunches" of electrons to form in step with the signal frequency. There are a number of such microwave devices. The reflex Klystron is the one which is used in the tellurometer to generate the microwave carrier. Its function, outlined in Fig. 35, is as follows. The cathode is a thermionic emitter of electrons. The anode is an "open" element with a strong positive voltage. The cavity can be visualized as a hollow, doughnut-shaped ring, the enclosed space of which is open through a gap around the circumference of the hole. The reflector is an element with a negative voltage relative to the cathode. Electrons emitted by the cathode are drawn by the strong voltage on the anode, thus gaining a high velocity. Since the anode is an open element the electrons will pass through

32

ELECTROMAGNETIC DISTANCE MEASUREMENT

output

+ I I

I f- - .. I cathode

-+ ------)~ --+

bunches

I I

reflector

I

anode cavity FIG .

35. Klystron.

it and continue on through the hole in the resonant cavity. The field associated with the electron beam enters the cavity space and sets up an oscillating field within the cavity (analogous to producing sound by blowing across a bottle opening). A cavity is equivalent to a tuned circuit, having the inductance of one coil turn and capacitance between the sides at the open tips. The resonant frequency of a cavity is therefore entirely dependent on the size of the cavity space. Once an oscillating field is set up within the cavity, the polarity at the opening changes sinusoidally in step with the oscillations. When this polarity is positive, electrons passing through the centre hole are accelerated and when it is negative they are retarded. As a result, in the "drift space" beyond the cavity there are electrons with different velocities. As faster electrons overtake slower ones, "bunches" are formed. The energy of the electron stream also becomes directed into intensified pulses associated with the bunches. As the bunched electrons continue through the drift space they feel the retarding influence of the negative voltage on the reflector. They lose velocity, stop, and reverse direction, passing back through the cavity hole and on to the anode. If they arrive back at the cavity opening at the instant the retarding cavity field is present, the bunched energy is given up to the field, which becomes stronger. The build-up of field strength within the cavity is such that some of the energy can be drawn off without undue damping. This is done by inserting one turn of wire inside the cavity for induction of EMF by the oscillating field. Optimum feedback of energy from the bunches to the cavity field is a matter of timing. If the bunches arrive back exactly at the instant the field

ELECTROblIC CONCEPTS AND DEVICES

33

changes from positive to negative, the cavity field will oscillate strongly at its resonant frequency. If the timing is slightly off optimum the field will still oscillate but it will be forced slightly off the resonant frequency. Since the timing of bunch return is a function of the reflector voltage, this voltage can be used to vary the cavity frequency within narrow limits. (Gross frequency changes require that the cavity size be changed.) Therefore, when a modulation voltage is applied to the reflector, the modulation waveform will appear in the output as a frequency modulation of the induced EMF.

Cathode Ray Tube 31. Figure 36 is a schematic diagram of the main elements comprising an electrostatic cathode ray tube (CRT). Electrons emitted by the cathode are attracted by high positive voltage on the anodes. The two anodes have balanced voltages which, together, set up an equipotential field.

+ I

cathode

~

I I I I I /I grid

+

V

V

_J_

/T

.

deflectors

focussing anodes FIG.

e

phosphor-coated screen

36. Electrostatic cathode ray tube.

This prevents electrons from reaching either anode, but will accelerate the electrons as they pass through the field, focussing them into a beam. The beam then passes between the deflector plates and if a voltage is present on these plates the beam will be deflected from a straight path ( toward the positive, away from the negative plate). Once past the deflectors, the beamed electrons travel through a force-free region and impinge on the screen coating causing the phosphors to glow. Electron velocity must be high in order to permit a large beam deflection with negligible change in travelling time to the screen. This requires a strong positive voltage on the anodes (1000 to 10,000 V).

34

ELECTROMAGNETIC DISTANCE MEASUREMENT

The grid element has a negative voltage (relative to the cathode) which can be changed to alter the beam intensity, or brightness. A sufficiently strong grid voltage will repel all the electrons and cut off the beam entirely. Although Fig. 36 shows two deflecting plates only, there are actually four of them positioned in two pairs perpendicular to each other. The signal used to produce the pattern on the screen is applied to the deflectors. (See Fig. 37.) Suppose that signal Vi is a sinusoidal voltage and V2 is zero. During the half-cycle when one of the horizontal deflectors is positive

signal V2 signal V1

FIG.

37. CRT deflector plates.

and the other negative, the beam will deflect toward the positive plate, being nearest to it at maximum voltage amplitude and returning to the centre as the voltage decreases toward zero. As the voltage reverses to the opposite half-cycle, the beam will deflect to the opposite direction and then return to the centre as the cycle is completed. This will repeat with succeeding cycles and the resultant screen pattern will be a straight, horizontal line. Similarly, if a sinusoidal voltage is applied to the vertical plates only, the pattern will be a straight, vertical line. Now suppose that similar sinusoidal voltages (same frequency and amplitude) are applied simultaneously to the two sets of deflector plates. If the voltages are 90° different in phase the resultant pattern will be a circle. This is explained as follows, referring to Fig. 38. The beam deflects from neutral position o to maximum a as the voltage on plate X 1 goes from zero to maximum positive voltage A . As the voltage on X 1 reduces from maximum, the voltage on Yi, being 90° later in phase, begins to build up. Thus the beam does not return from a to o but instead deflects toward Y1 along a circular path, reaching point b when the voltage on Y1 is at a maximum (B). Similarly, as this voltage decreases toward zero, the voltage on X 1 goes negative (X2 goes positive) and the beam deflects toward X 2 along a circular path, reaching c when the voltage on X 1 is at C. And so on to point d when the voltage on Y1 is at D. The process repeats with succeeding cycles and the screen pattern is a circle. 32. If a strong pulse of negative voltage is applied to the CRT grid

ELECTRONIC CONCEPTS AND DEVICES

A

_ _ ___._

r

B

35

waveform of voltage on horizontal plate X 1

; - waveform of voltage on vertical plate Y 1: I identical to horizontal _,__ _...,,__....:,..._ _- 1 - - - + - voltage but 90° later in phase

C FIG.

38

momentarily, the beam will be cut off and a break will appear in the circle. An elementary pulse-forming circuit can consist of a triode with a strong negative grid bias such that no current is drawn to the anode under static conditions. If then an AC voltage is applied to the grid with an amplitude such that for a fraction of each positive half-cycle the grid bias is reduced sufficiently to allow current flow, the result will be an intermittent flow of anode current, once per each AC cycle. In such case reference is made to "pulse recurrence frequency" (prf) instead of cycles per second. (See Fig. 39.)

fl!>, f/JJ.i current flow in pulses - ~ - - - - - ~ during conductic •1 intervals fraction of cycles when bias driven above cut-off

signal AC on grid

cut-off bias voltage on grid FIG.

39

36

ELECTROMAGNETIC DISTANCE MEASUREMENT

Phase Change and Discrimination 33. In certain electronic applications the phase of a sinusoidal wave must be advanced or retarded by a given amount or, as in the case of electromagnetic distance measurement, the amount of phase change undergone by a wave during propagation over a particular distance must be determined. In travelling through space at the speed of light an electromagnetic wave undergoes phase retardation in proportion to the distance travelled. For example, consider one cycle of x sinusoidal wave as shown in Fig. 40. At a distance of one-half wavelength from the source, the phase angle is 1r radians different from that at the source. The angular change equals 21r radians (360°) for each wavelength (},) distance from the source, and therefore, when X. is measured in metres, the angular change per metre is 21r/X. radians. In a distance of z metres the angular change will be 21rz/X. radians.

\

\

\

change = fraction of wavelength FIG.

'- . /

I

I

I

40

If the equation of a wave is y = A sin wt reckoned at the source, the equation of the same wave reckoned at distance z from the source will be y = A sin(wt - a) where a = 21rz/X. is the phase retardation angle. Note that since X. = v/f = velocity/frequency and/= w/21r,

21r 21r wz -z=-z=X. v/f V so that y = A sin(wt - 21rz/X.) = A sin(wt - wz/v) = A sin[u:(t - z/v)]. Therefore, if the phase retardation of a sinusoidal wave can be measured, either as an angle (a) or as a time interval (z/v), this measurement can be related to a fraction ofa wavelength, i.e., a distance. 34. A delay line is a variable impedance which changes, by a calibrated amount, the phase relationship between the alternating current applied to it and the voltage developed across it. A common type of delay line

ELECTRONIC CONCEPTS AND DEVICES

37

consists of an inductive element (a coil) with a movable "pick-up" which permits the number of effective turns to be varied (see Fig. 41). The pick-up can be in contact with the coil, or it can be a loop of wire into which EMF is induced with the phase pertaining to its location on the coil.

-

!

-

movable pick-up

E

FIG.

41

Every conductor has resistance, the magnitude of which is inversely proportional to the area of cross-section. By forming a coil of highly conductive material (such as copper) having a large cross-sectional area, the resistance per unit length can be kept quite small. A coil has relatively large self-inductance characteristics and thus presents considerable inductive reactance to the passage of alternating current. At higher AC frequencies there is also significant capacitance between a coil and elements of different voltage potential, the intervening space acting as a dielectric. Therefore some capacitive reactance also exists to impede alternating current flow. Recall that: (a) ER = IR expresses the voltage developed across resistance R by current I and in alternating current ER and/ are exactly in phase. (b) EL = IXL expresses the induced voltage due to alternating current I flowing through inductive reactance XL, EL leading I in phase by 90°. (c) Ee = !Xe expresses the voltage developed across capacitive reactance Xe by an alternating current/, Ee lagging I in phase by 90°. The vector diagram in Fig. 42 illustrates the relationship between these voltage components and the resultant voltage when R, XL and Xe are all E 1, (leading I by 90°)

(Er. - Ee)

I

I I

_ __.___ _ En (in phase with I)

Ee (lagging I by 90 ') FIG.

42

38

ELECTROMAGNETIC DISTANCE MEASUREMENT

present in a circuit carrying a common alternating current. The phase of the resultant voltage E relative to current I is found from tan : :~: 2 f 1

1-+l

lDf rm

+ +i----t -t H

Hlflli mt

t I

I

I

lTT

I

l

Tl

I.

FIG. 99

153. Battery charging. Caution. Do not permit flame or sparks near a charging battery. Due to the presence of hydrogen and oxygen during the gassing stage, explosions may result. Do not connect or disconnect batteries unless the charging current is stopped.

Nickel-cadmium batteries may be charged by the same methods as leadacid batteries. The more common systems used are the constant current, the constant potential and the modified constant potential methods. The characteristics of the constant current charging method will be obtained to some degree by the taper charge method discussed with lead-acid batteries. 154. Charging by the constant current method can be accomplished by using a rectifier or engine-generator battery charger. The current is maintained constant throughout the charge by the use of a slide-wire rheostat in the case of the rectifier charger or a field rheostat in the case of the generator set. The rheostats require adjustment during the charge, since the battery voltage rises. Schematic diagrams for such charging systems are given in Fig. 100.

iJ

BATTERY POWER SUPPLIES

-----+---

179

>-1-----