INSTRUMENTATION FOR MICROWAVE FIELD MEASUREMENTS
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
by
Jack Bacon, B .E .E ., M.Sc.
The Ohio State University I960
Approved by
d . ___ Adviser Department of Electrical Engineering ACKNOWLEDGMENT
Because the research reported here has extended over such a long interval of time, it is difficult to acknowledge all the individuals who have contributed to its success. In particular, the most valu able technical suggestions have been given by Professors R. L.
Cos griff, T. E. Tice, and F. C. Weimer. Although the advice of
R. A. Fouty was of a different kind, it has been no less valuable.
In the beginning he pointed out several areas where contributions could be made to advantage. His suggestions, which came when the writer was unfamiliar with the field of endeavor, proved to be in valuable.
No acknowledgment could be complete without recognizing the contributions made by the supporting staff of the Antenna Laboratory.
This includes particularly the drafting and editorial personnel.
Specifically, without the willingness of Miss Dorothy McGinty and
Mrs. Barbara Kerwood to work long hours of overtime beyond the call of duty the preparation of this manuscript in completed form would have been impossible in the allotted time. The encourage ment of my collegues and the forbearance of my wife has been no less a factor in the completion of this dissertation. The research reported herein was sponsored in part by the
Air Research and Development Command, Wright-Patterson Air
Force Base, Ohio, under contracts with the Ohio State University
Research Foundation. TABLE OF CONTENTS
Page
SECTION I - INTRODUCTION 1
SECTION II - IMPROVEMENT OF EQUIPMENT STABILITY 4
A. SELECTIVE AUDIO AMPLIFIER 4
1» Introduction
2. The Selective Audio Amplifier 6
3. Performance of the Amplifier 9
B. MECHANICAL RECTIFICATION 10
1. Introduction 10
2. Linear Rectifiers 13
3. Phase Discriminator 17
SECTION in - AUTOMATIC RECORDING 19
A. GENERAL CONSIDERATIONS 19
B. SQUARE ROOT RECORDERS 36
C. LOGARITHMIC RECORDERS 41
1. Commentary 41
2. Dual Detection Type 42
3. Audio Type 47
D. PHASE RECORDERS 51
iv Page
SECTION IV - ECHO AREA INSTRUMENTATION 63
A. GENERAL CONSIDERATIONS 63
B„ RADAR INSTRUMENTATION 68
1. Commentary 68
2. Innovations 7 0
3. Open-Loop Design 80
SECTION V - HIGH SENSITIVITY SYSTEMS 91
SECTION VI - RATE OF RECORDING 102
A. INTRODUCTION 102
B. CALCULATIONS 103
1. Null Depth 103
2. Beam Shifting 112
SECTION VII - CONCLUSIONS 115
APPENDICES 119
BIBLIOGRAPHY 189
AUTOBIOGRAPHY 199
v SECTION I INSTRUMENTATION FOR MICROWAVE FIELD MEASUREMENTS
I. INTRODUCTION
The need for precision instrumentation has long been recognized as essential to a well-rounded program of research in antennas, radar echo, radomes, wave propagation, and other related topics which re quire microwave field measurements. The instrumentation research described in the following pages has been concerned with either im proving the accuracy and reliability of existing instrumentation or with devising techniques for new types of measurements. Since automatic plotting of data is usually the only practical way to record information of this type, heavy reliance on servomechanisms is inevitable.
One illustration of the need for such instrumentation is the measure ment of aircraft antenna patterns by the method of electromagnetic
1 2 3 4 5 6 7 modeling. ’ ’ ’ ' * ’ This technique is based on maintaining the same ratio of aircraft size to wavelength in the model as in the full-sized system. Figure 1 shows a simplified block diagram of a typical model range used to measure antenna radiation patterns.
In order to improve the stability, accuracy, reliability, and dynamic range of the automatic antenna pattern-measuring systems, the principles described in the following pages may be applied. They
1 Aircraft Antenna
Detector
Support Tower
Turntable Transmitter Re cording Instrumen Modulator tation
Azimuth Information
Fig. 1. Instrumentation for model antenna measurements'. have been tested sufficiently in actual applications to guarantee improved
performance.
In addition to recorders which plot a parameter proportional to the voltage at the receiving antenna terminals, for certain types of interpretation and analysis it is often desirable to record patterns proportional to the logarithm of the input, i.e. , to record in decibels.8’9
The development of this type of recorder to a highly practical state is described in the following pages.
2 A key unit in both recording systems is a selective amplifier of improved design. Other specialized instruments which will be dis cussed include a practical automatic microwave phase plotter, a super sensitive synchronous detection system, and numerous im provements in both continuous-wave and pulse radar echo measuring systems.
The discussion which follows is not intended to be either a complete or a tutorial presentation of the subject matter. Rather it is intended to present the author* s personal contributions to the advancement of human knowledge of the field.
3 SECTION II IMPROVEMENT OF EQUIPMENT STABILITY
A. SELECTIVE AUDIO AMPLIFIER
1. Introduction
In a conventional pattern range ( see Fig. 1) the transm itter is amplitude-modulated by an audio-frequency voltage. The received signal is detected to recover an a-c voltage having the same frequency as the modulator and an intensity proportional to the incident power.
Receiving equipment used in early measurements of this type is indicated in Fig. 2. It consists of a square-law detector (bolometer
Narrow Input Square Root R dss Band ______^ Signal Amplifier Amplifier Polar r Recorder Azimuth Information
Fig. 2. Component parts of an early receiving installation. or crystal) , a narrow-band selective amplifier, and a linear recorder.
By introducing a square-root amplifier to compensate for the inherent squaring action of the detector, a plot proportional to the voltage at the terminals of the receiving antenna results. The linear or circular
4 motion of the recorder chart is synchronized with the azimuthal position of the turntable by means of a servo link.
In order to improve discrimination between the weak received signal and the spurious noise, it is desirable to decrease the band width of the selective audio amplifier. One method of doing this is shown in Fig. 3. This employs a General Radio Model 736-A wave
Wide Square Wave Band Wave Root ’ Signal Bolometer Analyzer Recorder Amplifier Amplifier
Fig. 3. Wave analyzer application in receiving equipment. analyzer as a narrow band filter. The instrument is a superheterodyne receiver with a 4 cps pass-band i. f. amplifier centered at 50 kc«1(* The
4 cps bandwidth is a good compromise between noise suppression on the one hand and-limitations associated with the reduction of the rate of recording antenna patterns on the other.
In order to improve the stability, accuracy, and dynamic range of the system, the various techniques described in the following pages may be introduced.
First, a narrow band audio amplifier may be used to supercede both the wave analyzer and the input amplifier, while providing a comparable degree of selectivity and gain. For simplicity, the superheterodyne principle is eliminated and selectivity is obtained directly at the audio frequency output of the r-f detector. An addition al advantage here is that the filtering begins at a low enough signal level that additional noise components are not generated because of nonlinearities in the preceding amplifier.
2. The Selective Audio Amplifier
System analysis and practical measuring experience define a practical standard of performance, e.g. , a gain of 93 db is usually sufficient. In the design now in common use, 0. 5 volts output results for an 11. 5 microvolts input with noise sufficiently low to provide a usable dynamic range below this level. Earlier results of other investigators11 indicated that the desired selectivity could be achieved by using some of the better toroidal inductors in resonant circuits.
The tube complement consists of a high gain pentode amplifier followed by four low-gain stages using dual triodes. RCA Red Seal tubes are selected for longevity and low noise. By virtue of small coupling capacitors in the triode stages, gain is suppressed while the driving impedance of the resonant circuits is increased to realize the full Q of the coils.
I-Ialf-henry inductors are used throughout. Using these, the amplifier has an output which deviates negligibly from linearity over an 80 db range extending from 6 volts downward. The slight deviation
from linearity which is observed with large signal levels is due to a
reduction in Q and hence a decrease in the resonant impedance QX.
High Q toroidal inductors are characterized by a Q which increases
with frequency over the normal range of 400 to 1000 cps. Tests of
several selective amplifiers tuned to spot frequencies throughout this
band indicate that the bandwidth is uniform at 4 cps. The clear im pli
cation here is that the Q is proportional to frequency over this range.
A sample frequency characteristic curve, centered at 1000 cps, is
shown in Fig. 4. Since the gain is nearly proportional to the magnitude
of the load impedance in each stage, one would expect the response
curve to have the form given by Eq. ( 1) . For a half-power bandwidth
of 4 cps, T = 0. 0308,
K (1) G =------_ |l+jwT|
From the well known relationship-of Eq. ( 2) , the corresponding Q is found to be about 97. Actually this is a bit low in comparison to quoted figures. The decrease is doubtless due to loading in the circuit,
Calculation of the response curve, based on Eq. ( 1) , shows good agreement over a wide range of values.
7 rtx mi
0 L - .
00 i
; ' 'j-~~ SELECTIVE AMPLIFIER - ■ FREQUENT RESPONSE CHARACTERISTIC j
SOOO 9 to t9 CP*
Fig. 4. Selective amplifier frequency response characteristic.
Tuning is accomplished by shunting the inductors with several mica capacitors in parallel with an additional 1400 to 3000 (J-jJ-f trim m er.
"Without the additional flexibility of a trim m er, tuning would be both difficult and time consuming. At 1000 cps the tuning rate is given by
Eq. ( 3) . In other words, the 1600 p(j,f tuning range
d£z cps (3) 9. 85 x lO"3 H e
8 shifts the center frequency approximately 16 cps. This is adequate
for easy alignment.
3. Performance of the Amplifier
Noise output may be determined by connecting a Hewlett Packard
type 400-C vacuum tube volt meter to the amplifier output. The results
are listed in Table I. Negligible increase in noise is observed when
TABLE I NOISE CHARACTERISTICS
Input Average Noise Equivalent Output Input Short Circuit 0. 8 x 10"4 1. 84 x 10"v
Crystal 3 x 10“4 6. 9 x 10'9
Bolometer 2. 8 x 10"4 6. 4.5 x 10“v
current is allowed to flow through either the bolometer or the short circuit. This is in accord with conclusions reached by theoretical investigators12 that no increase in generated thermal noise should result from a superimposed steady current. The increase in noise voltage output in substituting a bolometer for a short circuit is, in part, contributed by the thermal noise voltage as expressed in Eq. ( 4) ,
(4) E 2 = 4 k TR Af where k is Boltzmann* s constant ( 1. 372 x 10“23 joules/degree) ,
9 T is the absolute temperature, R is the resistance in ohms, and Af is
the bandwidth in cycles/second. This gives E2/R the proper dimensions
of watts. For the assumed set of conditions T = 350, R = 200, Af = 4,
E equals 3. 9 x 10"9 volts. This means that when using a bolometer the
actual noise level is approximately 4 db above the theoretical noise
level. This is sufficient to give the overall receiving system a
sensitivity equal to that obtained when a wave analyzer is employed.
The new amplifiers allow a vast decrease in size and weight. Further
more, a degree of stability is achieved which had heretofore been
noticeably absent. As an indication of their stability, the first units
were constructed and reported in 1950. 13 To the w riter1 s knowledge
not one of the amplifiers has needed retuning to date because of
internal drift. Except for the inclusion of improved components over
the years, the present models are still basically the same as the
earlier prototypes. Improved input transformers and tubes have made possible a reduction of the noise differential from the earlier figure of 4 db to about 2 db.
B. MECHANICAL RECTIFICATION
1. Introduction
Receiving system for antenna measurements almost without exception, require conversion of the received signal from a carrier to a noncarrier form. The need for conversion may arise simply
10 as a means to drive a d-c recorder. Again, it may arise because
of the need to convert the signal from a carrier of one frequency to that of another, e.g. , 1000 cps to 60 cps. Whatever the need,
stringent specifications are necessarily imposed on the stability, linearity, and dynamic range of the conversion circuits. The importance of these characteristics occurs because the process of conversion generally takes place in the open-loop portion of the system, as may be seen in Fig. 5. Consequently, any deleterious performance here affects the overall dynamic response of the receiving system.
In previous applications diode circuits were used exclusively.
Their deviation from the ideal was manifested in several ways. For one, the dynamic response became nonlinear for low signal levels.
Obviously this effect could be balanced out. However, other problems arise. Balancing introduces the possibility of drift. It also tends to make the dynamic response nonlinear for small signals. The use of semiconductor diodes or unusually high impedance circuits does not lead to a satisfactory solution to this problem either. Of all the diode circuits considered, about 25 db of linear dynamic range is all that can be achieved. With an 80 db range as a goal, it became clear rather quickly that other techniques would be necessary. The mechanical
11 Incident Selective ocac Square r-f Energy Amplifier R ooter Detector
ac ac RectifierRecorder
(a)
ncident ac Selective ac ac Rectifier r-f Energy Am plifier Detector ~~1
Position Indicator
Function Potentiometer
Square Root Servo ------1
(b )
Fig. 5. Pattern measuring systems. rectifier was found to possess the nearly ideal properties required.
Because the process of rectification is so intimately associ ated with phase detection it is a natural extension of the investigation to consider the application of mechanical rectifiers to this problem as well.
In order not to mislead the reader, it is well to point out that this is an old technique with a new look. It was first observed in
12 so-called "trickle" chargers for home radio batteries. The principal difference here is the end result to be achieved. In this instance the property of stability and linearity are exploited to the fullest. These characteristics have been developed to a high state of perfection in chopper elements developed for servo applications. Unfortunately most of them do not have the frequency range needed. So far only one mechanical chopper has been produced which will operate as high as 3 kc. With most signal sources being modulated at 1 kc for antenna measurements, these particular units have been found highly satis factory and trouble-free.
2. Linear Rectifiers
Rectification by mechanical means is a coherent or synchronous process. The reed is driven at the audio or modulation frequency and properly phased for maximum d-c output signal. The requirement of a synchronizing signal imposes no undue inconvenience in antenna instrumentation because the receiving equipment is usually adjacent to the signal source and modulator.
A great variety of circuits can be devised, these being of either full or halfwave type. A representative circuit together with the results achieved is shown in Fig. 6. 14 The lower limit is imposed by the noise level; the upper one is imposed by the large-signal nonlinearity
13 ■20 | C H •30 ChopM' Clreoit U 40 0 db r»pf#*«nt» 7 V input ond 21 V output 60•80 ■50 14 NOTES Mpchonicot Rpctifif R>«pon»a Relative A-C Relative Input A-C voltage in db 90 Fig. 6. Mechanical rectifier characteristics.
tllJJi J of the amplifier. Between these two extremes the response is linear with line splitting accuracy. The useful range is at least
86 db.
The circuit lends itself to either positive or negative output.
Both can be taken off simultaneously if desired. When properly adjusted for a given polarity across one load resistor, the opposite polarity will automatically appear across the other. In contrast with diode circuits, an additional advantage is apparent and is quite important in many applications; namely, the output impedance is vastly lower than that encountered in diode circuits.
Maximum rectifier gain results when the contacts are closed over an interval symmetrical with respect to the received signal sine wave maxima. The contact closure is approximately 30 percent of a cycle, according to the manufacturer's data. Figure 7 shows the optimum wave form appearing across the d-c output terminals with the filter capacitor disconnected. Due to the phase sensitive nature of the rectifier, any change in phase of the received signal over the dynamic range becomes apparent as error in the linearity.
A change in phase e shifts the limits of integration an equal amount.
The percent error introduced by incremental phase shift is given by Eq. ( 5) and is independent of the closure time,
I 1 5 Closure Closure
Fig. 7. Optimum, rectifier wave shape.
_+• e + e cos cat dcat -0 + £ (5) Percent Error = 100 1 = 100[l-cos e] + 0 cos cat dcot I -0
Since e would ordinarily be small, the approximation of Eq. ( 6) is valid. Accordingly, a phase shift of 8. 0° is necessary to cause a one percent error. A shift this great is far more than one would ordinarily expect,
(6) Percent E rro r ~ 50 e2
16 Note that closure over an interval shifted 90° from that yielding maximum output results in a null output. This suggests that perhaps the chopper could serve as an unusually stable phase
detector.
3. Phase Discriminator
In a system where a-c error signal is taken as the difference between two voltages, for instance when an a-c follow-up voltage is balanced against an input a-c signal, there is inevitably a quadrature component. It has been found that, in a positional system a balance to the noise level can seldom be achieved over the full dynamic range .
Inevitably a fundamental quadrature component remains, whose iragnitude may vary widely. It has the unfortunate effect of producing heat in the motor but no torque .
Quadrature error components are normally removed with a phase sensitive detector. These take various forms and are generally well described in the literature . 1S> 16 Actually their performance depends upon holding a fine balance between two d-c voltages, and hence drift is a problem. It is really this drift which establishes the lower limit of resolution. A typical circuit was found to have a long term drift of 25 mv. or so and a short term drift about one fifth this amount.
17 A synchronized chopper can be used as a phase sensitive detector with a substantial improvement in performance. Figure
8 shows one possible arrangement of components. An improvement
o Input o A/vy , o AAA Signal e0
o
Fig. 8. Phase discriminator. in the order of 33 db may be achieved over the short term stability of the diode discriminator. In antenna measuring instruments where the ultimate performance is often required, this results in a welcome improvement to the servo circuits . A consideration of some unorthodox applications of servo choppers forms the basis for several pertinent applications.14
18 SECTION III AUTOMATIC RECORDING
A. GENERAL CONSIDERATIONS
The desire to improve the performance of existing electronic square rooters prompted an investigation into alternate methods of achieving the same law of response over a greater dynamic range in a way that would be independent of the degradation of components.
The first effort to develop an improved instrument employed servo techniques. T 7 Although this initial effort never came to fruition, it provided a background for subsequent endeavors. Specifically, it indicated that the servo technique held promise as a way to ac curately obtain the square-root function. Where it fell short was in the dynamic range and transient behavior over this range.
Starting at this point the author carried the design through to com pletion and even to the point where it became a commercial instrument.
It was initially observed that the square-root servos in variably had a transient behavior which varied widely over the dy namic range of the instrument. Later, the same characteristic was noted in other types of recorders subsequently developed fox antenna measurements. Eventually it became clear that nearly
19 all recording instruments encountered in antenna work have non linear characteristics with certain common features. It turned out that with proper design procedure the transient behaviour of all these instruments could be made uniform over the dynamic range in spite of this nonlinearity.18
Automatic instruments employed in making antenna m easure ments are principally those which record either logarithmic or square-root functions of amplitude or linear functions of phase.
The major design difficulty is that of providing for uniform servo response throughout the full dynamic range. In the usual linear servo this consideration is no problem because the loop-gain is constant. In antenna instruments, however, the effective loop-gain is often a function of a generalized variable u.
A typical situation where the follow-up device is functionally related to the variable u is shown in Fig. 9. For certain types of
Motor fl
Fol low-up Component Gain = G (u)
Fig. 9. Nonlinear servo.
20 amplitude plotters u is identified with the output shaft position. In
other cases u is not related to the output shaft position but rather
is a function of some other signal associated with the system in
question. It is conceivable that u could be completely divorced
from the servo altogether. Since G(u) is a multiplier in the servo
loop-gain, a change in this quantity can be expected to cause serious
deterioration of the servo performance, independently of how u is
related to the servo itself. Under actual operating conditions,
variations between the extremes of complete insensitivity and a
state of self oscillation are possible. It is the intent of the present
discussion to show in a practical way how the influence of u on the
servo loop can be nullified.
Consider an amplitude plotter where the output is propor
tional to a nonlinear function of input and the follow-up component
is a potentiometer having fixed excitation. The pertinent example
shown in Fig. 10 is a square-rooting device. Assuming a perfect
servo = 0) the functional relationship E2 = k02 gives rise to a perfect square-rooter with 0= KQ E^. Small-signal gain of the
feed back path G{u=0) is defined as dE2 /d0. In this particular in
stance G(0) = k0.
Servomechanisms using nonlinear potentiometers in the man ner shown may have an incremental gain which is not simply
21 Amplifier
R > > r
Fig. 10. Uncompensated square-root servo. proportional to the slope of the follow-up potentiometer function.
Certain other factors must often be taken into consideration in de termining G(u). For instance, the impedance of the input generator may be a contributing factor in the determination of G(u). It is worthy of note that under certain circumstances even a so-called
linear servo may exhibit nonuniform incremental loop-gain. It is not the intent to consider how the various factors influence G(u) in
specific cases, but rather to consider how the servo may be made to have uniform dynamic stability in the presence of such an ele ment. Stated succinctly, the stability is maintained uniform by con
straining the incremental loop-gain to be constant.
22 It is not implied that the incremental loop-gain is always a variable in a servo designed to plot a nonlinear function of input
signal amplitude. Consider the particular type of logarithmic re
corder shown in Fig. 11. Here the input voltage E^ is applied to an
EXPONENTIAL a t t e n u a t o r
Preference
Fig. 11. Logarithmic servo.
exponential attenuator through amplifier K. The pick-off voltage
e is servo positioned for a constant signal level so that the recti fied voltage e equals the reference voltage V . This makes Eq.
{7 ) and Eq. (8) hold
(7) e = KEj£ = constant
(8) 6 = C log K E4 .
The symbols C and K are constants. Incremental gain of the at
tenuator is given, as before, by de/d0. Note that this becomes a
23 new constant due to the restraint imposed by Eq. (7). The servo performance is consequently independent of the input signal level over the usable dynamic range of the instrument. Recorders con structed using this principle confirm this fact.
There are cases where the independent variable u is identified with the input signal intensity, but not with the output shaft position.
A servo designed to plot r-f phase is a particular example. An elementary design is shown in Fig. 12. Here a balanced hybrid
PATH '
AMPLIFIER
MODULATOR
Fig. 12. Rudimentary phase servo.
24 junction is employed as the r-f phase discriminator. Under proper operating conditions, the magnitude of the audio error voltage £, for small values of 6, is given by Eq. (9). The angle & is the amount by which the phase of Ex and E2
(9) t - K Ex E2 5 differs from quadrature or 90°. Thus with a phase difference of tt / 2 radians, £=0 regardless of the amplitude of Ex .
The instrument operates by using £ to actuate a motor, which in turn moves an r-f phase shifter so as to minimize this error.
Thus as the phase of Ex varies, the r-f phase shifter "tracks" to maintain E2 at the constant phase difference of ir / 2 radians relative to Ex . The phase shifter position is taken as an indication of the relative input phase, by actuating a chart mechanism from the mechanical output.
Since the r-f phase is a linear function of the shaft position, the static sensitivity of the hybrid junction is proportional to d£/d0. The reference voltage E2 is normally constant in value, consequently the gain function in this case is proportional to the mag nitude of Ex , as shown in Eq. (10). Thus, u is identified with the input signal strength and independent of the shaft position.
25 (10)
Inasmuch as the magnitude of Ei may vary widely in actual oper ation, the utility of the instrument in this simple form is neces sarily restricted.
The discussion so far has indicated how the servo loop-gain in some pertinent examples in antenna instrumentation can become a function of an external variable. Some remedial measures are now considered which can be taken to maintain uniform transient re sponse over the dynamic range of a servo characterized by in cluding nonlinear elements .of the type described. Figure 13 is
* Amplifier 1 Compe nsator
Gain = C ( u ) = G_,(u )
External Variable U
Motor
E Nonlinear Follow-up Component Gain = G(u)
Fig. 13. Compensated servo with externally controlled nonlinearity.
26 a modification of the servo shown in Fig. 9. Under static conditions, where the input is maintained constant, Eq. (11) holds.
(U ) 1 E = - § = G
It is clear in this case that the loop-gain is proportional to tne quan tity C times G. Thus for small signals, the effect of the variable u = 0 on the system can be nullified if the quantities C and G are reciprocals. Although more extensive studies of nonlinearities in servos have been carried out at The Ohio State University Antenna
19, 20,21 Laboratory, the simplified solution indicated here has in every instance been satisfactory for stabilizing antenna instruments.
Two separate cases are considered in turn. In the first ex ample the independent variable u is identified with the output shaft position; in the second it is identified with an external voltage source.
When the variable u is identified with the output shaft position, the compensator can be simply an additional potentiometer attached to the output shaft. Consider again the square-root servo of Fig. 10.
It was pointed out in this example that G(9) is proportional to 0. To obtain a reciprocal relationship between C and G, it must be true that C = K/0. Figure 14 shows the compensator C attached to the output shaft. The reciprocal gain function is approximated by a
27 set of shunts attached at judicious points along the potentiometer resistance which serves as the compensator.
E COMPENSATOR AMPLI El ER
FOLLOW-UP COMPONENT
Fig. 14. Compensated square root servo.
It becomes obvious that a square-rooting servo can never be made to plot precisely to zero, because the follow-up gain G^S) becomes vanishingly small in the neighborhood of 0 = 0. To main tain constant loop-gain in the neighborhood of the origin would re quire that the compensator gain increase without bound. Certain compromises can be made in this region, however, without seri ously affecting the accuracy of the instrument. Modifying the law of response by altering G<0) so that it has a finite slope near the origin can be used, for example, without causing serious error.
Since in this region there is usually noise present which tends to
28 obscure the true reading, a slight distortion of the law of re sponse here has no significant degrading effect. An alternative to this solution is to stop the instrument short of zero.
Uniformity of transient response across the dynamic range of the instrument depends upon the accuracy with which the compen sator is adjusted. Figure 15 shows the uniformity of response
Fig. 15. Step function response for a compensated square root servo.
29 which can be achieved over an 80 db range of input signal or a 40
db range of output. The response is sufficiently uniform so that
there is negligible difference between its behavior and that of a
socalled linear servo. This same technique has also been applied
to an instrument servo where the loop-gain varied exponentially
with output shaft position over an amplitude range of 100 db.
The compensator in this instance consisted of another exponential
attenuator attached to the output shaft and having a gain function
which varied inversely to the gain of the follow-up component.
The finished design exhibited a uniformity of response very little
different from that of a truly linear servo.
In situations where the loop-gain is functionally related
to an external variable, say a voltage, the problem of stabilization becomes somewhat more difficult. A practical solution, which places no severe constraints upon changes in the variable u, consists of employing an auxiliary servomechanism to obtain the necessary compensation. A suitable slave potentiometer mounted
on the output shaft of the auxiliary servo provides the required compensation to the principal servo loop. Deleterious effects from the inclusion of a time-dependent variable, namely the compensating potentiometer, into the principal servo loop is
30 satisfactorily minimized by making the compensating servo re
sponse relatively fast in comparison to that of the principal servo.
The phase plotter shown in Fig. 1 2 is an example of where an
auxiliary servo can effectively provide the required loop-gain sta
bilization. The necessary modifications are shown in Fig. 16. It
Compensator Gain ir Tes t Path
Modulator
Fig. 16, Compensated phase servo, was previously pointed but that the error comparator has a gain proportional to Ej , but independent of 0. As a result, the
31 compensator gain function must necessarily be of the form K/Er
throughout the dynamic range of the instrument. The actual
response of an instrument employing compensation is shown in
Fig. 17.
TO PHASE PLOTTE R
( Inches)
Fig. 17. Compensated phase servo response.
In considering alternate ways to achieve suitable compen
sation for the independent variable u an external voltage, it be comes apparent that exponential potentiometers inherently have
some advantages. Consider Fig. 18. This is a device which has great flexibility in the type of gain function it can simulate. The top
32 AMPLIFIER RECTIFI E R
MASTER i POTENTIOMETER
MOTO ERROR AMPLIFIER
REFERENCE VOLTAGE
SLAVE POTENTIOMETER
Fig. 18. Generator for compensation functions, portion is simply an audio logarithmic servo wherein the follow- up potentiometer is exponential and has an attenuation rate c l . The output shaft which has a normalized angle of rotation 0, (0< 0< 1) is coupled to a slave potentiometer. The slave is also an expo nentially tapered attenuator, but has in general, a different rate of attenuation than the m aster. Let its attenuation rate be Not.
The variable u is represented by the voltage Ei applied to the master potentiometer. The servo positions the pick-off on the potentiometer so as to make its voltage constant. This makes Eq.
(12) valid.
(12) e = Ei£~ = constant.
33 The input signal to the compensator is the voltage V which may be applied to either end of the slave potentiometer. Assume that it is first applied to the A end. The output voltage from the compensator is the voltage v taken from the tap on the slave potentiometer.
Since the voltage distribution along this attenuator is also exponential and has an attenuation rate Net, the compensator output v is related to the input V by Eq. (13)
#i ov -rr _-Na0 (13) v = V t
The compensator gain function C(Ei ) is the ratio v/V. Com bining Eqs. (12) and (13) and rearranging terms gives
(14) C(EX ) = v/V = KEi "N where K is a constant. Thus a function Ei to the minus N can be generated, the N being determined by the ratio of the attenuation rates in the two exponential attenuators. No constraints are placed on N except that it be a positive number.
Now consider a slight modification to the circuit. Transfer the compensator input V from terminal A to terminal B. In this case Eq. (15) is applicable.
(15) v = Ve"Na(1-6) .
34 Upon substituting from Eq. (12) as before, leads to Eq. (16)
+N (16) C(Ei ) = v/V = KEi
As a result, the method described lends itself to the generation of
gain functions of the form given by Eq. (17)
t N (17) C(u) = KU
Here u is the generalized control voltage previously discussed in
regard to the compensation of loop-gain. It is clear that a wide variety of compensation requirements can be fulfilled using this technique. In addition, more complicated compensation functions
could be synthesized by combining the output of several slave com ponents where the exponents in general were different.
In the phase plotter it was required that the compensator gain -l be proportional to u . This was obtained by constructing both attenuators with the same attenuationrate and using A as the input.
The logarithmic property of the masterservo made it possible to easily obtain an 80 db dynamic range on the input control voltage without any difficulty.
An extension to the described technique is that of using the
compensator as a function generator in its own right. This can be
35 done using the pick-off voltage as the output, thereby synthesizing functions of the form given in Eq. (18).
+N (18) v = KEi
It should be possible, in principle at least, to construct poly nomials of the form shown in Eq. (19), if a number of the slave units were employed, each having a different attenuation rate. This would, of course, entail independent amplifiers to adjust the separate con
stants and an adder to perform the summation.
j=+m (19) v = \ A.El . L j J j=-n
A point worthy of note is the flexibility of design when used either as a function generator or as a compensator. Recall that in the slave potentiometer the exponent of £ is N a 0. Here N can be associated with either a or 9. By associating N with 0, the law of response can be altered merely by changing the gear ratio between the master and slave potentiometers.
B. SQUARE ROOT RECORDERS
Introduction of wide range mechanical rectification into an tenna instrumentation opened a new approach to the design of
square-root instruments. Actually, it was with the square-rooter
36 in mind that work on the linear rectifier was pursued. Because rectification precedes the square-root function in the servo ap proach, instead of following it as in the electronic technique, twice the db dynamic range of rectification is required. This quickly ruled out any of the diode rectifier circuits which came to the w riter's attention.
The instrument was constructed in two basic units. 2 2 The first was a synchronous rectifier; the second was the compensated square-root servo operating with a d-c input. As pointed out in the general discussion, it is not possible, in principle at least, to plot an exact square-root function all the way to zero. As a consequence of this, an a-priori range of 80 db was agreed upon. Accordingly, the lower rotation stop was set at .
Square-root action was obtained in the servo by comparing the input voltage with a like follow-up potential derived from a pair of linear potentiometers, as shown in Fig. 10. This well-known tech nique does not represent the only means of achieving the desired response; however it appeared to be the most feasible. Single section nonlinear potentiometers having the same law of response possess neither the range nor accuracy obtainable with the ganged dual linear components. In addition, a more subtle difference can
37 exist between the two methods of developing the follow-up voltage, under certain conditions. This concerns the compensation. The point is made in Appendix I.
Consider Fig. 10 again. If R » r it follows that E2 ^ k© .
Because of the servo response, it can be written that
(20) 9 = k | r [.
The accuracy to which the 62 follow-up function is approximated depends upon the ratio R/ r . Only for an infinite ratio is the function theoretically correct. An actual value of 300 was chosen. This gave a corresponding maximum deviation from square-law of: -OS per cent. Further improvement would have: been of marginal benefit.
Appendix II shows in just what way the error increases as the ratio
R/r is decreased.
In accordance with the discussion in the General section, a compensator potentiometer with a shaped voltage distribution curve of 1/0 was incorporated. The function was simulated by a piece- wise straight line approximation. Figure 15 shows the degree of uniformity of response which can be achieved across the dynamic range with little effort. The semi-block diagram of Fig. 19 in dicates the way in which the compensator is integrated into the
38 To Chart Sync. Sync Low Mechanism Amp. Rect. Resistance
Signal Signal High Amp. Resistance
Compensator
(-0 SO
Gear Box
Amp. Amp
Fig. 19. Square root servo block diagram
t- —
Motor Gen. servo amplifier. A more detailed discussion has been given in the literature.1 8
In addition to the transient response, Fig. 15 also indicates somewhat roughly the accuracy which has been achieved in the re corder. As may be seen, from 0 to -40 db the steps are in 2 db jumps. Ten db steps complete the span down to -80 db . Because of the heavy pen lines, detail is rather masked. More refined measurements of output shaft position were made by carefully measuring the resistance of a potentiometer affixed thereto. These are presented in Fig. 20. Here it may be seen that for purposes of
100
fl0<
JO
-t— r— r r.r
Fig. 20. Accuracy plot. measurement the lower stop was released to extend the range below
-80 db. This was just for academic interest, because a range of
40 80 db represents all the coverage usable in a polar plot.
Because the law of response of this instrument is deter mined exclusively by potentiometers, the long-term accuracy of the machines has been highly satisfactory. The first one was com pleted in the summer of 1953. Others followed in sequence shortly thereafter and with the benefit of occasional service, they have operated with their original accuracy ever since. The same basic design has been preserved in a commercial version. Approxi mately 100 of these have been produced and distributed to roughly half as many different measuring sites. Except for minor com promises for the sake of production, the original prototype has been faithfully duplicated.
C. LOGARITHMIC RECORDERS
1 . Commentary
Owing to the natural enhancement of the low signal levels in
a logarithmic plot, as compared to say a direct field strength plot,
interest developed in recorders of this type. These were to com plement the square-root instruments, not supplant them. Actually,
arguments exist in favor of each method of taking data. The choice
depends upon what factors take precedence and the use of the re
corder data.
41 Techniques for obtaining the logarithmic response had been
described in the literature. 8’ 9 However, owing to the state of the
art at that time satisfactory recorders were not commercially
available at the time this study began.
2 . Dual Detection Type
The first approach employed a dual-detection principle con
ceived to circumvent certain deficiencies inherent in the more con-
23, 2 4 ventional methods of developing a logarithmic response. It
entails detecting two widely separated square-wave-modulated r-f
frequencies in the same crystal. The basic circuit employing this
principle is shown in Fig. 21. The key element is a detector of
Chart Mechanism
Piston Local Attenuator Oscil lator
Audio
Servo Modulator Amplifier Transmitter And Motor Modulator
Synchronizing Oscil lator
Fig. 21. Basic dual detector circuit.
42 unusual design indicated as "d." Unlike a crystal mixer, where two co-existing r-£ signals produce sum and difference frequencies, the two r-f signals in this case are alternately present due to phasing *• of the square-wave modulation. Each r-f signal gives rise to a separate audio voltage component in the detector output. These components are out-phased and together they become the audio error signal. In principle, r-f signals of equal strength produce a null error regardless of the power level. The detector output controls a servo-system which continuously positions the piston attenuator for minimum error signal. Consequently an indicator coupled to the piston positioning shaft automatically records the relative level of the received signal in db. This is true because a one-to-one db correspondence exists between received and local oscillator signals for a balanced condition.
In view of the high transmission losses incurred in r-f cables at microwave frequencies, the preferred detector location is at the antenna. A unique design has made it possible to convey both the local oscillator and audio error signals in opposite directions
over the same cable. This means that only one cable is necessary to link the receiving antenna to the recording instrument.
43 A suitable dual detector capable of presenting a normal crys
tal load to each frequency source is shown in Fig. 22. At the re-
10-cm Stub
10-cm Choke
Crystal 80 me Signal
Error Output Fig. 22. Dual detector detail.
ceived signal frequency, stub S and choke C represent an approxi
mate open and short circuit respectively. At the local oscillator
frequency the impedance values are interchanged, i.e., stub S and
choke C represent respectively a short and an open circuit. The
interchange of impedance values occurs due to the wide frequency
separation of the two r-f signals. The design center frequencies
of the received and local signals are respectively 3000 me and 80 me.
When viewed from either input terminal at the proper frequency, the detector presents a normal crystal load. Furthermore, the d-c
short on the left of the crystal allows the right terminal to be used
44 for the additional purpose of extracting audio error signal. As a result, the connecting cable is made to convey 80 me energy to the detector and extract audio in return. The detail block diagram of
Fig. 23 shows the location of this element in the system.
Signal Separator Dual Piston 80 me <4 - - - k----- 10 cm Detector 1 1 Input l ^Audio 1 Compensator vL Potentiometer
OSC
Sync. For Trans. Mod.
Fig. 23. Logarithmic recorder detail block diagram.
From a servo point of view, the follow-up signal is obtained from, a special motorized attenuator which supports an oscillator mounted at the. input end. Through proximity of the oscillator tank coil to the open driven end of the attenuator, an evanescent field is set up in the tube. The level of output, which is automatically adjusted to match that of the received signal, is determined by the location of the pick-up probe . Position of the attenuator is taken as a measure of the received signal strength. Consequently, a pen mechanism attached to the movable piston gives a measure of the
45 received signal strength in db. A more complete description has been given in the literature, 2 5 however this is the basic principle of operation.
As was shown to be true in the square-root recorder, the follow-up assembly is characterized by having gain functionally related to the shaft position. Unfortunately in this case the gain varies over twice the db range required in the square-rooter for the same variation of input signal level. This alone makes the instrument somewhat more difficult to compensate. The variation in gain as a function of 9 can be shown in a simple manner. For example, power at any point in the attenuator tube is given by
(21) p = Pe -Ct 9 .
Because the detector "d" is square-law in response, it is true that
( 22) = K d0 P
This is just the follow-up sensitivity S. As a result, a 40 db
4 (or 10 :1) range in power causes the same range in voltage sen sitivity. This means that a compensator in the error path must have a change in gain of 104, or 80 db. The 2:1 difference in db comes about because one case concerns power and the other
46 voltage. However the ratio in each instance is the same. Knowing
the overall variation in gain is of little use without also being ap
praised of how the gain varies over the dynamic range. In this
case it is clear that the gain varies exponentially. A ladder at
tenuator gives the exact variation needed to obtain constant incre
mental attenuation across the dynamic range of the instrument. The
location of this component in the circuit is shown in Fig. 23 .
In final form the instrument operated over a dynamic range
of 50 db. This limit was imposed by the audio compensator which
had to vary exponentially over 100 db. Because of the complexity
and difficulty in operation, the design was not pursued beyond the
prototype stage. Rather, effort was directed toward the design of
a dependable audio-type instrument to do the same work.
3 . Audio Type
Maximum flexibility in a logarithmic recorder is realized when the instrument is controlled by the audio signal. Admittedly,
nonlinearity in the preceding amplifier and non-square performance
in the detector may cause plotting error. However, this problem
is not as acute as may be suspected. In return for this risk of
error, great simplification is achieved. To wit, the only change
necessary to cover the gamut of frequencies from megacycles to
47 to kilomegacycles is the interchange of detectors. For simplicity this cannot be surpassed.
Audio-type logarithmic recorders first came to the w riter's
q attention by way of published reports. Although the principle was
sound, improved simplicity and accuracy were needed. It was ap
parent that with care, an instrument using this principle could be
built having improved mechanical and electrical characteristics.
It was to this end that effort was directed.
As a matter of expediency it was decided that the instrument
should have an input compatible with the output of the Selective
Amplifier previously described. In this way a pattern range could
quickly be changed from square-root recording to db recording
merely by an interchange of cables. With this in mind, both the
operating dynamic range and the maximum signal level were set.
These were respectively 80 db and 5 volts. Owing to the square-
law detector, the r-f operating range was one half of this, or 40
db. Actually, the machine was calibrated in units of 0-40 db rather
than 0-80 db for compatibility with the input r-f signal.
It was not known at the beginning what accuracy could be
achieved. However, ratings on the available commercial poten
tiometers were not so impressive that improvement was beyond
48 hope. Available figures gave a 40 db range with 0 .5 db accuracy.
Since this accuracy was not considered adequate, it was decided that a suitable attenuator would have to be constructed as part of the project. Considerable effort went into this. Ultimately a
component was developed which employed a ladder network rather than nonlinear approximations. It possessed a continuously vari able range of 80 db with the error held to 0.Z db. This a-priori error figure was a compromise between accuracy and effort. It turned out that a tap spacing of 4 db yielded this figure . The re lationship of accuracy to tap spacing has been worked out in some detail and is presented in Appendix III. A more elegant discussion of error in ladder attenuators is given in Appendix IV where it is shown that a substantial decrease in the number of taps can be achieved for the same accuracy by a loading technique .
Rudiments of the system are.shown in Fig. 11. It is not the intent here to go into all the construction details, especially since this has been adequately covered in a publication.26 However, for completeness a more detailed diagram appears in Fig. 24. Con sistent with the General discussion, it may be noted that no com pensation is required in this servo loop. The uniformity of transient response in its absence is clearly indicated in the accuracy diagram
49 1000 cps Inpul Pick-Off Amp. Input 20 Sections, At 4 d b / g eCfjon
Gear Mon itor Bo x Pol. 1000' Reference ■P Rectifier Am p. ignol
Selsyn
Motor
Amp.
Geors " ~~IT~
Line i------1
Fig. 24. Audio logarithmic recorder detail.
50 of Fig. 25 where the full dynamic range is covered in 1 db steps,
relative to a 40 db scale .
Completeness demands establishment of the operating prin
ciple again, even at the risk of reiteration. The motor positions the ladder pick-off voltage for constant level. Thus,
(23) e = K Ele 'Gx .
Because e is a constant quantity it is possible to write
(24) x^Klog-f^
Proper scaling of the chart gives K a value of 20. As a result, a direct reading in db is achieved. Accordingly, it is valid to say that if xi ~ Ej and x2 ~ E2 :-then
Eix (25) xi - x2 = 20 log E< 12
A representative pattern taken on one of these instruments is shown in Fig. 26. The db units are compatible with the r-f signal in tensity .
D. PHASE RECORDERS
Earlier interest in the measurement of r-f phase resulted in the development of an S band instrument capable of automatically
51 Minimum Signal
40 30 20
Paper Advance
Maximum Signal
Fig. 25. Accuracy plot.
52 OJ
CL c r
CO
CL
Fig. 26. Field strength intensity pattern. 53 p 7 measuring the relative phase in free space. Except for minor differences in detail, the instrument had a strong resemblance to the rudimentary phase servo shown in Fig. 12. Although it lacked later refinements;- moderately successful operation was achieved.
An accuracy of 4° for a 20 db variation of input signal intensity was quoted at the time . The principal insufficiency was the absence of a means of maintaining the servo gain constant as the input sig nal intensity varied.
Later the author developed the X-band system of Fig. 27 for
2 8 j 2 9 j 30 measuring the phase of the near fields of antennas and radomes. 5 ’
Because the phase and amplitude of an input signal can be viewed as varying independently, it was initially decided to include a com pensator to assure uniformity of servo performance in spite of possible wide changes in signal strength. This led, in principle at least, to a design which closely resembled that shown in Fig. 16.
The compensation feature represented the most significant im provement over earlier designs. The complete instrument in cluding this innovation is shown in Fig. 27.
A hybrid T together with a suitable subtraction circuit served as the phase discriminator. The behavior of these components is reviewed in Appendix VI. Here it is sufficient to observe that under
54 I Probe j Horn Selective Log Compensating Amplifier Servo Potentiometer Number I
Crystal Hybrid Defector Junction
Selective U n i I i ne Amplifier Modulator Bolometer Number 2 Circuit
Synchronous Audio Rectifier Modutator Synchronizing Voltage Signal
Servo Amplifier
Motor
Slotted Line Termination Phase Shifter
Pad
Klystron Osci llator
Fig. 27. Complete system block diagram.
55 proper operating conditions the erro r output is given by
(26) £ = KEi E2 5
5 is the amount by which the phase of Ei and E2 differ from
quadrature. Because of the automatic tracking feature in the in
strument, 5 is normally very small. Ideally, it would vanish altogether.
In accordance with the General discussion, the compensator is required to vary the gain inversely with the intensity of Ei .
(Fortunately E2 remains constant, hence causes no additional complications.) The method used is that indicated by Fig. 18 and the related text. For completeness, the specific application is considered further in Appendix VII. The action of this circuit is fast compared to the phase servo proper. If this were not true, a large increase in hybrid junction gain could promote instability until the compensator had time to react. On the other hand, the main servo could be made momentarily insensitive to phase changes which were accompanied by a rapid decrease in hybrid junction gain.
Ideally, the follow-up component should have a phase vari ation which is both linear and frequency invariant. These two factors are most nearly realized in the Hewlett-Packard Model
56 X-885A X-band phase shifter. Unfortunately this component was not available to the author when the automatic phase plotter was constructed. As a result, a matched slotted line was employed instead. Although this has the ideal linear phase variation, un fortunately it is frequency variant. However, because the in strument was intended for operation at a fixed wavelength of 3 . Z cm no difficulty was encountered. Without doubt an instrument being constructed at the present time would use a rotary phase shifter in preference to the slotted line to obtain the frequency in variant feature .
Because of the linear phase variation, it is possible to obtain a plotted phase pattern with linear characteristics by linking the pen mechanism to the slotted-line carriage with strings . A. know ledge of the operating frequency together with the waveguide char acteristics can be used to calculate the phase calibration. An alternative and somewhat easier method is to set the instrument in operation, overpower the servo and moye the carriage in excess of
X. / Z . As soon as this critical distance is exceeded, the servo will automatically seek a new quiescent point X. removed from the original position. The X. distance can be used as a scaling factor for all measurements taken at the same frequency.
57 As in any equipment relying upon the balance of two signals for its operation, stability and purity of the signal are of utmost
importance . Two principal measures have been taken to provide a signal of suitable quality.
In the first place, slow frequency drift caused by temperature variation has been minimized by fully submerging the oscillator in a deep container of transformer oil. The tank employed was a
standard galvanized refuse container. Only convection currents were relied upon to provide the necessary cooling, thereby elimi nating mechanical modulation caused by oil turbulence . The total oscillator power of approximately 60 watts causes the ambient temperature to rise to about 40° C. Provision was made to main tain this temperature during periods of inactivity by energizing a
60-watt light bulb adjacent to the tube. The technique of operating the tubes in this manner for improved performance has been described in the Antenna Laboratory reports. 32
Secondly, r-f modulation is applied by varying the impedance of a waveguide section at a point where high isolation exists be- tween the modulator and the klystron. 33 A standard crystal de tector mount is employed for this purpose. Approximately one volt produces full modulation, i.e ., an audio signal in excess of
58 this value does not appreciably increase the percent modulation.
A ferrite modulator may also be used, but these are generally not
as available as crystal mounts .
As evidenced both by the depth of null attainable in the hybrid
junction discriminator and by spectrum analyzer observations, a
modulated r-f signal of greater purity can be achieved with this
technique than that attainable with direct klystron modulation. In
asmuch as 100 percent modulation cannot be achieved using imped
ance variation, a somewhat smaller useful signal results . Vari
ations exist among crystals, of course, but a decrease of 6 db could
be considered a typical figure.
The usable frequency range of the instrument was 8.2 to 12.4 kmc. This was established by the commercial specifications on the waveguide components. Since none of the automatic equipment op
erated at the r-f frequency, any microwave band could have been used with an appropriate choice of waveguide components .
An over-all measure of the accuracy was obtained by intro
ducing a slotted waveguide phase shifter in the received signal path
similar to that used in the phase servo itself. By propelling the
carriage at a constant velocity and synchronizing it with the paper
notion, an input signal should ideally plot a straight line . Figure 28
59 IZO ° 360° (DEGREES)
Fig. 28. Linear test pattern,
shows typical test results. These were made at a power level 20
db below maximum . It is difficult to state exactly the magnitude of
error, but a deviation of ll/2 division seems a reasonable figure.
This corresponds to +4° at a wavelength of 3.2 cm. Some of this
is due to an inaccurate standard and further improvements are
possible .
The error included contributions from both the servo and
the two slotted waveguide phase shifters. Based on an SWR of 1 .05
•and negligible probe loading, the shifters themselves each has a
phase error as great as 1.2°. This indicated that a large contri
bution to the total error was made by the automatic mechanism.
The principal cause was noise which tended to obscure the true
balance that otherwise could be made more precise simply by in
creasing the servo loop gain.
As a result of the phase shifter being noncyclical, the phase
range of the instrument was necessarily limited by the total
60 excursion of the probe carriage. In this case the range was 10 cm, which meant that the phase range for a free space wavelength of 3 .2 cm was about 14 radians .
Pen velocity was limited principally by the maximum motor speed as reflected through the mechanical linkage. The gear ratio was purposely kept high in order to obtain reasonable servo per formance while at the same time incorporating a 4 cps narrow band amplifier within the servo loop to combat noise present on the low level signals. A maximum writing rate of about 1 .25 inches per second was achieved. This corresponds to about 0.93 seconds per radian phase shift at a wavelength of 3 .2 cm in free space. Even though the response seems slow, the figures were considered acceptable at the time.
A workable power range of -50 to -85 dbw (db referenced to. 1 watt) was established. This represented an expedient com promise between development time and sensitivity. Certainly a concerted effort to improve these figures would achieve positive results. Although a phase measuring instrument does not exist which has been developed to the same state of perfection as ampli tude recorders, much valuable phase data have been obtained. A typical sample of results was shown in Fig. 17 in the General section.
61 For completeness, it should be pointed out that this design is
inherently both an amplitude and phase plotter together. However,
because of the availability of other amplitude measuring instruments,
this feature was not exploited. To take out amplitude information on
a db basis it would merely be necessary to record the position of the
compensator potentiometer.
Subsequent modifications by another investigator 5 at 5 the
Antenna Laboratory led to a design suitable for plotting both in-
phase and quadrature components of an r-f signal. This extended the usefulness of the instrument with regard to radome work. The method by which this feature was achieved is shown in Appendix
VIII.
62 SECTION IV ECHO AREA INSTRUMENTATION
A. GENERAL CONSIDERATIONS
Up to this point the discussion has centered around various instruments used in measuring the amplitude and phase of the near and far fields of antennas. Now attention will be focussed on instru ments used in connection with the measurement of the radar echo of various targets. In general terms, the target is illuminated by a signal from the radar transmitter and it is desired to measure the energy scattered or diffracted in various directions. In most cases the principal concern is with back-scattering, or reradiatinn toward the illuminating source called monostatic return. Just as in the case of aircraft antenna measurements, the principle of electro magnetic modeling has been applied with marked success. Target types have included model airplanes, missiles and classical shapes.
In addition, the same techniques have been extended to measuring the radar return of targets having echo areas of a statistical nature, such as natural terrain. The special problems incurred in measuring terrain return are discussed in more detail in Appendix IX.
The equipment used for radar echo measurements falls into two general categories, namely, continuous wave (CW) and pulsed,
63 which relies mainly on radar techniques. Both types serve a definite need and there are advantages and disadvantages to each.
The "best" type to use depends mainly on the target to be measured.
For most applications the objective is to measure the electromagnetic scattering from the body as a function of its aspect angle.
The basic parameter which describes the reflection property of the target is its echo area, cr . It is defined by the well-known radar range equation Pip Gp> GR X.^ (27) PR (4ir) 3 R4
It may be seen that for given measuring conditions
(28) PR = K or , where the constant K is determined by measuring the return from a known reference standard such as a sphere or a triple -bounce corner reflector.
In a typical system, the pulse width is 1/6 microsecond and the range is 275 feet, which gives about 3/8 microsecond clearance between the transmitted and received pulses. For larger targets the range must be increased to secure proper illumination.
A simple CW system is shown in Fig. 29. In general, the
CW system, in spite of the terminology, may or may not illuminate
64 Audio Signal /^Detector Narrow Band R e c o rd e r .Modulator Amplifier
Echo Target
Incident Hybrid Signal
Signal Source
Fig. 29. CW echo measuring system.
the target with unmodulated r-f energy. Whether it does or not
depends where in the system modulation takes place. Audio
modulation of a free-running klystron introduces the possibility
of excessive incidental frequency modulation which prevents an
adequate balance in the hybrid junction. In Fig. 29 this source of
error is eliminated by introducing the modulation in the received
signal path where it has no opportunity to affect the purity of the
signal source. It has been estimated that a null depth in the order
of 95 db is required to attain the required accuracy over a 40 db
dynamic range for routine measurements. 32 When it is noted that
50 kc shift in frequency will decrease the null depth by 15 to 20 db,
65 the need for high frequency stability becomes apparent. Because of the inherent flexibility and economy associated with a free-running system, all CW installations are now excited in this manner. An acceptable degree of stability is attained by immersing the tubes in deep tanks of oil where convection currents provide the necessary cooling. Operating in this way nulls in the order of 100 db can be held for a period of time adequate for measurements,
One of the characteristic features of CW systems is that the echo and incident signals are not separated on the basis of time, hence close-range measurements can readily be made. This is why it is possible to use low level energy sources of the klystron type.
The pulse system, being exactly what its name implies, is basically a pulsed radar ( see Fig. 30) . In contrast to the use of
CW, high power signal sources are required here. It is typical to use a magnetron oscillator to generate narrow pulses of r-f energy which are used to illuminate the target under study. A directional receiving antenna channels the returned echo into the receiving system proper. A servomechanism maintains the input to the receiver constant by continuously positioning an attenuator to counteract variations of input intensity. This attenuator is a wave guide type and is located between the receiving antenna and the
66 Echo
Chart
Video Transm itter Receiver Gate And
Motor Servo Amplifier
Sync Variable
Generator
Fig. 30. Radar echo measuring system.
receiver input port. Its shaft position is taken as a measure of the
relative echo signal strength. Although separate antennas are used for transmitting and receiving, the lack of congruency here has negligible effect, owing to the small dispersion angle. For all practical purposes the system shown is monostatic. This is due to the rather long target range, which is one of the salient features.
The necessity for this relatively long separation of target and source
67 arises because the received echo is sorted out from the spurious clutter by time gating. To wit, only return which arrives during an a-priori determined time interval can activate the system.
Figure 30 shows a block diagram where, in the interest of clarity, some of the detail has been deleted.
B. RADAR INSTRUMENTATION
1. Commentary
Contributions by the author to this important area of electro magnetic studies have been principally restricted to the pulsed radar technique. These have dealt with a widely diversified set of topics which have, over a period of time, significantly improved the performance. Initially the instrument took the form shown in Fig. 31.
The end result is described in Report 406-2. 34 An AN/TPQ-2
K-band radar (\ = 1. 25 cm) formed the nucleus around which the system was built. Actually, small changes were necessary to the radar itself. Mostly it was a matter of adding auxiliary circuits to accopimodate the automatic features incorporated.
The initial system in the form shown was deficient in several respects; hence improvements and modifications were made.
Eventually interest became aroused in recording logarithmically at speeds exceeding the reasonable upper limit of the existing system.
68 xTarget
. Azimuth Information pedestal Sample AFC AFC Detector Line Mixer IF Amplifier 3J3I Magnetron Oscillator Chart Local Frequency Mechanism Amplifier Oscillator Correction Pulse Voltage Modulator R.F. Attenuator Mixer Synchronizing Pulse Constant Field Generator Power 1 Armature .F. Amplifier j Control Boxcar And Circuit Line Circuit Detector Constant Variable Speed Speed Differential Motor Motor
Delay Circuit
Fig. 31. Initial radar echo measuring system. The approach taken was to employ an open-loop method, wherein the logarithmic response would be achieved in the i. f. strip. 3 5
This was to be followed by a linear time gate operating on the video pulses. The goal never reached fruition, principally because a suitable i. f. amplifier36 was not available. Substantially more improvement is necessary before logarithmic intermediate frequency amplifiers can be considered satisfactory for this purpose. The most significant positive contribution which materialized from the author' s efforts here was the development of a video gate having an unusually wide, linear dynamic range. This turned out to be a problem of no small magnitude. Previously the time gate had operated at constant signal level. As a result, the problem had never occurred before. A noticeable absence of published information on this subject made it fertile material for the literature.37
2. Innovations
(a) Motor drive
Originally the attenuator and pen linkage were actuated by a shaft whose velocity represented the differential between that of two different motors, 34 One of these was synchronous; the other was not. Adjustments were made so that the quiescent speed of the d-c error motor was identical to the synchronous speed of the other.
Error became manifested as an incremental change of velocity on the
70 shaft of the d-c machine. Dynamically the performance was creditable. However, as it turned out, the advantages of the design33 were more than counterbalanced by several objections. Perhaps the most innocuous among these was noise. The steady grind had a tendency to wear out more than just the gear teeth. Perhaps one of the most serious disadvantages was attrition. The high-speed differentials developed slack which resulted in poor dynamic per formance and plotting accuracy. Over and above degradation in per formance, considerations of power and bulk dictated a more economical design. Consequently, the equipment was modified eventually to include a single a-c error motor and a companion amplifier. Without laboring the point, the attendant savings here are evident. While these modifications were clearly prosaic (they have been included only for documentation) , they did represent a significant improvement and reduced the maintenance substantially.
(b) Energy enhancement
It may be noted from Fig. 31 that the video output of the i-f
strip controls the erro r motor. While the detail is absent, the implication is clear. A train of fractional microsecond pulses having less than a volt of amplitude must be converted into a large d-c signal to regulate the motor armature. Specifically, the input pulses had an
71 amplitude of about 0.4 volt; the output was about 40 volts. Originally the pulses were amplified and then passed through two cascaded pulse stretching circuits to increase the energy content. The latter took the form of cathode followers with charging capacitors in the cathode circuits. The first one was self-quenching, so to speak, i. e. , the charge was dissipated by the time the next pulse arrived. The same condition did not prevail in the second stage. Here the charge held almost unattenuated until the next pulse was due. To restore zero initial conditions for each pulse, it was necessary to incorporate a discharge circuit on the capacitor of the second stage. This took the form of a triggered thyratron. The end result was that the output consisted of a train of semi-rectangular blocks of energy whose height varied with the input pulse amplitude. Because of the output pulse shape, the filtered d-c average value recovered was nearly that of pulse height itself. This was the voltage which controlled the power amplifier. The necessity for such a large value was due to the low gm of the subsequent motor-controlling power tubes.
The circuit, while satisfactory in principle, had a history of being unstable. Jitter was the most prevalent defect. The apparent source of this was the discharge circuit associated with the second pulse stretcher.
t 72 A new concept was looked for that would improve results.
The method finally employed was to filter out the fundamental
component of voltage, occurring at the pulse repetition frequency,
and amplify it. In this way the problem devolved from one of
handling pulses to one of handling sine waves. The end result was
a far simpler design in which the only evidence of instability was
that attributable to the input pulse train. After sufficient ampli
fication, the a-c signal was rectified. The d-c output, which was
at least an order of magnitude less than in the former case, was
chopped to yield a 60 cps signal. With further amplification, it
provided-drive for the error phase of the motor. Essential parts
of the design are shown in Fig. 32.
Video Band Pass Rectifier Video Filter Pulse Input
. _L Frequency T Fig. 32. Pulse filter.
That no intelligence is lost by this approach can readily be
shown. The argument can be further fortified with a theorem 38
which says:
73 Periodic sampling at intervals 1/2B of a wave, the spectrum of which is confined to all fre quencies less than B cycles per second, pro duces upper and lower sidebands of 2B and of each harmonic of 2B. If any one of these side bands is selected and sampled at the same instants, it will be found to produce the same set of samples as does the original wave.
In other words, echo information which is superimposed on the incoming pulse train appears as amplitude modulation on the fundamental signal. Because the.sidebands are restricted to a few. cps in width and the pulse repetition frequency is about 5 kc, there is no possibility of the upper sideband of one harmonic mixing with the lower sideband of the next higher harmonic. As a result the theorem applies.
Consider a set of pulses of narrow duration. Although these are shown as having fixed amplitude in Fig. 33, eventually A will be
A
T
Fig. 33. Pulse train. made to be time variant. The spectrum here can be found by-
standard techniques,
00
(29) E(t)=A- +^Kn cos n cot T n=l
where
( 30) K„ = — \ A cos n cot dt T J _ K/7 - 6/2
which yields 5 ^ sin mr ( 5 /T) (31) Kn=2A(- \ T / nrr ( 6/T) the end result is that
( 32) ^ E( t) = A ^ + A^T cos n cot
n=l Now let the amplitude A be viewed as time variant. In other words,
(33) A = Aq + \ Am cos mpt L-J n=l The spectrum then becomes
^00 00 00 E(fc) =“ y ■^■m cos mPt C°S ^ C°S nCjt n=l n=l ii=l (34)
+ AQ cos ncot + A0 n=l
The first term represents the original modulating wave. The last two
75 together can be interpreted as saying that each harmonic frequency
of the pulse train has associated with it an upper and lower sideband
having the respective frequencies nw + mp and mw-mp. Such a pair
exist for every harmonic of the modulating signal and every existing
harmonic of the pulse train. As a result, if the modulating signal
is A( t) the spectrum will look somewhat like that of Fig. 34.
A(t
T T Fig. 34. Modulated pulse train.
Since every harmonic of the pulse frequency carries amplitude
modulation in accordance with the modulating signal, no information
can be lost by recouping any one harmonic together with its sidebands.
The most convenient one, of course, is the fundamental.
The end result proved to be sufficiently stable that
imperceptable variation in the output amplitude occurred when a
stable pulse source was used for an input test signal. Because
actual input signals tend to be rather jittery, any variation in output,
under normal operating conditions, could be safely attributed to variations of input. This technique has been satisfactorily employed
in both a K- and Ka -band radar system for several years. ( c) Gating
Without some method of separating the received target return
from spurious clutter, the radar system would be unsatisfactory.
Leakage of the main transmitter pulse together with return from every
object in the illuminated area capable of producing an echo constitute
the undesired signals. An acceptable method which sufficiently
discriminates in favor of the actual target is to include a range gate.
This is really a synchronous switch which livens the receiver at those instants when the target echo is due to return. While this method is the best devised, even it cannot give infinite discrimination against
out-of-gate signals. Indeed, it cannot discriminate at all against
spurious echo which has time coincidence with the target itself. In this latter category come such signals as return from the target
supports and trailing edges of preceding pulses. However, in spite
of these inherent flaws, it is a highly valuable adjunct without which the system would be impractical.
Originally the gating action was accomplished in the i-f amplifier. Shortly after the system was put into operation it became evident that imperfections characteristic of i-f gates were present.
Perhaps the most serious difficulties were the lack of gate-edge sharpness and nonuniformity of sensitivity throughout the alive interval. As a result of the former, it was necessary to keep the receiver alive longer than the received pulse width for satisfactory acceptance of the target echo itself. This extra width permitted the passage of strong adjacent spurious signals, the presence of which is not uncommon. The lack of uniform gain throughout the open interval, which varied by as much as 6 db, was a potential source of instability, This was because a relative shift in the gating and received signal pulse positions had the same effect as a change of gain.
The g.-ting signal was inserted in much the same manner as age. , i. e. , by the injection of a variable controlling voltage in the i-f return of several stages. While this method is entirely satis factory for the slow variations of controlling voltage normally encountered in automatic gain control, it has inherent limitations for pulse applications. This is pursued at some length in Appendix X.
After considering alternative possibilities, it was decided that superior gating action could be achieved using video gating. 39 >40
Experimental results justified the decision to substitute a gate of this type. Several alternative proposals were considered. It turned out that the most propitious method in this case was to employ a pentode. The synchronizing pulse supplied what corresponded to
78 screen yoltage. Incoming video pulses were applied directly to the
number one grid. The vast difference in gm owing to the presence
or absence of screen voltage was relied upon to achieve the desired
gating action. Actually, isolation in the order of 50 db was achieved
with little difficulty under conditions similar to those of actual use.
It turned out also that the gain of the gate was practically flat no
matter how wide the synchronizing pulse was made. The gate edge
definition showed a marked improvement over that observed in the
i-f case. Figure 35 shows the final circuit employed. It was found
1000
Gated Output
6AK5
Gate Puttee
100
100
Fig. 35. Gating circuit. that because of the small, but finite, gm existing between the screen grid and the plate, it was possible to obtain a pedestal pulse in the output due to the gating signal. This phenomenon was only evident
79 when the screen pulses exceed ten volts. In actual operation the level was set at about eight volts. With this value only the faintest indication of a ripple occurred at the gate edges. This was presumably due to differentiation. No difficulty was encountered because of it. As a matter of fact, these band edge m arkers contained no harmonic components which would pass through the subsequent filter.
As a practical expedient, the gate, the energy enhancement circuit, and the subsequent rectifier were assembled as one unit.
3. Open-Loop Design
Logarithmic response in radar echo-measuring equipment, as already discussed, is generally obtained by servo-positioning an attenuator located between the antenna and the receiver input so as to maintain constant signal level into the receiver and attendant equipment. Such a design has several obvious points to recommend it, the most important of which is perhaps freedom from requiring wide dynamic linearity in the various circuits. The principal de ficiency occurring in this otherwise sound design is the relatively slow response, which is due to the limited pass band normally associated with servo recorders.
The advent of logarithmic i-f amplifiers opened what appeared to be a new approach to data taking in db units. A design centered
I 80 around one of these amplifiers would of necessity be an open-loop
system. Such is the case in Fig. 36 where it may be observed that
Echo Return Receiver (R-F Section)
High Speed Recorder
Fig. 36. Open-loop logarithmic recording system. the component parts operate over the full dynamic range of the signal itself. By deleting the servomechanism, a substantial improvement in speed is realizable, albeit at the expense of accuracy. This in itself may not produce excessive degradation in the final results, especially in a system that eventually records median values as the end result, or resorts to some other type of data smoothing.
Nonetheless, overall accuracy in an open-loop system is critically dependent upon there being no deviation from the true law of response in any of the component blocks. As it turned out, the two principal sources of error were the i-f amplifier and the time gate. From published data36 it was not anticipated that the former would present any insurmountable hurdles, but such did not prove to
81 be the case. Actually, considerable time and effort were invested in the logarithmic i-f amplifier. Although a satisfactory prototype was never obtained, the experience gave a feeling for the problems involved in the successive detection technique ( ref. Appendix XI) .
Fundamentally there appears to be no reason why such a logarithmic system cannot eventually be developed. Antenna instrumentation would be advanced measurably if an i-f amplifier design having suitable accuracy and stability were available for use with fractional microsecond signals. As a consequence, further effort in this area is amply justified.
The other source of nonlinearity'was the time-gate.
Fortunately more success was achieved here. It was found that gate circuits satisfactory for operation in constant level systems turned out to be nonlinear when operated over a wide dynamic range. The subsequent discussion is concerned with a satisfactory solution to this latter problem.
Compatibility requirements were such that the gate must accept 0. 2 microsecond pulses at a 2. 5 kc repetition rate and a a maximum amplitude of at least one volt. A d-c output was required to operate a commercial recorder of the Brush or Sanborn type.
Initially the operating range requirements were somewhat tenuous, but the minimum span considered acceptable was 40 db with an allowable error of + 0. 5 db. Actually, the dynamic range specifi cations were exceeded by a wide margin.
For obtaining gate action it was initially intended to exploit the wide difference in gm of a pentode for conditions of screen voltage and no screen voltage. This wa,s the method previously employed. However, the linearity requirement ruled this method out as a practical technique. It was found that the sm aller tube types, suitable for constant-signal-level operation, lacked the linear dynamic range necessary. Larger tetrodes possessed suitably linear characteristics, but consumed excessive power and required large signal levels to control them. Because of these objections diode circuits were considered.
Upon noticing the fast rise time obtainable in circuits employing Zener diodes, it appeared that such elements would be practical in this instance. Accordingly, the simple arrangement shown.in Fig. 37 was tested. Pulse levels were chosen so that the synchronizing signals broke down the diode to operate the gate. This represented the "on" time. Input signals arriving simultaneously with the sync pulse appeared, in part, across the mutual terminating resistance. It was necessary, of course, to hold the input signal level below the breakdown voltage of the diode. This condition imposed no undue disadvantage. Operating
83 nput Signal Sync. Signa Zener Zener Voltage Voltage o
Zener Diode
Output Gated Signal
Fig. 37. Zener diode gate. in this way, the out-of-gate signals made no measurable contri bution to the output. The electrical characteristics are covered later. However, it can be stated here that both the linearity and rejection ratio achieved exceeded that attained using gated tubes.
Output from the gate proper was handled in a manner previously used with a measure of success. Instead of resorting to pulse stretchers to enhance the energy contained in the signal, a filter was used which recovered only the fundamental component of the pulses together with existing sidebands. Amplification followed the filter,, A quick calculation shows that for perfectly rectangular pulses having the aforementioned pulse width and repetition rate, the ratio of recovered signal amplitude to pulse amplitude should be about 0. 001. In other words, for one volt
84 pulses the recovered signal amplitude should be in the order of one mv. Actually, this is somewhat optimistic because the pulses were not actually rectangular, Nevertheless, a usable signal amplitude could be recovered, A band-pass filter was employed to obtain the desired frequency selectivity without appreciably degrading the speed of response.
The introduction of a filter furnished an additional advantage.
An examinatinn of the gate output signal showed that it consisted of a synchronizing pedestal upon which the input signal was superim posed, Normally both pulse trains would have the same repetition rate, and as a result each would contribute its fair share to the total output of the filter.
In considering various methods of separating the contribution of the signal pulses from that of the pedestal pulses, balancing was immediately discarded. As a technique, it is always open to suspicion in precision systems because of inherent drift. For low signal levels this unbalance can easily yield an output as great as the signal itself. In the absence of such circuitry, drift is a nonexistent problem.
Upon considering alternative methods of separation, it became apparent that if the gate circuit were pulsed with a synchro nizing signal having twice the repetition rate of the input signal, the pedestal would contribute negligibly to the output. Experiment 85 readily verified this. The resulting pulse train, examined at the gate output, showed the signal superimposed on alternate pedestal pulses.
A Fourier expansion for such a set of pulses readily indicated that the synchronizing pulse train had no components of energy in the passband of the output filter.
The unanswered question was whether at the second gate opening any radar return existed. An inspection of the radar echo on the oscilloscope showed none to be evident, at least in comparison to the usual echo return. Actually it would have been surprising to find significant return at the midregion inasmuch as this represents a range of about 105 and the usual target is located only about 300 feet from the antennas.
For clarity, Fig. 38 shows a block diagram of a system where
X Torget
Tf on^miM And LOCO! Moouiolor Osc
2 5 kc Rep. Rote 60 me ReD Rote .00 l.f. Divider Circuits
Limn Pulses Of 2 5 kc Rep. Role Gote Ckt Pulses 0t 5 kc Pulse Gen Sync Rec’ Rep. Ro>e
2.5 kc Sine Wove Recorder
Fig. 38. Over-all open-loop recording system.
86 the gate serves a principal function. Particular emphasis is made
to indicate how the pulse trains having a two-to-one repetition rate
are introduced.
Essential detail of the composite gate circuit is shown in
Fig. 39. In the interest of preserving linearity and minimizing
spurious coupling, the number of components has been kept to an
absolute minimum. Circuits which rightfully should be considered part of the gate assembly have been located elsewhere in the over
all system. This explains why no phase control or amplifier is
included in the synchronous rectifier driving circuit.
Bristol Chopper
[Monitor Bond Pott p.Iter 2^7 ft Center F«e <4.
• HOFFMAN ZFNER DIODE.
I N 707
Fig. 39. Linear gate.
In view of the intended application of the gate, it is clear that linearity should be of paramount importance. Figure 40 shows that for a range of at least 50 db the over-all deviation from linearity does not exceed + 0. 3 db. Measurements made at the
87 6 ,0 0 0 -
4tOOO ■
1,000
600
200
<00
60
0.4
0 .2
- 7 0 - 5 0 - 4 0 -20 -10 0 Rtloflv« Input Slgnol Strength In db
Fig. 40. Linearity characteristic s. filter output show that the recovered a-c is linear over at least another 5 db. This indicates that with improved shielding to eliminate spurious coupling from the chopper, a linear range of
55 db is potentially available. However, since effort to achieve this extra five db would have yielded a marginal benefit, it was not accomplished, Substantial improvement would have to be made
88 elsewhere in the radar before an extra five db of range in the gate would be of any significance to the overall performance.
Capacity of the circuit to reject out-of-gate signals was measured by applying full input signal to the gate and measuring its effect on the residual output under out-of-gate synchronization.
This was done for the received pulse occurring both early and late.
The effect was negligible in either case. With just 0. 005 micro second clearance between the synchronizing and input pulses the residual output dropped to -58 db, relative to the in-gate value.
As the time spacing widened, the isolation increased to about -61 db. These figures could not have been attained except for the excellent recovery characteristics of the Zener diodes.41 In comparison to results achieved using vacuum tubes, the Zener diode circuit has a more clearly defined boundary between the in-gate and out-of-gate region. This characteristic is particularly advan tageous in echo measurements because considerable clutter appears near the target echo return.
Transient response of the system is fairly well determined by the transfer characteristics of the bandpass filter employed. This is true because the time constant associated with the rectifier introduces negligible effect. The filter itself has a 15 percent half power passband with the center frequency set at 2. 5 kc. Supposing the original servo had a 5 cycle significant bandwidth, this band width has been widened by a factor of about 50 in the present design.
Provided no other factors entered into consideration, the rate at which pattern information could be recorded would increase by this same factor. Unfortunately this is not the case. Nevertheless, a sizable improvement in the rate of taking data is potentially available using a well-engineered open-loop system.
In lieu of a pulse generator whose pulse amplitude could be modulated, a sine wave input signal was employed for actual bandwidth measurements. The half-power bandwidth was found to be about 190 cps. This agreed favorably with the quoted specifi cations on the filter used.
The detail of design is not presented as being necessarily the ultimate. Rather, the aim has been to stress the effectiveness of using filtering and double gate opening together with mechanical rectification to produce an effective solution to the problem of linear gating.
90 SECTION V HIGH SENSITIVITY SYSTEMS
With the trend toward higher frequencies, the problem of insufficient dynamic range in instrumentation for r-f measure ments becomes a problem of first magnitude proportions. The contributing factors are two-fold, inasmuch as the available power and detector sensitivity both decrease markedly as the frequency rises. Whereas, for example, 10 watts can be readily obtained at 1 kmc, 10 mw is a typical figure at 70 kmc. To make matters worse, the threshold of sensitivity for a crystal video detector with a 4 cps selective amplifier is about -117 dbw at 1 kmc while at 70 kmc it has dropped to a mere -80 dbw.
Improvement in sensitivity is achieved most readily by replacing a square-law detector with a linear one, as used in conjunction with the superheterodyne principle. For practical bandwidths, this leads to an improvement in sensitivity in the order of 25 db. The relative merits of these two detection pro cesses have been studied at some length by other investigators at the Antenna Laboratory. 42,43
Methods proposed for achieving even greater sensitivity vary widely in sophistication. Chronologically, they could be listed as (1) the ultra-narrow-band superheterodyne, (2) the
91 parametric amplifier, and ( 3) the maser. The first system was published entirely by investigators at Bell Telephone Laboratories. 44
It had certain attractive features which appeared to make it adapta ble to r-f measurements. Although conceptually this system was preceded by the parametric amplifier, the latter did not become
i a practical reality until later, owing to the lack of suitable time- varying reactors.
Circumvention of the principal obstacle encountered in the design of ultra-narrow band superheterodyne receivers was first achieved by Bell Laboratory investigators. 44 Specifically, the problem is that of attaining a stable frequency difference between the received signal and the local oscillator when this difference represents a small percentage of the input frequency. The. magnitude of the problem using conventional techniques is brought into sharp focus when numbers are mentioned. For example, it has been possible to obtain a 4 cps passband with K-band operation.
To do this the local oscillator input is obtained from a sampled portion of the transmitted signal which has been linearly shifted in phase. That a new frequency is generated is indicated below.
For example, let
( 35) e = E sin (ojt + 4>(t) )
92 If «|>(t) = Kt then
( 36) e = E sin (to + K) t „
Here it is clear that a new frequency (to + K) has been generated, whereas the original frequency was to.
The linear shift in phase is accomplished using a special rotating waveguide section. Description of this device is given in
Appendix XII. For clarification a block diagram containing the essential parts of the entire system is shown in Fig. 41.
w Direct Path 0 uj K-Banri 8 Narrovh Pass-Band Source Detector (D, Ampl ifier It)
© ------a| J* 0-2 Rotating Meter Phase Shifter
Fig. 41. Essentials of the ultranarrow band superheterodyne receiver. *i • * ___ A similar system was constructed as a thesis project at the Antenna Laboratory. 46 >47 This also operated at K-band. A sensitivity figure of -135 dbw was achieved whereas the theoretical value of sensitivity came out to be -137 dbw. The calculations were
93 based on a previous study of detector properties which was carried out here. 4 3
The limiting factor in achieving greater sensitivity is the crystal noise which contains a 1/f term. It is clear from this that increasing the i-f frequency should improve the sensitivity, other factors being the same. Unfortunately, practical difficulties arise in trying to achieve such a condition. In the first place it is impossible to rotate the phase shifter sufficiently faster to produce a significant improvement. In the second place an attendant increase in absolute bandwidth normally accompanies an increase of the center frequency.
To obviate these difficulties, while at the same time obtaining the benefit of a higher i-f frequency, a modification to the original system was conceived.48 This was constructed by the writer with the result that repeatable sensitivity of -160 dbw was achieved. Figure 42 shows the essential features of the system. Here it may be observed that due to a local oscillator, the lowest level mixer, M2, is operating into a 60 me i-f strip.
In addition, the crystal mixer, M3, which operates into the low frequency amplifier carries a sufficiently high signal level that it does not establish the system, sensitivity. In principle at least,
94 Coupler f u -yfrv- i i © Amplifier T“ at, K-Band Oscil lator/ <>'a|
(m a 2 Local V i Oscillator Rotating Narrow Phase Pass-Band Shifter I.F. Amp ifier f+ 8 Amplifier u+8 A f = 25 kmc 2 0 u = 6 0 me y Nominal Frequencies 8 = 210 cpsj Meter
Fig. 42. Modified ultranarrow band superheterodyne receiver.
the receiver behaves as if it were a K-band superheterodyne with
a 60 me i-f having a passband of 4 cps. There is one very im
portant difference, however. In this case no particularly severe
requirements are placed on the frequency stability of the local
oscillator. All that is required is that the local oscillator be
sufficiently stable to keep the signals within the i-f pass band.
It is interesting to compare the sensitivity of -160 dbw
with an extrapolation of the quoted sensitivity of the Polarad
receiver operating also at K-band, For a bandwidth of 3 me
the sensitivity is said to be -65 dbm or -95 dbw. A reduction
95 in bandwidth from 3 me to 4 cps corresponds to a decrease in noise power of 58. 8 db. Accordingly, such a reduction in band width would yield a sensitivity figure of about -154 dbw, which is comparable to that obtainable with this system.
It is interesting to compare the experimental figure of
-160 dbw with the KTB noise power for an ideal 4 cps passband.
The latter corresponds to a noise power, p , of -198 dbw which is about four orders of magnitude lower than that obtained.
Unfortunately at this time an explanation of this difference can be based only on theoretical plausibilities.
Available information indicates that at K-band the sensi tivity should be about 15 db less than the corresponding KTB noise power.49 This is based on a 5 db noise figure for the subsequent i-f amplifier. Inherent noise in the crystal makes up the difference. On the basis of these figures a system pos sessing a four cps passband should have a sensitivity threshold of -183 dbw. This still leaves a difference of 23 db to be explained.
It was suggested to the writer that the discrepancy could be possibly attributed to a difference in performance between this synthetic 4 cps system and one where the 60 me i-f amplifier were really 4 cps wide. Such was not found to be the case, as is shown by calculations in Appendix XIII. 96 Turning to an alternative explanation, the amount of noise available from a klystron local oscillator was investigated. Basing an estimate on published data of the OSU Electron Devices Labo ratory, it seems plausible that the noise level has been established by the local oscillator itself.
Consider, for example, the results published on the X-13
Yarian tube. 50 Because this is an X-band tube rather than K- band, it is to be expected that the figures will show the tube to be somewhat less noisy than one operating at the higher frequency.
Unfortunately, no figures have been found which apply directly to
K-band. Nontheless, the available figures are well worth considering. At 30 me removed from the center frequency of this tube the noise power density is given to be 25 x 10-12 watts/mc/ sec. /mw of oscillator signal. In other words, a band of frequencies
4 cps wide located 30 me from the carrier would contain a noise power equal to -160 dbw, provided the carrier power were attenu ated to 1 mw. Since this is just about the normal signal power supplied to a crystal mixer from the local oscillator, the noise figures can be taken as being directly applicable without scaling.
Owing to the incoherence of the noise, the power in both sidebands would, accordingly, be -157 dbw. It has been found that the noise
97 power density decreases as the square of the frequency separation between the sideband and the central carrier. On this basis the noise power in both 4 cps sidebands 60 me removed from the carrier would be reduced to -163 dbw. If several db of noise are allowed in going from X- to K-bands, a figure remarkably close to the -160 dbw experimental result obtains. Indeed, if the K-band tubes were twice as noisy an exact correlation with the measured results would have been achieved. Even without holding to such exact corroboration, it is safe to view the local oscillator noise as setting the actual system sensitivity.
With an experimentally determined noise figure 2 3 db worse than that presumably attainable, the question arises as to how this theoretical improvement can be achieved. The apparent answer, in the light of previous considerations, is to use a balanced mixer.
For those doubting that such a degree of balance can be achieved, reference is made to the literature. 51 It appears that with careful tuning and meticulously matched crystals, the necessary degree of balance can be achieved. It is interesting to observe here that the
Polarad receiver, which possesses a projected sensitivity of -154 dbw for 4 cps passband, does not employ a balanced mixer either.
The reason for this is that the receiver tunes over such a wide
98 range that maintaining balance over the full frequency coverage would be a near impossibility.
Owing to practical considerations, a workable system requires additional components to keep the several signals
separated. In particular, it has been found necessary to nullify the degrading effect of modulated echo from either end of the
rotating phase shifter. Because the principal concern has previously been sensitivity, the necessary isolation has, in the past, been achieved with attenuators located fore and aft of the rotating phase shifter. A practical system would require the replacement of these attenuators with isolators, or some other equivalent device capable of achieving reverse attenuation without introducing forward loss. The avoidance of this problem heretofore has not been viewed with alarm. However, a usable system must necessarily entail this added refinement before it can be classified as a satisfactory system for r-f measurements and having the inherent sensitivity attainable.
A scheme characterized by eliminating the local oscillator and yet possessing the desirable characteristic of operating the low- level mixer, Mlf into a 60 me i-f amplifier rather than into one at the shift frequency 5 Jb 200 cps, is suggested by the author. A simplified block diagram is shown in Fig. 43. On the basis of
99 Waveguide Modulator u = 6 0 me
K-band Osci I lator
Amplifier Significant Frequencies
Rotat ing Phase Shifter (4 cps Passband)
Meter
Fig. 43. Modified detection system. being square-law, a number of signals are produced in the output.
These are derived in Appendix: XIV. Three out of the set are of particular interest. One is the carrier at 60 me; the other two are respectively an upper and lower sideband located 5 above and below the carrier. The strength of these sidebands is linearly related to the signal strength of the received signal f + 5.
Except for a quick check to verify that signals could actually be detected using this technique, no work has been done on the system. This means, as of this writing, no experimental
100 determination of sensitivity has been made. Because of the simplicity, this system would be useful for r-f measurements provided the sensitivity turns out to be sufficiently high. As a result, further investigation here appears to be amply justified.
Several versions of the ultranarrow-band superheterodyne have been constructed over the years at the Antenna Laboratory. 52
The principal purpose for building these devices has been to eventually obtain an exceedingly sensitive system for mm use.
101 SECTION VI RATE OF RECORDING
A. INTRODUCTION
Pattern information emanating from a selective audio ampli fier in a receiving system occurs as amplitude modulation on an audio frequency carrier. Current practice is to use 1000 cps in the majority of cases . Now the dispersion of the sidebands is directly proportional to the rate at which the antenna is rotated. To say it another way, the sidebands spread out as the receiving antenna is turned more rapidly. Because the bolometer amplifier passband is restricted to a few cps in width, it would be possible for the higher sideband components to be badly attenuated at higher speeds of rotation.
It is a well known fact that detail in a wave shape is inextri cably associated with the high frequency content. As a result, the null region deteriorates first with increased angular velocity of the antenna. Actually, degradation of the null is the first evidence that patterns are being recorded at an excessive speed.
A second important effect occurs in that the true heading of the minor lobes and nulls becomes shifted due to amplifier delay.
102 Without considering the purpose of the pattern data, it is difficult to say which phenomenon is the more important. However, it is well to point out that because delay is not so evident as the loss of
null depth, it may be inadvertently ignored.
The purpose of the following calculations is to evaluate these
effects.
B. CALCULATIONS
1. Null Depth
While pattern data may differ in detail for a wide variety of
antennas, two characteristic features are generally retained.
Grossly speaking, these are the rounded lobes and the notched
nulls. In the null region the patterns can be fairly well represented
by a pair of straight lines forming a V. Even though the slope may
actually vanish for zero signal intensity, it is well to recall that
the recorders at most plot down only 80 db. The subsequent cal
culations are based on the validity of this V being fairly represent
ative of the state of affairs near the points of minimum signal level.
Figure 44 shows a portion of a pattern for which the signal
vanishes along a definite non-zero slope. Because a practical re
cording system cannot plot down an infinite number of db from
maximum, it is only necessary to rotate the antenna slow enough
103 t = a
Fig. 44. Pattern notch, that the null be as deep as the dynamic range of the instrument.
Actually, a range of 80 db is not hard to achieve. (This cor responds to a 40 db range of received signal strength using a square-law detector.) The pertinent question thus becomes:
How slow must the pattern be rotated to guarantee a notch depth of, say N db?
Proceeding on the supposition that a V input is representa tive, the time required to rotate the antenna from A to B is de termined in such a way as to be consistent with an a-priori choice for N. The upper bound on the angular velocity of the antenna fol lows directly.
Let the peak amplitude of the pattern be unity and the slope of the V in volts/second be s. Then
104 (37) T = —
It turns out that for a V input the minimum level to which the output of the amplifier drops is linearly related to s. Thus,
(38) e = Ks, m
As a result
(39) T -=. e','m
Since N is the number of db corresponding to 1/e , it is true m that
1 . 11 5N (40) = e e ^ m
The expression for T now becomes
115N (41) T = K e’
Provided K is known, the time T can be found at once from this last expression.
The ensuing calculations deal with the response of an actual amplifier to a V input signal. This leads to the evaluation of K for use in Eq. (41).
105 Anticipating the Laplace transform approach, the V function is described by f(t) where
(42) f(t) = (1 - 1 ) U(t) + — (t-a) U(t-a) . a a
It starts with a value of unity at t = 0 and vartishes for t = a.
Letting F(s) represent the Laplace transform of f(t), it follows that
2 £-as (43) F(s) = as as*
Inasmuch as the bolometer amplifier contains five cascaded and isolated resonant circuits, the transfer function can be closely represented by G(s) where
1 (44) CHs) = (t s +1 r
This of course does not take into consideration any nonzero initial conditions. On a noncarrier basis the amplifier can be simulated with the structure shown in Fig. 45. This is particularly true
—VW
A* I C =J= C =£
Fig. 45. Simulated bolometer amplifier.
106 here where the side bands extend only a cycle or two on each side
of the 1000 cps carrier.
Because all stages operate identically, and it is desired that
eQ(t = 0) = 1, corresponding to that of the input, a revaluation of the transfer function is necessary. Consider the first section
alone, where an initial potential Vc = 1 is applied to C. For an input F(s) the output across C is given by
(45) E = —Fi.gl -- + ------01 SCR+1 SCR+1 *
The output from successor sections is found by using the response
of preceding stages as input. Carrying out the process until
E0(s) from the last stage is obtained, it is found that
5 (46) Ep(s) = T (TS + 1) H. P 's + 1)J J=1 where T = RC. The corresponding eQ(t) becomes the formidable array of term s given below. _t 3 4 -i " T (47) e (t) = 1+— - 1 - 5T + 4t + l *—■ + - ^ + ----- U(t) + ° a a L 2 T . 24T
10T + 2(t-a) +2
+ 107 d en(t) In principle at least, it is possible to set ^— equal to zero, find dt the time where the minimum occurs, substitute back into Eq. (47) to obtain an en . This would come down in terms of T and a, which means that the minimum output would be related to the slope in a known way. Carrying out the process in this special case leads to transcendental equations, not amenable to easy solution. As an alternative, eQ(t) was plotted in the neighborhood of the minimum value for several descrete magnitudes of a. The results are shown in Fig. 46. Here it is evident that the slope of f(t), given by 1/a, is linearly related to the minimum value of eQ(t), as was axiomatically stated earlier. In particular, (48) s =i = ^ eD . a 1 m Earlier considerations of the bolometer amplifier revealed that T = . 0308. Using this value, the K of Eq. (41) becomes . 0553. Thus 115N (49) T = . 0523 e° Figure 44 is a reasonable representation of the amplifier output for a dipole antenna when a linear detector is employed. The slope of V in volts/radian is thus one inithis case, which 108 0 . 0 8 0 .0 6 0 .0 4 0.02 0 4 8 12 16 18 Fig. 46. Slope of ramp input versus minimum output. 109 implies that ABi corresponds to 1 radian. Basing calculations on an assumed reasonable plotting range of 50 db for a linear detector, it turns out that T is 16. 5 sec. The equivalent time for 1 tower rotation is thus 103.5 seconds or 1.72 minutes. When a square-law detector is employed the V is not so evident. Here, the slope actually vanishes for the' sine function being considered. However, at -80 db for example it still has a significant value. It turns out to be . 02 volts/radian, which implies that T = 50 radians. The corresponding time obtained from Eq. (49) is 523 seconds. On this basis the time for one tower rotation is just 66 sec. As a comparison, the time for one tower rotation using a linear detector and 40 db of signal range is 54.5 seconds. Thus for the same r-f power range, in this instance, it takes about 20 percent longer to record the data using a square law detector. It is possible to compute the slope on a logarithmic scale at the -80 db signal level, which is compatible with the time T of Eq. (41). However, because of the nearly perpendicular approach of the intensity pattern to the -80 db level, the information has little to offer beyond academic interest. Figure 47 shows the null region on a'db scale. The slope is given by —~ db/unit time. 8T 110 80 - e 0> - +A-- 0>> o c C — O' co 80 Time Fig. 47. Notch on the db scale. Because calculations are based on the maximum voltage -4 being one volt, ez equals 10 volt. From earlier considerations it is true that (50) £.L..l.eA = I 5T T Although ez is known, ex remains to be found. It is de termined from the relationship (51) -80 + A = 20 log ex . Or, A (52) log ei = -4 + 20 The value of ei follows directly, -4 + ~ (53) ex = 10 20 = I0"4 e+*115A % 10'4(1+ .115A) . Substituting in Eq. (50) yields 111 .115 x 10 "4A (54) 1_ 5T T . Replacing T by its equivalent yields A (55) =166 db/sec 5T which is the maximum slope at the -80 db level if a -80 db notch is to be achieved. Because of the approximations involved, it is not expected that the figures resulting from these calculations be precise. On the other hand they should at least provide a first order estimate where none existed before. The figures obtained here have been substantiated approximately by measurements . 2. Beam Shifting The magnitude of shift incurred in the received beam of an antenna pattern can be viewed either from the Laplace transform or steady state points of view. The same conclusions are reached in each case . In the theory of the Laplace transformation technique there is a theorem which states that if f(t) is Laplace transformable to -a s 57 F(s), then f(t-ct) U(t-ct) is Laplace transformable to F(s)e The bolometer amplifier response to an input f(t) is given by 112 (56) F(s)------. (TS + l)5 —a s If this expression could be approximated by F(s)« , for a valid region in s, then the time delay would be nearly a . — CL s “ 5 Expanding both e and (Ts + 1) gives the results - a s , , a2 2 a 3 s3 ' , (57) £ = 1 - a s + — s - — ----- + • • * UL LA (TS + 1)"5= 1 - 5T+ 10T2 s2 - 1OT3 s3 + • • Owing to the frequency constraint imposed by the depth of null condition, Ts « 1 . This validates the approximation that a % 5T. From a steady state viewpoint, the bolometer amplifier re sponse to a sinusoidal input E sin cot is given by E (58) E0 = , —«/ 2” Sin(a>t " 5*]- [1 + I co J Here tan (59) Eq = Em sin co(t - 5T) . For the dipole case it was shown that about 1 minute is re quired for a tower rotation. This means that the frequency is nearly 1/60 cps. On this basis a delay of 5T, or .154 seconds corresponds 113 to a beam shift of .92°. While this may not be excessive in the ex ample taken, the shift associated with high resolution antennas could be excessive. It has been shown by other investigators at the Antenna Lab oratory that error between the input and recorded output can be greatly reduced by shifting the axes to compensate for the delay. Accordingly, it would seem that a device connected to the recording table which would retard its proportional to speed would be a useful improvement. This would be an arrangement analogous to the spark-advance mechanism in an automobile distributor. 114 SECTION VII CONCLUSIONS A criterion was established for maintaining uniform stability in a class of nonlinear servomechanisms normally encountered in instrumentation for electromagnetic field measurements. This criterion which concerns the design of appropriate compensators intended to keep the incremental servo loop-gain constant in spite of variations in feedback gain, was used in the subsequent planning of practical recording instruments. Particular examples of where the information is applied are the linear and logarithmic amplitude plotters, together with a linear phase plotter. At their inception these represented an improvement over existing instruments intended to perform the same function. For the first time it became possible to plot the strength of an r-f signal over a linear range of one hundred to one with less than one percent error. The phase plotter made it possible to automatically record the relative phase of an r-f signal in the presence of an independent variation of amplitude up to 40 db. The phase accuracy is + 4°, with improvement possible. Although the amplitude feature of this instrument was never utilized, it is inherently possible to obtain both amplitude and phase information simultaneously. 115 With a view to developing an unusually sensitive receiving system for eventual use in the mm region, an ultranarrow band pass receiver was constructed for operation at K-band. The equivalent bandwidth is 4 cps which was achieved by means of an unusual arrangement of mixers together with a linear waveguide phase shifter. The noise level occurs at -160 dbw which is 23 db worse than theoretically possible. The decreased sensitivity is attributed to local oscillator noise. Because it has been an observed fact that the recording of pattern data at excessive speeds results in the loss of null depth, a quantitative investigation of the phenomenon was undertaken. This was carried out using a V function to simulate the selective amplifier input or detector output. By comparison of the V function with the null region of a dipole pattern, it was estimated that for a 40 ub dynamic range of r-f and using a linear detector 54 seconds are required to record the pattern. In contrast, 66 seconds are required using a square law detector for the same dynamic range. Thus for the case considered, 20 percent more time is required to obtain a pattern using square law detection if the same bandwidth of filtering is employed ahead of the recorder. Two factors cause a difference in the recording time. One is that the db dynamic range at the detector output is doubled because of squaring; the other is 116 that the pattern shape is different after squaring. Consideration was given to the azimuthal shift in the recording of antenna lobes. This arises because of the time delay- occurring in the narrow band selective amplifiers. The equivalent delay is 0. 154 seconds. As a result, a dipole pattern rotated in 1 minute has an azimuthal shift of 0. 92°. Revision of the radar echo measuring circuitry, tp the extent of deleting an i-f range gate and replacing it with a video counterpart, improved the performance until no observable instability can now be attributed to the gate itself. The out-of-gate discriminatinn is about 50 db using a vacuum tube gate. The use of a Zener diode gate increases the discrimination to about 60 db. Unfortunately, the Zener diodes were not available at the time the first gate was constructed. The need to obtain logarithmic echo data at a higher rate of speed than is normally possible using a conventional system prompted an investigation into the use of open-loop systems. It was found at the time that suitable component parts were not sufficiently developed to permit the completion of a workable system. As part of the project, a Zener diode gate was developed which has a linear dynamic range of 55 db together with an out-of-gate discrimination approxi mately 60 db. The principal difficulty was that logarithmic i-f 117 amplifiers were not available which had sufficient stability to make the system reliable. It is the opinion of the writer that such a system is now feasible provided sufficient interest is aroused to solve the remaining problems. In addition to the broader problems dealing with systems, several innovations in detail circuitry and techniques have proved fruitful. In part these include ( 1) the introduction of mechanical rectification which extended the dynamic range of rectification from about 30 db to 86 db. This extension makes the square root recorder possible. ( 2) The introduction of an arm-loading technique in the design of continuously variable ladder networks to allow greater separation of taps for the same error. As an example, for a 0. 23 db maximum interval error, the tap separation can be increased from 4 to 10. 5 db using this method. The proper loading and tap spacing have been calculated for a range of allowable values of maximum error. These are presented for ease in application. 118 APPENDIX I The objective is to show how loading on the follow-up com ponent affects the loop gain. Stress is placed on the nonlinear case. Consider the input circuit of Fig. 48 to be that of a general nonlinear servo where the total potentiometer loading is lumped into Rj. Both the error circuit and the input generator tnay contribute to this total value. AAA/ AAAAAA/— Fig. 48. Input circuit. E rro r signal, is the result of current flowing through ctRlo This in turn is due to an inequality existing between eQ and e1# Allow the follow-up potentiometer to be a Thevenin generator with the following characteristics; ( 60) e =V f{0) oc ' ' ( 61) R0 = R g (6 ) 119 It does not follow that f( 0) uniquely defines g( 0) . A specific appli cation to the square-law case demonstrates this fact. Referring to Fig. 48, the output error voltage is given by Eq. ( 62) and the follow-up sensitivity by Eq. ( 63).. a Rx( V£(G) - ex) ( 62) R+Rg( 0) aVf'(0) (63) S = — = aH( 0) 1 + N g( 0) d0 balance where N = R/Rj^ . Equation ( 63) shows that the variation in sensitivity with 0 depends not only upon the potentiometer law, but also upon how it is generated. Magnitude of the latter effect is governed by the amount of potentiometer loading which is present. Thus as N -► 0, meaning of course that the loading becomes negligible, H( 0) ->■ f*( 0) regardles of how the function is generated. In considering Eq. ( 63) further, it is apparent that for N large even a servo with a linear follow-up potentiometer will not posses exactly uniform gain across the dynamic range of 0. Howeve in usual circumstances the circuits are so designed that no compen sation is necessary in this case. A further point is that the compen sation of a nonlinear servo may be sufficiently sensitive to the impedance of the input generator that care must be taken in using a simulator for test input signals if response identical to the regular input generator is to be achieved over the full range of 0. In other words, the mock-up test generator shown in Fig. 49a may not actually give results identical with those obtainable using the generator shown in Fig. 49b. In regard to the sensitivity expression given in Eq. ( 63) , N would vary for the first generator and not for the second. V (a) (b) Fig. 49. Servo command generators. Two possible arrangements of potentiometers which will generate a square-law response are shown in Fig. 50. The one at ( a) , which has been discussed, employs two "piggy-back" linear components. The one at (b) is a nonlinear resistance made with a uniform winding density distributed across a triangular shaped mandrel. Both circuits yield an f { 9) = 02. On the other hand, the g( 0) is different in each case. 121 In ( a) the output resistance is given by 0R( 1-0) R (64) R„o %- = 0R(l-0) R and (65) g(0) ~ 0(1-©) . In (b) the output resistance is given by 02 R( 1-02)R ( 66) Rq = ------= R02 (1-0 2) R and (67) g(0) = 0 (1-0 ) . Although g( 0) varies between 0 and 0.25 for 0 < 0 < 1 in each case, the curve shapes are somewhat different. R»> r (a) (b) Fig. 50. Square-law-generating potentiometers 122 APPENDIX II The objective is to compute the maximum error in the square- law response of the follow-up potentiometers owing to finite ratios of resistance. It turns out that maximum error always occurs for 9 = 1/2 regardless of the potentiometer resistance ratio. Consider Fig. 51. 8 r : l e Fig. 51. Square-law potentiometer circuit, Provided no loading occurs, i.e., R/r -*■ oo (68) e = 02E . Consider finite loading, 0ZE R (69) 0(1-0) + R /r r The percent error between Eq. ( 23) and Eq„ ( 24) is given by 0 ( 1- 0 ) (70) £ = 100 0(1-0) + R /r 123 d Setting £ = 0, the point of maximum error is seen to occur at d0 0 = 1/2. Using this value in Eq. ( 70) , a formula for £ vs R /r max follows. A plot is shown in Fig. 52, obtained directly from Eq. ( 26) 100 (' 71) ' § 3 max 1 + 4 R /r 0.1 H. Fig. 52. Maximum square-law error in terms of potentiometer loading. 124 APPENDIX III The objective is to determine, in the case of a ladder network, the maximum db error existing over an interval in terms of the total attenuation across the interval. Error arises because a linear function is used to approximate an exponential one. Let (92“®i ) a- typical interval on the attenuation curve, with V and V the boundary potentials. The exponential function is characterized by having uniform interval spacing between taps, provided equal db potential differences exist between adjacent tap points. Thus in Fig. 53, if N is the db difference between VL and Y o> Of a p 8Z Position Fig. 53. Typical attenuation interval. 125 it is independent of either 0JL or 02 alone. It depends only on the quantity ( 02- 0x) , as is shown in Eq. ( 53) . V e~r0i (72) N = 20 log ______-r0 V e 2 or (73) N = 20 r[0 2 - 0 j log e If position is calibrated directly in db, then ( 74) r = 0.115 . In the typical interval ( ©2 - 0^) , (b-a) is the linearization error to be maximized, i. e. , the maximum error between the true and approxi mate curves is to be found for a typical interval of fixed bounds. -Y2l Using geometrical correspondence and equating e to Ye , an expression results which gives the following value for b, (02 - 0,) £-^ + 8, €-r02 - 0 2£ 'r01 (75) b = 6-re2 _ Upon subtracting a from each side and maximizing, an expression for a is obtained. 1 T r( 0 - 0 ) (76) a = — in 2 . £-r0, _ £-r0 2 126 This is the particular value which corresponds to maximum error. After solving for b, the maximum error (b-a) can be shown to equal -rfi . --r0 r 0 _ (1-r 0 ) 6 1 - (1 — r0L) e 2 x (77) (b-a) ------jgn 'r(V S i) ~r02 -r0i e - e ,e-r0! _ G-r0 2_ max By letting r| = r(0 -0 ]L) and simplifying, Eq. ( 38) results, (78) fjM =(b-a) = 8. 68 -1 + - In 1-e-H max The end results shown in Fig. 54 are obtained directly from this last equation. Notice that by using a 4 db interval, and thus requiring 20 intervals to cover the 80 db span, the maximum error referred to the received signal is about 0.11 db. This, of course, is just half the db error indicated by Fig. 54. 7 6 5 4 3 2 0 0 I 2 3 4 5 6 7 db Interval Fig. 54. Maximum linearization error versus interval length. 127 APPENDIX IV The objective is to develop a method for minimizing the positional error occurring in ladder networks. The discrepancy arises because a linear function is used to approximate an expo nential one between the end points of tap intervals. To be specific, the network under consideration is shown in Fig. 55. Here the Lood Resistance Fig. 55. Ladder attenuator. load resistance r is specially chosen with a view to minimizing the positional error across the tap intervals. As has been pointed out, 54 a significant measure of improvement can be realized using this criterion for choosing r. The results are organized so as to permit easy determination of the greatest spacing consistent with a maximum allowable position al error over the interval as well as the normalized values of the 128 load resistance r and generator resistance r . In situations where high accuracy and wide dynamic range are required, the possible improvement becomes an important consideration. A typical tap interval having 5 db insertion loss is shown in Fig. 56 to demonstrate the actual improvement which can be N s Normellaetf Voit*«« OiiHikiihtn Acr*«t - 0.1711 A 3A Tap interval Variant \ s \ — 01 Le«4<»9 — V S i /• ld«dl v\ > Cuf *• \ V \ V> V > \ s s — \ V \ \ sN V® > \ V7 N s K ■ 0. 84 ft S Optimum \ s, I s | ^K • 5 - 0.»7|« - Ideal Curve —— - 0 02 0.4 OJ OK LO Fig. 56. Normalized voltage distribution across a 5-db tap interval for various degrees of loading. realized using various degrees of loading. Both the true exponential curve and various approximations, each associated with a particular value of load resistance, may be seen. Here K is the ratio of load resistance to series resistance between tap points. The advantage 129 to be gained using optimum loading may be observed by noting the large reduction in error for this case. The improvement is even more evident in Fig. 5'7 where error is plotted against position. For optimum adjustment the positive and negative maximum errors are obviously equal in magnitude. 01 a t ot Fig. 57. Error across a 5 db interval for various degrees of loading. 130 There are two facets associated with the optimum design. One phase is concerned with determining the maximum improvement realizable with optimum loading; the other phase is concerned with determining the optimum load. This information is condensed into graphical form for ease in obtaining the tap spacing for no loading, the tap spacing for optimum loading, and a normalized value of the load resistance, once a maximum allowable error over the interval is established. A typical ladder section is shown in Fig. 58. Ri is the effective H R. A/WWV Fig. 58. Typical ladder section. resistance across the terminals as shown; ^ is the normalized distance between taps. The circuit is constrained to have N db insertion loss between tap points, when the measurements are made by reading the pick-off voltage at the extreme positions, i.e. , when ^ equals zero and one. This leads to Eq. ( 79) . 131 Vi L, = n ON ( 79) . JL = where a = 0. 11 51 29 . . . . The number of db indicated by Eq. ( 79) is independent of the value r. This follows directly from Eq. ( 82) . The extreme voltages, as read on the pick-off are given by Eq. ( 80) and Eq. ( 81) V I r ( Ri + Rs) (80) .. . ^ .r_P = 2Rtr + Rx2 + RXR + rR £ v » U - i ______(81) E 2R. r + R. 2 + R R + rR 1 i i s £ Dividing Eq. ( 80) by Eq. ( 81) and comparing with Eq. ( 79) it is apparent that ON R s ( 82) £ = 1 + . Ri As a consequence of the total attenuation per section being independent of r, the only possible effect this quantity can have is to shape the response curve over the interval. This property is exploited to the advantage of the designer in the subsequent calcu lations. 132 A general expression for the voltage distribution across the tap interval, expressed as a function of load value and position, is given by Eq. ( 83) . This degenerates into Eq. ( 79) and ( 80) re spectively when ijj equals zero and one. V(r ,f) r(Rj+ [l-^]Rs) (83) ------— ------= —------' ( Ri +^Rg) ( r +Rx + [l - ^]RS) + r( Rj + [1 - ^]RS) Expressing the load resistance in terms of the series resistance so that (84) r = KRg and employing an expression for Ri obtained from Eq. ( 82) , a more useful expression for V(r , -ft) results, especially after being normal ized to have a value of unity at ^ = 0, as has been done in Eq. ( 85) V( K, N, $ (85) L. E Normalized [K(e2ciN- + [1 + irf 6°” - 1) 1 [ 6°®*+ ( K - f) ( e0^ - 1) ] + K[ -1 ] [s0®1- f ( e ^ - l) ] } An exponential distribution which passes through the same end points as those of Eq. ( 85) for identical values of N in each instance is given by Eq. ( 86) . 133 Ve(N,ft -aN ^ ( 86) e E The angular difference ^ , which makes Eq. ( 85) and Eq. (86) equal in value, is the significant error in the application of ladder networks to logarithmic servos. In the particular case where K -*■ oo (an infinite impedance load) the maximization process can be readily carried out. It leads directly to Eq. ( 87) which is plotted as a function of N in Fig. ( 59) . (87) Max Notice that the results shown on the K = oo line of Fig. 59 correspond exactly with those calculated in a less sophisticated manner in Appendix III. The more general case of finding the value of K which minimizes the greatest error over the interval (and also that corresponding value of greatest error) does not lend itself to easy computation. As a consequence, only the results are included. These have been carried out to a higher order of accuracy than can readily be shown on the graphs. The essence of a large amount of calculation is shown in Figs. 59 and 60. The data are presented in OPTIMUM K . I Kgpy) 0.06 interval error vs INTERVAL 0.006 0.006 0.004 NOTE CURVE • A Corrttpond* To An Inhnrtt Imptdonc* Termination On Th« Afl«nuo 4 6 6 10 12 14 16 18 20 22 N, The db 'ntervol Between Topi Fig. 59. Interval error vs interval, for Kopt and Kq OPTIMUM K vs INTERVAL 0.6 0.2 0.15 0 2 4 6 8 10 12 14 16 2 0 ^ <3b Interval Between Topi. Fig. 60. Optimum K vs tap interval. 135 such a form that, once having established an allowable greatest error, the maximum db span between tap points for both cases considered can readily be determined. A comparison of Curves A and B in Fig. 59 shows the sizable improvement which can be realized by .using the optimum loading technique. As an example ^consider an allowable maximum error of 0. 2 3 db. According to Fig. 59 the maximum span between tap points for an infinite impedance load is 4 db, but with an optimum load the span can be increased to 10. 5 db. Referring to Fig. 60, the K0pt corresponding to 10. 5 db span is 0. 368. Thus if the attenuator had a resistance of 1000 ohms between tap points, the proper termi nation would be 368 ohms. It has been shown that loading the attenuator has no influence on the loss per section. Thus it is possible to adjust the ladder initially in the usual way with the load absent from the circuit. Obviously then, no additional complications in the adjustment procedure are incurred. Unlike the unloaded attenuator, consideration must be given . to the generator impedance when the pick-off arm is loaded. Without this precaution the first sections of the attenuator may deviate markedly from the proper value of attenuation. The correct 136 generator impedance is given in Fig. 61 in terms of the series NORMALIZED GENERATOR IMPEDANCE VS db INTERVAL BETWEEN TAP POINTS \\ Rg = hR, \ \ \ S.\ \ \ \ 0 2 4 6 6 10 12 14 16 10 2 0 d b Interval Between Tap Points Fig. 61. Normalized generator impedance vs insertion loss per section. resistance between tap points occurring in the attenuator. This is equivalent to Rj appearing in Eq. ( 82) and Fig. { 58). The constraint upon input impedance is no particular disadvantage in the case of a logarithmic servo, where, in all likelihood, the driving amplifier is included as part of the servo recorder in order that the instru ment impedance may be made very high. However, where the ladder network may be excited from a general source, the input impedance must comply with that given in Fig. 6l to insure correct 137 insertion loss, particularly in the first section of the attenuator. It should be pointed out here that because the pick-off arm is normally positioned for constant signal level in the logarithmic servo, the first sections of the attenuator are sampled only for low input signals. As a result, it may be possible to relax the accuracy requirements in this region because of the inherent experimental inaccuracy in obtaining the original input data. This consideration would naturally permit greater mismatch of the input impedance. In determining the effect of generator impedance mismatch on the accuracy of the first ladder section, many methods of data presentation could be employed. Figure 62 shows that percent error 40 20 / / X> In* ertio n Lo 31 Error In a £ Tt e F rst Sect on 1 / 10 * / Greater Than In 8.0 / The Region Above / 6.0 The Curve . 4.0 / trlic E rror ! \n n L 3SS , 1 R The e 2.0 M rst bectton is Less than £m In The Region Below The Curve. 1.0 0.8 / / 0 2 4 6 7 10 12 14 I t 18 20 db Intervol Between Top Points Fig. 62. Tolerance requirements on the generator impedance. 138 in the nominal generator impedance which causes the insertion loss of the first ladder section to be in error by an amount just equal to the maximum interval error previously evaluated. In the example where 10. 5 db intervals were considered, a tolerance of 8 percent on the generator impedance could be allowed, based on the above criteria. This value is obtained directly from Fig. 62. The true generator impedance is obtained either from Eq. ( 82) or Fig. 61.' Using the assumed value of 1000 ohms for Rs, the generator impedance turns out to be 427 ohms for 10. 5 db loss per section. A 100 db attenuator constructed using the design data presented had no more than the anticipated allowable error. Whereas the unloaded ladder required taps every 4 db for the required accuracy, the modified design allowed a tap span of 10 db without any degradation of performance. Actually, the span could have been increased to 10. 5 db. The difference between 25 and 10 tap sections on such an attenuator represents a sufficient saving in both time and expense as to justify the modified design in many applications. 139 APPENDIX V The objective is to show to what extent the positional error in ladder networks can be reduced by the introduction of an op timum second order term . The results obtained are compared with those achieved in Appendices III and IV. It turns out that the error in this case is just about half that obtained in previous in stances. Although the calculations have not been carried out as yet, it would seem reasonable to expect that a combination tech nique using a second order coefficient together with arm loading would achieve further improvement in accuracy with negligible increase in complexity. Fortuitously the second order term in the voltage distri bution across a tap interval can be introduced without resorting to curvature in the card shape. The fact that sawtooth segments produce the desired effect is both a convenience as well as an economic advantage . Consider first a linear card of normalized length 1 .0 and width w. Let it have n turns per unit length and p ohms per unit wire length. Accordingly, the resistance of the total length is given by ((88) R-j. = 2p nw . 140 Now consider a sawtooth card made in such a way that its median width is still w. Figure 63 shows such a design. Using the e, -.II5N a = kw Ax Fig. 63. Tapered form for approximating an exponential voltage distribution. same winding as in the linear case, it turns out that the resistance Ibj, does not change. This can be concluded from a heuristic argument by noting that the total resistance of pairs of turns equally spaced on each side of the x = 1/2 point have constant resistance. This is true because one turn is longer than 2w the exact amount by which the other is shorter than2 w . In anticipation of finding the voltage distribution across the tapered interval, consider how the resistance R(x) varies with x. Resistance in an elemental length of winding Ax located a distance 141 x from the left end is given by (89) AR( x ) = 2£pnAx . The length, i, is given by (90) I = 2x(w-a) + a Accordingly, (91) AR( x ) = 2p n[ 2x(w-a)+a] Ax After integration it is found that (92) R(x) = Rrpffl-RJx2 + kx] . Inasmuch as the terminal voltages on the left and right are respec- —a s / jc) tively ei and ei^ , the normalized voltage distribution follows e i from the equation pair (93) < e(x) = ei - iR(x) It is given by (94) e (x ) 1 - (1 - e a )[(l-k)x2 + kx] e i where a = .115N and N is the number of db insertion loss in the 142 span. In addition, k is the ratio ± which is the maximum to median w card width. To find the optimum value of k which minimizes the posi tional error between Eq. (94) and the true exponential having the same insertion loss requires the solution of a transcendental equation. This has been handled graphically by assuming a range of k values for discrete values of N. That value of k which yields equal positive and negative values of error is taken as optimum, as in Appendix IV. As it turns out, both the error and k ^ vary with the insertion loss N. These are shown respectively in Figs. 64 and 65. Comparable error curves from appendices .III and IV.are superimposed for easy comparison. It turns out that using this design is approximately half that obtainable using the arm Joading technique of Appendix IV. Accounting for finite card thickness can be accomplished easily, once the ratio k = a/w for the infinitely thin card is de termined. Let k = a /w where the primed quantities are the corresponding counterparts for a card of thickness 5. The re lationships between the primed and nonprimed quantities are E In db 3 . 0 7 . 0 .9 0 .5 0 Fig. 64. E rror versus insertion loss. insertion versus rror E 64. Fig. b neto Loss Insertion db 144 .c 20 2.2 2.0 -4- Q. O 20 22 db Insertion Loss Fig. 65. kQpt versus insertion loss. Accordingly, <96> k - . From which, X97) k = k + T(k-l) . Here T is the ratio 25/w , or twice the card thickness to the median width. 145 . APPENDIX VI The objective is to show that the gain, J , of the hybrid junction phase discriminator is proportional to Ex , the received signal. £, is the error output voltage; 5 is the phase deviation of the angle between Ex and E 2 from it / 2 radians. Let Ex and E 2 be two r-f signals applied to the hybrid junction 2 2 as shown in Fig. 66. KVx and KV 2 are the corresponding outputs KV, x — d - d - 2 KV, Fig. 66. Hybrid junction circuit, of detectors d -1 and d- 2 . Referring to the phasor diagram of Fig. 67, it is evident that (98) Vi = E 2 + Ex 146 (99) V2 = E2 - Ei . Also it is true that (100) Vi = Ei + E2 - 2Ei Ez c o s ( j _ 6) ^ 2 2 (101) V2 = Ei + E2 + 2Ei E2 c o s ' ( | - + 5) . -E Fig. 67. Vector diagram of hybrid junction voltages. Since 5 is constrained to be small, (102) K [V 2Z - Vi2 ] = Kfj ~ 4Ei E2 5 whence the gain, , js proportional to Ex E 2 . Inasmuch as E2 is maintained constant (103) 1 - k E L 147 APPENDIX VII The objective is to show in detail how the error gain was made to vary inversely with signal strength. Ex shown in Fig. 68 is the actuating r-f signal. Because of SQUARE LAW AMP. RECTIFIER DETECTOR i 6 t. , Vi , u ■4f / EXPONENTIAL LADDER ATTENUATOR ------AMPLIFIER 0 OUTPUT REFERENCE VOLTAGE T N PUT EXPONENTIAL LADDER ATTENUATOR Fig. 68. Compensator circuit. the automatic control feature, the pick-off voltage V is given by (104) V = AKEi2 e"a9 = k . 148 The error gain is given by /£j 0 Because of the exponential property of the compensating potentiometer, and the fact that the attenuation rate is just half that found in the follow-up potentiometer, it is true that -2 e (105) £0 = £ ie By substituting in Eq. (105) from Eq. (104) for the exponential term, it turns out that there is an inverse relationship of the type required. K (1°6) f O TT. Hence to Kn (107) .G = — = — Ei 149 APPENDIX VIII The objective is to show how a phase plotter may be modified to yield both in-phase and quadrature components of r-f phase. 59 Consider the basic design shown in Fig. 69. 1000 cps Signal Modulator Test Pad Probe Klystron Load Hybrid j v w Junction Slotted Wave Guide 000 cps Reference Signa 1000 cps Li near Selective Recorder Rectifier Am pi ifier Fig. 69. Equipment for measuring the real and imaginary components of electric field. 150 Because of the properties of the hybrid junction, the signals arriving at detectors dt and d 2 are respectively , «* = A + E (108) < E = A - E s. -2 For details concerning adjustment of the equipment so that the hybrid junction operates properly, reference is made to the original paper. If the phase angle of signal A is arbitrarily called zero, then Ej = A + jE | cos a. + j |E | sin a (109) E2 = A - |E | cos a - j jE j sin a The output voltages Y l and Y z of detectors dj and d 2 are proportional to |E 1|2 and |E 2 j2 respectively. That is, Yi = [A + |e j cos a ]2 + [ (e j sin a ]2 <110> , , Y 2 ~ [A - |E j cos a ]2 + [ JE f sin a ]2 The audio transformer Tj takes the difference between Y x and V2, yielding V 3 where V3 = 4 | A | |E | cos a . Since A is held constant, V 3 is proportional to Re[E] . 151 The imaginary component of E is extracted in a similar manner, except an initial shift of 90° is given to A by moving the test probe down the slotted guide tt /2 radians. In this case Ej= |E | cos a + j [ A + |E | sin a] ( 111) < E 2 = -(e ) c o s a + j[A - |E | sin a] and Vx = [ |e I cos a ]2 + [A + |E I sin a ]: ( H 2) < V = [ IE I cos a ]2 + [A - |e I sin a ]2 In this case (113) V3 = 4 j A | | E | sin a and hence V is proportional to Im [E] . The results achieved using this system were found to be remarkably accurate. In addition, the high sensitivity figure of -125 dbw was achieved with careful adjustment. Comparisons were made with test sections possessing known phase distributions, To wit, sections of matched and shorted guide were employed. The result of these tests is shown below in Fig. 70. 152 in a l- UJ (VOLTS x 0.2 4 . 0 0.6 el opnn o eeti fed nest i nre waveguide, snorted in intensity field electric of component Real n ace waveguide. matched in Fig. 70. Real components of field intensity. field of components Real 70. Fig. R E F E R EPO N C E W I E R m w IN L OE Imw SIGNAL POWER (LENGTH) X MEASURED SINUSOIDAL 153 UJ Ct > o ^ J U o z l- x elcmpnn o lcrc il i e iy1 sity ten in field electric of ponent com Real 0.8 0.2 0.6 4 . 0 1.2 MAX. SIONAL POWER POWER SIONAL MAX. R E F E R E N C E POWER POWER E C N E R E F E R (LENGTH) X SINUSOIDAL MEASURED O.lmw Imw A PPEN D IX IX The objective is to show how conventional echo measuring equipment can be extended in scope to permit the recording of te r rain return. Initial terrain measurements were made by using mobile radar operating at X-band. For convenience, a truck was employed to hold the equipment. Antennas were mounted on top; equipment was mounted inside. An auxiliary power plant furnished energy to operate the sys tem . In principle the instrumentation differed little from a regular radar echo measuring set. However, to obtain a statistical average of the echo area interrogated additional circuitry was required. The important components of the complete system are shown in Fig. 71. The method of determining this averaged value for a certain section of terrain was to use a comparison technique. To be specific, the input attenuator cx was adjusted until the counter in dicated that half the transmitted pulses were lost. A target of known echo area was then substituted for the interrogated terrain. As before, the attenuator cx was adjusted until half the transmitted 154 Terrain X - Band Video Transmitter And Rece iver Counter Gate Modulator Sync , Pulse G en era to r Fig. 71 . Radar terrain measuring equipment, pulses were lost. By comparison of the two attenuator settings, it was possible to assign a numerical value to the statistically aver aged echo area of the sampled terrain. In order to measure terrain return at higher angles of incidence, a cw system mounted on the boom shown in Fig. 72 was constructed. The doppler design of Fig. 73 provides a simple effective method of alleviating the hybrid T balance problems of a conventional cw sys tem. With this system the hybrid junction is not required to op erate at a delicate balance. Indeed, it is purposefully unbalanced 155 mt-m: Fig. 72. Terrain measuring equipment. 156 to permit a controlled amount of oscillator power to reach the de tector and serve as local oscillator signal. The shift in frequency between the received and transmitted signals comes about because measurements are made with the truck in motion. In order to discriminate against spurious audio signal components in the re ceiving system and yet not place undue restriction on the truck speed, band pass filters were used in the linear amplifier. Actually there were two pass bands with a rejection region between 60 and 120 cps to eliminate trouble from the power lines. The pass bands extended from 10 to 50 cps and from 140 to 600 cps. These regions corresponded to moderate rates of speed for the truck. Actually, the truck speed is determined from the relationship AfX (114) V------z 2 cos 0 cos in cps, X is the wavelength in feet, 0 is the incidence angle, and 4> is the azimuth angle between the forward motion and the antenna beam direction. Upon going to a doppler system it was found that the klystron tubes were sufficiently stable without using oil as a coolant. It turned out that high velocity air did an adequate job. 157 V Ste p Linear Square Electronic Attenuator Entegrator d > - Amplifier Detector Unbalance Crystal Monitor Mixer (^Frequency Mixer Output E. Tuner H Lens Pad Load -VW- •AAMA J. Ferrite ^ Tuner A/St An ten na Isolator Powe r Di rectiona Monitor Coupler Recorder Klystron Fig. 73. Block diagram of cw doppler system. Workable systems have been built and used at X, K^, and Ka bands. Zoned dielectric lenses provided the necessary uniformity of phase front required at the 20 ft. measuring distance. To indi cate the latitude of freedom inherent in the measuring head, it is merely necessary to note that terrain was measured at ten and sometimes five degree intervals over an incidence angle range of 10 to 80 degrees. In the absence of a pulsed oscillator a somewhat different method of averaging became necessary. This was accomplished by using an integrator together with a power level recorder. As in the case of radar, a triple bounce corner was employed. Owing to 158 the doppler feature, however, the detail of standardization became somewhat different. In order to introduce a Af frequency shift, the corner reflector was mounted on the end of a revolving four foot arm . The observed response to this provided the reference required for comparison with the measurements of actual terrain. 159 APPENDIX X The objective is to consider some of the factors which influence the performance of an i-f gate. In order that the discussion be germane to the original system, the specific values have been taken from the published circuits.43 Originally gating was accomplished by modulating a fixed cut-off bias applied to three i-f amplifier stages as shown in Fig. 74. Its o o o 2 2 0 K w v A A / V - o - 3 0 0 V Gating 2 7 0 0 Pulse 2 5 K Fig. 74. I-F gating circuit, value was -33 volts. Except in the presence of the 30 volt gating pulse, the tubes were surely cut off. It was stated that the series resistance was employed to effect a match between the pulse gen erator and the termination. This statement seems open to doubt. However, accepting its presence, consider the pulse deterioration due.-to the selected components. 160 The gating pulses, represented in detail in Fig. 75, can be ex pressed as a summation of unit step functions. Thus, 00 (115) e^t) = ^ U(t-nT) - U(t-nT-5) . n= 0 The Laplace transform expression becomes ,-nTs (116) E i(S)=- (i - e-5s) y s L j n =0 H 8 f— K Fig. 75. Gating pulse detail. The simplified circuit this pulse train excites is shown in Fig 76 The output voltage developed across C is given by eQ(t) ~ EQ(s) 2 7 0 0 Oj ■ -VW ------ ei (f ) 25k =: e0(t) r 2 35/i/xfd Fig. 76. Simplified charging-circuit, 161 K (117) E0(s) = (1 - e_a s) ,-nTs s(s+(3) where Ri + R 2 K = ; P = Ri Ci C Ri R^ This leads to the time expression (118) eQ(t) = IS \ [(l-e _<3 (t "nT))U(t -nT) - (1 (t-rxT- 6)) . P ! n =0 * U(t-nT-B)] . Because P T » 1 the circuit has virtually no memory from one pulse to the next. As a result, the first pulse (n = 0) can be considered typical of any in the sequence. If the circuit values p = 11.7 x 10 6 & = .4 x 10-6 T = ZOO x 10“6 K = 10.6 x 106 and n = 0 are used, the expression for e (t) reduces to ! (t’< 5) = .907(l-e"4>68[t/ 5l (119) < :Q(t> 5) = 96.5 £-46.8 [t/5] The results are shown in Fig. 77 for an assumed interval of . 4jjl sec. 162 0.4 fi. Sec. P 0.8 0.2 Sec. 0 4 8 1.2 1.6 2.0 Fig. 77. Effective gating pulse . In reality, the effect of the pulse distortion is worse than the results plotted in Fig. 77 may indicate. This is because only the top portion of the pulse is effective, owing to the large neg ative bias which keeps the tubes cut off. Widening the pulse in order to create a flatter plateau is no satisfactory solution. This allows spurious echo signals to get through. It is reasonable to expect that decreasing the capacitance would square up the pulse. Here again difficulty is encountered. The capacitance is needed to make the bottom ends of the i-f transform er coils appear at ground potential with respect to the 60 me i-f signal. Further more, these i-f amplifiers are models of compactness. Modi fications come at the risk of dire results. This is because they 16a rely on stray reactance to bring the coils into resonance. Actually the stray capacitance together with that of the tubes is all that tunes the coils. As a result, even moving wires has a noticeable effect. It is reasonable to expect that substantial improvement in the gate squareness would result from a decrease in the series resist ance in the pulse cirsuit. This was tried. No spectacular overall improvement was observed. In fact, no value of series resist ance existed which made the gain constant over the entire open interval. For high series resistance, of course, the pulse rise deteriorated. On the other hand small series resistance suitable for obtaining a fast rise time caused a different objectionable side effect. In this instance the gain showed a marked variation with higher sensitivity near the leading edge. It is presumed that this effect resulted from the pulses themselves containing energy in the i-f pass band. If square pulses are considered, for example, this argument is perfectly feasible. If such were true, damped oscillations could be established in the resonant circuits which would modify the response . 164 It is not implied that satisfactory i-f gating is an impossi bility. The best that can be said is that one was not found in the time available. Consequently i-f gating was abandoned in favor of a system which showed more promise of immediate improve ment. 165 APPENDIX XI The objective is to show the principle employed in successive detection logarithmic i-f amplifiers. As a starting point consider how a logarithmic device responds. Let e- be' a particular input. The corresponding output u is given by eQ where (120) e0i = k l o g eii « If the input be multiplied by A, the difference between the initial and final values of output, Ae0l, is given by ( 121) Aeoi = k log A . Similarly, if the input be multiplied by An the difference between the initial and final values of output is given by AeQ where n ( 122) AeQ = n k log A n or ( 123) Ae0 = n Ae n °i With these principles in mind, consider the block diagram shown in Fig. 78. All the A^ amplifiers have the same gain A. The boxes D indicate detectors which have their separate outputs summed in the box 2 . 166 Let ei be that value of e^ which just brings the nuth 1 chain into saturation. The corresponding value of e is e where (124) e_ = k e. °i 0 Fig. 78. Successive detection logarithmic amplifier. st If the input be multiplied by A, the (n-I) chain just comes to saturation. The corresponding output is eQ where (125) eQ =2ke. The difference between the initial and final values of eQ is given by Ae^ where ( 126) Ae = kei l l , n -1 Similarly, if the input be multiplied by A ~ , the first chain just reaches saturation. The corresponding output now becomes 167 (127) eQ = n k The difference between the initial and final value of eQ is Ae where °n-l (128) AeQ = n k e- - k e: = (n-1) k e. un-l xi ■Li i x or (129) Ae =(n-l)Ae n -1 l This is the identical behavior of the truly logarithmic device. The difference between the ideal and the electronic approximation is that the latter is only accurate at spot points. Elsewhere marked deviations exist. In considering Fig. 78 it is apparent that a gross redundancy of circuitry is incurred. The same end result can be achieved by using just one amplifier chain and tapping off witha detector between every amplifier stage. This is shown in Fig. 79. n-l Fig. 79* Single chain successive detection logarithmic amplifier. 168 In actual operation only about 30 db of reasonably precise logarithmic response was achieved. While this was short of the 40 db goal, it would have been usable as a start if the stability had been satisfactory. Unfortunately it was not. However, this defect does not automatically stamp it as hopeless. Undoubtedly further effort would bear fruit. 169 APPENDIX XII The objective is to show how a new frequency (co + 5) can be produced by a waveguide device which used oo for an input fre quency and employs a specially designed rotating phase shifter. Three separate cascaded sections, known as A, B, and C make up the instrument. The signal traverses these in that order. The center- section, B, is rotated at a constant velocity by a syn chronous motor. The end sections are stationary. Because they are designed to transform from linear to circular polarization or vice versa, they are generally referred to as X/ 4 sections. The rotating part is sometimes referred to as a X /2 section for reasons which will subsequently become clear. It is a known fact that the velocity of propagation for a wave traveling in a round guide is a function of the tube diam eter. As a result, a compressive force which tends to make the guide cross section elliptical will cause the tube to have different rates of prop agation for signal components along each of the orthogonal principal axes of the ellipse. Because the phase velocity and hence the guide wavelength is greater for a smaller tube than a large one, the com ponent of the initial wave which is resolved along the larger axis 170 will lead its counterpart along the smaller axis. By choosing the length properly, (or controlling the ellipticity) it is possible to have one component lead the other by 90°. Because the two com ponents are already spaced orthogonally and adjusted to have equal amplitudes by virtue of having the principal elliptical axes tilted at 45° with the incident wave, the end result is a circularly polari zed wave at the output. It turns out to have right or clockwise polarization in this case. Figure 80 shows the vector relationships at both the input and output of this quarter wave section. The rotating section B is constructed similar to the quarter wave section. A notabie ""difference exists, however, in that the compression and length are adjusted for 180° relative phase delay between signal components oriented along the two major axes of the ellipse. Figure 81 shows the vector relationships which hold for this rotating section when excited with the circular polari zation emanating from section A. The fixed coordinate excitation signals E ^ and Ej can be represented in simple form by Efj, = E sin wt (132) Eiy = E sin(wt + \) 171 i END OUTPUT ENDINPUT J E jx = 0.707E j Sin cut J Erx - 0 .7 0 7 E, Sin (cut— Erx • X 9 X \ • ' • E ry \ Resultant (cw Rotation ) N X y Fig. 80. Vector relationship in the quarter wave transition guide. 172 •IX ox INPUT OUTPUT Fig. 81. Vector relationships in the rotating guide section. The resolution of this pair onto the rotating axes E_^_ and Eg yields the set (133) E . = E^ cos 0 - Eg, sin 0 iy v Eg = E^y sin 0 + E|x cos 0 Appropriate substitution leads to the compact form E ^ = E cos(tot + 0) (134) J Eg * E sin(mt + 0) By introducing the fact that 0 = p t, owing to the constant rotation, the terms become E ^ = E cos(co+ p)t (135) Eg = E sin(w+ p )t Provided E^ and Eg correspond to the major and minor axes respectively, the output signals become Ea = -E cos(co+ p )t (136) Eg = E sin(to+ p )t Here the common phase delay has been deleted. A resolution of this set back to the stationary output axes EQX. and EQy produces circular polarization with the new frequency being u)+ 2p . Thus, E0y = -E cos(oo+ 2p )t (137) E qx = Esin(co+ 2p )t . Here it may be noted that polarization is in the opposite sense to what it was originally. Section C returns the left circularly polarized wave into one having linear polarization suitable for transmitting down a normal rectangular wave guide. This is accomplished by carrying out the reverse process to that which occurs in the initial section A. As a point of caution, the major and minor axes of compression in section C must be properly chosen to make the resultant linearly polarized wave align itself correctly for propagation in the output waveguide. Otherwise, no output will result owing to the E vector 174 being normal to the correct direction for propagation. However with the correct adjustment, negligible insertion loss is experienced in transforming the input signal of frequency cj to that of oj + 2p . Because the shift is directly related to the angular velocity of the halfwave section this method provides a way of establishing a carefully controlled frequency difference between two r-f signals, to a degree which is virtually impossible by other means. 175 APPENDIX XIII The objective is to compare the signal-to-noise response of an amplifier having a regular 4 cps passband with one having a synthetic passband of the same width, as considered in the text. Figure 82 shows the rudiments of the two systems. f * 6 0 me 4 cpc Pass Bond Output^ e + e n 60m c 1 F Amplifier Conventional Filtering - 60 me t 200 c ps r w 10 me Pass Band 60 me 1 F Amplifier e + e n Reference f = 60m c Output -*■ 4 cps Pass Band 2 0 0 cp s Audio Amplifier Synthetic Filtering. Fig. 82. Comparable filtering systems. To express relationships in literal form the definitions of useful terms are established at the outset. Accordingly, (x>Q ~ i-f center frequency ~ 2ir 60 x 106 2 a~ wide i-f bandwidth ~ 2 ir l0 x l 0 6 (138) p ~ shift frequency ~ 2ir 200 2 5~ narrow i-f bandwidth 2 7T 4 audio am p. bandwidth 176 Now consider a uniform spectrum of noise applied to the inputs of both systems. It can be represented by (139) en =^ En cos (“n1 + ‘W • The power associated with en is proportional to en2. Indeed, if calculations are on a per-ohm basis the power is exactly en . Proceeding on this basis, the power becomesjust ( i4 °> pn=y ^ = - y En 2 2 2 Nown is summed over all the noise terms occurring in the passband. Let this number be N for the bandwidth 2 a. Eventually N will be viewed as going to infinity. The stipulation that the power density remain constant will be imposed also. This noise signal could be thought of in several ways. It could be considered representative of the internal disturbance arising in an amplifier having a non-ideal noise figure, for example. On the other hand, it could be thought of as an external noise voltage feeding a perfect amplifier. It could even be viewed as a combination of these. For N components to exist, the frequency terms necessarily occur 2a/N cycles apart. In addition, the En are equal in magnitude 177 for all n because the noise power is assumed to be uniformly distri buted. Accordingly, NE (141) n = e 2 = p n n or 2 2p.n (142.) N N Now impose the condition that the noise power contained in the band of frequencies coQ - 5 to (143) p = N - n a Equating this to the signal power yields a A' (144) En 6 N where A is the amplitude of the signal. Now the noise power in the band 2a is given by NE 2 A2 a (145) n - This states the obvious fact that the noise power exceeds the signal power by the ratio of the bandwidths. 178 Having agreed upon an S/N = 1 for the bandwidth 2 6, allow the bandwidth to be expanded to 2a. The effective signal input now becomes n= +N/2 < 146) es = A cos ooQt + En cos [u>nt + <|>n] n= -N/2 here 2otn '(1 4 7' ) to n = o to 4 N and a (148) E A N' 6 Suppose now that Keg and Eq are applied to a square-law device. Because of the signal levels, it is assumed that the element contributes no noise of its own. Actually this may be somewhat optimistic. A practical assumption is made as to the relative magnitude of the local oscillator power ° E ^ . It is taken to be 2 two orders of magnitude greater than the noise power. Thus, (149) = 100 “ 2 2 6 or (150) Eq2 = 100 K2A2 - 6 Now the detector input becomes 179 n= + N/2 (151) e^ = K A cosu0t + ^ Encos [a>nt + n=-N /2 The output is proportional to e^2 and no generality is lost when the constant is taken equal to unity. Because of the subsequent filter, the significant output response is taken as that occurring between p - 5 and p + 5. Other terms vanish due to filtering. Accordingly, n= + N/2 2 ed2 = A2 cos2 coQt + -j^T En cos (cont + (j)n) j- + EQ2cos 2[to0 + p]t + n= -N/2 n= + N/2 2Aco's Uot ^ En cos [wnt + <|>n] + 2AEQ cos ojQtcos [to0 4- p]t + n= - N/2 n= + N/2 (152) 2E0 cos [o>0 + p ] ty En cos [wnt + c]3n] n= - N/2 Out of the first and third terms no significant contributions are obtained. However, term five yields a result which represents the uncorrupted signal of frequency p. (153) 2AEQ cos 0Jo't cos [a)Q+p ]t = AEQ cos [2coQ+p ]t + AEQ cos pt Only AE q cos pt falls within the allowable passband. 180 Let ( 154) eg = AEq c o s pt The associated power is p5 where (155) p = 50 A4 — B Consider the frequency content of term four. n=+N/2 n=+N / 2 (156) 2AcosuQt^ Encos [ojnt+ + En cos ( f“o " wn]i - 4»n) Because for any n, cc>n is constrained to fall between > - a and coo a > [“ o^^n-J contains no frequency component in the passband p - 5 to p + 5 . The terms of importance are given by e4 where n= +N/2 (157) e4=A^ Encos [co0 - wn] t n= -N/2 where ( p - 6) < [oo0 - con] < ( p + 6) Owing to the eventual interest in power, the phase (j> has been dropped. Since the term s are assumed to be of equal amplitude, it is merely a matter of deducing the number of significant terms to evaluate the power here. The number of terms is just twice those 181 6 contained in an interval 25, or just 2N — to be specific. The power, a p4, due to these noise components is just A2E 2 5 , (158) p4 = _____£_ 2N _ = A4 2 a Consider now the significant energy content in term six. n= +N/2 2Eq cos (coQ + p) t ^ ' En cos [o)n t + cj)n] = n= -N/2 n=+N/2 E_ "V” Je cos (to + go +p)t + Ecos( + p - to ) t j- o £ 1 n ° n r/ n ' o v n' J n= -N/2 As before, 4>n has been deleted. Now there is no possibility of the first term contributing to the passband p - 5 to p + 5. However, the second one can contain terms of significance. Accordingly, let (160) e6 = E0^T En cos (ojQ + p - u>n) t where p - 5 < go + p - ton < p + 5 . 2a N N Introducing the fact that = to_ 4- ___ nfor - — < n < — leads to N 2 - - 2 n=+N/2 (161) e6=Eoy E cos(p-i^n)t . „ n N n=-N/2 Now obviously all these term s are not within the allowable passband. 182 Limiting e& to only the significant terms constrains n further. Specifically, N5 N5 - ---- < n < + ---- 2 a 2 a With these limits e6 is expressed as n=+N5/2a (162) e6 = E Y En cos ( p - n) t . N n=-NB/2a The noise power p6 associated with this set of term s is given by E02A2 (163) p6 Term two contains both square and cross product terms which are separated out to begin with. N N N n= + 2 i-+ 2 j-+ 2 (164) Encosunt | E^cosoj^t^T E^ cos cj^t N ^ N T - — n — — i — — j t — ~ z 2 J 2 When i = j a set of terms e2a result. Thus N , N i= — 1~ 2 2 1 + cos 2cd.t 2 1_ (165) S2 a = y E^cos2^ = \ Ei; LmJ _ T \T N . N 2 1="2 2 Clearly, no contribution to the passband p-5 to p+5 can arise here. However, for the cross product terms where i ^ j, this is not true. 183 Let N N N N i=+ 2 j = + i=2 i=2 ( 166) e_,='S' E-cos g o . t) Eicosco-t= ) " V 2E-E.cosG0,-t cos c o - t 2b z_. „ 1 1 L- N J J 2 N . MN 1 J 1 J l - — 2 j=-z 1-“ 2 J -~2 In more comprehensible form (jL67) e-2b=y T EiEj tcos ( wi + a)j) t + cos (toi-coj) t] . N N 1= ~J J=~2 i t j Now, o j - and g o - are each constrained to fall between w 0 - a and go + a, J o As a result, go ^ + g o j can never fall in the band p-b to p + 5, This means that any significant term s which are to arise must appear from the second part. Accordingly, let N 2 1! H- + j= + / - V V (168) e2h2b -= Z ) ) EiEj cos (wi - coj) t . L . N N 1_ “2 j= - The only terms of concern are those where p- 5 < GO. - co- < . p-f5 . r — x J — r 184 Upon introducing the relationships 2a coi = w0 + — i N (169) , 2a “j = wo + — 1 N Equation (168) reduces to Eq. (170) . N . N ^ 2 J=2 2a (i7°) e2 b = J T EiEj cos. i=“2 j=-J Again, because E^ and Ej are equal constants, the problem devolves into one of determining the number of effective quantities in the double sum of Eq„ (170) . The total number of terms appearing in the passband 5 p-5 to p+o is given by — N. On this basis the total number of a significant cross product terms equals r| where (171) t] ~ — N2 a Accordingly, the noise power associated with this set of terms is p2 where 26: .a-., A4 a (172) p2 = _ .N 2 (g)2 _ _ = J A4 a ’ u ' 2N2 5 185 Thus V a E0 2A2 (173 ) Pn=^pn= - A-+ + A* . Replacing EQ and combining the noise power becomes (174) Pn = A4 - + 50 + 1 e 6 The uncorrupted signal of frequency p was found to have a power of (175) P s = 50 A4 - Thus, whereas the S/N was set at 1 for the conventional filtering, in the synthetic filter it has decreased to (176) - = ------:------% 0.98 . b .it,-- 1. 02 + 02 - a There is no question but that the analysis is somewhat artificial and does not account for all the facts involved. However in spite of the simplicity it does show that the synthetic system should have an overall noise figure not significantly greater than a conventional system. 186 APPENDIX XIY The objective is to show the array of terms which emanate from a square-law crystal mixer for input signals germane to the system of Fig. 70. The simplest expression describing the stronger signal is given by (185) ex = E(1 + m cos ut)cos cot . The simulated received signal, on the other hand, is given by (186) ez - e cos[(co + 5)t + c|>] • The sum of ex and ez constitute the mixer input. Accordingly, the output is given by (187) eQ = K(ex + e2 )* . The array of terms appearing in the output are listed in Table II. The tabulation is arranged in ascending order of frequency. The three terms of particular importance are uii'dferlined. They-con- stitute an amplitude modulated signal with a carrier centered on the i-f frequency. The modulation frequency is that of the shift imparted by the rotating phase shifter. 187 TABLE II Freq. Phase Amplitude 0 5 4 Ee u-5 -([> Eme u 0 E2 m u + 5 +4 Eme E2 -~2 iijTp2 m-^2 2co- 2u 0 8 Ez m 2u>- u 0 *7 Eme 2co- u + 5 4* E2 , E2 m2 2 co 0 + 2u>+ 8 4 e 2 2co+ 25 24 Z— c* EZ m 2co + u 0 2 E2 m2 2co+ 2u 0 8 2co+ 2u + 6 4 188 BIBLIOGRAPHY Hines, J. N. , Rumsey, V. H. , and Walter, C. H., "Traveling Wave Slot Antennas, " Proc. IRE, November 1953. Final Engineering Report 233-4, March 1947, Antenna Lab oratory, The Ohio State University Research Foundation; prepared under Contract W 33-038-ac-1349 3, Air Research and Development Command, Wright Air Development Division, Wright-Patters on Air Force Base, Ohio. Sinclair, G. , "Use of Models for Investigating the Patterns of Aircraft Antennas, " Ph. D. Dissertation, The Ohio State University, 1946. Sinclair, G. , Jordan, E. C. , and Vaughn, E. W. , "Meas urements of Aircraft Antenna Patterns using Models, " Proc. IRE, December 1947. Brown, C. H. , King, R. , "High Frequency Models in An tenna Investigations, " Proc. IRE, April 1934. Gruber, J. R. , "Investigation of the Method of Measuring Antenna Patterns by Utilizing the Reradiated Electromag netic Field,'." Thesis, The Ohio State University, 1946. 189 7. Interim Engineering Report 301-1, June 1947, Antenna Lab oratory, The Ohio State University Research Foundation; prepared under Contract W-33-038 a c l6520(17380), Air ■ Research and Development Command, Wright Air Develop ment Division, Wright-Patterson Air Force Base, Ohio. 8. Tyson, O. A. and Edwards, W. J. E. , "A Portable Servo Recorder for Antenna Patterns, " Naval Res. Labs. , July 1949. 9. Brochure, "Power Level Recorder, " Leeds and Northrup Co. , Phil. , Penna. 10. Bulletin, "736-A Wave Analyzer, " General Radio Corporation, Cambridge, Mass. 11. King, D. D. , Taylor, J. , and Falkner, W. H. , Jr., "Bolometer Amplifier, " Electronics, February 1948. 12. Goldman, S., Modulation and Noise, McGraw-Hill Book Company, Inc. 13. Bacon, J. , "A Selective Bolometer Amplifier, " Report 301-24, September 1950, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract W-33-038 acl6520(1 7380), Air Research and Development Command, Wright Air Development Division, . Wright-Patterson Air Force Base, Ohio. 190 14. Bacon, J. and Cos griff, R. L. , "Applications of Servo Choppers Synchronized with Input Signals, " Report 301-30, April 1951, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract W-33-038 ac 16520(17380), Air Research and Development Command, Wright Air Development Division, W right-Patterson Air Force Base, Ohio. 15. Greenwood, Holdam, and MacRae, "Electronic Instruments, Vol. 21, Rad. Lab. Series. 16. James, Nichols, and Philips, "Theory of Servomechanisms, Vol. 25, Rad. Lab. Series. 17. Interim Engineering Report 301-8, April 1948, Antenna Lab oratory, The Ohio State University Research Foundation; prepared under Contract W-33-038 ac 16520(17380), Air Research and Development Command, Wright Air Develop ment Di\ >.sion, Wright-Patterson Air Force Base, Ohio. 18. Bacon, J. , "The Stabilization of Nonlinear Servomechanism Encountered in Antenna Instrumentation, " IRE Transactions on Automatic Control, Feb. 1957. 19. Cosgriff, R. L. , "Analysis and Measurement of Antenna Parameters, " Report 478-1, January 1952, Antenna 191 Laboratory, The Ohio State University Research Foundation; prepared under Contract AF 18(600)-88, Air Research and Development Command, Baltimore, Maryland. 20. Cosgriff, R. L. , "A Study in Nonlinear Servomechanisms, " Ph. D. Dissertation, The Ohio State University, 1953. 21. Cosgriff, R. L. , Nonlinear Control Systems, McGraw-Hill Book Co. , Inc. 22. Bacon, J. , "A Wide Range Square Root Recorder, " Report 478-19, November 1953, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract AF 18(600)-88, Air Research and Development Command, Baltimore, Maryland. 23. Bacon, J. , "A Sensitive Wide Range Logarithmic Re corder, " Report 301-33, September 1951, Antenna Lab oratory, The Ohio State University Research Foundation; prepared under Contract W-33-038 ac 16520(17380), Air Research and Development Command, Wright Air Develop ment Division, Wright-Patterson Air Force Base, Ohio. 24. Bacon, J. , "A Logarithmic Recorder of Unique Design, " M.S. Thesis, 1951. 192 25. Final Engineering Report 301-25, October 1950, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract W-33-038 ac 16520(17380), Air Research and Development Command, Wright Air Develop ment Division, Wright-Patterson Air Force Base, Ohio. 26.- Bacon, J. , "A 40 DB Audio Logarithmic Recorder for Antenna Measurements, " Report 478-10, April 1953, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract AF 18(600)-88, Air Research and Development Command, Wright Air Develop ment Division, Wright-Patterson Air Force Base, Ohio. 27. Hines, J. N. , "An Automatic Phase Plotter, " Report 301-31, April 1951, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract W-33-038 acl6520(17380), Air Research and Development Command, Wright Air Development Division, Wright-Patterson Air Force Base, Ohio. 28. Richmond, J. , "Electromagnetic Transmission Through Dielectric Sheets, " Ph. D. Dissertation, The Ohio State University, 1955. 193 29. Bacon, J. , "An X~Band Phase Plotter, " Report 531-7, September 1954, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract AF 33{6l6)-277, Air Research and Development Command, Wright Air Development Division, Wright-Patterson Air Force Base, Ohio. 30. Bacon, J. , "An X-Band Phase Plotter, " Proceedings of the National Electronics Conference, 1954. 31. Brochure, "Waveguide Phase Shifter, " Hewlett Packard Co. , Inc. 32. Tice, T. E. and Hines, J. N. , "An Investigation of Reflection Measuring Equipment, " Report 478-13, June 1953, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract AF 18(600)-88, Air Research and Development Command, Baltimore, Maryland. 33. Caligiuri, J. F. , "A Reflection Pattern Recorder, " Thesis, The Ohio State University, 1951. 34. "Automatic Recording of Back Scattering Patterns, " Report 406-2, May 1952, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract AF 33(038)- 10101, Air Research and Development Command, 194 35. VanVoorhis, S. N. , "Microwave Receivers, " MIT Rad. Lab.. Series, Vol. 23. 36. Chambers, T. H. and Page. I. H. , "The High Accuracy- Logarithmic Receiver, " Proc. IRE, 1954. 37. Bacon, J. and Burgess, J. Q. , "A Time-Gate for Echo Measuring Radar Installations, " IRE Transactions on Instrumentation, December 1959. 38. Black, I-I. S. , Modulation Theory, Van Nostrand Co. , Inc. 39. Bacon, J. , "K-Band Radar Modifications, " Report 475-12, June 1954, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract AF 18(600)- 19, Air Research and Development Command, Wright Air Development Division, Wright-Patterson Air Force Base, Ohio. 40. Bacon, J. , "Instrumentation for K^-Band Radar Echo Measurements, " Report 475-13, June 1954, Antenna Lab oratory, The Ohio State University Research Foundation; prepared under Contract AF 18(600)-l9, Air Research and Development Command, Wright Air Development Division, "Wright-Patterson Air Force Base, Ohio. 195 41. Zener Diode Brochure, Hoffman Electric Corp., Semiconductor Div. , Evanston, Illinois. 42. Cos griff, R. L. , "A Study of Detectors and Amplifiers Used in Antenna Instrumentation, " Report 487-5, December 1953, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract AF 18(600)-160, Air Research and Development Command, Wright Air Development Division, Wright-Patterson Air Force Base, Ohio. 43. Cosgriff, R. L. , "Sensitivity of Microwave Detectors with Low Frequency Output Signals, 11 Report 667-37, October 1957, Antenna Laboratory, The Ohio State University Research Foundation; prepared under Contract AF 33(616)- 3353, Air Research and Development Command, Wright Air Development Division, Wright-Patterson Air Force Base, Ohio. 44. Ring, D. H. , "A Microwave Double-Detection Measuring System with a Single Oscillator, " a paper presented at the AIEE-IRE Conf. on High Freq. Measurements, January 1953. 45. Hefner, H. , "Masers and Parametric Amplifiers, " Microwave Journal, March 1959. I 96 46. Yaw, D. F. , "A K-Band Superheterodyne System Using a Rotating-Guide Phase Shifter, " Thesis, The Ohio State University, 1955, 47. Yaw, D. F. , "A K-Band Reflection-Measuring System Using a Rotating Guide Phase Shifter, " Report 444-19, February 1955, Antenna Laboratory, The Ohio State University Re- Research Foundation; prepared under Contract DA 36-039 sc 5560, Signal Corps Supply Agency Laboratory Procure ment Office, Fort Monmouth, New Jersey. 48. Kouyoumjian, R. G. , suggestion proposed to D. F. Yaw and set forth initially in Reference 51. 49. Ginzton, E. L. , Microwave Measurements, McGraw-Hill Book Co. , Inc. 50. Boone, E. M. , et al, "Research and Development on Milli meter Wave Generation, " WADC Technical Report 57-180 (ASTIA No. AD 142214). 51. Pound, R. V. , "Microwave M ixers," MIT Rad. Lab. Series Vol. 16, McGraw-Hill Book Co. , Inc. 52. Hardman, W. E. , "A Sensitive Detection System for Elec tromagnetic Radiation with a Wavelength of Four Milli meters, 11 Report 889-2, November 1959, Antenna Laboratory, 197 The Ohio State University Research Foundation; prepared under Contract AF 33(616)-6137, Air Research and Develop ment Command, Wright Air Development Division, Wright - Patterson Air Force Base, Ohio. Gardner, M. F. and Barnes, J. L. , Transients in Linear Systems, John Wiley and Sons. Bacon, J. , "An Improved Design for Audio-Type Exponential Attenuators, " IRE Transactions on Instrumentation (PGI) November 1955. Richmond, J. H. , "Measurement of Time Quadrature Com ponents of Microwave Signals, " IRE Transactions on Micro wave Theory and Technique, April 1955. 198 AU T OB IOGRAP H Y I, Jack Bacon, was born in Durham, England, September 3, 1916. I received my secondary school education in the public schools of Dayton, Ohio. All my college training has been received at The Ohio State University. The B. E. E. degree was received in 1940. Following a number of years industrial experience, I returned to The Ohio State University as an employee in the Antenna Laboratory. A part time program of graduate work lead to a Master of Science degree in 1951. Thereafter my employment duties were divided between teaching and research. A part-time program of graduate work was continued which eventually term i nated at the completion of all the requirements for the degree Doctor of Philosophy. 199