National Bureau of Standards

Library, N.W. Bldg

JAN 2 1 1963

^ecknlcai vtote 103

EQUIPMENT CHARACTERISTICS AND THEIR

RELATION TO SYSTEM PERFORMANCE FOR

TROPOSPHERIC COMMUNICATION CIRCUITS

A. F. BARGHAUSEN, F. O. GUIRAUD, R. E. McGAVIN,

S. MURAHATA, AND R. W. WILBER

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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\

1
NATIONAL BUREAU OF STANDARDS

technical <^iote

103

JANUARY I5.I963

EQUIPMENT CHARACTERISTICS AND THEIR

RELATION TO SYSTEM PERFORMANCE FOR

TROPOSPHERIC COMMUNICATION CIRCUITS

A. F. Barghausen, F. O. Guiraud, R. E. McGavin,

S. Murahata, and R. W. Wilber

Boulder Laboratories

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, DC. - Price $1.00
TABLE OF CONTENTS

Abstract vi

1 . Introduction 1

2. Antenna System 2

2.1. The Transmission Line 3

a. The Voltage Standing Wave Ratio (VSWR) .... 4

b. The Attenuation or Line Loss 5

2.2. The Antenna 11

a. The Voltage Standing Wave Ratio (VSWR). ... 11

b. The Radiation Pattern and Gain 12

c. Measurement of Antenna Beamwidth and Gain . . 25

3. Duplexer 27

3.1. The Operating Characteristics of the Duplexer ... 31

a. The Insertion Loss or Coupling Factor .... 31

b. The Bandpass Characteristics 32

c. The Isolation 34

4. Comparison of Different Transmission Systems 36

4.1. Methods of Modulation 36

a. Amplitude Modulation (AM) 36

b. Single Sideband Modulation (SSB) 37

c. Angle Modulation 38

d. Phase Modulation 38

e. Frequency Modulation (FM) 39

4.2. Comparison of the Different Systems of Modulation . . 41

a. Bandwidth Requirements 41

b. Signal-to-Noise Ratio 45

c. Frequency Stability Requirements 48

d. Power Requirements 48

li
e. Distortion 49

f. Final Amplifier Efficiency 49

The FM Transmitter 51

5.1. Oscillator and Modulator Sections 51

5.2. Frequency Multipliers 57

5.3. Power Amplifiers 57

5.4. Power Supplies 58

5.5. Measurement of Frequency Deviation in an FM

Transmitter 58

The SSB Transmitter 62

6.1. Modulators 64

a. Rectifier Modulator 64

b. Vacuum-Tube Modulators 65

6.2. Single -Sideband Generation 66

a. The Filter Method 69

b. The Phase -Shift Method 69

6.3. Oscillator Requirements 70

6.4. The rf Power Amplifier 71

a. Distortion 72

6.5. Regulation of the Output Power 72

6.6. Inter modulation Distortion 74

a. Two-Tone Test 76

b. Noise -Loading Test 79

Klystron Amplifiers 82

7.1. Power Output Efficiency 82

7.2. Bandwidth 88

7.3. Gain 90

in
8. Power Combiners for Transmitters 90

8.1. Tuning Procedure 92

8.2. Circuit Reliability 92

9. The Receiver 93

9.1. The rf Amplifier 96

a. Noise in the rf Amplifier 97

9.2. Noise Figure Measurement 98

a. Signal Generator Method 100

b. Noise Generator Method 101

9.3. The Mixer 104

a. Conversion Gain Measurement 105

b. Noise Figure 108

c. Excitation Requirements 110

9.4. The Local Oscillator Ill

9.5. Automatic Frequency Control (AFC) 112

9.6. The Intermediate Frequency (IF) Amplifier . . . .114

9.7. The Automatic Gain Control (AGC) 115

9.8. The Limiter in FM Receivers 116

9.9. Demodulators 116

a. SSB Demodulation 118

b. FM Demodulation 120

9.10. The Squelch 121

10. Low Noise Devices 121

10.1. Parametric Amplifiers 121

a. Theory of Operation 124

b. The Semiconductor Variable Capacitance . . . .125

c. Negative Resistance Amplifier 128

d. The Up-Converter 130

IV
e. Electron-Beam Amplifier 130

f. General Considerations 133

10.2. Maser 141

10.3. Tunnel Diode Amplifiers 141

a. Theory of Operation 141

b. The Reflection-Type Amplifier 143

c. General Consideration 144

11. Combiners 144

11.1. Methods of Combining 147

a. The Selector Combiner . 147

b. The Equal Gain Combiner 147

c. The Maximal Ratio Combiner. 148

11.2. Comparison of Combiner 151

11.3. Pre -Detection and Post-Detection Combiner .... 158

11.4. General Considerations 160

12. Power Supplies 161

12.1. Unregulated Power Supplies 161

12.2. Resonant Regulator Power Supplies 161

12.3. Magnetic Amplifier and Saturable -Core -Reactor

Power Supplies 162

12.4. Transistorized d-c Power Supplies 163

12.5. Series -Tube Regulated Power Supplies 163

13. Repeaters 164

13.1. Active Repeaters 165

13.2, Passive Repeaters 165

a. Back-to-Back Directional Antennas 166

b. Single Flat Reflectors 167

c. Multiple Flat Reflectors 167

15. Acknowledgments 168

References 169
ABSTRACT

The performance of a tropospheric communications system,

either within the line of sight or beyond the line of sight, is directly

dependent on the operating characteristics of the equipment.

i Performance predictions of a communications system are made

on the basis that equipment will operate in a prescribed manner. The

degree of success of the communications system will depend largely

upon how well these predicted values correspond to the actual operating

value s

.

Consideration is given to those portions of the equipment that

have definite effect upon the operating performance. Specific items

of equipment and methods for determining their performance are

considered. Representative results in light of the present state of

the art permits an evaluation of an actual system in terms of realizing

an "optimum" system.

In systems that do not have the "optimum" characteristics

desired, consideration is given to laboratory devices which may

alleviate these deficiencies. Future systems should consider incorporating these devices as development permits.

VI
EQUIPMENT CHARACTERISTICS AND THEIR

RELATION TO SYSTEM PERFORMANCE FOR

TROPOSPHERIC COMMUNICATION CIRCUITS

by

A. F. Barghausen, F. O. Guiraud, R. E. McGavin

S. Murahata and R. W. Wilber

1. INTRODUCTION

The performance to be expected on a tropospheric scatter path

can be predicted according to the methods outlined by Barsis, Norton,

Rice, and Elder [ 1961] and Florman and Tary [ 1962] . However,

these performance predictions are made on the assumption that the

equipment used on a particular path will perform in an expected manner,

Transmitter power, antenna gains, line losses, receiver noise figure,

and a variety of other parameters are assumed to have certain values.

The degree of success of operation will depend largely upon how well

the correspondence between the assumed values and the actual values

can be achieved.

This report considers these aspects of the equipment which

difect the performance of a tropospheric circuit. While this report

is divided into various sections to permit evaluation of specific parts,

it should be emphasized that the performance of the total system is

the desired result. Consequently, the assumption is that each part

operates the same after incorporation in the system as it did before

incorporation.

Each section considers both the purpose of the specific part or

it;em, and methods for determining its performance.

In general, tropospheric circuits can be divided into two types:

Those which are concerned with the propagation of radio energy

to a point far beyond the radio line of sight.
-2-

Those where propagation is over relatively short distances

where the receiving terminal is within the radio line of sight of the

transmitting terminal.

The same principles generally apply whether beyond line of

sight or within line of sight is considered. The requirements and

tolerances recommended are more stringent for long paths, whereas

some latitude may be allowed for the shorter path. In this connection,

it may be assumed that, unless otherwise stated, no distinction is

being made between the two, and application, in so far as it is

practical, will be uniform.

2. THE ANTENNA SYSTEM

The antenna system is here defined as the entire transmission

system, which includes the antenna and the transmission lines. The

antenna system is the transformer between the medium carrying the

radio energy and the terminals, the transmitting or receiving equipment. The efficiency of the system is dependent upon how well this

transformation takes place.

The antenna itself acts as a converter between the energy in a transmission line and the energy in a free -space wave. According to

the princple of reciprocity, the characteristics of the antenna will be

the same whether used as a transmitting or a receiving antenna. In

point-to-point communication, directional antennas are used since

energy directed to other than the intended terminal is wasted. The

type of antenna to be used depends upon the type of path considered.

Within-line-of-sight paths do not require high-gain antennas such as used on the long paths; however, very often a high -gain antenna will

be used to take advantage of the narrow beamwidth to eliminate multipath reception and interference on a line -of -sight path. In the absence

of such necessity, line -of-sight paths utilize low-gain antennas, the

most common types being Yagis, dipoles, folded dipoles, horns, corner

reflectors, and small parabolic antennas. Due to the power requirements for beyond line of sight, high-gain narrow-beam antennas are

used, and in tropospheric propagation, the parabolic antenna fed by a horn primary antenna is in almost universal use.
3-

The most important parameters affecting the efficiency of an

antenna system are:

The line losses or attenuation of the transmission line, from

transmitter to transmitting antenna.

The impedance matching of the components of the antenna

system.

The radiation pattern of the antenna.

In some cases, the polarization is an important factor.

With the exception of the radiation pattern, the evaluation of

the antenna system characteristics is the same, whether the path is

within or beyond the line of sight.

However, it should be realized that the impedance and the radiation pattern are not necessarily independent quantities, and the adjustment to correct one possibly will have an effect upon the other. None

the less, in considering these two parameters and the measurement of

them, it is assumed, for convenience, that they are independent, it being understood that the goal to be achieved is an antenna having the

proper radiation pattern as well as the proper impedance.

2.1. The Transmission Line

Before the antenna is measured for its characteristics, it is

important to determine whether the characteristics of the transmission

line by itself are such as to introduce errors into the measurement.

Two parameters are of interest here: the VSWR of the transmission

line which is a measure of the relationship between the transmission

line characteristic impedance and its terminating impedance, and the

line losses or attenuation. A transmission line calculator, as described

by Smith [ 1944], is recommended for this work.
-4-

a. The Voltage Standing Wave Ratio (VSWR)

If an ideal transmission line is terminated in its characteristic

impedance, the VSWR, as measured from the sending end, will be

unity. However, if the transmission line is poorly assembled or if there are discontinuities due either to non-uniformity or to injury to

the transmission line or to the presence of foreign matter in the transmission line, then a VSWR of unity would not be measured in all

sections of the line even though it were terminated in its nominal

characteristic impedance. It is important, therefore, to measure

the VSWR of the transmission line. This measurement consists of

terminating the transmission line with a load known to be equal to the

characteristic impedance of the transmission line and measuring the

VSWR at the sending end of the transmission. Such terminations for

any size and type of line are available commercially and should be used

for this measurement. The VSWR of the transmission line should be

measured with this termination in place. If the VSWR should be found

to be significantly different from one (e.g., in excess of 1.05:1), then

the transmission line should be checked section by section to insure

that all flanges are clean and undamaged, that all connections are

proper and tight, and that the line is free from all foreign matter.

All faulty sections of line should be replaced. Unless these precautions

are taken, any further measurements should be made with caution.

Several methods can be employed to measure the VSWR of the

transmission line. Fundamentally, all methods can be resolved into

the two common types: measurement of Emax and Emin by use of a

slotted line, and measurement of the impedance or admittance at some

point along the transmission line.

Two types of slotted lines are available: slotted coaxial transmission line, and slotted waveguide. The same principles of operation

apply whether coaxial line or waveguide is used for the slotted section.

In essence, the slotted waveguide line is merely a section of waveguide

in which a slot is milled in the center of the broad wall so that the

disruption of the surface current flow is a minimum, and its presence

does not appreciably modify the original field pattern. It is usually

long enough so that several minima and maxima can be observed. A

sliding probe is loosely coupled through the slot to the electric field
-5-

wJiich induces a voltage in the probe proportional to the probe depth.

This voltage is then fed through associated circuitry and appears as

a reading on an output meter. The relationship between this reading

and the value of the field at the point being measured depends on the

model of slotted line used. The manufacturer's recommendations

should be consulted. The probe is moved through points of maximum

field and minimum field, the ratio of which is the VSWR.

It must be remembered that the accuracy of any measurement

is dependent upon the accuracy of the instruments used. Consequently,

the slotted line should have a very good VSWR of its own if it is not

to impair the accuracy of these measurements. Slotted lines having

a VSWR of 1.05 are available. If the slotted line has a VSWR of 1.05,

then it is capable of use in matching the VSWR of any device to within

1. 10 in the most pessimistic configuration. A slotted line is a precision instrument and must be handled with care. The manufacturer's

recommendations should be consulted to insure no damage due to

excessive currents, to insure that the detector is used in its calibrated

range, and to insure negligible error due to excessive probe depth.

The slotted line should be protected from water or dust if its accuracy

is to be maintained.

The second method, that of measuring the impedance or admittance at some point in the line, is usually used at the lower frequencies,

The use of the slotted line is not recommended below 300 Mc/s, and

even 400 Mc/s might prove to be inconvenient due to the wavelength.

Essentially, this method utilizes a bridge circuit and null detector.

The bridge is supplied with a known impedance which is used to balance

out the impedance of the device under measurement. At balance, a

null output from the bridge arrives at the detector. The bridge is then

calibrated in either R + jX, Z /Q , or G + jB.

b. The Attenuation or Line Loss

It is not good practice to assume that the manufacturer's specifications are sufficient to determine the line loss of a system, especially

where long sections of transmission line are used. Discontinuities and

departures from a perfect transmission line can cause attenuation due
-6-

VSWR OF LOAD AS A FUNCTION OF VSWR MEASURED

AT INPUT AND THE ATTENUATION OF THE LINE

4.0

3

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db

db

20 2.5 VSWR AT LOAD

3.0 3.5 4.0

Figure 1
-7-

to reflection within the transmission line. These reflections will not

necessarily modify the VSWR measured at the efid of a long transmission

line, since, in theory, if the transmission line is infinite in length, a VSWR of one will be measured for any load terminating the transmission

line. Consequently, the longer the transmission line, the more optimistic will be the measurement of the VSWR at the sending end of the

line. For an accurate determination of the VSWR at the termination,

but measured at the sending end of the line, a knowledge of the

attenuation through the transmission line is required (see figure 1).

One accurate method of measuring the attenuation in a transmission line can be described as follows. The transmission line to

be measured is made a part of a longer transmission line having the

same characteristic impedance. Then the power loss through the

combined system at the operating frequency is compared to the power

loss which occurs in the system without the transmission line under

test in the system. The difference in these two power losses is the

power loss resulting from the attenuation of the transmission line under

test. The receiving end of a large rigid transmission line would be

terminated with a reducer from the transmission line down to some

convenient flexible coaxial cable having the same characteristic

impedance. It should be emphasized that the reducer (e.g., from

3-1/8 or 6-1/8 inch line down to RG8/U or RG17/U) must be of good

quality, especially as regards the impedance match through the

reducer. The flexible line is then connected between the reducer and

the detector, which can be either a receiver or a bolometer bridge.

If the transmission line is short (50 meters or less in length), it is

not necessary to move the detector out to the end of the transmission

line, and the flexible line can be long enough to reach back to the input

of the transmission line to be tested. However, if the transmission

line to be tested is long (greater than 50 meters), the attenuation in the

flexible cable may be large, especially at the higher frequencies. Then

the attenuation of the combined system may include only a very small

additional attenuation due to the transmission line under test. The

flexible line may be sufficiently unstable that the changes in attenuation

rate due to flexing and heat change can be greater than the attenuation

of the transmission line being tested. Therefore, under conditions

such as these, it is recommended that the detector be placed at the

end of the transmission line and be connected through a short piece
-8-

ATTENUATION RATES OF

STANDARD TRANSMISSION LINES

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RG 95/u AL

WR 187

20 30 50 70 100 200 300 500 700 1,000 2,000 3,000 5,000 7,000 10,000 FREQUENCY

Figure 2
of flexible line. The second measurement with the transmission line

out of the circuit will then require that the detector be moved to the

input of the transmission line. (To insure accuracy in this measurement, the detector must be stable and should be powered from a regulated voltage source; if regulated a-c is not available at the end of the

transmission line, a voltage regulator should accompany the detector).

When the transmission line under test is taken out of the system from

the generator, the signal is fed only through the flexible coaxial cable

from the signal source to the detector or recorder and the input level

reduced until the same output level is obtained. The difference in the

two power levels is then the attenuation which was introduced by the

transmission line under test.

The db attenuation can be determined directly if a precision

variable attenuator calibrated in db is inserted in the line and remains

in the system for both measurements. It is essential that the impedance match of the attenuator be constant irrespective of the value of

attenuation inserted into the system. The measurements with the

attenuator, the transmission line, and the flexible coaxial line are

then compared to the same system minus the transmission line under

test. The original level is produced in the second measurement by

inserting attenuation from the variable attenuator until the level received is identical to the previous measurement. The value of the

attenuation necessary to restore the level to the previous level is the

amount of attenuation that the transmission line introduces into the

system. If the measured attenuation is greater than that as found from

figure 2 by more than several percent, then the line attenuation may be

excessive, and the line should be checked carefully for causes of the

departure. Other methods have been proposed from measuring the

attenuation of the transmission line and its effect upon measurements

of other parameters of the system. However, most of these methods

assume a uniform rate of attenuation down the line. This is not necessarily encountered in practice, especially with rigid transmission line

which is made up of many sections. Discontinuities where sections

are bolted together can give rise to a serious problem both as to attenua^

tion and VSWR. This is not reflected in an assumption of a uniform

rate of attenuation. Consequently, the direct method of inserting and

removing the transmission line under test in an overall transmission

system is recommended.
•10

POWER LOSS IN db DUE TO VSWR

IN TRANSMISSION LINE

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5
11-

Additional references for recommended study may be found in

King et al. [ 1945] , Skilling [ 1951] , and Wind and Rapaport [ 1955] .

2.2. The Antenna

One of the most important parts of a communication system is

the antenna. Therefore, a reliable and accurate determination of its

operating characteristics is imperative to evaluate the system performance. The primary technical aspects of the antenna can be

treated in the following categories. While the mechanical aspects

of the antenna are not listed, they are of utmost importance, but are

beyond the scope of this report.

a. The Voltage Standing Wave Ratio (VSWR)

The procedure for measuring the VSWR of the antenna and the

transmission line is the same as the method employed to measure the

VSWR of the transmission line itself. In this case the antenna replaces

the termination. A properly designed and erected antenna will have a low VSWR. Without any major adjustments to the antenna, VSWR of

1.3:1 should be easily realized in practice.

This VSWR is the measure of the match of the antenna to the

transmission line. From the standpoint of radiation efficiency, this

may or may not be a real problem. If the plate circuit of the transmitter can be tuned to match the impedance at the input end of a lossless transmission line, then all the power from the transmitter will

be delivered to the antenna and be radiated. However, if the transmitter cannot be matched to the impedance at the input end of the

transmission line, which the antenna terminates, some of the power

is reflected into the plate circuit to be reradiated or to be absorbed

there. The reradiated power can cause distortion due to its phase lag

and the absorbed power can cause a heating problem at the transmitter.

In any case, power is lost and the full transmitter power is not utilized.

Figure 3 illustrates the loss in power that can be expected if the

antenna system has a mismatch which is not compensated by transmitter tuning. One of the chief disadvantages of large standing waves

on a line is the degradation of the power -carrying capacity of the line.

An excessive VSWR will increase the possibility of voltage flashover.
-12-

The power dissipation capabilities are not vital at the receiver

input. However, the VSWR is still of importance. Although it can be

shown that the optimum operation of the receiver is obtained when the

receiver is mismatched to the transmission line, the conditions for

this mismatch for optimum operation are not arbitrary. Consequently,

as far as the transmission line is concerned, it is more advantageous

to maintain a matched or flat line in the direction of the antenna and

to produce the proper mismatch condition at the input stages of the

receiver. This question is considered in detail later in this report

where the noise figure of the receiver is considered. Therefore, as

far as the antenna system is concerned, VSWR's which approach unity

are desirable in all cases.

Methods are available to correct for large VSWR's. However,

a properly designed antenna system should not exhibit an excessive

VSWR when the system is optimized; a VSWR in excess of 3:1 should

be rare. Where parabolic antennas are used, matching devices are

necessary to optimize the VSWR since in most cases the uncorrected

VSWR will be limited due to the energy from the reflector that intercepts the transmitting horn. The energy from the reflector acts as a reflected wave and sets up a standing wave. A proper mismatch must

then be introduced to re -reflect this energy back to be radiated. Such

provisions usually are incorporated in the transmitting horn in the

form of tuning stubs.

b. The Radiation Pattern and Gain

The radiation pattern of an antenna is the graphical representation of the radiation intensity [ Schelkunoff et al., 1952] . The isotropic

antenna, a fictitious ideal antenna, is a radiating point source. Other

antennas do not radiate equally in all directions, and hence do not have

the spherical pattern of the isotropic antenna. With direction antennas,

the energy is concentrated in one direction, so that the power density

along one direction is much greater than that in any other direction.

If the antenna is located in free space, then the ratio of the field strength

experienced at a point in the direction of maximum radiation to that which

would be experienced if the same power were radiated from an isotropic

antenna is the free -space gain of the antenna.
-13-

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-14-

Since the isotropic antenna is an ideal antenna, the comparison

is made relative to an antenna whose gain with respect to an isotropic

antenna is known. For example, a vertical dipole has a gain of 2.15

db over an isotropic antenna. An additional parameter closely related

to the gain of the antenna is the beamwidth. The 3-db (or half -power)

beamwidth of the antenna is defined as the width of the cone of energymeasured from a point on each side of the axis of maximum radiation

where the power density is decreased to one -half. This total width

is the half -power beamwidth of the antenna.

The gain to be expected from a parabolic antenna as shown in

figure 4 can be estimated from the following expresion from FTR

Handbook [ 1949]:

G

db= 201°«10 fMc + 201°«10 D

ft52 - 6 <"

where

f = frequency in megacycles per second Mc

D„ = diameter of the reflector in feet

ft

G,. = g3-!*1 in decibels over an isotropic antenna

db

N.B. These calculations assume a reflector efficiency

of 54%, a reasonably attain figure.

If the parabolic reflector is illuminated uniformly, the approximate relation between the half -power beamwidth and the gain is

expressed by the following:

142

(j) = ; degrees (2)

•s/G
where

-15-

<!> plane angle between half -power points of the

radiation pattern of the antenna

n/G

antilog

antilog

G

db

10

G

db

20

Example

f

Gain

Mc

D

£t

db

1000 megacycles

60 feet

20 log (1000) + 20 log (60) - 52.6

60 + 35.6 52.6

G

db

43 decibel

Beamwidth

4> 142

n/g"

n/g"

4g~

antilog

antilog

141.3

db

20 —43

J = antilog 2.15

<i> 142 , ^o S 1.0

141.3
-16

However, since uniform illumination is not often used because

side -lobe suppression is better achieved with a tapered form of

reflector illumination (i.e., the energy incident at the edge of the

reflector is reduced in a particular manner below that incident at

the center of the antenna), the beamwidth is usually somewhat wider.

A convenient approximation for a 10 -db tapered illumination is

(j) Si. 15 cj). (3)

where

<t>-

half -power beamwidth with a 10 -db taper

half-power beamwidth with uniform illumination

It should be evident that if the antenna beamwidth is very narrow,

considerable accuracy is required in the pointing of the antenna. An

example of the importance of the proper alignment can be given by

comparing the beamwidth of typical parabolic antennas of certain gain

figures.

For example, the relationship between gain and beamwidth can

be illustrated as follows:

TABLE 1

Gain Half -power

beamwidth

30 db

35 db

>44 db

5°

30

< 1°

Small departures of the true direction can cause a considerable

power loss due to misalignment. Therefore, two parameters are of

exceptional importance: the gain of the antenna and the direction of

the beam.
17-

Of all the parameters of a tropospheric scatter system, probably the most difficult to measure is the actual pattern and gain of

the antenna. In the practical case, a true determination of the gain

and pattern of the antenna is all but impossible, and any method will

yield only an estimate of the true condition.

The gain figure used in the transmission loss formula is the

free-space gain or at least an estimate of it. The free-space gain of

an antenna is the ratio of the signal received at a distance from the

specified antenna to that which would be received from an isotropic

antenna if both antennas were located in free space. However, the

antenna to be measured is not located in free space, and the pattern

will be affected by the ground in the foreground of the antenna. In the

general case, the effect of the energy reflected by the ground is very

difficult to analyze and still more difficult to eliminate. With extremely

large antennas, it is not practical to move them to a site where freespace conditions can be approximated, and the determination of the

pattern and gain will depend upon the ability to determine the effects

of the ground reflection.

In free space the radiation from a parabolic antenna is a plane

wave. If the same antenna is placed in close proximity to the ground,

the radiation from the ground in the region close to the antenna can

distort the wave front such that it is no longer a plane wave. This also

distorts the free-space pattern. In most cases, especially where large

parabolic antennas are used, this distortion is a second-order effect.

However, this effect should be considered where the antenna is close

to the ground and where the immediate foreground is rough and broken.

Even if the wave front is not affected by the ground, the radiation pattern will be distorted because of ground reflection. Any point

in space will receive energy both directly from the transmitter and

indirectly through reflection from the ground in front of the antenna.

This produces a familiar lobe structure. If the ground were perfectly

smooth, the effect would be amenable to analysis. In the practical

case, however, the ground is seldom smooth. In general, the exact

effects of the reflection from the ground in the vicinity of the antenna

is difficult to determine, and under conditions usually encountered in

ordinary field measurements, exact determinations can be considered

to be impossible.
-18- o

or

<r

UJ ui

--1. q:

III o X LL hh- < ^

7" LJ

<d.

T ^ LlJ Ld Q:

LxJ (- UJ £ ZOh- < —

UJ

DQ ^7- Q ^< UJ > x

rr

n iLlI

u o q: o l±j lu UJ <

hi UJ UJ

(• •>

x q: 2T i- o <1— Q o

CD z -z. < LJ

h- ^ </) ~) UJ ^ h- 2^ or ^

UJQ ij 1 j 1 1 1 I j 1 

V i ^

°K

'<

*> 1 1 s 1 '^\

'f >

'/ S,

<\ s

Hi?' v °2X

^\ uZ ^> ! V j ^S . V ?>\u«h^^\c\

CO

cc

UJ

fUJ3

z.

CO

ccUJa23< m 2

<U UJ u

h- 3

-z. GO < •rt L^ 2o

cc

u_

Ulo2<

h-coa

S31DADV93W Nl ADN3D03yJ
19-

However, an "estimate" of the free-space gain can be determined. The degree of accuracy of this estimate is related to the

terrain over which the antenna is used. If the terrain is extremely

rough and broken with significant prominences along the transmission

path, or if there are structures in the near vicinity of the transmission

path, then the estimate probably will be poor. If the transmission path

directly in front of the antenna is approximately smooth and free of

obstructions (including the area immediately surrounding the antenna)

the estimate will be accurate, i.e. , within several db of the actual

free-space gain.

The measurement consists of transmission to a receiving

terminal established along the transmission path some distance in

front of the transmitting antenna. A comparison is made between

signals received at the receiving location from the antenna under test

and from a standard antenna. Before such a measurement can be

undertaken, possibilities of further error must be evaluated. Two

important considerations are necessary: the minimum distance required

between the two antennas, and the evaluation of the effect of ground

reflection.

Even if the two antennas were located in free space, error

would be present in the measurement of the gain of the antenna under

test due to the finite distance between the two antennas. Although a usual determination assumes that only plane waves are considered,

where the antennas are separated by a finite distance, the wave front

arriving at the receiving antenna from a point source is not a plane

wave but has a radius of curvature. This phenomenon can most easily

be understood if we consider the large antenna to be the receiving

antenna. If the wave front which arrives at the large antenna in free

space is not a plane wave, then the field at the edge of the antenna

differs in phase from the field at the center of the antenna by a small

amount, A . If an accurate pattern is to be measured, A must be

kept negligible. A commonly used criterion given by Silver [ 1949]

is that the difference between the spherical wave and the plane wave

at the edge of the antenna reflector should be less than X/16. By this

condition, then, the minimum distance from the antenna to be tested

must be greater than 2d^/X where d is the diameter of the antenna

and \ is the wavelength of the carrier frequency as shown in figure 5.
•20-

Using this minimum distance, the measured power gain in free space

would be in error by no more than 1%, with respect to a perfectlyplane wave front. For example, if a 60 -foot parabolic antenna is

being tested at a frequency of 1000 Mc/s, then this minimum distance,

such that the error will be not greater than 1%, would be 2.23 km

(1 . 39 miles) between antennas. In comparison, if the minimum distance

used is d^/X, the apparent gain is reduced by 5%, and the side lobes of

the antenna appear to increase. If at all possible, the condition mentioned previously, that is, 2d^/X, should be maintained. At times this

might be impractical since, if the same antenna were being used at

4000 Mc/s, this minimum distance is 8.92 km (5.54 miles). If the

antenna is located on a coast line, then extreme ranges such as this

would necessitate the use of a ship or slow moving aircraft such as a helicopter for the target terminal.

As has been pointed out previously, the presence of the ground

renders the measurement of the radiation pattern difficult. If the

immediate foreground of the parabolic antenna is reasonably smooth

and if the immediate area around the antenna is free from obstructions,

the assumption of a plane -wave emission from the parabolic antenna

is at least a reasonably approximation.

The second effect, that of the distortion of the pattern due to

the addition of the direct radiation and the ground reflected radiation,

can be evaluated if the ground within sight of the antenna is not extremely

rough and broken. If the ground were perfectly smooth, a regular lobe

structure would be formed where a field maximum occurs when the two

components are in phase and where a field minimum occurs when the

two components are out of phase. Where the ground in the sight of the

antenna is broken, no easy method of analysis is available except insofar

as an approximation to a smooth surface is valid. An exhaustive analysis

of the surface, point by point, would be necessary to determine the actual

ground reflection. If the roughness is not too excessive and is fairly

regular, then uniform reflection can be assumed. The amplitude of the

reflection coefficient could then be assumed to have a mean value over

most of the reflecting region.

A better appreciation of the problem can be had from a brief

consideration of phase addition of the two components when propagation

is between two terminals over a smooth earth.
-21-

D

and

E

E

E

rh

T

hR

X

D

D 1

= field due to the wave arriving over path D',

= field due to the wave arriving over path R,

= resultant field at R,

= reflected path distance,

= transmitting antenna height,

= receiving antenna height,

= point of reflection,

= flat earth distance from base hm to h , T R

= distance of transmitting antenna to receiving

antenna.

Assuming that the reflecting surface is reasonably flat, we have

by simple geometry:

D'

2

= (h T

- hR

) Z + D

2

(4)

r 2

= (hT

+ hR

) 2 + D

2

(5)
If

-22.

r 2

- D'

2

= 4 h

T

hR

(6)

h and h < < D, then R + D'«ZD

X R

4h h 2h h

r - D' = T R « T R

(7) r + D1 D

v

'

the difference in path length is approximately equal to 2h h /D. X R

If horizontal polarization is used, a phase shift of 180° occurs

upon reflection at x for any path consideration. If vertical polarization is used, a phase shift of 180° occurs only for regions where the

angle between the reflecting surface and the reflected ray is small, a condition almost universally found in this type of measurement. Xhere'

fore, if the path length difference is \, then the two signals arrive out

of phase and cancel.

If 2h h /D = 2n\/2, where n = 1, 2, 3...., a minimum (8) X R

occurs

.

If 2h h /D = (2n - 1) X/2, where n = 1, 2, 3 , a (9) X R

maximum occurs.

If this path length difference is then converted to phase differ'

ence between the two paths,

9 = 4 77 h h /D\ radians. (10) X R
-23

The energy reflected from the ground is a function of the ground

constants, the dielectric constant, and the conductivity. In general,

not all the energy is reflected in a specular fashion nor is the phase

angle undisturbed. (The change in the phase angle has been considered

above.) The amplitude of the reflection coefficient p will always be

less than one. Therefore, the amplitude of the reflected wave will be

the amplitude of the wave striking the reflecting surface multiplied by

the reflection coefficient. In addition, the antenna pattern must be

considered, which can be represented by f (i\>), the power density in

any given azimuth or elevation angle. In this text this will be referred

to as the antenna function. Especially where narrow-beam antennas

are concerned, the power density in the direction of the reflecting

region will be less than that along the direct path. The amplitude of

the reflected wave must be multiplied also by this antenna function.

Then the amplitude of the reflected wave will be

ER

= p£(i|i) E

D

(11)

Using the law of cosines to determine the vector sum of the direct and

the ground -reflected waves yields

E

2

= E^ [1 + (pf(^) ) 2- 2pf(i|i) cos 9] (12)

where is the angle between the direct and the ground-reflected waves

The values of maximum and minimum field strength caused by alternate

reinforcement and cancellation of the direct and reflected waves can be

determined by the expressions

Emax=V 1 + pfW] (13)

E

mi„ =ED

[l " pfW] (14)

That is, the value of the measured field can vary between these two

limits if the attenuation with distance is ignored.
-24

From the composition of the lobe structure determined by the

above equations, it can be shown that the minimum fields are verysharp, whereas the maximum fields are approached through a shallow

gradient. This indicates that the maximums are the more useful since

positioning of the antenna is less critical, and the integration of the

field over the aperture of the antenna approaches the integration of a constant. It can be seen that there is a point where the measured

field will be equal to the field produced by the direct wave Eq, which

is the free -space field. But this point has the disadvantage of being

located on a rather steep part of the curve of the lobe structure and

is undesirable because of the above reasons.

Then the estimate of the gain of the antenna should be determined by comparing the field measured with the antenna under test to

the field measured with a standard antenna, where the measurement

is made at the maximum of the field pattern at the receiving antenna.

This measurement is based on several assumptions: one, that the

reflection coefficient is the same for both the test antenna and the

standard antenna and, two, that the antenna pattern functions are

approximately the same. The former assumption is reasonably since

both antennas observe the same terrain; the latter assumption may be

questioned especially where very narrow-beam antennas are being used,

The effect of the latter assumption may be reduced by moving the

receiving site farther out along the transmission path. (This does have

the disadvantage, however, in that the height of the first maximum is

increased.) The degree of error introduced due to the antenna function

can be evaluated according to the following:

Let

E

: 2

Then

E : the field measured with the antenna under test,

max

E = the field measured with the standard antenna,

max.

E E

max D f- 1 + pf n (^)

*\TM E ^ L 1 + pf, M) J max D

L* La

1

2

(15)
•25-

The maximum error due to a difference in the antenna functions

of the two antennas will be 3 db, this occurring when the quantities

within the braces is equal to either 2 or 1/2. This, of course, is a

limit and will never be encountered in practice. It will be rare when

an error as great as 2 db is introduced due to this condition.

Example:

Assume h or transmitter antenna height of 10.7 m (35 feet)

D = 2.5 km (1.55 miles)

X = .3 meter, i.e., f = 1000 Mc/s

Then the maximum fields occur where

2 h h —T—R ._ .. X MZn-Dj

The first maximum occurs where

2h h

1 = [2(1) -1]T D

L v

' J 2

hR-Th~

T

3

hR = Z ' 5

4

(

(

1

1

Q

o

) 7)'

3) = 17 * 5 meters < 57 ' 4 feet>

Then under these conditions the maximum field at the receiving

location should be measured at approximately 18 meters above the

ground.

c. Measurement of Antenna Beamwidth and Gain

The method proposed is based on a comparison between the signal received from a standard antenna whose gain is known and the antenna

under test. The standard antenna can be one of many types. Standard
-26-

horns are available commercially having known gains and radiation

patterns, and should be considered especially for the higher frequencies.

However, for the lower frequencies a standard horn is quite large and

heavy, and the use of corner reflectors is recommended as described

by Cottony and Wilson [ 1958] . Corner reflectors have the advantage

that they are relatively light even at the lower frequencies, can be

collapsed to lie flat, and can be so constructed that they can maintain

their characteristics through many assemblies and disassemblies.

It is assumed that the receiving location can be seen from the

transmitting location. A theodolite or transit set up at the base of

the antenna to be tested should be pointed along the transmission path.

Either radio communications or visual signals should be used between

the two sites. A mobile unit should proceed out to the proper distance

and should be positioned on the radial by an operator at the transit.

A signal is radiated from the standard antenna. The receiving antenna

is raised, passed through the maximum field, and then returned to the

position where the maximum field is measured. This height should be

close to that calculated. It will be noted that the field pattern will not be

a smooth curve but will in general display a certain amount of variability due to the roughness of the reflecting surface. In the region

of the maximum this variability should concentrate about a mean value,

which mean value should be taken as the value of the maximum. If the reflecting surface is inordinately rough, a lobe structure will be

difficult to detect, and the field will vary with no apparent predicability

.

(If such a condition exists, the accuracy of this measurement may be

poor.) After the value of the field produced by the radiation from the

standard antenna has been logged, the standard antenna is lowered

and the signal is applied to the antenna under test. The above procedure

is repeated and the value logged. The maximum field in the second

measurement should occur at the same antenna height that it did in the

first measurement. The above two readings of received fields are

then corrected taking into account the differences in line losses, and

the ratio of these values is the estimate of the gain of the antenna.

This ratio is usually converted to db.

The gain of the antenna to be tested may be 20 db over the gain

of the standard antenna, and the dynamic range of the receiver may

not permit an accurate comparison of signals as much as 20 db apart.
•27-

It is suggested that accurate attenuators be inserted at the input to the

receiver when measuring the high-gain antenna. The attenuation thus

added must be taken as part of the apparent gain of the antenna under

test.

An estimate of the field to be expected at the receiving terminal

from the radiation from the standard antenna can be accomplished bycalculating the free -space field to be expected at the distance D using

the methods described by Rice, Longley, and Norton [ 1962] .

This value is then used as the value of the field due to the direct

wave, E„.

An estimate of the beamwidth between half -power points in the

horizontal or vertical plane patterns can be made by repeating the above

measurements on each side of the radial over a sufficient angle to

incorporate at least twice the theoretical beamwidth of the antenna.

The limitations on this measurement are the same as those for the

original measurement. If the lobe structure of the antenna is difficult

to detect, the determination of the beamwidth will be a poor estimate.

The value of the gain loss should be equal on each side of the transmission path. If these two measurements are significantly different,

then two additional points, midway between the points already measured,

should be used to produce two additional gain determinations. These

five points should fall on a relatively smooth curve from which estimates

of the beamwidth and pointing accuracy can be determined.

The reader is referred to Kraus [ 1950], Schelkunoff and Friis

[1952], and other standard reference books for a more detailed treatment on the subject of antennas.

3. DUPLEXER

A duplexer is a device which makes possible the use of a single

antenna for simultaneous transmission and reception. Where pulse

techniques are used and the requirement for simultaneous transmission

and reception from the same antenna is not present, electronic switching

devices may be used for the transmitter and receiver circuits, respectively, as described by Smullen and Montgomery [ 1949] . This manner
-28-

THE OPERATION OF A DUPLEXER

ANTENNA

TRANSMITTER

ri

RECEIVER

~l

TRANSMITTER i —1-

1

BANDPASS

FILTER

BANDPASS

FILTER

RECEIVER

.J

DUPLEXER

BAND 1=ASS CHARACTERISTICS OF A DUPLEXER

- V

UJ A I

\

O i \ /

1

I \ 2 \ /

1 \ < \ /i i \ h- i \ /

1

1 \ h- \ /

\ > \ /

\ Q \ /

\ <

IV J\ \^

FREQUENCY —~

Figure 6
29-

of operation presupposes that the antenna is used for transmitting at

one instant of time, whereas it is used for receiving at another instant

of time . However, a cw system imposes more restrictive conditions

on the duplexer than would a system involving pulse transmission.

Where cw is used, a duplexer must effectively keep the transmitter

isolated from the receiver at all times and yet maintain maximum

coupling between the transmitting and receiving antenna circuits. If the transmitted and received signals on the same frequency and polarization, it can be shown that a lossless 3 -terminal network cannot

satisfy these requirements. A 4 -terminal network, however, can

satisfy these requirements, such a network being in the nature of a magic T. However, the use of this device requires that the fourth

terminal, the one not connected either to the transmitter, receiver,

or antenna must be terminated in a matched load. This matched load

dissipates half the transmitted power and half the received power,

indicating that if the device is essentially lossless, then there is still

an insertion loss of 3 db whether the transmitted direction or the

received direction is considered. Not only is this loss undesirable

from the aspect of circuit efficiency, but this loss imposes severe

requirements on a terminating load, especially where high-powered

transmitters are being used.

To avoid these restrictions, the transmitted signal and the

received signal are usually separated in frequency, and the frequency

difference between these two signals makes possible their isolation

one from the other while maintaining a good coupling factor to the

antenna. Essentially, the device is so tuned that the receiver leg

appears to have an admittance approaching zero at transmitting frequency whereas the transmitter leg has an admittance approaching zero at

the receiving frequency. The antenna must be sufficiently broad-banded

such that both the transmitted frequency and the received frequency can

be matched with a low VSWR.

Figure 6 illustrates the principle of operation of such a duplexer.

The transmitter and receiver legs are connected in parallel to the

antenna. The bandpass filter on the receiver leg is so constructed that

it presents the characteristic admittance of the line at the center frequency of the received signal, yet presents an admittance approaching

zero at the transmitted frequency. Likewise, the bandpass filter in

the transmitter leg is so constructed that at the junction it exhibits the

characteristic admittance of the line at the center frequency of the
-30

transmitted signal, yet presents an admittance of essentially zero at

the received frequency. Therefore, practically speaking, the receiver

leg does not exist as far as the transmitter frequency is concerned nor

does the transmitter leg exist as far as the received frequency is concerned.

Figure 6 is the parallel combination; a series coupling is also

possible but is not often used.

It is evident that the isolation between transmitter and receiver

is directly related to the quality of the bandpass filter used in each

leg. From the standpoint of admittance matching, the object of the

design is to keep the susceptance of the off resonant branch as small

as possible as well as having the conductance essentially zero. With

respect to the resonant frequency of each branch, the insertion loss

is desired to be maintained at a minimum over a wide band, which the

attenuation of the resonant frequency of the opposite leg be maintained

at a maximum. It can be seen that the bandpass filters are required

to have a fairly flat top as well as having very good selectivity, that

is, sharp skirts to the response curve.

Essentially, then, the duplexer is merely two bandpass filters

terminated in the transmitter and receiver, respectively, and connected

to the antenna in parallel. The coupling between the transmitter leg

and the receiver leg is therefore a function of the characteristic of

these band-pass filters and the separation in frequency between the

transmitter leg and the receiver leg.

This type of duplexing can be extended to include almost any

arbitrary number of transmitters and receivers operating in this

fashion, with each addition to the junction being characterized by its

own particular band -pass filter. Systems called multicouplers as described by Cline and Schiffman [ 1959] have been devised where as

many as 20 inputs, transmitters, and /or receivers, can be coupled

into the same antenna. The method is exactly the same except that the

antenna must be capable of more and more broad -banded operations

as the number of inputs increase. Where many of these inputs are

required, a simple junction as illustrated in figure 6 will not suffice,

and these inputs usually are distributed along a transmission line.

This requires more complicated matching since the sections of transmission line between the inputs can be critical as far as length is
-31

concerned with respect to the operating frequency of each input. Line

stretchers can be used between the inputs to tune the overall complex

for the optimum operation over the frequency ranges desired.

Attention will be concentrated on the simple duplexer whereby

a single transmitter and a single receiver are coupled to the antenna.

Since, in the usual case, the duplexer is not field tunable and in manufacturing they are fixed tuned to operate over the required frequency

band, it is not necessary to consider the different methods whereby

this goal is achieved. It is sufficient to refer to the manufacturer's

instruction book to ascertain the methods used to achieve this result.

A duplexer can be made in different ways. Probably the most common

utilizes coaxial transmission line for the bandpass filters. From the

aspect of simplicity of design, the duplexer utilizing waveguide is

advantageous since the filters can be built into the waveguide by means

of irises. Irrespective of the type considered, the principles are

exactly the same; therefore, what is considered with respect to waveguide duplexer s applies equally well to coaxial duplexers. From the

aspect of measuring the characteristics of such a duplexer, it can be

considered to be a 3 -port black box with an antenna terminal, a receiver

terminal, and a transmitter terminal.

Other similar duplexers are described by Cohn and Coale [ 1956]

and Lewis and Tillotson [ 1948] .

3.1, The Operating Characteristics of the Duplexer

a. The Insertion Loss or Coupler Factor

The measurement of the coupling factor between the antenna and

the transmitter and receiver ports, respectively, is a measure of insertion loss of the attenuation factor of the duplexer. A method for measuring this insertion loss or coupling factor will take into consideration

any directive qualities which the duplexer may have inherent in its

design. Essentially such a method consists of the following: a monitored

signal is fed from the antenna into the duplexer and is monitored at the

receiver port. Conversely, a signal can be injected into the duplexer

at the transmitter port and monitored at the antenna port. The difference between the input and output signals is a measure of the attenuation
-32-

or the coupling factor of the duplexer. A receiver whose power level

can be monitored is used as a detector on the receiving leg, and a

signal generator tuned to the center frequency of the receiving circuit

is connected to the antenna terminal. A signal at the center frequency

of the receiving system whose level is accurately monitored at the

signal generator is then fed through the antenna port and received at

the receiving port. The level of the signal is then recorded at the

receiver. If an output meter is not available at the receiver, then

some provision can be made to measure the AGC voltage, and this can

be used as the level determining reading. The signal generator is then

connected directly to the receiver, and the circuit remains the same

with the exception that the duplexer is removed from it. Again the

same monitored signal would be received at the receiver, and its level

would then be noted. The ratio of these two levels would then be the

insertion loss or the coupling factor for the duplexer. The same

method would be used on the other leg of the duplexer with a signal

generator connected to the transmitter port and the receiver connected

to the antenna port. If an insertion loss greater than 1 /2 db is experienced, the duplexer may not be in proper operating condition. Since

no provision is present to adjust the duplexer, then an excessive insertion loss could be interpreted that the duplexer was not well designed.

It should be remembered that for this measurement the port which is

not being measured must be terminated in the characteristic impedance

of the line

.

b. The Bandpass Characteristics

The method of measuring the insertion loss of the dupelxer

may be extended to measure the bandpass characteristics of the duplexer

if a variable frequency receiver in the range of operation is available.

Since the usual 1/2-db bandwidth of the duplexer should be known, a number of points within the region of the center frequency should be

sufficient to determine the flatness of the curve over its desired bandwidth. The signal generator could be tuned to several discrete frequencies and the receiver tuned to meet these frequencies. A comparison of the output of the receiver is then graphed to determine the bandwidth characteristics of the duplexer. It is recommended that these

measurements include frequencies other than those contained within

the 1 /2-db bandwidth. The nature of the selectivity of the filter can be

well estimated if the 20 -db bandwidth is measured. This would entail

measuring several additional points where the receiver response may

be down 20 db below the response experienced at the center frequency.
-33-

Q<

cr

LlI

CO<

LUX

crLUX

Q_Oo O CO

CO uj

_l

cr

Q<

00

LU

CO >

CO LU

O- LU

LU * ><

_1

LU

cr
•34-

c. The Isolation

Since the attenuation necessary between the transmitter and

receiver leg is extremely high, that is, in excess of 100 db, ordinary

methods of measuring this isolation will not be adequate. Performance

of the duplexer can best be determined while it is in the actual operating

circuit. The necessity for a good degree of isolation can be illustrated

by consulting figure 7. The response curve to the left is the idealized

frequency response curve of the transmitter leg. The response curve

to the right is the idealized frequency response curve of the receiving

leg. It can be seen that the response of the receiver leg to the transmitter frequency should be maintained at a minimum. The response

of the receiver leg to the transmitted energy is illustrated by the

shaded portion in the transmitter bandpass. The amount of area under

this curve is indicative of the amount of energy from the transmitter

that appears in the receiver leg. The isolation of the receiver leg

from the transmitter leg is indicated by the distance A, the attenuation

from the peak power of the transmitter. This attenuation should be

maximum. Two effects will follow if this attenuation A is not sufficient.

One is that increased noise will appear in the bandpass of the receiver

and, secondly, if the energy associated with this unwanted signal in

the receiver leg is sufficiently high, it can effectively block the receiver

at the rf stages. This situation is idealized in that it assumes all the

energy from the transmitter will be contained within the indicated bandwidth, which, of course, is not necessarily true.

The method to be utilized here will be an approximate determination of the change in noise level and in minimum detectable signal

caused by the duplexer. The receiver will be connected to the receiver

port, the transmitter to the transmitter port, and the antenna to the

antenna port of the duplexer. Then, with the transmitter off, a re- cording of the noise output of the receiver should be made; that is, the

receiver, after the initial warm-up time has elapsed, should be allowed

to operate merely on the noise from the system. Then the transmitter

should be turned on and should be adjusted to maximum operating power

with full modulation. The noise level of the receiver should then be

again recorded for comparison with the first recording. If no discernible difference (i.e., less than 1 db) is evident between the two

recordings, then it can be assumed that the isolation between the transmitter and the receiver is sufficient.
-35-

Blockage of the receiver due to excessive energy from the

transmitter will be very apparent in that the receiver will tend to

saturate, causing the noise level of the receiver to change markedly,

indicating the duplexer to be inadequate.

This measurement of the output of the receiver should be made

immediately after the IF amplifier or immediately after the detector.

Then the degree of isolation is not only a function of the duplexer but

is also a function of the selectivity of the receiver.

If a significant difference is noticed between the two recordings

of the noise level of the receiver, then it is still to be determined

whether or not this increased noise in the receiver on the second

reading was due to the lack of isolation of the duplexer or due to the

leakage and radiation of the transmitter. A method to determine this

can be outlined as follows. The receiver is disconnected from the

duplexer, and both the receiver and the duplexer are terminated in

good quality matched terminations. With the receiver input then

terminated with the matched load, a record of the noise level is obtained,

The transmitter is then turned on and adjusted to full power and full

modulation. A second record of the noise level of the receiver is

obtained. If there is any difference between these two readings, i. e. , greater than 1 db, then it can be assumed that stray coupling between

the transmitter and the receiver is excessive, and the determination

of the performance of the duplexer would be in error. It is extremely

important for the accuracy of this determination that grounds be maintained between the duplexer and the transmission line to the receiver

such that the paths of stray coupling experienced while the duplexer

was in the system will not be disturbed. If excessive coupling is noted

between transmitter and receiver when they are not connected through

the duplexer, then steps must be taken to eliminate this stray coupling

problem before the duplexer can be measured. After the problem of

stray coupling has been eliminated, the measurement of the isolation, as outlined above, can be accomplished. If the increase in the noise

level due to operation through the duplexer is in excess of 1 db, the

isolation should be considered inadequate.
-36

4. COMPARISON OF DIFFERENT TRANSMISSION SYSTEMS

Generally, most tropospheric scatter communications systems

will employ either frequency modulation (FM) or single sideband

suppressed carrier, amplitude modulated (SSBSC-AM). While other

transmission systems are used such as pulse code modulation (PCM),

only FM and AM modulation systems will be considered.

4. 1. Methods of Modulation

Information can be transmitted on a carrier by varying any of

the parameters of a sinusoidal wave in accordance with a modulating

voltage. Thus, a carrier is described by

M(t) = A cos (w t + <b ) (16)

c c c

where

M(t) = instantaneous value of the carrier at time t A = amplitude of the carrier

c

co = the angular frequency of the carrier = 2 tt f where f is the frequency

c£> = the phase angle of the carrier when t =

c

a. Amplitude Modulation (AM)

Amplitude modulation is accomplished by letting the modulating

signal vary the amplitude of the carrier wave about its mean value.

Thus, Ac (equation (16)) is caused to vary in accordance with the modulating signal. If we represent the modulating signal as a time varying

function V(t), then the amplitude modulated carrier is

M(t) = A [ 1+ K V(t)] cos (co t + <b ) (17)

c c c
-37-

where

K = a constant determined by the modulator

If a sinusoidal modulating wave is assumed, that is,

K V(t) = a cos p t (18)

where

a = amplitude of the modulating signal whose

maximum value is 1 .

then

M(t) = A [ 1+ a cos p t] cos (go t + <j> ) (19)

b. Single -Sideband Modulation (SSB)

If (19) is expanded, it will be noted that three terms appear.

aA

M(t) = A cos (go t + cb ) + ——- cos (go t+ A + pt)

c c c 2 c c aA < 2°>

Q + — cos (go t + 6 - pt)

2 c c

The first term is the carrier, and the other two terms are the sidebands.

Single -sideband (SSB) systems suppress the carrier and one of the sidebands such that the output contains but one of these components. The

carrier can be suppressed by use of a balanced modulator such that the

carrier does not appear in the output. The two sidebands are then passed

through a special SSB filter which passes one and rejects the other.

Then (20) becomes

aA

M(t) = —— cos [ (go + p) t + 6 ] (21)

c> c c
38-

c. Angle Modulation

Angle modulation has two principal subdivisions: phase modulation and frequency modulation. Since true phase modulation does not

utilize the spectrum as effectively as frequency modulation, phase

modulation, today, is used primarily as a means of obtaining frequency

modulation.

d. Phase Modulation

Phase modulation is defined as angle modulation in which the

instantaneous phase angle of the carrier is varied in accordance with

the amplitude of a modulating wave, and the frequency deviation, F , or the change in the carrier frequency, is proportional to both the

amplitude and frequency of the modulating wave. Thus, the phase

modulated carrier is given by

M(t) = A cos [co t + <j> KV(t)] (22)

where

V(t) = time varying modulating wave

K = a factor of proportionality determined by the

design of the modulating system

If the modulating signal is a sine wave, then (22) becomes

M(t) = A cos [w t + a <j> cos p t] (23)

where

<(> = phase shift produced by the maximum amplitude

of the modulating signal a = relative amplitude of the modulating signal,

which can vary from to 1

.

It can be seen that the instantaneous frequency deviation is a function of both the amplitude and frequency of the modulating signal.
-39

e. Frequency Modulation (FM)

By contrast, in FM, the instantaneous frequency of the carrier,

the time derivative of the instantaneous phase angle 9(t) is varied by

the amplitude of the modulating wave. The frequency deviation is proportional only to the amplitude of the modulating wave. The frequency

of the modulating F determines the rate of change of the carrier

frequency. Frequency modulation requires that the instantaneous

carrier frequency be varied about its average value f = co/2 tt in proportion to the amplitude of the modulating signal, and between the

limits of f + Fi and fQ

- Fj is the frequency deviation or peak swing

of the carrier produced by the maximum values of the modulating

signal. If a sinusoidal wave with an angular frequency p is used to

modulate the carrier, the instantaneous carrier frequency is

f = f + a F, cos p t (24) o d

where

a = the relative amplitude of the modulating wave

which may have any value between and 1

The carrier can be described by M(t) = Ac cos (u> t + cf> c

), where the

value of the argument is dependent upon the following integration:

(J> = 2tt \ a F cos ptdt (25)

o. -> ^ +. sin p t § - 2 ir a F t -

(26)

c d p t F

F*

cj> = a —— sin p t (27)

m

where Fm = frequency of the modulating wave = p/2ir .

Then substituting (27) into (16), the equation of the frequency

modulated wave is
-40

M(t) = A cos (go t + a —7— sin p t) (28)

c c Fm

Thus, an FM wave varies in instantaneous frequency above and

below the center (carrier) frequency. Taking the limit of (26) as t approaches 0, the instantaneous carrier frequency to c

t + 2tt a F^ t shows that only the amplitude of the modulating signal determines how

the FM wave varies from the center frequency. Equation (28) shows

that the frequency of the modulating wave determines the rate of change

of the carrier frequency.

As an example, if the amplitude of the modulating signal of one

volt caused 100 kc/s change in frequency, the FM wave would swing

from a maximum frequency of 100. 1 Mc/s to a minimum frequency of

99.9 Mc/s. If the frequency of the modulating signal is 200 kc/s, this

would happen at the rate of 200, 000 times per second.

The amount by which the frequency differs from the center frequency is proportional to the amplitude of the signal. If the amplitude

of the signal is doubled, the amount of frequency swing will double.

If the peak amplitude remains at one volt and the modulation frequency is doubled, the frequency will still vary between the limits of

100. 1 and 99.9 Mc/s, but the frequency rate would increase to 400, 000

times per second.

The frequency difference between the modulated wave and the

center frequency is called the frequency deviation of the wave. The

maximum amplitude of the modulating signal determines the maximum

frequency deviation of an FM wave. In the final result the amplitude

remains constant; only the frequency changes.

The reader is referred to Fibbs and Johnstone [ 1956], and

Hund [ 1942] and Arguimbau and Stuart [ 1956] for a more comprehensive

treatment of the processes and applications of frequency modulation.
-41

4.2. Comparison of the Different Systems of Modulation

The three most common types of modulation, AM, SSB, and

FM, can be compared. The comparison is made here not from the

aspect of propagation but from, the aspect of the equipment; the evaluation of systems of modulation with respect to propagation characteristics

is considered by Florman and Tary [ 1962] . The comparison can be

made on the basis of bandwidth, signal-to-noise ratio, frequency

stability requirements, power requirements, distortion, efficiency,

and simplicity of equipment.

a. Bandwidth Requirements

Bandwidth reduction is one of the most significant advantages

of SSB over any other system of modulation. For example, two SSB

voice circuits will occupy the same spectrum space as a single conventional AM voice circuit. Narrow-band PM and FM will require

considerably more spectrum space than does AM.

An AM system occupies a bandwidth equal to twice the highest

modulating frequency. For example, in an AM multiplex system of

24 channels plus 4-order wire channels, each channel requiring 4 kc/s,

then the total bandwidth required is 2 x 28 x 4 = 224 kc/s.

Since the bandwidth of a single sideband system is only half that

of AM, the required bandwidth for a comparable SSB system would be

112 kc/s.

The bandwidth required for an FM system is a function of the

sidebands necessary to convey the desired intelligence with an acceptable amount of distortion. Even with a sinusoidal modulating signal,

the expansion of (28) into the Bessel function is

OO

M(t) = A > J (m ) cos (oo + n ) t (29)

c Lu n p c p n = - oo
-42-

where

m = a Fm

J (m ) = Bessel function of the first kind, of order n n p for the argument m

P

(For mathematical simplicity, both positive and negative n must be

considered for each sideband.)

The sidebands of an FM signal extend over an infinite bandwidth.

All of these sidebands are not required. Practice has shown the distortion caused by clipping of sidebands is well within acceptable limits if only those sidebands with an amplitude greater than 1% of the unmodulated carrier amplitude are considered. The number of sidebands

increase with the modulation index (m), where

F

m = — (30)

m

From (30) it can be shown that as the modulation frequency

(F ) increases the sidebands decrease. Alternately, the sidebands m

increase as the frequency deviation (Fj) increases. The frequency

deviation (F^) is determined solely by the amplitude of the modulating

signal.

For a modulating signal of constant amplitude, the bandwidth

occupied is equal to twice the frequency of the highest significant sideband which is given by the number of significant sidebands multiplied

by the modulating signal frequency. Thus, as the number of significant

sidebands decrease with increasing frequency, the bandwidth tends to

remain constant. The bandwidth is a function of the modulation index,

and it can be shown that

BW=2F 1 ifF 1/ x » F

d d(max) m

B W = 2 F if F,, m d(max) « Fm
-43

O

\-

< 2

-I o

CO ^

a: . uj ^

>-o

Ld

=>O

LU < a:

O u_ £

x

E! O

Q

<

DQ

UJQ

00

QO

SaNV93QIS AG CGIdnDDO HlQIMQNVa
-44-

RELATIVE SIGNAL-TO-NOISE RATIOS OF

AM AND FM SYSTEMS

AS A FUNCTION OF FIELD STRENGTH

CO

CO<

UJo

/ V

—s~ s~ '

1 f

DETECTED SICiNAL — EQUAL TO NO ISE

7^

INCREASING FIELD STRENGTH

Figure 9
-45-

Figure 8 is an illustration of the relationship between the bandwidth, the frequency deviation, and modulating frequency. For example,

if an FM multiplex system of 24 channels plus 4 -order wire channels

were desired, then for 4-kc/s channel bandwidths, the following can

be found from figure 8: m = F

d = B W =

224 kc/s

1052 kc/s

m

B W =

0.6

67.2 kc/s

590 kc/s

b. Signal-to-Noise Ratios

One of the primary advantages of FM over other forms of modulation is the improvement of the output signal-to-noise ratio for a given

input as illustrated in figure 9- This advantage is accomplished only

if the signal level is greater than the FM threshold level. An FM system requires a larger signal input for a minimum output than does the

aforementioned systems. Black [1953] has shown that once this threshold level is exceeded, the output signal-to-noise ratio of an FM

system can be expressed as

N

= 3

FM

F

d

- z m -1 2F n m

= 3m7 P

2 c 2F n m

(31)

where

n

m

= the average carrier power

= noise power density at the input to the detector in

watts /unit bandwidth

= frequency deviation

= the modulating frequency

2F n is then the noise power at the detector input. While it may seem that the signal-to-noise ratio could be made to increase

indefinitely merely by increasing the frequency deviation (F ), this

is not so, since wider bandwidths imply increased power to maintain

the signal level above the detector threshold.
46-

The comparable signal-to-noise ratio for an AM system can

be determined by considering an AM wave (equation (19)) applied to

an ideal detector. The output signal will be proportional to the modulation. The output signal power can be expressed

2 2

S = c a P

o c (32)

where

c - a proportionality constant

a = the. amplitude of the modulating wave

P = the average carrier power

The noise present in an AM system assuming an ideal low-pass

filter of bandwidth B, and a purely random character for the noise is

N = 2c Bn

o

(33)

where

n = the noise power density at the input to the detector

in watts /unit bandwidth

B = bandwidth

Then the signal-to-noise ratio can be expressed

S

N

a

2

P

o -J AM 2Bn (34)

If 100% modulation is assumed, a will be equal to one and

N

o J AM 2Bn (35)
-47-

Assuming an ideal detector, equal average carrier power, equal noise

density at the detector, and with 100% AM modulation.

FM versus AM

N

o -JFM

= 3

N

L o J AM

m

= 3 m (36)

If the modulation index m is in excess of 0.6, FM systems

are superior to AM, and the rate of improvement is proportional to

the square of the modulation index.

FM provides a 4-to-l advantage beyond that expressed above

if peak powers are considered rather than average powers. Consequently,

when the comparison is made between FM and SSB, this further FM

enhancement must be considered since only peak power comparison is

reasonable where SSB is concerned. This does not mean that FM enjoys

this total increase over SSB, since SSB enjoys an 8-to-l advantage over

conventional AM. This indicates that the enhancement of FM or SSB is

only half that which is enjoyed over AM.

FM versus SSB

r- S

o N L o FM 3 4 3

r S

O

—

SSB

2 F

2

m

"" 2

N I- o

m (37)

If the modulation index m is in excess of 0.8, FM systems are

superior to SSB, and the rate of improvement is again proportional to

the square of the modulation index. However, this apparent enhancement should be viewed with caution. It is emphasized that this comparison is valid only when the signal is well above the threshold of the FM

system. Especially in tropospheric scatter circuits where a continuously

variable signal is present, the power requirement may be prohibitive

if the received signal is going to be maintained above the FM threshold

100% of the time. This FM advantage must be considered in the economy

of the particular circuit under consideration. If the signal is expected
-48-

to fade below the threshold of the FM system, then this advantage

vanishes and the performance of the FM system deteriorates rapidly

to below that expected of other systems.

c. Frequency Stability Requirements

The requirements for frequency stability are quite stringent

where SSB systems are used. These requirements arise due to the

suppressed carrier. At the receiver the carrier must be reinserted

for demodulation. It is very important that the exact relationship between the carrier and the sidebands be preserved. This places narrow

limits upon the frequency variations of the oscillators both at the transmitter and at the receiver. For voice communications, a deviation of as much as 50 c/s can cause loss of intelligibility under conditions of

poor signal strength. As the frequency of the transmitted signal

increases, the percentage tolerances on the oscillator frequency

become increasingly difficult to maintain. To overcome this difficulty,

many SSB systems transmit a reduced carrier which furnishes the

control for the frequency of the oscillator at the receiver.

Neither conventional AM nor FM has this tight frequency tolerance,

The only requirement in the FM case is that the oscillator frequency

variations must be small with respect to frequency changes caused by

the modulating signal. A frequency stability of .002% is usually adequate

for an FM system.

d. Power Requirements

Since in SSB only one of the sidebands is transmitted, there is a great saving in the amount of power necessary at the transmitter.

This is equivalent to an increase in the effective power gain. Under

comparable conditions, the SSB system provides a power gain of up

to 9 db over a conventional AM system. Furthermore, an improvement

in the signal-to-noise ratio can be expected since SSB requires lesser

bandwidths

.

The FM system is more difficult to analyze because good performance can be expected only as long as the input signal at the receiver

is in excess of the threshold level. Near or below this level the
49

performance deteriorates. Hence, for a fading signal, it can be

expected that SSB will have approximately a 10 -db average power

gain over the FM system.

e. Distortion

Distortion in the high-power amplifier can become a very

serious and limiting factor in the method of modulation. In all systems

harmonic distortion will be present, but due to the resonant circuits

in the output of the amplifier a minimum of these distortion products

will be present in the output. A far more serious type of distortion is

that which is produced when a linear amplifier is driven out of its

linear range, as would be that case in SSB. Distortion products are

produced which fall close to the desired signal and cannot be filtered

out. These unwanted signals can destroy intelligibility. As a compromise, the tube is usually derated and operated over a smaller

range, thus reducing its efficiency. FM, PM, and AM do not suffer

from this deficiency, since the final amplifier in these systems does

not require these linear characteristics.

f. Final Amplifier Efficiency

In general, AM tropospheric scatter circuits will utilize high

level modulation. This places greater demands on the modulator

because the modulator will be required to produce one -half of the power

in the carrier. There is some compensation, however, since the final

amplifier can then be operated in a class C condition, or, if the final

amplifier utilizes a klystron, it can operate in the saturated region.

This has the advantage that the efficiency of the final amplifier is at

a maximum, and the amplifier can be operated at rated continuous

carrier output. The efficiency of a saturated klystron power amplifier

may be in the range of 40%.

In the case of SSB, the amplifier must be operated only over

its linear range. In the case of the klystron, the peak power is usually

limited to about 80% of the maximum saturated output, thus reducing

excessive distortion. The efficiency will be dependent on the character

of the modulating signal. For example, two tones, not synchronized

in phase, will have an average-to-peak power ratio of 50%. However,
-50-

Ld

CO

<

O

CO

<

GO

CO

cr:

rv- Ll_J

Q_ Q_

i

co

<3»

cr:

(=3 *C

CO

cez U_l

U_l ; SE Q_

<=> n CX_ =>CO

u

00

J

CO

CLJ
-51-

as the modulating signal becomes more complex, this ratio decreases.

Gaussian noise, which more closely approaches voice, reduces this

ratio to approximately 15% for the 1% peaks.

Where FM and PM systems are used, the final amplifier is

usually operated at saturation. However, the maximum efficiency

may be reduced if the klystron is broad -banded to accommodate the

wider bandwidths required in FM. In general, under comparable

conditions FM will display a 6-db advantage over AM if the peak power

output of the amplifier is the limiting factor, and a 3-db advantage if

the limitation is in terms of the rms power output.

5. THE FM TRANSMITTER

In order to transmit information as electromagnetic wave it is necessary to convert intelligence to a modulating signal, to superimpose this modulation on a carrier wave, and to deliver this modulated wave to the antenna system. FM transmitters are largely

conventional and consist of three basic parts: the oscillator-modulator,

the frequency multiplier, and the power amplifier. In the first section

the carrier frequency is generated and frequency modulated, in the

multiplier section the carrier is increased in frequency to that of the

operating frequency, and in the amplifier section the power is increased

to the desired operating level as shown in figure 10.

5.1. Oscillator and Modulator Sections

Frequency modulated waves are produced by varying the carrier

frequency at the modulating signal rate above and below the unmodulated

carrier frequency. This can be achieved by using a reactance tube or a voltage variable capacitor to alter the frequency of the transmitter

master oscillator. The reactance tube or voltage variable capacitor

is controlled by the frequency of the modulating signal. Phase modulation is produced by allowing the modulating signal to shift the phase

of the carrier, the change of the phase angle being proportional to the

instantaneous amplitude of the modulating signal. Phase modulation,

as such, is seldom used since it does not utilize a given frequency

channel as effectively as does FM transmission. However, phase

modulation is important as a means of obtaining frequency modulation,
-52-

PHASITRON

r

AUDIO INPUT

3 PHASE RF INPUT

CATHODE

ANODE No. I ANODE No.2 ELECTRON

DISC

SHIELD TO REDUCE

INPUT OUTPUT

CAPACITANCE —-Lvwv-3 C—

.

(TO FREQUENCY

MULTIPLIERS

PHASE DEVIATION OF THE OUTPUT VOLTAGE

WITH RESPECT TO FIELD STRENGTH OF THE MODULATING COIL IN GAUSS

CO

CO<

CDX

o

UJ

CL

h-coO

_lUJ

20

10

-10

-20

-240 240 PHASE DEVIATION OF OUTPUT VOLTAGE IN DEGREES

Figure 11
•53-

the phase modulator requiring an integration circuit or a pre -emphasis

network to remove the effect of the frequency of the modulating signal

on the total frequency deviation and produce frequency modulation.

A direct method of generating FM is to control the frequency of

an ordinary oscillator such as the hartley oscillator by a modulating

voltage. The most common method of doing this is by means of a

reactance tube, although the voltage variable capacitor has a promising'

future in such applications. If a reactance tube operates on a crystalcontrolled oscillator, the resulting modulating is closer to phase

modulation than to frequency modulation because the frequency deviation

that can be secured by varying the tuning of a crystal oscillator is quite

small. Although a reactance tube operating on a free-running oscillator

is capable of producing wide deviation, the frequency of such a transmitter is susceptible both to variations in power supply voltages and

to changes in parameters due to aging and temperature. Such susceptibility results in very poor frequency stability. This can be improved

through the use of push-pull reactance modulators, but in the end the

desired stability must be achieved through the use of automatic frequency control in which the average transmitter frequency is compared

against a crystal -controlled oscillator. This results in considerable

added complexity to the transmitter. The sensitivity of the reactance

tube modulator depends on the trans conductance of the modulator tube

and certain circuit factors, but in general this modulator is capable of

causing a frequency deviation of several hundred cycles with a distortion

of a few hundredths of a percent at the oscillator frequencies commonly

used.

This problem of frequency stability can be avoided through the

use of a fixed frequency oscillator and appropriate phase shifting network on the output of the oscillator controlled by the modulation. One

such method utilizes a specially designed tube called the Phasitron to

introduce comparatively wide phase variations in the crystal-controlled

RF carrier, as described by Bailey and Thomas [ 1946] . The Phasitron

is capable of producing phase deviations of up to ± 450° with a distortion

of 1.35% at 50 c/s (see figure 11). Phase deviations of ± 200° or 3.5

radians are commonly used. With this type of service, distortion is

about 1% and the frequency swing ±175 c/s, with a modulating frequency

of 50 c/s. The noise is more than 78 db below the signal at full

deviations (100% modulation).
-54-

o

3Q

O

O

<

CEUJ

(NJ

u

Cuo
-55-

The Phasitron is so constructed that a sinusoidally varying

electron disc is formed. At the periphery of this disc are concentric

anodes The inner of the two anodes is punched with holes arranged

in such a manner that the rotating disc of electrons strikes the inner

anode half the time, and half the time it passes through and strikes

the outer anode.

Thus, if a tuned circuit is connected across the two anodes, it will be excited at the oscillator frequency. The Phasitron is surrounded

by a varying magnetic field produced by the modulating frequency in a solenoid. The action of this field is such as to advance or retard the

rotation of the disc about its axis and to produce in its rotational motion

either a slight increase or a decrease in its peripheral velocity.

The modulating solenoid is very nearly a pure inductance with

a constant voltage applied to it. The resulting current through the coil

and the rotation of the electron disc are then inversely proportional to

the modulating frequency. Thus a constant deviation is acquired and

FM results.

The Serrasoid modulator as described by Day [ 1948] is

widely used today. It can provide phase shifts of up to about ± 150° or a corresponding frequency excursion of ± 130 c/s with a distortion of

a few tenths of a percent. The noise originating in the modulator can

be kept about 80 db below that level obtained with 100% modulation. By

using some harmonic of the output pulse, Serrasoid modulators have

been successfully used at rf frequencies as high as 5 Mc/s and with

modulating frequencies as high as 300 kc/s.

The Serrasoid modulator, (see figure 12) consists of 3 tubes

which generate a stable, very linear sawtooth wave and a modulated

gate which generates a pulse whose time phase is proportional to the

instantaneous audio signal. The rf oscillator draws plate current during

only a small part of the cycle. This signal is then differentiated and

clipped by a cathode follower. These pulses are used to time the sawtooth generator. Because the linearity of the modulator depends upon

the straightness of the sawtooth wave, great effort is made to achieve

the desired waveform. The sawtooth generator is directly coupled to

the modulators or gate tube. This tube is normally cathode -biased so

that conduction begins when the sawtooth wave reaches about half its peak

value. Once conduction starts the sawtooth is clipped. The bias of
•56-

the modulator is varied by the modulating signal, thus varying the

clipping level of the sawtooth wave and the time of conduction of the

modulator tube. The negative going portion of the wave is differentiated and amplified. The phase of the resulting pulse can thus be

advanced or retarded because the audio signal alters the bias on the

modulator tube. These pulses are then applied to the frequency

multipliers and reshaped to sinusoidal waves.

Table 2 illustrates the comparison among the different types

of modulators considered here.

TABLE 2

Type of

Modulator Deviations Obtainable Distortion Noise in db Comments

Phase in

degrees

Frequency

in c/s

Below Full

Modulation

Reactance

tube acting

on a freerunning

oscillator

± 9000 < .05% Poor stability

without complicated stabilizing

circuitry, excellent deviation,

usable at high rf

frequencies

Reactance ± 25

tube acting

on an amplifier tank

circuit

± 22 Poor deviation

Phasitron ± 450 ± 390 < 1 . 5% > 78 Good deviation,

low noise

Serrasoid ± 150 ± 130 < 1% 80 Low noise, good

high frequency

response, usable

at high rf frequencies .
-57-

Most manufacturers have their own favorite modulating methods. In

addition to those listed above, these may include the use of cathode

ray tubes or methods for varying the transconductance of a tube. In a specific piece of equipment, the manufacturer's instruction manual

must be consulted to determine the type of modulation used and to obtain

detailed information as to the action of the circuit and its adjustments.

The reader is referred to Terman [1947], Camies [1959], Fibbs and

Johnstone [ 1956] , and Black [ 1953] , among others, for additional

information.

5.2. Frequency Multipliers

Modulation is accomplished at low rf power and in most cases

at a comparatively low frequency. The modulator output is used to

drive a series of low level, receiving tube, class C, multiplier stages.

In the final stages of the multiplier the power level is increased to that

necessary to drive the power amplifier.

The frequency multipliers perform one additional important

service. The modulators produce frequency shifts of relatively small

magnitude, and this is increased to the desired frequency deviation in

the multipliers. The deviation is given by

where

F

d

= Mf

d

(38)

M = the frequency multiplication factor of the multiplier

chain

f = the frequency deviation produced by the modulator

5.3. Power Amplifiers

The power amplifiers used in tropospheric scatter systems are

either conventional tubes or klystrons. Since linearity is not required

in the power amplifiers in FM transmitters, conventional tubes are

operated class C, and klystrons are operated at the peak of their mode

curves with high efficiency. The power output of an FM transmitter

may usually be increased at any time by the addition of larger power

amplifiers to the existing equipment.
-58-

5.4. Power Supplies

The requirements of the power supplies for an FM transmitter

are not particularly stringent. Aside from the oscillator and modulator

section, the regulation of the power supply is not important since the

load does not change with modulation. Ripple should be low (0.1% or

better)

.

The oscillator and modulator power supplies should be well

regulated and have very low ripple since poor power supply performance at these points can alter the modulation or the frequency of the

transmitter.

5.5. Measurement of Frequency

Deviation in an FM Transmitter

It is important to know the frequency deviation of an FM transmitter for several reasons. Perhaps one of the most important is

that the rf spectrum occupied bears a direct relationship to the frequency deviation. The relationship between the modulating index,

frequency deviation, and the modulating signal is given by

F.

m^^r2- (39)

m

where

m = modulating index

F. = frequency deviation

d

F = frequency of the modulating signal

Elaborate equipment has been designed for the purpose of measuring frequency deviation. If such equipment is available, it is simply

a matter of following the instruction manual supplied by the manufacturer,

to determine the frequency deviation. If such equipment is not available, or if the results found by the use of such equipment are to be subjected
-59-

to confirmation, then the following method is recommended. The

Bessel zero method will allow the determination of the frequencydeviation using only an audio oscillator and a receiver tunable to the

carrier frequency of the transmitter. The receiver must have an

internal beat frequency oscillator (BFO).

For certain values of modulation index, specifically 2.405,

5.520, 8.654, 11.792, 14.931, etc. (where the Bessel function passes

through zero), the total transmitter power is contained in the sidebands,

none being present in the carrier. It is possible by increasing the

amplitude of the modulating signal and thus varying m, to cause the

carrier of the FM signal to disappear. The frequency deviation can

then be calculated from (39) where 2.405 (corresponding to the first

disappearance of the carrier) has been substituted for m.

A standard communications receiver with a BFO is required,

and the receiver is tuned to an unmodulated transmission from the FM

transmitter. The BFO should be adjusted until a tone such as 500

cycles per second is heard in the output of the receiver. "When the

frequency of this beat is set, the BFO adjustment should be fixed and

the ear allowed to become accustomed to this pitch. This is extremely

important as later the frequency deviation will be varied by changing

the amplitude of the modulating signal, resulting in a number of sidebands at various frequencies. This will produce many tones in the output of the receiver. All of these conflicting tones, with the exception

of the desired 500 -cycle tone, must be ignored at all times. This may

require some practice. Next, a signal Fm from the audio oscillator

is fed into the FM transmitter. As the amplitude of this audio signal

is increased, the sideband frequencies and their innumerable beat

notes are produced. However, as the amplitude of the audio signal

is increased from zero, F^ increases, and a steady attenuation of the

beat note arising from the carrier will occur. At some point this beat

note will disappear completely and reappear once again as the amplitude

of the audio signal is further increased. If the amplitude of the audio

signal is "rocked" on both sides of the apparent zero, two points will be

found where the beat signal can be just perceptible. The center point

between these two positions will be the desired level.

With these factors in mind, it is now possible to determine the

amplitude of a given audio signal necessary to produce the maximum

allowable frequency deviation. The first step is to calculate the modulating frequency that will produce the maximum allowable frequency
-60-

deviation when the modulation index is 2.405. This can be obtained

from (39). The audio oscillator should be set to this frequency. If the computed value of modulating frequency is too high to be within

the audio bandpass of the transmitter primary stages, or if it is too

high for the audio oscillator, then a value 5.520, 8.654, etc., should

be used for m corresponding to the second, third, etc., occurrence of

carrier disappearance.

When acceptable modulating frequency can be obtained, this is

applied to the transmitter from the audio oscillator. The amplitude of

the modulating signal is increased slowly until the audio beat of the

carrier disappears appropriately. When this occurs, the maximum

allowable frequency deviation F^ has been reached and the corresponding amplitude of the modulating signal can be read using a vacuumtube voltmeter. This level must not be exceeded during the operation

of the transmitter. If some value of m other than 2.405 such as 5.520

or 8.654 were used, the first disappearance of the carrier beat note

corresponds to a relatively low frequency deviation. The amplitude of

the audio signal must be increased further until the carrier has disappeared the same number of times as the order of the value of m.

In other words, the carrier should disappear twice for an m value of

5.520 and three times for an m of 8.654.

If the above method requires an excessively high value for m

or if a receiver tunable to the transmitter frequency is unavailable,

the following method may be used. In this case, a receiver with a BFO which will tune to the lower frequency signal immediately after

the point of modulation is used. A portion of this modulated signal is

coupled into the receiver. This may be done by means of a small pickup coil coupled to a transformer. Since the frequency multiplying stages

of the transmitter increase both the carrier frequency and the frequency

deviations by the same factor, it is possible to determine the frequency

deviation at the receiver pick-off point by using (39) and substituting for

Fj the maximum frequency deviation which can be tolerated at this point

and for m a value of 2.405, it is possible to determine the desired

modulating frequency. This audio frequency is then applied to the transmitter and the amplitude of the audio increased until the beat note disappears. This amplitude of signal then corresponds to the maximum

allowable frequency deviation. Here, again, a higher order of m such

as 5.520 or 8.654 may be used, remembering that the same order of

disappearance of the carrier must be used as is used for m. In other

words, the carrier must disappear twice for a value of 5.520 for m or three times for a value of 8.654, etc.
-61-

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The previous method considers the modulating signal, both as regards amplitude and frequency necessary to produce the desired frequency deviation. It can be seen that this method can be used for many

values of the modulating index m, and, consequently, care must be

exercised in the selection of the value of m. The following example

will illustrate the use of this method:

Example: Given an FM system whose maximum frequency deviation

is to be ± 150 kc/s, the modulating frequency is to be 20

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TABLE 3

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5.520 150 kc/s 27.17 kc/s

8.654 150 kc/s 17.33 kc/s

11.792 150 kc/s 12.72 kc/s

From Table 3 it is evident that the value of m to be used must

lie between 5.520 and 8.654, that is, between the second and the third

order values of m. In this case the modulating frequency corresponding

to m equal to 8.654 is sufficiently close that a good estimate will be

found by using a single value of m. (Greater accuracy can be attained

if interpolation is used.) Consequently, if the modulating signal generator

is adjusted to 17.33 kc/s and if the amplitude is increased until the beat

note disappears the third time, then the permissible level of the modulating signal is that signal level experienced when the carrier disappears

the third time. If this signal level is not exceeded, then the frequency

deviation will not exceed the imposed limits. Excessive frequency

deviation can produce distortion at the receiver due to sideband clipping.

6. THE SSB TRANSMITTER

A block diagram of a typical multichannel SSB transmitter for

operation in the UHF region is shown in figure 13. The transmitter

consists of an exciter for translating the signal from the multiplex

equipment to the UHF region and for amplifying it to a power level
63-

BASIC RECTIFIER- MODULATORS

RING MODULATOR

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-64-

sufficient to drive the intermediate power amplifier. For one typical

24 -channel system, the multiplexed signal occupies a baseband between

12 and 112 kc/s. A pilot tone is located at 116 kc/s. This composite

signal is fed to a 16 Mc/s balanced modulator along with a 16 Mc/s

carrier signal. The 116 kc/s pilot signal is used by the receiver for

correction of amplitude variations due to selective fading. The desired

sideband is selected by means of a high Q filter following the modulator.

This output signal is amplified, and some of the 16 Mc/s carrier signal

is reinserted and used in the receiver for automatic gain control (AGC),

automatic frequency control (AFC), and demodulation of the SSB signal.

The signal is again translated this time to the final operating frequency

by the UHF converter. Tuned coaxial line resonators form the UHF

filter which passes the upper sideband; additional filtering is provided

in the intermediate power amplifier (IPA) and final power amplifier

(PA). The UHF signal is then amplified to the desired power level in

the IPA and PA. At the output of the PA, a sample of the signal is fed

back to the 16 Mc/s amplifiers to provide automatic power output

regulation of the SSB transmitter.

6.1. Modulators

Radio frequency sidebands are obtained by combining the audio

signals and the rf carrier in an amplitude modulator. There are many

modulator circuits; however, they can be grouped according to their

circuit components into rectifier modulators and multi-element vacuumtube modulators.

a. Rectifier Modulator

Rectifier modulators may be one of three general types --ring,

series, or shunt, depending on the manner in which the diodes are

connected in the circuit. The basic circuits for these modulators are

shown in figure 14. In each circuit the rectifiers are made to work as switches by using large rf switching signals which greatly exceed the

audio signal levels. These modulators are almost always connected as balanced modulators so that there is a minimum of the rf switching

voltage in the modulator output. If the system is symmetrical, the

carrier frequency will balance out and will be absent in the output.
-65-

The output of these modulators consists of a series of pulses

whose repetition rate and polarity are determined by the carrier signal

and whose amplitude is proportional to the audio signal. A spectrum

analysis of these pulses would show an upper and lower sideband displaced by the modulating frequency about the carrier frequency. A

similar set of sidebands will be placed about the second harmonic of

the carrier and still more about the higher harmonic carrier frequencies

Of the three types of rectifier modulators, the ring modulator

has the highest efficiency where the output can be twice the output of

the shunt or the series modulators. The split-ring modulator, where

it is possible to balance independently two sets of diodes, can be used

where carrier balance is important.

Rectifier balanced modulators have their greatest advantage in

that they are more stable than vacuum-tube modulators. If they are

made from good quality, well balanced components, intital carrier

balances exceeding 40 db can be obtained with the level of the third

order inter modulation products holding 50 db below the desired sideband output.

b. Vacuum-Tube Modulators

Multi-element vacuum-tube modulators, whose output is a function of the instantaneous waveform of the modulating signal, fall

into two types: the product modulator and the square -law modulator.

A product modulator output is proportional to the input modulating signal and to the carrier signal. An example of a product

modulator is a double -grid vacuum tube where the carrier is impressed

on one grid and the modulating signal on the other. Modulation takes

place due to combined action of the grids and not due to any nonlinearities of the tube.

In the square -law modulator, modulation takes place as a result

of the nonlinearity of the tube. An example of such a modulator is a

triode in which the shape of the "grid voltage versus plate current"

curve has at least second-order curvature. (This characteristic is

present in all vacuum tubes and is a cause of distortion in amplifiers.)
66

If the carrier signal and the modulating signals are imposed on the

grid of the triode, and if the tube has purely square -law characteristics, then the output signal will contain only the desired sum and

difference frequencies with no other products except the second

harmonics of the input signals.

Modulation also can take place by using a circuit in which the

output is proportional to the polarity of the modulating signal. An

example of such a modulator is a plate -modulated triode operating

class C. The modulating signal is used to vary the plate voltage

applied to the class C amplifier. The resulting output is a series

of pulses whose repetition is that of the carrier frequency, and the

amplitude is proportional to the modulating signal. A tuned circuit

is then used to suppress the harmonics of the signal. A double -grid

vacuum tube can also be used as a switching type of modulator by

increasing the amplitude of the carrier signal applied to one of the

grids. This signal can be large enough to drive the plate current of

the tube to cutoff in one direction and saturation in the other, resulting

in an output signal similar to the waveform of the rectifier modulator.

Vacuum-tube modulators have the advantage in that a conversion

gain can be realized, whereas in the rectifier modulators a loss in

gain is incurred. But vacuum-tube modulators are somewhat unstable

as to gain and impedance, which makes them undesirable as balanced

modulators. However, the product and square -law modulators are

particularly useful as frequency changers since they generate a minimum of unwanted products.

6.2. Single -Sideband Generation

The two basic systems of generating single -sideband signals

are the filter system and phase -shift system.

Both systems produce a single sideband of an amplitude modulated radio-frequency carrier, and both are capable of good overall

system performance.
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a. The Filter Method

The filter method of producing single sideband, which is the

most familiar SSB generator, consists of a balanced modulator followed

by a selective bandpass filter (see figure 15). The balanced modulator

produces two sidebands. Theoretically, the rf carrier is balanced out

and does not appear; however, practical design considerations determine the extent of the carrier suppression. Present balanced modulators can easily suppress the carrier to from 30 to 40 db below the

peak envelope power (PEP) of the sidebands. Further suppression of

the carrier by the SSB filter can result in an additional 20 db of carrier

suppression. Total carrier suppression of from 50 db to 60 db can,

therefore, reasonably be expected from the transmitter system.

The rapid increase in attenuation required of a sideband selecting

filter in order that it may adequately suppress the undesired sideband,

limits the frequency at which a single sideband signal can be produced

by this method. Many inductors and capacitors have low Q factors and

can be successfully used for sideband filters only at relatively low

carrier frequencies, up to about 50 kilocycles per second. Mechanical

filters have been built to operate up to 60 kc/s for a single voice channel,

and crystal filters have been made to reject sideband and image responses

as close as 1 to 2% of the desired frequency. This permits a first conversion frequency of 10 to 20 Mc/s in multichannel operation. With

such filters, it is possible to construct bandpass filters at 10 to 21 Mc/s

which pass a desired sideband extending from 10 to 100 kc/s or more

from the carrier frequency while rejecting the other sideband by 40 db

or more. The signal may then be heterodyned to the desired frequency

and amplified to the desired power level. The major advantage of the

filter method lies in its stability and in its suppression of the unwanted

sideband.

b. The Phase -Shift Method

The phase method produces SSB through the use of a balancing

process. In this system, a modulating signal is applied to two balanced

modulators through a wideband 90° phase difference network. The rf

carrier is also applied to these modulators through a 90o phase -shifting

network (see figure 16). Therefore, each of the two input signals,

carrier plus modulating signal, are applied to the balanced modulators
-70-

in phase quadrature. The two double -side band suppressed carrier

signals thus generated will combine in the common plate circuit of the

combining network. Since the signals are in phase quadrature, one

set of sidebands will add while the other set will cancel. The amount

of suppression of the unwanted sideband in the phase -shift system is

primarily dependent upon the design and adjustment of the wide -band

phase -shift network. This network must maintain the two audio input

signals exactly 90° displaced in phase over the entire band, and the

amplitude of the two signals must be equal.

The significant advantage of the phase -shift method is that the

undesired sideband is removed without the need for expensive filters.

Furthermore, this method can be used at a higher rf carrier frequency,

reducing and at times eliminating the number of heterodyning steps

necessary to reach the operating frequency.

6.3. Oscillator Requirements

At the receiver the detection process consists of a frequency

translation of the SSB rf signal down to the baseband spectrum. To

accomplish this translation process the carrier which is suppressed

prior to transmission must be reconsituted with the receiver signal at a frequency close to that of the original carrier. In practice, a deviation between the local and the transmitter carrier frequencies of as

little as 50 c/s can cause loss of intelligibility of signals under conditions of low signal-to-noise ratios.

This implies a rather stringent requirement on the frequency

control of SSB which results in a general increase in the complexity

and cost of equipment. For example, if it is assumed that half of the

maximum allowable 50 -c/s departure between the local and the transmitter frequencies is distributed equally between the two ends of the

path, then the minimum oscillator stability that can be tolerated would

be 6 . 75 parts in 10^ at an operating frequency of 400 Mc/s, whereas

this tolerance shrinks to 2.5 parts in 10" if the operating frequency is

1000 Mc/s. Furthermore, if the signal is to be relayed again by SSB,

then the stability requirements become even more restrictive.
71

Although the development of small ruggedized frequency standards is progressing rapidly and stabilities of one part in 10^ are

commonplace, some form of AFC is recommended. The method

currently in use involves the transmission of some carrier power

at all times but reduced to at least 20 db below the transmitter peak

power. This signal is used as a slow acting AFC to control the frequency error at the receiver. This carrier of low pilot is used at

the receiver for AFC and the demodulation of the SSB signal.

6.4. The rf Power Amplifier

The most important consideration in regard to the power amplifier of an SSB system is its linearity. In an rf tuned amplifier, both

the input and the output voltages tend to approximate sine waves due to

the flywheel effect of the relatively high Q tank circuits. Distortion in

the rf amplifier will cause distortion in the SSB envelope. Class A

amplifiers are used to maintain distortion at a minimum at low power

(less than 2 watts). Class A amplifiers can be operated rather easily

over the linear portion of their characteristic curves. As long as the

maximum output voltages are maintained at less than one -tenths of the

d-c voltage, the signal-to-distortion ratio can be maintained at 50 db

or more. (The signal-to-distortion ratio is the ratio in db of the desired

signal to the largest distortion product.) As the power levels in the

transmitter increase, class AB amplifiers are used since class A

amplifiers are not practical at high power. Efficiencies of 55-70% at

full output can be obtained with class AB amplifiers. Recent power

amplifier developments permit adjacent channel operation, using power

amplifiers with signal-to-distortion ratios of from 35 to 40 db. By

using rf feedback and envelope distortion cancelling techniques, ratios

approaching 50 db have been achieved with high-frequency 20 -kw peak

envelope power amplifiers.

The dynamic regulation of the power supplies become important

when using class AB amplifiers. When the load on an unregulated

supply is suddenly increased, there is an interval during which the

only available energy is that stored in the output filter capacitor. Since

the current cannot change rapidly through the power supply filter choke,

there may be a momentary drop in the output voltage which may be

longer in duration than the modulation peak causing distortion. This

behavior will not be evident on a d-c meter but can be observed on an
•72-

oscilloscope . In class A operation, or in linear klystron amplifiers,

this requirement on the power supply is not as rigorous since the load

current is constant at all times. In class AB operation, plate current

is drawn only as the modulation is applied and will vary from a small

no -signal current to a large value on modulation peaks.

a. Distortion

Two principal causes of distortion in the rf power amplifier

are: grid current loading and non-linearity of the amplifier tube.

When grid current is drawn in class AB operation, the effective

impedance of the previous stage, the driver, changes in accordance

with the amount of grid current. This is equivalent to imposing a varying load on the previous stage. If distortion is to be avoided, the

regulation of the previous stage, the driver, must be excellent. The

driver must be capable of maintaining the waveform under conditions

of varying load. The usual method used to provide better regulation

consists of adding fixed resistance across the grid circuit of the driven

stage, thus presenting a load to the previous stage that will be modified

only slightly when grid current flows. Also, it is desirable that the

grid circuit of the class AB circuit be high C; this improves regulation

and, in addition, simplifies the coupling from the previous stage. A

stable bias supply is also required, since it is important that the bias

remain constant and independent of grid current flow.

The non-linear characteristics of the amplifier tube generate

distortion products that can be derived from the dynamic characteristics

of the amplifier tube. The shape of this curve, the choice of the

operating point, and the level of excitation will determine the amount

of distortion which will be produced by the tube.

6.5. Regulation of the Output Power

The loading of a multichannel SSB circuit depends upon the

traffic on the individual incoming channels. Since not all voice channels

will be busy at all times, it is desirable to pass the benefits of the full

power capabilities of the system to the channels in use. To allow full

utilization of the transmitter output capabilities, the output signal is
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sampled and applied to two detectors, a peak detector and an rms

detector, whose outputs are fed back as AGC to the rf amplifiers in

the exciter section of the transmitter. The rms detector circuit monitors the effective output of the power amplifier and limits it to a preset

level while the peak detector limits the peak power output of the final

amplifier.

Figure 17 shows a block diagram of an output power regulator.

A diode power detector reproduces the envelopes of a sample of the

rf output of the power amplifier. The peak value of the envelope is

measured by a peak detector. If the level of the input signal to the

power amplifier is sufficient to drive the output of the final amplifier

to saturation, the peak of the envelope will have a certain maximum

value. A certain fraction of this peak provides a reference voltage to

one input of the differential amplifier, while the entire envelope is fed

to the other input. The diode clippers and low-pass filter produce a voltage proportional to the percentage of time the envelope exceeds the

preset fraction of the peak envelope. The low-pass filter also determines the response characteristics of the regulator. The output of the

filter is amplified by another differential amplifier which has a reference voltage on one input. The output of this amplifier is a negative

voltage which controls the gain of one of the amplifiers in the exciter

of the transmitter. The pilot-level control circuit allows the power

amplifier output to be held at any desired level when no channels are

in use. A transmitter is usually considered lully loaded when its peak

power capability is being exceeded 1% of the time. The distribution of

the signal amplitudes will depend on the number of channels in use and

the type of information on the channels. For example, with unprocessed

voice, 1% peaks will approach 8.2 db as a limit above the average power

as the number of voice channels increase, the figure 8.Z db being obtained

after four voice channels have been combined for the composite signal.

6.6. Intermodulation Distortion

The limiting factor in power output capability of the single -sideband transmitter is intermodulation distortion generated by the nonlinear

characteristics of the power amplifier. This distortion will increase

as power output increases and will appear as splatter or crosstalk in

and around the transmitter spectrum.
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a. Two-Tone Test

Two Jest tones of equal amplitude have become a standard test

for intermodulation distortion. One tone is insufficient to produce

inter modulation while more than two tones produce so many intermodulation products that analysis becomes impractical. Tones of equal

amplitude place more demanding requirements on the system than is

likely to be encountered in normal use.

The idealized spectrum for a two-tone single sideband signal

will consist of three frequencies: the suppressed carrier and the two

tones translated to the desired frequency about the carrier. In practical

circuits there are new frequencies generated by the nonlinearities in

the amplifier. The frequencies not eliminated by the selective circuits

of the transmitter are the different frequencies of odd order. The frequencies of these spurious signals are of the form, nfj - (n - 1) f?

and nf£ - (n - 1) i\, where fi and f^ are the frequencies of the two test

tones and where n + (n - 1) is the order of the product or the order of

curvature causing the product. It can be seen that many of these products will fall within the pass band of the transmitter and will be spaced

along the passband by the difference between the frequencies of the two

test signals as shown in figure 18.

In the two-tone method of measuring intermodulation distortion,

it will be these spurious signal power levels which will be measured in

comparison to the amplitude of one of the test tones at the transmitter

output. The signal-to-distortion ratio then is defined as the ratio of

either of the two desired test tones to the largestundesired product.

This ratio is usually expressed in db. The third-order intermodulation

products should be the largest unless unusual cancellation occurs. The

higher-order products should become progressively smaller.

When two sinusoidal voltages of equal amplitude but unrelated

in phase are applied to an SSB transmitter, the peak envelope power

(PEP) will be 6 db greater than that experienced with a single tone.

(PEP is the average power of the combined signal measured over one

rf cycle.) The average power dissipated by the load is half the PEP

when the test signal is composed of two tones of equal amplitude. This

neglects the vestigal carrier power which is very small. (If the carrier

is suppressed 20 db, then the power in the carrier is only 1% of the

average power in one tone.)
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INTERMODULATION PRODUCTS IN A

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THIRD-ORDER PRODUCTS

FIFTH-ORDER PRODUCTS

SEVENTH-ORDER PRODUCTS

FREQUENCY

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•79-

Any two frequencies will serve for this test; however, a 3-to-5

frequency ratio is often used as a suitable ratio to alleviate some

troublesome problems occurring with many other ratios. Care should

be exercised in the selection of frequencies so that:

(1) The frequency spacing is sufficient --harmonics,

and the sum and difference frequencies do not

interfere with the measurement.

(2) The frequency spacing is not so small that difficulty

will arise in the separation of components for

measurement.

(3) The frequency spacing is not so large that most of

the distortion products will fall outside of the bandpass. This situation will bear no resemblance to

actual operation.

Figure 19 is a block diagram of the equipment configuration for

the two-tone test of inter modulation distortion.

b. Noise -Loading Test

Although the two-tone test for the measurement of intermodulation distortion is very versatile, measurements using Gaussian noise

as the test signal more nearly represent the typical complex signal

actually transmitted. As shown in figure 20, a transmitter loaded with

noise over a discrete bandwidth B will have third-order intermodulation products that appear in a band equal to three times the desired

bandwidth with the same center frequency. The fifth -order inter modulation products will fall inside a bandwidth equal to five times the

desired bandwidth and have the same center frequency. The seventhorder intermodulation products will fall inside a bandwidth seven times

that of the desired bandwidth and so on. The amplitudes of the products are usually in approximately inverse proprotion to the order of

the product. By using results of two-tone test an approximate plot of

the shape of the curves describing the amplitudes of the products may

be predicted.
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81-

Using Gaussian noise as the test signal requires that the intermodulation distortion ratio be defined for equivalent bandwidths, that

is, the signal-to-distortion power ratio, expressed in db, becomes the

ratio of the desired noise sampled over a given bandwidth to the spurious

noise in an equivalent bandwidth adjacent to the noise -loaded band.

Figure 21 shows a block diagram of a typical fixed frequency

noise -loaded intermodulation test described by Icenbice and Fellhauer

[ 1956] for a system having a baseband bandwidth of 12 to 112 kc/s and

is directly applicable to single -sideband systems with other basebands

by proper selection of filters.

If random noise is fed to the transmitter through a bandpass

filter which passes equally all noise frequencies in the band to be tested

except the low and high channel, the noise can equally load all but a few kilocycles per second of the transmission band to any degree of

modulation desired. Three bandpass filters with equal bandwidth and

insertion loss are used at the detection end of the system. Care should

be exercised in the selection of the bandpass filters. The skirts of

the distortion measuring filters should not overlap the skirts of the

noise -loaded band so that an appreciable amount of noise energy will

be injected directly into the measuring filter. If the overlap occurs

at a point where the measuring filter is 60 db down from its peak, then

little error will occur in distortion measurements as low as 50 db.

The amount of residual noise can be measured by injecting the

noise signal directly into the filter and measuring its output.

One bandpass filter is chosen near the center of the noise passband for a reference signal, and the other two filters are selected to

pass the spurious intermodulation products on the low and high side of

the band-limited noise. The noise is measured across a load resistor

with a true rms voltmeter through the reference filter. Once the reference level is established, the other two filters can be switched separately into the true rms voltmeter load circuit, and their level in db

below the reference measurement is taken. The two levels in db below

the reference represents the low-frequency and high-frequency intermodulation distortion generated in the loaded system.
-82-

A receiver operating at the transmitter output frequency is

used for detection of the signal. A sample of the transmitter output

is taken using a directional coupler. This signal may require further

attenuation to avoid overloading of the receiver or detector. The output of the receiver or detector is then fed to the filters. Impedance

matching must be carefully observed between receiver and filters.

7. KLYSTRON AMPLIFIERS

The klystron amplifier is particularly well suited to long distance communications circuits where high gain and high power are the

principal requirements. In addition, such factors as bandwidth, circuit

simplicity, and ease of adjustment all combine to render this type of

tube superior to conventional three- or four -element tubes.

7.1. Power Output Efficiency

The power output of a klystron is coupled from the output cavity

of the tube into an unbalanced coaxial transmission line or waveguide

by means of either a coupling loop or capacitive probe or, in some

cases, a combination of both. Usually, in the latter case, the coupling

probe consists of an open-end loop adjusted so that the capacity between

the open end of the loop and the wall of the cavity is sufficient to resonate the output coupling circuit. In the case of external type cavities,

care should be taken to be sure the output coupling probe is not damaged

or deformed prior to its installation.

A curve of power output when plotted against rf power input is a Bessel function of the first order and the first kind. Since the first

part of this curve is practically linear, the klystron can be used as a

linear modulated amplifier in single -sideband transmitters. Under

these conditions, operation of the tube must be limited to the linear

portion of the Bessel curve in order to prevent modulation distortion.

If this distortion is to be kept at an acceptable level for a multichannel

system, linearity should be maintained to within about 1%. This limitation reduces the peak power output of the tube for SSB service to approxi

mately 80% of its saturated output capabilities. When speaking of

klystrons, the term "saturated output" is the maximum power output
-83-

POWER OUTPUT AS A FUNCTION OF DRIVING POWER

KLYSTRON 3K 20,000 LK

MIDDLE CAVITY DETUNED TO f + f AND ALL OTHER CAVITIES TUNED TO f

r>

Q.h-Z>o

a:UJo

0.

Z>UJ

V)

z>

f + 9 Mc

f +6 Mc

f + 3 Mc

(b)

10 20 30 RF DRIVING POWER

40 50

Figure ZZ
-84-

which can be obtained from a tube for any given beam voltage and

current. Figure 22 shows the relationship between useful power output and excitation for a typical tube. The reader is referred to articles

by Bruene [ 1956] and Icenbice and Fellhauer [ 1956] for additional

information on klystron linearity.

The efficiency of a large klystron may range from about 15%

to over 50% depending upon bandwidth requirements and the system in

which it is used.

When used as an amplifier in an FM transmitter, the average

carrier output level will be confined to the region around the peak of

the curves. The actual departure on either side of the saturation peak

will depend upon the required bandwidth. For this type of operation,

the tube conversion efficiency can be quite high since the average power

output level is high.

When the conventional type of klystron tube is used as a modulated linear amplifier in a single sideband system, its efficiency is

quite low. If its average power output is measured by the accepted

method of applying two sinusoidal audio voltages of equal amplitude

simultaneously to the balanced modulator, the measured output will

equal 50% of the peak envelope power. If now all factors are considered, the expected overall efficiency for SSB service would be:

Average = (40%) x (80%) x (50%) = 16% of beam

measured efficiency peak ratio aver- power input

output of tube at excursion age power

saturation limitation to peak

level to maintain envelope

linearity power, under

conditions

specified

Actually, in a multichannel voice communication system, the

ratio of PEP to average power may be more on the order of 6 or 7 to 1 rather than 2 to 1 which will further reduce the overall long-term

average conversion efficiency. Since this is the efficiency of the amplifier only, and since additional power is required to operate the exciter,
-85-

>

X

tl

i n

J,

,xi h h

r^TJT U U'U

o

tro

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tf UJ

o

o

C/) Z

o

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0-
-86-

final amplifier filament or bombarder supply, heat exchanger and

losses within the high voltage beam supply, such as a transmitter could

conceivably have an overall efficiency of 5%.

A number of ideas have been considered for improving the

efficiency of a klystron when used for SSB service. The first is that

of using a special connection for the collector known as the depressed

collector. This is shown in figure 23 (B). The objective is to reduce

the collector potential and thereby lower the energy of the electron

beam by the decelerating action of the field at the collector gap. The

reduction of collector potential below that of the beam voltage is limited

by the allowable increase in drift tube current. A further refinement

of this idea is demonstrated in Eimac's type X625B klystron where

the collector is segmented. This is shown in the drawing of figure

23(C). Each segment is at a different potential with minimum collector

voltage at the collector end of the tube. Such an arrangement will

reduce the beam power input to the tube, thereby improving its conversion efficiency. The idea of the depressed collector has proven

quite effective, particularly in low-powered klystrons. In larger tubes

where the beam potential is quite high, the depressed collector may

not be as effective due to the high velocity of the electrons.

Other schemes for achieving high efficiencies in SSB service

have been investigated. Those having the most promise were conducted

with tubes which contained a modulating anode. Such arragnements

are not yet being employed in present day commercial equipment.

Efficiency is an important consideration. For example, in FM

service, the Varian type VA 842 tube will provide an average power

output of 75 kw over a bandwidth of 3 Mc/s at an efficiency of approximately 43%. This amounts to an input of about 175 kw. It should be

pointed out that only the input to the final tube is considered and that

other power requirements will raise the primary power needed to well

over 175 kw. Such a transmitter would require a heat exchanger

capable of dissipating the full 175 kw of power since, in the event excitation is removed, the full beam power input to the tube must be dissipated by the collector.
-87-

_ioooo<\J

roO

crhy

LU

Li. O>Oz

UJo

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A0N3I0IJJ3
88-

It will be noted from the curves of figure 24 that the efficiencyarid power output of a klystron are functions of beam voltage. There

is an optimum voltage for best efficiency and power output for a given

tube since voltage determines the velocity of the electron bunches

through the drift tubes and cavities. Because the bunching action of

the electrons takes time, for a given frequency, there is an optimum

balance between the velocity of the electron bunches and the distance

which they must travel if they are to give up their energy in the output

cavity at the optimum moment.

It will also be noted from figure 22 that maximum output and

efficiency do not occur under the synchronously tuned condition but

when the middle cavity is detuned to the high side of resonance.

The efficiency of a klystron is affected to some extent by the

electron beam configuration which is controlled by adjustment of the

magnetic focus coil currents. Slight adjustment of the individual coil

currents will affect both the output and tube body current. Improper

adjustment of the beam focus will cause excessive body current and

reduced output. This is due to the fact that many electrons are allowed

to leave the confinements of the main beam and strike the body of the

tube, thereby never reaching the output cavity and collector.

The beam power input to a klystron is constant regardless of

whether it is operating as a linear amplifier in a single -sideband

transmitter or as an amplifier for an FM transmitter. For this reason,

regulation of the d-c beam power supply is not at all critical. In contrast to this, if a conventional three- or four-element tube is used as a linear amplifier in SSB service, regulation of the plate supply must be

very good to prevent distortion on modulation peaks.

7.2. Bandwidth

The bandwidth of a klystron is usually specified under one of

two headings, namely, "synchronously tuned" or "stagger tuned." The

term "synchronously tuned" refers to the condition where all cavities

are tuned or resonated at the driven frequency. The term "stagger

tuned" describes the method whereby the cavities are not all resonated

at the operating frequency.
-89-

HYBRID NETWORK FOR PARALLELING THE

OUTPUT OF TWO TRANSMITTERS

TRANSMITTER #

ANTENNA

z =50n

Z = 50 a

ir

-/-A

TRANSMITTER #2

TUNING ADJUSTMENT

Z n =50n

Z = 50ft

MATCHED LOAD(L)

Figure 25
-90-

Where the bandwidth requirements do not exceed two or three

Mc/s, the most common and efficient means of achieving this is to

detune the center cavity, or cavities, slightly to the high side of

resonance. The curve of figure Z2showsthat such an adjustment will

increase the bandwidth and at the same time provide more useful

power output at slightly less gain. In the event this technique will

not provide adequate bandwidth, a further broadening of the passband

can be had by loading the center cavity by means of an external resistance. This is not always practical since the technique requires that

the cavity be provided with a coupling probe.

Another effective means of increasing the passband of the tube

is that of detuning the input cavity to the low-frequency side of resonance and, when necessary, loading this circuit by means of an

external resistance. This method should not be used unless the first

suggested method proves inadequate. Any detuning or loaded operation

will increase the excitation requirements. Such techniques will usually

serve to increase the bandwidth substantially.

7.3. Gain

In general, the power gain of a klystron amplifier is quite good,

ranging between 10 and about 60 db. Gain is dependent upon the number

of cavities contained within the tube, how they are tuned, and whether

they are resistance loaded for increased bandwidth. Most tubes used

in forward scatter communications transmitters contain three cavities

which have power gains ranging between 25 and 40 db even under broad

banded operation.

8. POWER COMBINERS FOR TRANSMITTERS

One of the first requirements of a transmitter in a forward

scatter communications system is that it be capable of generating the

necessary power to assure, for a given percentage of time, a predetermined grade of service at the distant receiving terminal. Such a prerequisite can be met either by use of a single transmitter large

enough to supply the full power requirement or by two or more similar

transmitters, each capable of developing its share of the required

power. In the latter case the output of the transmitters must be combined by means of a hybrid network shown in figure 25 and similar to

that described by Tyminski and Hylas [ 195 3] .
-91-

The hybrid ring network is an rf coaxial containing three equal

arms of approximately one -quarter wavelength each and a fourth arm

approximately three-quarters of a wave long. The latter usually contains an adjustable phasing section for use in balancing the bridge at

the operating frequency. The four junctions of the bridge are terminated as shown. The matched load L should be capable of dissipating the

full output of one transmitter. The characteristic impedance of the

four arms of the bridge is usually 70 ohms where 50 -ohm terminations

are employed. This provides a suitable load impedance for the two

transmitters

If it is assumed that the bridge is in balance and that the power

output of the two transmitters is equal and in phase at their respective

bridge junctions, the combined output from the two transmitters, less

slight losses in the bridge elements, will be dissipated in the antenna

since voltages at the antenna junction of the bridge are in phase.

Because of the added half -wave of line in one leg of the bridge between

the transmitters and the load L, phase cancellation occurs at that

junction. Consequently there is no power dissipated in L. Any power

appearing at L would result from unequal power levels or phase angles

at the two transmitter junctions of the bridge or from an improperly

balanced bridge.

Failure of either transmitter will result in a 6-db reduction in

power at the antenna. Half of the output of the operating transmitter

will be expended in load L since phase cancellation no longer occurs

across its junction terminals. (A 3-db loss in power due to the

failure of one transmitter plus an added 3-db loss due to half of that

transmitter's power output being dissipated by load L accounts for the

6 db.)

In practice, a means is provided whereby the hybrid ring can

be removed from the circuit. In the event one transmitter fails, the

operator can choose a period of low traffic to switch the transmitter

to the termination L for trouble -shooting while the operating transmitter can be switched directly to the antenna, thereby raising the

power level at the antenna by 3 db over the loss encountered if the

hybrid ring remained in the circuit.
-92-

8.1. Tuning Procedure

If the combiner is to function properly and efficiently it is

important that the bridge be carefully balanced at the operating frequency.

This may have been done at the factory. If so, it is probable that the

three-quarter wave element cannot be adjusted in the field. If this is

not the case, and the element length is variable, the following procedure

can be followed:

(1) T\ and T% should be disconnected at their respective

bridge junction and the junctions left unterminated.

(2) A small amount of power at the operating frequency

is supplied to the bridge at the antenna junction.

(3) A voltmeter or power meter is connected to the

terminal load L.

(4) The variable arm of the bridge is then adjusted for

minimum voltage or power across load L. This

will approach zero as the bridge is brought into

balance

.

Connections are then restored to normal following a check of

the bridge balance. If the transmitter characteristics are similar the

bridge will remain in balance with the transmitters connected for

normal operation.

There may or may not be provisions for adjusting the phase of

one transmitter with respect to the other. In some cases the phase

characteristics of the two transmitters are so nearly alike that a control is considered unnecessary. Where a control is provided, the

transmitter output levels should be equalized and the phase -matching

section adjusted for minimum power at the termination L. By making

adjustments to the individual power levels and phase control, the output can be reduced to practically zero.

8.2. Circuit Reliability

When considering the reliability of a system, there are several

obvious advantages to be gained by using the combined output of two

smaller transmitters rather than one large transmitter.
-93

First, if the power requirement is substantial, the reliability

of large amplifier tubes and their necessary high-voltage power

supplies and components is much less than for smaller tubes and

correspondingly smaller components.

Second, should one transmitter fail, the circuit is not completely

interrupted as would be the case where one larger transmitter was

involved. As was pointed out earlier, the loss of one transmitter would

reduce the transmitted power by 6 db which may or may not seriously

impair circuit performance, depending on circuit loading and propagation conditions. This loss in output could be reduced to 3 db by

removing the power combiner from the circuit.

Another point of interest is the possibility that during periods

of high fields which occur most frequently during summer months, it would be possible to use a single transmitter with the second transmitter serving as a standby. This will reduce the primary power

requirements below that which would be required by operating a single

large tube at reduced plate or beam voltage.

This method of combining the power output of two transmitters

can be extended to four transmitters if the requirements warrant it.

Such an arrangement would contain three hybrid rings similar to that

shown in figure 25 .

9. THE RECEIVER

Many of the aspects of performance with regard to the receiver

have been considered by Florman and Tary [ 1962] . It is recommended

that the information contained in this report be used in conjunction with

the above reference since a complete critique of the performance of

the receiver demands a consideration of the standards given therein.

The typical communications receiver may be viewed as an instrument composed of a variety of basic sections so interrelated as to perform an overall reception-detection function. These basic sections of

the receiver differ considerably in components, circuitry, and frequency

of operation. Therefore, the overall performance characteristics of

the whole receiver are directly dependent upon the performance characteristics of the individual basic sections.
-94-

00

CO

CO

CO

z>CO

orLd>

Ld

U_

U_

LdO

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CO

Ld

orx

iCOQ

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CD

CJ

<L> i_ <

n/s
-95

It is well known that the ultimate usefulness of the receiver is

limited by its ability to discriminate between the weakest signals which

must be detected and noise. Thus, one of the most important parameters which can be determined for the individual basic sections of the

receiver is the noise figure, where it expresses the relative ability

of the receiver to amplify a weak signal without introducing appreciable

noise. This, in turn, is related to the threshold effect in FM systems.

A graphical illustration of the threshold effect in FM systems

as contrasted to SSB is shown in figure 26. As illustrated, the

weakest signal in an FM system produces nothing but noise in the

receiver output. As the signal level is raised, the output continues

to be noise until a transition point or threshold is reached. At or above this level, the signal becomes available at a fairly good signalto-noise ratio, while signals below this level are unusable. This level

is dependent on the noise figure and bandwidth of the particular receiver

involved. In any typical tropospheric scatter communications system,

the threshold level increases as the number of channels increases.

It has been demonstrated that scatter signals are reliable

since they are always present. However, the amplitude of the received

signal is constantly fluctuating over a fairly large range, the amount

of fluctuation being dependent upon the particular path and carrier frequency. When FM is used over a scatter path, information is completely lost at the point at which the signal fades below the threshold;

thus, the system must be operated with a minimum received median

signal sufficiently above the threshold so that information will not be

lost during deep fades.

When diversity signals are continuously combined, whether in

FM or SSB, according to the proper operating mode of the combining

method used, the signal-to-noise ratio of the combined signal will be

better than that of the best signal. A combination of four signals all

having the same signal-to-noise may result in a combined signal-tonoise ratio 6 db better than that of any one signal by itself. By controlling the amount of any given signal that is allowed through its

combiner in accordance with its own signal -to -noise ratio, optimum

combination can at all times be achieved.
•96

9.1. The rf Amplifier

Almost all rf voltage amplifiers are operated under class A

conditions. The major factors on which voltage gain per stage are

dependent are the specific characteristics of the tube used, the input

and output impedance, and the bandwidth to which the stage is designed.

In some circuits, noise figures also must be considered as a limiting

factor in the determination of voltage gain. However, beyond the first or second stage in cascade amplifiers, the noise is usually low enough

in relation to the signal amplitude to be neglected.

At frequencies up to 250 Mc/s, circuits similar to those used

at lower frequencies are practical. The voltage gain in amplifiers

with a bandwidth of 2 or 3 Mc/s will range from 40 to 50 at 30 Mc/s

and 8 to 10 at 215 Mc/s Triodes can be used successfully in this

frequency range, but it is more common to use pentodes such as the

6AK5 or 6 CB 6 . The voltage gain of a triode is considerably lower

than a pentode, making it necessary to use a greater number of amplifier stages to obtain a given total gain. A factor limiting the use of

pentodes at high frequencies is their noise figure. In general, pentodes

operating at frequencies up to 250 Mc/s give greater gain than triodes.

Because of their poor noise figure, pentodes are not used in the upper

part of this frequency range where the noise level is approximately

that of the desired signal.

In the frequency range from 300 Mc/s to 1000 Mc/s, the use of

triodes and distributed -property circuit element becomes essential.

Reasonably good gain and noise figure can be obtained with triodes.

Above 500 Mc/s, concentric -line circuits and special lighthouse,

rocket, pencil, or disk-seal planar type triodes are used to obtain

voltage gain with an acceptable noise figure. One of the features of

the concentric -line circuit is the ease with which a shielding and

isolating effect can be obtained in grounded grid configurations. No

practical pentodes have yet been developed for use as voltage amplifiers

in such circuits. The voltage gain expected with triodes in circuits

containing concentric -line sections usually does not exceed 3 to 12.

Although higher gain can be obtained at the lower end of the frequency

range, the gain declines rapidly as the frequency increases because

of the lowered circuit Q and decreasing tube efficiency.
97

There are not many electron tubes that will operate satisfactorily at 1000 Mc/s and above as rf amplifiers. Therefore, the use

of rf pre-selection and a crystal mixer has been commonly employed.

The rf pre-selector is a tunable filter with low insertion loss to the

operating frequency and high loss at unde sired frequencies.

a. Noise in the rf Amplifier

The limiting factor in the operation of rf amplifiers, especially

at frequencies above 300 Mc/s, is the noise generated by the amplifier.

Consequently, low noise devices such as parametric amplifiers and

masers are being considered as rf amplifiers. Since the significant

part of the noise generated in a cascaded operation is contributed by

the first several stages, the use of such low noise devices is equivalent

to improving the sensitivity of the receiver, thus permitting the detection of extremely weak signals.

Probably the only parameters of significance affecting the performance of rf amplifiers are the noise figure and gain. Throughout

this report all discussion relating to the noise figure assumes that the

input noise is equal to KT B and that this input noise is the only noise

contributed by the testing instrument or device --where the testing

instrument output impedance is at room temperature (T = 290°K).

Although all parts of the receiver contribute noise to the output,

the initial stages are the chief contributors. Unless the mixers and

IF amplifiers have exceptionally high noise figures, the rf amplifier

can be considered to be the determining factor. This is clearly indicated by the following expression for the total noise figure of multistate networks connected in cascade:

F, - 1 F - 1 F - 1 IA x ^ ^ 2 3 n (41) F, = F + + + + — v ; l---n 1 G. G, G G, G ---G

1 1 Z 1 Z n - 1

where Fj represents the noise figure of the first stage,

F^ the second stage, etc.;

Gj represents the gain of the first stage, and

G£ the gain of the second stage, etc.
-98-

Thus it is evident from the expression that after any high-gain

network the overall noise figure is not influenced to a great extent byadditional networks even though their individual noise figures are

relatively high.

Consequently, for this measurement it is sometimes assumed

that the rf amplifier is the major contributor and that the noise figure

reflects the noise added by the amplifier alone. Such an approximation

may not be valid, especially where parametric amplifiers and masers

are used, since their contributions to the noise of the overall receiver

are very small with respect to the mixer and the IF amplifier.

9.2. Noise Figure Measurement

Utilizing the concept of available power, the noise figure F of a network is defined as the ratio of the available signal power at the

input to kTB, divided by the available signal-to-noise ratio at the output, which, written in equation form, is

S./kTB

1S /N

o o

(42)

where S = available signal power at output,

N = available noise power at output,

o

S. = available signal power at input,

kTB = available noise power of signal generator.

Simply stated, the noise figure is the ratio of the signal-to-noise

power at the input divided by the signal-to-noise power ratio at the

output, as given by Wind and Rapaport [ 1958] . Thus, if the network

were ideal, no noise would be added and the output noise would be the

input noise from the signal generator increased only by the gain of

the device, resulting in a noise figure of 1 and a perfect receiver

since we now have the same available signal-to-noise ratio at the

output as we have at the input.
-99-

Since the noise power per cycle available from a source at

absolute temperature T is kT, where k is Boltzmann's constant, the

noise power NQ

, available at the output of an ideal receiver, is

N = kT \ G(f) df (43) ° J

where G(f) = the gain function of frequency f.

The noise figure can be expressed as the power ratio in db of

the actual output noise power N available to that which would be available if the amplifier merely amplified the available thermal noise of

the source at a reference temperature. This can be expressed by the

following equation:

° kT \ G(f) df

J

which, converted to db, is F = 10 log, _ N/N . 1 (J o The reference source temperature T is taken equal to 290°

Kelvin (room temperature), and k is equal to 1 . 38 x 10~23. Therefore

kT = 4.00 x 10" watts per cycle of bandwidth. If a receiver is

operated with a source at this temperature, and if thermal noise alone

corrupts the signal available from the source, then the noise figure

gives directly the degradation in signal-to-noise ratio produced by

excess noise in the receiver.

For receivers using conventional front ends, the measurement

is conducted using the entire receiver. The output is measured either

immediately before or immediately after the detector. Since power is

to be measured, a square-law detector is advantageous. In the absence

of a square -law or approximately square -law detector, the measurement can be made with a precision 3-db attenuator between the IF and

the detector.
-100-

a. Signal Generator Method

The noise figure of a receiver may be measured using a conventional signal generator capable of delivering a known variable

amount of power to the input of the receiver. It is important that the

output impedance of the source generator be the same as the impedance

of the transmission line from the antenna.

With the signal generator connected to the input terminals of

the receiver and the power output at zero, the total noise power developed by the receiver will be

N = FkT \ G(f) df (45)

J

as measured by a square -law detector connected to the output terminals

of the IF amplifier. A square -law detector is defined as a detector in

which the output voltage is proportional to the rf power or to the square

of the rf voltage applied at the input.

The signal generator is now tuned to the frequency f , and the

output available power level, S is adjusted until the total power output

of the receiver P is equal to 2N. This is accomplished by doubling

the initial reading of the square -law detector. In the absence of a square -law detector, the measurement can be accomplished using a 3-db precision attenuator between the IF amplifier and the detector.

The initial power measurement is made without the attenuator. The

second measurement is made with the attenuator between the IF amplifier and the detector, and the initial power level at the detector is

restored by increasing the input power.

In equation form this can be represented by

P = FkT \ G(f) df + SG (f ) (46)

where P = total output power,

F = noise figure,

k = Boltzmann's constant,

T = source temperature,

G(fo) = receiver power gain,

S = available signal power from signal generator.
101-

By adjusting the power level such that P = 2N, where N is defined by

(45),

FkT \ G(f) df = SG (f ) (47)

which reduces to

F = T=—

kfB < 48)

1! w L

G(f)d£ G< f

0< "0

since

oo

1 I B = \ G(f) df = effective noise bandwidth. (49) G( V J

Thus by (48) we can measure the noise figure of a receiver and

determine the value of B in (49) by measuring the power gain as a function of frequency and integrating the curve graphically.

Extreme care must be exercised in the selection of a signal

generator to insure that the available power output S is an accurate

value at the low levels required. However, with the advent of improved

circuitry and reliable power standards, such generators are available

through commercial manufacturers

b. Noise -Generator Method

The signal generator method of noise -figure measurement is

considered to be reliable and is recommended as the most accurate

method. However, it is time consuming, and other methods are availabel which should suffice to determine the noise figure for circuit

operation requirements.

Essentially, this method consists of a comparison of normal

noise with the noise occuring when the generator is artificially changed

to a new temperature.
-102-

A temperature -limited diode is employed for this purpose at

VHF and UHF frequencies, while the argon discharge tube in a waveguide is used at microwave frequencies. The requirements of the

noise source are that its noise spectrum is flat with frequency over

the passband of the receiver and that a known amount of noise power

is generated. The latter is accomplished by associated circuitry.

Therefore, the noise power output of the receiver Nj, with the

noise source off, and the noise power output with the source on, N£>

are used to determine the noise figure.

Allowing for the contribution due to noise sources in the receiver

alone which add to the total available output noise, (44) can be rewritten

in the form

p » n oo N = kT \ G(f) df + (F - 1) kT \ G(f) df (50)

1 J J

where the first term is the amplified source noise and the second term

is the amplified excess receiver noise. If X is equal to the ratio of the

available power per cycle from the noise source to kT, then, when the

noise source is turned on, the following equation results:

p oo p oo N = X kt \ G(f) df + (F - 1) kT \ G (f) df (51)

Z J J

This is represented in ratio form

N

2 X + F - 1 , X - 1 N

i which reduces to

1 + —=— (52)

2 -1 N

l

It is evident that this is a much simpler relationship to determine than the values needed for the signal generator method.
-103-

Here only the value of X for the source and the observed output power ratio N^/Nj are needed.

Precaution is necessary in two areas, namely, the noise source

must present nearly the same impedance to the receiver when turned

on or off, and the image frequency rejection of the receiver must be

adequate.

The impedance must be matched closely; otherwise variations

of receiver output noise with source impedance will affect N2/N1 .

Most present-day superheterodyne receivers employ preselector cavities or bandpass filters to reject the unwanted energy at

the image frequency. However, if a receiver is used where precautions are not taken to reject the response at the image frequency,

such as wide -band radar receiver, the measurement of the noise figure

obtained by the noise diode device may be 3 db lower than that obtained

by the signal-generator method. To avoid this condition it is recommended that a pre-selector cavity or bandpass filter be inserted at

the receiver input to attenuate the response at the image frequency.

Thus for this measurement the noise generator is connected to

the receiver input and a suitable output indicator, such as a true rms

voltmeter, is used at the IF output. The rms voltmeter reading is

obtained with the noise source turned off. The noise source is turned

on and increased until the voltmeter reading is increased by 3 db.

The noise output necessary to increase the rms voltmeter reading by

3 db is a measure of the noise figure of the receiver. Noise generators

are available with meters calibrated directly in db of noise power output.

Basically, the above discussion is related to the work by Friis

[ 1944] and Oliver [ 1958] . Further work has been published by Haus

and Adler [ 195 7] and Brodzinsky and MacPherson [ 1959] with relation

to the problems presented by negative resistance devices and low noise

MASER's, but such studies are considered to be beyond the scope of

this report.
-104-

9.3. The Mixer

Since all receivers used in either FM or SSB are usually of

the heterodyning type, one or more mixers will be encountered. The

mixer or converter may be defined as the device which converts the

rf signal frequency to the intermediate frequency. The mixer combines the input signal with a local oscillator signal to yield the IF.

At the lower frequencies tube -type mixers are used. At HF

a single tube can be used for both the oscillator and the mixer,

whereas at VHF such a technique is not practical due to the inefficiency

of the oscillator portion of such a converter. Above HF, especially

where frequency stability is required, a crystal oscillator plus multipliers are required to produce the local oscillator signal. Tubes are

used as mixers up to frequencies of 700 Mc/s. At frequencies above

700 Mc/s, crystal mixers are used since they have lower noise figures

than the tube type

.

The diode-, triode-, or pentode -type tubes are most often used

as mixers or converters at frequencies up to approximately 700 Mc/s.

The diode mixer gives noise figures which are appreciably

higher than those obtained with other types of tubes. However, the

simplicity of the circuitry has advantages, and the resulting noise

figure will be sufficiently good for many purposes. On particular disadvantage with the diode mixer is that, since the average impedance

is low, the local oscillator must furnish a considerable amount of

power which results in a problem of local oscillator stability and

possible unwanted interaction between the local oscillator and mixer.

Triode and pentode mixers will result in considerably better

gain and noise figures than the diode mixer. Essentially all of the

characteristics which apply to these tubes at VHF frequencies as conventional amplifiers will also apply for their operation as mixers.

The important difference is that the power gain and noise figure which

can be obtained from a given tube as a mixer can never be as good as

the power gain and noise figure of the same tube operating as an amplifier.

The output impedance is higher for the pentode mixer than for

the triode mixer, and consequently the maximum power gain of the

pentode mixer is higher than the maximum power gain of the triode mixer,
-105-

For these tube -type mixers, the problem of local oscillator

injection must be considered and is different for each type. In the

diode mixer optimum performance is obtained by biasing the tube

beyond cutoff and then using a large local oscillator signal to swing

the tube into the conducting region. For the triode and pentode mixers

the optimum local oscillator voltage on the input grid is about seventenths as large as the cutoff bias. For the triode mixer this operating

bias is usually obtained through a high-resistance grid leak. However,

if for any reason the local oscillator fails, excessive mixer current

will result, and damage may occur to the tube. In the pentode mixer

where the operating bias is obtained by a high-resistance grid leak, a screen-dropping resistor is used to prevent damage due to this

excessive mixer current if the local oscillator fails.

On parameter of interest especially from design considerations

is the conversion transconductance, which is comparable to the trans

conductance of a tube in the conventional sense. Conversion transconductance is defined

di

s

3i = change in plate current

3e = change in signal voltage

s

That is the change in IF current output for a change in input

signal voltage. If signal voltage is small and the local oscillator

voltage large, the conversion transconductance of the mixer will be

a function only of the local oscillator voltage.

a. Conversion Gain Measurement

Tube -type mixers are capable of conversion gains greater than

one, but crystal mixers have conversion gains less than one since no

amplification takes place in the crystal itself. The conversion gain or

loss is a function of local oscillator injection. For tube mixers, it is

difficult to specify the relationship between the conversion gain and the

local oscillator injection since it will differ for each type of tube used

as a mixer.
-106-

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-107-

The conversion gain is an important parameter in determining

the noise figure of a mixer. The measurement of the conversion gain

of tube -type mixers is a simple procedure requiring only a calibrated

rf signal input with a method of measuring the output IF current through

a resistive terminating load.

In a crystal mixer the conversion loss is a function of the local

oscillator power, measured in terms of the d-c crystal current. This

relationship is especially sensitive where the local oscillator power is

low. Consequently it is necessary that the proper level of excitation

be used. If the power level is considerably different from the recommended value, biasing will occur which will vitiate the measurement.

Table 4 should be consulted for the recommended local oscillator

excitation for silicon crystals. (Although germanium, crystals are

used for mixers, silicon is far superior. Noise figures differ by as much as 20 db between the two types.) The output impedance of the

crystal is another important characteristic. The crystal mixer should

be terminated in its characteristic impedance (sometimes called the

IF admittance). Table 4, page 109> includes the recommended value

of the terminating resistance.

The d-c incremental method of measuring the conversion loss

can be expressed as follows: an amplitude modulated signal from an

rf signal generator is supplied through a calibrated attenuator to the

crystal mixer. The attenuator must be matched to the crystal mixer.

The output of the signal generator is set to the proper power level as

measured with a bolometer bridge. The mixer is terminated with its

proper characteristic impedance in series with a milliammeter (see

figure 27). The input power is then varied a small amount, and the

resulting change in the output current is noted. The conversion loss

is calculated from the following expression:

(AP) 2

L

db= 101°g 10 2

< 58 > 2 P R (AI)

where

L nl = the conversion loss in db, db

AP = the change in the input power from the local oscillator,

A I = the change in crystal current,
-108-

P = initial power from the local oscillator (table 4),

R = the load resistance (table 4).

For example, assume

P =1 mw,

A P =0.1 mw,

R = 400 ohms,

A I =0.2 ma,

then L.,, = 5.06 db.

db

Table 4 contains the value to be expected from a number of

silicon diodes used as mixers. If conversion losses are in excess of

these values, that is, if the measured values are greater by more than

1 db from those in the table, the crystal should be replaced.

b. Noise Figure

Especially where a receiver is to be operated without rf amplification prior to the mixer, it is important to determine the effect of

the mixer on the overall noise figure. Where tube-type mixers are

used, the noise figure can be defined as

F2" * F = F. + —== (59)

1 G,

where

F = the best noise figure at the rf frequency,

F_ = the noise figure of the IF amplifier,

G = the conversion power gain of the mixer (less than one)

This relationship is valid exactly only for diode mixers. The

noise figure of receivers using triode and pentode mixers is also a function of the loading of the mixer. This expression, however, is a good approximation for any kind of tube -type mixer.
-109-

TABLE 4

Crystal Local Oscillator Terminating

Type Excitation Impedance

(milliwatts) (ohms)

Test Data

Max. Conv. At Test

Loss db Freq. (Mc/s)

s- Band (300 - 4000 Mc/s )

1N21 0.5 400 8.5 3060

1N21A 0.5 400 7.5 3060

1N21B 0.5 400 6.5 3060

1N21C 0.5 400 5.5 3060

X-Band (4--12 Gc/s with ±1.0 db nf)

1N23 1.0 400 10.0 9375

1N23A 1.0 400 8.0 9375

1N23B 1.0 400 6.5 9375

1N23C 1.0 400 6.0 9375

L-Band

1N25 1.25 200 8.0 1000

K-Band (16-25 Gc/s ± 1 . db nf)

1N26 1.0

1N26A 1.0

1N26B 1.0

500

500

500

8.5 23948

7.5 24000

7.5 24000

Ku-Band (7-20 Gc/s with ± 1 . db nf)

1N78 1.0

1N78A 1.0

1N78B 1.0

1N78C 1.0

500

500

500

500

7.5 16000

7.0 16000

6.5 16000

6.0 16000
•HOWhere a crystal mixer is used, the expression for the overall

noise figure involves the concept of noise temperature as follows:

t + t + F* - 1 F =

l—— (60)

where

= ratio of the effective noise temperature of the crystal

to the ambient temperature (assumes local oscillator

to be noiseless),

t

1 = the ratio of the increase of the effective noise temperature to the ambient temperature (assumes a practical

local oscillator with some noise),

1

F = the noise figure of the IF amplifier,

G = the conversion gain of the mixer (less than one).

The methods for measuring the noise figure of devices using

mixers as the front end is identical to that used in the preceding

section on the measurement of the noise figure of rf amplifier. A

pre -selector should be added prior to the mixer for image rejection.

It should be apparent that a receiver having a mixer with less-thanunit conversion gain as the front end is not efficient with regard to

optimum noise figures; the noise figure of the IF amplifier becomes

a significant contributor to the overall noise figure. Radiofrequency

amplifiers, especially of the low noise varieties, will offer significant

improvement in the noise figure, especially at UHF and above.

c. Excitation Requirements

The excitation requirements of a mixer are important. In

order that the mixer may work properly, it is necessary that ample

local oscillator power be available. However, too much local oscillator power can be harmful since the noise figure is not a linear

function of the local oscillator power. For example, in the case of

the crystal mixer, a minimum noise figure occurs where the crystal

current equals 0.3 to 0.5 ma in the general case. In general, if the

crystal current is maintained within these limits, the noise figure
Illwill tend to be optimum. Note that some compensation must be made

between the optimum noise figure and the optimum conversion loss.

However, the local oscillator should be capable of considerably more

power than is required to provide optimum mixer operation. This

permits more decoupling between local oscillator and the mixer,

providing increased local oscillator frequency stability.

9.4. The Local Oscillator

The local oscillator (LO) supplies the signal to convert the rf

signal frequency to the IF frequency. In some cases the frequency is

generated in a single stage. At the low frequencies the problem is

somewhat simple, and conventional negative grid tubes can be used.

Above 1000 Mc/s a lighthouse tube or a similar type is used, and above

4000 Mc/s reflex klystrons are in almost universal use. However, if

extreme frequency stability is required, the crystal oscillator is probably the best source of the primary frequency. Since the upper frequency limit of crystal oscillators is relatively low, multipliers are

almost always used with them to attain the desired frequency of the

local oscillator. Where crystal oscillators and multipliers are used,

the reader is referred to the section on FM transmitters for a consideration of frequency multipliers.

The frequency stability is probably the most important parameter

when considering the local oscillator. This is as true of the receiver

as it is of the transmitters, where tolerances are held close regardless

of the type of transmission. In normal AM reception the oscillator

may drift as much as several kc/s with little noticeable effect except

for a small decrease in the gain. The modulation intelligence will

remain the same because the sidebands still retain the same relationship to the carrier. In SSB transmission, however, the requirements

for frequency stability are somewhat stringent. It has been pointed

out that a 50 c/s difference between the transmitter and receiver

carrier can cause a loss in intelligibility, which implies a frequency

change no greater than 25 c/s at the receiver. This would imply a

frequency stability of the order of one part in 10° at 400 Mc/s.

Present FM systems can operate satisfactorily with stabilities of the

order of one part in 10".
-112-

If extremely close frequency tolerances are desired, a crystal

oscillator should be considered. Crystal oscillators using premium

components, good mechanical construction, and stable crystal ovens

with a high degree of temperature compensation can yield stabilities

of 5-8 parts in 10* per day. Such oscillators are commercially

available.

Even if reflex klystrons are used to supply the actual local

oscillator signal, a crystal oscillator can be used to control the frequency of the klystron. A highly stable oscillator will maintain

sufficient accuracy to satisfy the requirements of FM and conventional

AM. Only in the case of SSB is there a danger of lack of adequacy.

The use of a crystal oscillator also renders the system somewhat

inflexible as far as operating frequencies are concerned.

Many receivers are not fixed frequency and the first local

oscillator must track with the incoming signal. A highly stable variable oscillator must be used. Such a system may employ automatic

frequency control (AFC). High degree of stability is possible using

a good AFC circuit which is controlled by a pilot transmitted with the

signal. The advantage of AFC is that it can compensate for transmitter drift. Its disadvantage is that it depends on the existence of

the carrier at all times especially where a suppressed carrier is used.

If the carrier is absent in times of very low signal, a time constant

can be employed in the AFC circuit to eliminate, at least partially,

this disadvantage

.

9.5. Automatic Frequency Control (AFC)

Automatic frequency control is used to stabilize the frequency

of the receiver. Since the chief cause of frequency instability is that

attributable to the local oscillator, the control is usually accomplished

in terms of the control of the frequency of the local oscillator.

The most common method of achieving AFC is the difference

frequency method which utilizes the difference between the carrier and

the local oscillator frequencies to provide a correction signal to the

local oscillator thus maintaining a constant IF frequency. A loop is

completed between the output of a discriminator and the local oscillator. The frequency of the local oscillator is adjusted to maintain
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-114-

the frequency of the IF amplifier. The correction voltage is developed

when the change in the IF frequency is due to either the local oscillator or the transmitted carrier.

Figure 28 illustrates a typical AFC loop, which employs the frequency difference method. The output of the IF amplifier is applied to a discriminator, whose output becomes the correction voltage for the

local oscillator. The slope of the discriminator curve determines the

correction voltage as a function of the frequency deviation. The correction voltage is either applied directly to the local oscillator or

amplified and then applied. In most cases the correction voltage is

applied to a reactance tube, acting as a variable capacitor in the

oscillator tank circuit. In some applications a servo system is used

to operate a variable capacitor or inductor. Recently variable capacitance semi-conductors have proven useful in AFC circuits.

In the case of SSB the difference between the carrier frequency

as found from the pilot is compared to the frequency of a locally generated carrier. The same general principle applies. The two carriers

are applied to a phase discriminator, the output of which is used to

control the frequency of the local oscillator.

In some cases sophisticated circuits are used to search for the

carrier when the transmitted carrier drifts out of range of the normally

operating AFC circuit. These are used only when extensive carrier

drift is to be expected or where poor quality oscillators are used on

either end of the transmission path. Such circuits become operative

whenever the carrier of the local oscillator drifts out of the "lock

range" of the AFC. One disadvantage to such circuits is encountered

where the fading is occurring near the threshold level of the receiver.

When the carrier is unavailable, the search circuit begins to hunt,

causing erratic action. This action can be improved by insertion of a delay to cause the search circuit to become operative only after a specified interval of carrier absence.

9.6. The Intermediate Frequency (IF) Amplifier

The intermediate frequency amplifier is a high-gain circuit

located between the mixer and detector or demodulator . The main

purpose of the IF amplifier is to provide gain and to restrict bandwidth.
-115-

The number of stages required is governed by the gain and bandwidth

requirements. Gain requirements are dictated by the signal available

and the output required at the detector or demodulator.

Bandwidth requirements vary with the type of system. FM

receivers require broad bandpass characteristics, AM requires

narrower bandwidth, and SSB requires the least of all. For example,

FM systems require approximately 24 to 40 kc/s per voice channel as

compared to 8 kc/s for AM, and 4 kc/s for SSB.

The choice of intermediate frequency is a compromise. A

common rule for selecting the IF frequency is that it should be no

more than 10% of the operating frequency. This allows for an optimum balance between IF selectivity and image response.

9.7. The Automatic Gain Control (AGC)

Since a scatter communication path is characterized by a signal

that fades in intensity over a considerable range, it is especially important that adequate automatic gain control (AGC) be utilized. The

primary function of the AGC is to prevent overloading of the IF amplifier at times of strong signal without losing the sensitivity at times of

weak signal. In most receivers AGC is usually applied to the first IF

amplifier. Since the purpose of AGC is to prevent distortion, care

should be taken in applying this feedback voltage to the IF amplifier.

If the feedback is applied to an adequate number of stages, strong

signals may produce so much bias that the amplifier will be essentially

at cutoff. This action causes distortion. When AGC bias is applied

only to the first one or two amplifier stages, the signal-to-noise ratio

may be impaired when signals are weak and noise is controlling the

AGC. On the other hand, control must be applied at a sufficient early

point in the amplifier to preclude the possibility of overloading or

limiting ahead of the control point. The optimum arrangement allows

a signal to obtain a reasonable level, then holds this signal level within a linear region until the final amplification to the desired level for

demodulation.

In some diversity systems the AGC accomplishes an additional

objective. The combiner in a diversity system depends upon the output of several receivers. For proper combining action, it is necessary
-116-

that proper balance be maintained among the different receivers. In

times of high signal, when the signal-to-noise ratio is high, the error

rate is low even if the balance between receivers is not optimum.

However, when the signal is low, the balance between the receivers

is very important. Also, the energy in one of the passbands may

consist of more noise than signal and the AGC is operated chiefly on

noise; this results in AGC action to maintain the noise level constant.

Consequently, it is advantageous to maintain the gains of the receivers

such that their noise outputs are equal.

Due to individual differences between receivers, each receiver

should be adjusted so that the AGC action of several receivers are

identical. The noise level of the receiver may then be set to approximately the same value. The signal-to-noise ratio of weak signals is

more sensitive to the setting of the AGC than it is to the setting of the

gain. Small departures from identical gain characteristics usually

have little effect on the diversity action and, consequently, little

effect upon the signal error rate.

9.8. The Limiter in FM Receivers

Since the IF stages amplify both FM and AM signals, the

limiter stage has as its prime function the elimination of amplitude

modulated noise pulses that are superimposed on the FM signal prior

to detection. Complete limiting requires the removal of these noise

peaks from both the positive and negative portions of the signal voltage

The most widely used method of obtaining this limiting action uses

grid-leak bias and low screen and plate voltage to limit plate current

on the positive and negative peaks of incoming signals.

Incomplete limiting is experienced when the signal level drops

below the threshold. This can be observed when AM noise pulses

appear at the detector output with a drop in the input signal level.

9.9. Demodulators

The function of the demodulator of the receiver is to recover

the amplitude and frequency of the modulating wave that was impressed

on the carrier at the transmitter. Since the treatment here has been

confined to FM and SSB operation, only these systems will be considered,
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The standards of performance for this part of the receiver are

considered extensively by Florman and Tary [ 1962] . This section will

review the methods of demodulation and the general principles involved.

a. SSB Demodulation

To recover the information on a SSB signal, it is customary to

reconvert it to an AM signal and demodulate it in conventional fashion.

This demands that a carrier be resupplied to the SSB signal. This

insertion of the carrier occurs at the demodulator. This carrier can

be generated locally from an oscillator which is independent of the

transmitter carrier, or it can be the received suppressed carrier or

pilot signal. The former method has the advantage that it does not

require the presence of the pilot signal to accomplish demodulation;

its disadvantage is that it is incapable of compensating for any

carrier drift, and hence may be incapable of maintaining the necessary

frequency relationship between sidebands and carrier. The latter

method has neither the advantage nor the disadvantage of the former,

and requires the presence of the carrier at all times. The carrier is

usually suppressed below the level of the sidebands, and selective

fading may at times affect the carrier to a greater degree than it does

the sidebands. There may be times when the sidebands are available

and the carrier is not.

It is practical to provide both methods, one to be used during

times of strong signal and the other available for times of severe

fading (see figure 29). The output of the IF amplifier is fed through

a narrow-band pilot filter. The output of the filter is applied to a balanced demodulator through an amplifier which raises the level of

the pilot carrier to a level roughly ten times the level of the sidebands.

A balanced demodulator may be used for detection to reduce the possibilities of inter modulation distortion. The amplification of the carrier

is necessary to prevent distortion due to overmodulation. Companion

to this circuit would be an oscillator operating on the carrier frequency

having exceptionally good frequency stability. Since it was pointed out

that a 50-c/s variation between the locally generated carrier and the

transmitter carrier may cause serious distortion, the frequency stability of this oscillator must be exceptionally good. Stabilities less

than 5 or 6 parts in 10^ day are not usually considered adequate for

frequencies of 1000 Mc/s or more. An AFC circuit can be incorporated in a system such as this as illustrated in figure 29.
119

THE PHASE-SHIFT DISCRIMINATOR

23

out

(A) SIMPLIFIED CIRCUIT

OUTPUT

VOLTAGE

INPUT FREQUENCY

(B) THE OUTPUT VOLTAGE AS A FUNCTION OF INPUT FREQUENCY

Figure 30
-120-

b. FM Demodulation

The phase -shift discriminator is the most widely used of all

forms of FM detectors in communication systems. Its chief advantage is its linearity over the total range of frequency deviation

encountered in FM systems.

The phase -shift discriminator operates on the principal that

the inductive voltage induced in a resonant circuit by another resonant

circuit will vary in phase as the frequency of the inducing voltage

varies. Figure 30(A) is a typical simplified diagram of the phase - shift discriminator. Changes in input frequency vary the phase angles

between the inductively coupled voltages and the primary voltage which

is capacitively coupled. The phase-shift discriminator converts

these variations of phase into variations of amplitude. The input

voltage is coupled to the center tap of the transformer through a coupling capacitor Cj . This capacitor must be large enough to provide effective coupling so that Ei is always present at the center tap.

The phase -shift discriminator thus converts an FM input of

constant amplitude and changing frequency to an output which varies

in amplitude in accordance with the input variation in frequency.

Figure 30(B) is a typical characteristic curve for the phase -shift

discriminator.

To give undistorted output the input to the phase -shift discriminator must be free of any variations in amplitude. Therefore, in all

FM systems the input to the phase -shift discriminator is preceded by

one or more limiting stages to eliminate variations in amplitude.

The need for limiters in some types of FM receivers is

eliminated by using a variation of the phase -shift discriminator called

a ratio detector. The basic difference between the phase-shift discriminator and the ratio detector is the fact that in the ratio detector

the polarity of the two diodes are arranged so that their load voltages

are additive. Thus, the output voltage is proportional to the ratio of

the voltages at the diodes. Amplitude variations in the signal input

will increase or decrease these voltages but their ratio will remain

constant for a particular frequency.
-121-

9.10. The Squelch

Squelch is employed in some systems to disable the output of a receiver when the signal fades into the noise. The squelch circuit, as ordinarily used, is merely a tube that is biased to cut off so that nothing

can pass through when no signal is being received. As soon as a signal

is received, part of the voltage built up across the diode load resistor

is used to remove the blocking bias, so that a signal can be passed.

Since the voltage due to the signal is higher than that due to noise, the

squelch tube can be so biased that it will not operate on noise voltage

but will go into action as soon as the higher signal voltage is received.

Over-bias setting will desensitize the receiver so that it will

require a large signal to remove the blocking voltage. Under -bias

will permit noise peaks to trigger the squelch circuit so that bursts

of noise will ride through.

10. LOW NOISE DEVICES

With increasing requirements for reliable communications over

long-distance tropospheric scatter circuits, attempts have been made

to improve the performance of the receivers operating on these circuits

In this way definite improvement in the noise figure of the receiver

will show a marked improvement in the signal-to-noise ratio of the

entire communications system which includes the antenna and transmission line as well as the entire receiver itself. Thus, since the

ultimate objective is the overall system performance, improvements

in the individual components, to such an extent that they are no longer

the predominant source of noise, is important.

Such devices which will accomplish this for the receivers are

now available in the form of parametric amplifiers, MASERS, and

most recently tunnel diodes.

10.1. Parametric Amplifiers

In general, parametric amplifiers or reactance amplifiers may

be classified as regenerative, up-converters, traveling -wave diodes or electron-beam amplifiers. Many of these devices possess common
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RLC CIRCUIT ANALOGY TO PARAMETRIC

AMPLIFICATION AND RESULTING WAVEFORMS

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Figure 32
-124

features in that they do not obtain power from a d-c supply from a time -varying rf signal supply. The signal output is obtained from this

rf drive by means of a nonlinear time -varying element termed tne pump,

a. Theory of Operation

The physical operation of a parametric device can be related

to the swinging pendulum as described by Russell [ I960] . Referring

to figure 31, the ball at the end of the string has its highest potential

energy at point A, while at point B, its lowest point, all energy is

kinetic. If the string is shortened while the ball is at point A, the

parametric concept takes place, in that the potential energy is increased and work is being done on the system. The string is returned

to its normal length when the ball reaches its lowest position (point B)

and potential energy is converted to kinetic energy with the result that

the velocity of the ball is greater at this point than it was before. Repeating this process will result in an increase in the overall amplitude

with more energy being transferred to the system.

A simple method used by Reed [ 1959] to illustrate the principle

of variable -capacitance parametric amplification is shown in figure

32. If a small signal voltage s at the resonant frequency is applied

to the circuit, a sinusoidal variation of voltage and charge is set up

across the capacitor. Since it is desired to amplify the signal voltage

and since the capacitor voltage is inversely proportional to the capacitance by the expression V = 3- , separation of the capacitor plates will

increase the capacitor voltage for a given charge. If the plates are

separated at the maximum sinusoidal displacement and returned at the

time when there is no charge on the plates (when the wave crosses the

axis), work will be transferred to the signal as shown in figure 32.

For maximum energy transfer the capacitance must be varied or pumped at exactly twice the signal frequency.

In practice, it is difficult to maintain an exact phase relationship between the uncontrolled signal and pump oscillator frequency.

An exact condition is not necessary if something less than maximum

energy transfer is acceptable. If the frequency of the signal f

g is

different from half the pump frequency fn

/2, conditions for maximum

If energy transfer are no longer satisfied and the pump and signal will

now vary in their phase relationship. However, there will be a net
-125-

flow of energy from the pump to the signal resulting in an amplified

signal exhibiting a beat phenomenon and modulated waveform. This

type of waveform consists of the original signal f and a lower and

upper sideband equal to the sum f + f and difference f - f of the

p s p

o pump and signal frequency. These sidebands are usually referred

to as the idler, image, or difference frequency.

The idler is unavoidable and cannot be suppressed without also

suppressing the entire amplification. Also, the closer the idler is to

the signal, the more difficult it is to separate it from the signal by

filtering. In the practical amplifier it is desirable to keep the signal

frequency a few megacycles away from half the pump frequency. This

means that the parametric amplifier must be broadband to contain the

signal and idler or image bands. Therefore, the amplifier must provide twice the bandwidth and amplify twice the noise associated with

conventional amplifiers. However, by proper filtering action either

the signal or idler frequencies can be separated.

b. The Semiconductor Variable Capacitance

A semiconductor has certain properties which enable it to act as a time -varying capacitance whose value is a function of the voltage

across it. The voltage or pump source is in the microwave frequency

range

The P section of a diode has a high density of free holes or

positive charge carriers, while the N section is rich in free electrons

or negative charge carriers. With the P and N sections in contact,

electrons diffuse from a region of high to low electron density while

the holes diffuse across the junction from the P to N material. The

resulting increase of negative charge of the P section and increase of

positive charge in the N material causes a potential gradient or electric

field at the interface so as to oppose and stop further diffusion of

electrons and holes across the junction. As a result, a narrow region

at the interface called the depletion layer will be swept free of mobile

charge carriers. This is a non-conducting or dielectric region,

bounded on both sides by conducting regions. This is the criterion for

a parallel plate capacitor having a separation equal to the depletion

layer width.
-126-

EQUIVALENT CIRCUIT OF A VARIABLE-CAPACITANCE DIODE

C(V)

Rs

wwv

TYPICAL

C= 0.4- 2.0/x/xf

R

s=0.8- 5.0 OHMS

Figure 33
127

SINGLE-TANK NEGATIVE-RESISTANCE AMPLIFIER

Figure 34

TWO-TANK NEGATIVE-RESISTANCE AMPLIFIER

Figure 35
-128-

If the junction is now given a reverse bias, which means the

negative battery terminal is connected to the P section and the positive

terminal to the N section, then the electrons will move to the positive

terminal while the holes move to the negative terminal, causing an

increase in potential difference across the junction. As a result, the

depletion layer increases in width, resulting in a decrease of capacitance and an increase in terminal voltage. Similarly, a forward bias

will force the majority carrier distributions toward each other, the

depletion layer will shrink, and the capacitance will increase. Thus,

we have a capacitor whose terminal capacitance will vary with the

applied voltage. The variable capacitance diode is an excellent device

for both high-frequency operation and low noise while the transistor,

consisting of similar materials, does not excel to the same extent.

Frequency limiation of the variable -capacitance diode as described by Uhlir [ 1958] is nearly unlimited since the change in width

of the depletion layer under an applied voltage is so small that transittime effects are negligible up to high frequencies. Before transit-time

effects are reached, two limitations arise as is shown in the equivalent

circuit in figure 33. C(v) is the variable capacitance while C represents the fixed capacitance which is a function of the contact area

depletion-layer width, the applied bias, and the type of encapsulation.

RS represents the diode resistance due to the impedance of the semiconductor material. Consequently, at very high frequencies C can

shunt out the variable -capacitance voltage with a resultant power loss

and increase in the thermal noise in the resistor Rg.

c. Negative Resistance Amplifier

Figure 34 shows a generalized scheme in which straight-through

amplification can be achieved, as described by Bateman and Bain

[ 1958-1959] . One tank is tuned to an external pump oscillator frequency. When power is applied to the pump tank the diode capacitance

will vary at the pump frequency rate around the capacitance value

associated with the particular value of applied reverse bias voltage.

The varying capacitance allows some of the pump power to be released

to the signal and output tanks.
129-

nnnh

to

CJ> CJ>

n = «= S <o

=3 <M gE Q 1/5

<=> i . i ro

COO . CO Ce C3

l_l 1 i^^i i >CO 2 SE 1 1 I •a: ce

CD "*"'

=L i i lO

UmJ

CJ> 1 1 CO irini

LcJ ^ 1 LO Q- $ C3 CM «=c —- :=» c=> +1 CO <=> "=> Q= 3 CJ> Ll_ <=>

-^- C=5 CDLO

Ld oI CD

Q_^<^ ,_^ < 2

UJ o

coi h-<

:z tr o o to ct Q_ ro h- DC CD u O l_ Ld o 3

_l

Ld

X

L.

_J h- < -z. h- Ld

Z.

N

Ld

Ld

Q_X

Ld

-z. <
130-

With the purap frequency approximately equal to twice the signal frequency, an amplified version of the signal f s and the difference

or idler frequency fp

- f s = fQ appears in the single tank. The circuit

may then be used as an amplifier or converter depending on whether

f s or f is utilized. Both f

g and f have equal amplitude and simutaneously appear at the single tank output terminals. In wideband operation,

it is recommended that fp be located at a higher frequency, thus preventing f s and f from being within the passband. This will also move

the image of idler frequency f Q up with a result of no gain until the

idler is separated by tuning another tank circuit to f Q , thus effectively

discarding this source of energy. The schematic of the two tank circuits is also shown in figure 35.

d. The Up -Converter

The up-conversion or sum-frequency amplifier differs from

the negative -resistance amplifier in that the output frequency is the

upper sideband fp + f s where p is the pump frequency and s the signal

frequency. In contrast, the negative-resistance amplifier utilizes

the lower sideband fp - f s only.

Since the gain is proportional to the frequency ratio (fp + f )/f

g

, the pump frequency must be many times greater than the signal frequency. In the up-converter, the signal frequency is shifted in the

amplification process while the negative -resistance amplifier may be

used at the original frequency or at a lower sideband frequency. The

up-converter has unconditional stability whereas the negative -resistance

amplifier requires either exceptionally good matches or a circulator

for stable operation.

e. The Electron-Beam Amplifier

The electron-beam amplifier is sometimes referred to as a quadrupole amplifier since the principle of operation is based on a tube

in which quadrupole fields act parametrically on the fast cyclotron wave

of an electron beam to produce amplification.

Figure 36 is a block diagram showing the operating principle

of the electron-beam parametric amplifier developed by R. Adler

[ 1958] of the Zenith Radio Corporation. The beam is surrounded by
131-

¥

LU

CL

<

<

LU

OQ

I -z. o

tr

ho

LU

_l

LU

LUX

LU

_J

a.o

Lul CO D^ U-l

' —i <c t; = Q_ U_ <=> «

Q_

<

crLU

a.o
132-

a uniform magnetic field and flows parallel to the flux lines. The

magnetic field intensity produced within the tube is such that the

corresponding cyclotron frequency is approximately equal to the

signal frequency to be amplified.

The input coupler extracts noise and inserts signal simultaneously by demodulating the noise components appearing on the electron

beam and modulating the electron beam with a new fast wave equal to

the input signal. The modulated electron beam then passes through

the quadrupole structure which is fed by a pump signal equal to twice

the cyclotron frequency where parametric action of the quadrupole

field on the modulated beam results in amplification. The output coupler

merely extracts the amplified signal from the electron beam.

There are several similarities and differences between electronbeam and diode -type parametric amplifiers which should be pointed

out. In the electron-beam amplifier if the pump frequency is not

synchronous with twice the signal frequency, an idler frequency is

formed which is very close to the desired signal frequency and will

appear as a beat on the desired amplified signal. This beat frequency

may range from a few cycles per second to several megacycles per

second, depending on the idler frequency generated by the pump and

signal frequencies. For communications purposes this unwanted beat

frequency is eliminated by what is called synchronous pumping where

the pump frequency is exactly twice the signal frequency and optimum

phase control between the two frequencies is maintained. However,

experiments by Adler et al. [ 1958] have shown that the electron-beam

amplifier is a wideband device with good gain stable qualities when

compared with many cavity-type, solid-state amplifiers.

An experimental type electron-beam amplifier constructed by

the Zenith Corporation and described by Adler et al. [ 1959] is diagrammatically shown in figure 37.

The signal frequency was 560 Mc/s, and the pump frequency

was 1120 Mc/s. The rf elements are shown together with a schematic

of the tube structure. The electron gun consists of a series of small

apertures where the first aperture selects a small portion of the electron stream, and the potentials between succeeding apertures cause

this beam to diverge and become parallel to the axis. The last two

apertures reduce the beam to a diameter of 0.016 inches. The beam
-133

voltage was 6 volts at 35 microamperes to obtain 6 orbits in the coupler and 4 orbits in the quadrupole. The magnetic field was 200 gauss

corresponding to a cyclotron frequency of 560 Mc/s. The amplifier

has the following characteristics:

Gain = 30 db

Bandwidth = 40 Mc/s

Noise figure = 1 . 5 db

f. General Considerations

The operation of the up-conversion amplifier may be considered

analogous to the Manley-Rowe theorem [ 1956] describing the fundamental power relation for nonlinear (and lossless) reactance. This

theorem states that when a strong pump frequency p and a weak signal

of frequency s are simultaneously impressed on a nonlinear reactance,

the following power relationship result:

P P P

f (f + f ) (f - f ) _JL + _P__i P s =Q (54)

f f + f f - f

s p s p s

where only the signal and the two lowest sidebands, f - f and f + f , p s p s are considered, and values of P£ , P /£ + f ) and P(f _ f

\ are the

powers at the frequencies f

s

, f + f s and fp

- f

s

. A positive value of

P denotes net power leaving the amplifier and a negative value denotes

power absorbed by the amplifier.

For the negative -resistance amplifier, the circuit does not

respond to the upper sideband fp

+ f

s

; therefore the middle term of

(54) drops out, and we have the following relationship:

P P

f (f - f ) -*- -*- - (55)

f f - f s p s
•134-

Therefore, Pf must be positive in order to have amplification at the

signal frequency f

g

, and P/f _ f

\ must also be positive, showing that

if amplified signal power leaves the amplifier, image power or lower

sideband power must also leave the amplifier.

From (55) the image power is related to the signal power by

f - f P = -2 L P

(f - f ) f f (56)

p s s s

This suggests another mode of operation of the negative -resistance

amplifier where the amount of gain is reduced at the signal frequency,

and the overall gain is increased by extracting the useful signal at

frequency fp - f s

, which makes use of the frequency-ratio gain

(f -fs )/f

g

. This has the effect that the amplifier stability and gain are

less critically dependent on the quality of matches, and the image noise

is reduced.

A negative -resistance amp ifier of this type has been built by

G. Herrmann [ 1958] of the Bell Telephone Laboratories and is diagrammatically shown in figure 38. In this amplifier a certain amount

of up -conversion gain is used in addition to the negative -resistance

gain, and the lower sideband is used as the useful signal output. The

amplifier has the following characteristics:

Gain = 18 db

Bandwidth = 5 Mc/s

Noise figure = 1 . 2 db at 90OR

Another similar amplifier was constructed at the Federal

Telecommunications Laboratories. The amplifier operates at a signal

frequency of 900 Mc/s, pump frequency at 9900 Mc/s, and the useful

lower sideband frequency of 9000 Mc/s with a gain of 18 db and a noise

figure of 1 db.

If the circuit responds to the signal upper sideband only, then

from the previous power expression P/£ _ f ) = and then P/£ ^ £ \ =

fp + f

s

- P^ . The negative sign shows that power out at one frequency

s s
-135-

LU

LUO

C/) LUmi LU>

i-<

UJ

UJ

LT

LU

Q.X

LU 3

a.

COo < </> 7» ^

CD

CO o Q o UJ IO

U. CD

_l

Q.s<

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Q

1§o_ an * Q o — o w

CD t

UJ PI

a:UJ

CO

ro

u.

CO

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a. f O

Ijn

UJ Q_ ^ S »- ^ O 3 -1 3

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-136-

crUl

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Q_ iZ> coV

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cr i- o iii < S Q <

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ac

COMMUNICATIONS RECEIVER

VHF- CONVE

CO

V4—

QC

LtJ X1 «*1

CO

as

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a_

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Q. +

CO

vt— Q.

'1 acUJ

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bo
-137

BLOCK DIAGRAM OF RECEIVER

USING DOWN— CONVERTER

PARAMETRIC AMPLIFIER

w

fc

DOWN CONVERTER

CRYSTAL CONTROLLED

PUMP

COMMUNICATION

RECEIVER

Figure 40
-138

cr

LU

LU

LU

Q

O

LU

cri LU>

I-<

LUO o < <

cr<>

cr>

CO3

LU

Q.

CO

cr

cr<x
-139-

ccUJ

u_

-J

Q_2<

UJ ljJ >.— so y- — < o

(Tz *

p. " UJ <

<r cc <§

u.o < QCLU S CD OS '— < Z < *

GC/S 1

(100 o o ^oo

CD

as.

—i "-" «e s»

RYST

ECEl « o= CO

t> 1

Z LU

=C o ce O UJ

i2 o_ o> _,CO

CO

t»^

<=>

<z> CO

CT>

en

<=> *-» 1— OS

-* UJ

:d i- = OSo

Q= « Oi— a:

i2«C *o I as ca

«*: , I i CO

<L3 z

C3

a>w
-140-

is desired, and power must be absorbed by the system at the other

frequency. If Pf is put into the system, the (f + f )/f times as much

power can be extracted at frequency f„ + f s

.

Figure 39 shows a practical configuration using an up-converter

and a crystal mixer in which the output appears at the signal frequency.

The combination converter and mixer performs the same function as

a straight-through amplifier. It has the desirable feature of permitting

a self-controlled oscillator to be used for the pump without introducing

frequency variations in the output. It has one disadvantage in that the

overall noise figure will be somewhat greater than that which can be

obtained from a two -tank amplifier using the same diode and pump frequency.

Figure 40 is a block diagram of a receiving system using a regenerative amplifier. As can be seen, few components are required

for a complete system. In a regenerative amplifier, f is smaller

than f s ; thus the ratio f s /f may be quite large. To compensate for

large values of f s

/f , it is necessary to have extremely tight coupling

between the load and output tank. A further disadvantage is that very

high regeneration is required to give useful gains. When f Q

/f s is

small, a narrow bandwidth will result and the device will tend to have

very poor gain stability. As a result, regenerative amplifiers with a high ratio of £ /£ s may be difficult to adjust and maintain.

A low-noise negative -resistance amplifier now in production

is shown in figure 41 . It was developed and tested by F. S. Harris

[1958] of Microwave Associates for use in the 400-500 Mc/s region.

This amplifier uses one varactor diode mounted in a coaxial cavity.

The pump frequency is several times the signal frequency. Separate

coupling loops are provided for the input and output. The output frequency is exactly equal to the input frequency regardless of drifts in

the pump frequency. Measured noise figures of approximately 1 db

have been obtained in this frequency range.

A block diagram of a regenerative amplifier is shown in

figure 42. The signal to be amplified (500 Mc/s) is mixed with several

hundred milliwatts of 10 Gc/s pump or carrier frequency in the varactor

diode. Sidebands are generated at 10, 500 Mc/s and 9, 500 Mc/s. With

500 Mc/s inputs upper sideband up-converter have noise figures of 2-3

db while regenerative amplifiers using the lower sideband have overall

noise figures of 1 db.
-141-

10.2. MASER

The development of the MASER (Microwave Amplification byStimulated Emission of Radiation) and parametric amplifiers has led

to important contributions in the advancement of microwave engineering.

Although the MASER in its present form is only a few years old and

much research is yet required, it shows great promise in its application to such fields as radio scatter systems, satellite communications,

and radio astronomy, where extremely low noise amplification is

important.

These new amplifiers differ in principle and operation from the

more familiar klystron and traveling-wave tube amplifiers in that

MASERS utilize the property of bound electrons instead of free electrons,

and radiofrequency energy rather than direct-current energy is used

as a source of power.

Since the amount of noise produced in a device is a direct result

of the temperature of the working substance and since no electrons are

obtained from thermionic emission from a hot cathode, MASERS are

among the lowest noise producing devices thus far developed.

10.3. Tunnel Diode Amplifiers

Recent experimental research by Esaki [ 1958] , Hall [ I960]

and Summers [ 1959] has shown that the tunnel diode exhibits proper'

ties which may render it quite useful as a low noise rf amplifier in

scatter communications circuits.

a. Theory of Operation

The current-voltage characteristics of the tunnel diode shows

that a negative -resistance region exists in the direction of forward

bias. This negative resistance, according to theoretical and experimental results, extends well into the high microwave region. The

linear portion of the negative -resistance characteristic is utilized to

construct linear rf amplifiers . Basically, this negative -resistance

characteristic is identical to that found in some types of parametric

amplifiers where the negative resistance is developed by the pump

signal.
-142-

TUNNEL DIODE EQUIVALENT CIRCUIT

Re

-vww

L-s

VOLTAGE -CURRENT CHARACTERISTICS

VOLTAGE

CIRCULATOR COUPLED TUNNEL DIODE

AMPLIFIER

r

INPUT Jr\

OUTPUT -#

1

DIODE MODULE POWER

SUPPLY

CIRCULATORS

MATCHED

TERMINATION

Figure 43
-143-

The equivalent circuit for the tunnel diode and the representative current-voltage characteristic curve is shown in figure 43. R

is that resistance existing across the function for a given forward bias

point indicated by A on the voltage -current characteristic curve. The

ohmic losses in the leads and the diode itself are represented by R s , and the associated lead inductance is indicated by Lg

. The diode

junction capacitance which shunts the negative resistance R is indicated by C. Therefore, the design of a linear rf amplifier is based

on tuning the reactive elements of the tunnel diode with an external

circuit similar to the equivalent circuit shown in figure 43. Amplification takes place when the coupling to the source and load are such

that the equivalent positive conductances exceed, by a slight amount,

the negative conductance of the diode.

The above description is oversimplified but should suffice for

the purposes of this report. Further study of the theoretical and

quantum mechanical phenomena of tunneling may be obtained from the

above references and publications by Hines [ I960], Van der Ziel

[1960], Tieman [ I960], and Neilsen [ I960] .

b. The Reflection-Type Amplifier

Recently the Micro State Electronics Corporation has developed

a tunnel diode amplifier employing a reflection technique to overcome

the coupling factors between the diode and the source and load impedances .

The basic requirement of this type of amplifier is a suitable

network to separate the incident wave and amplifier reflected wave.

This may be accomplished by a circulator on hybrid network. Shown

in figure 43 is a block diagram of a complete tunnel diode amplifier

using a four-port circulator (two three-port circulators combined)

which has been manufactured by the Micro State Electronics Corporation

and is commercially available. Experimental models have indicated

noise figures of 3 to 6 db in the 1000 to 6000 Mc/s range with a gain

of 17 to 20 db and bandwidths on the order of 10% in the lower range

and 5% in the upper range.
144-

c. General Considerations

The tunnel diode amplifier offers certain advantages over other

low noise devices in their application to scatter communication circuits .

Since the tunnel diode amplifier is a completely solid-state

unit, it has exceptional reliability requiring only d-c activation for

operation. In addition, because of its small size and light weight it can be readily mounted at the antenna terminals, thereby eliminating

the excess noise contributed to the system by the transmission line or waveguide

.

One of the main disadvantages of the tunnel diode amplifier is

its stability versus environmental temperature change. Ambient temperature changes on the order of ± 20°C can cause major variations

in the gain and noise figure of the device. Consequently, extreme

care must be exercised in controlling its operating environment, and

the unit must be temperature compensated in some way.

11. COMBINERS

Diversity techniques are applied to tropospheric scatter systems to overcome the continual rapid fading encountered. Diversity

techniques are based on the statistical character of scatter signals,

and make use of the phenomenon that two or more signals arriving

over different paths or at different frequencies do not fade in unison.

The relative merits of space diversity (signals arriving over different

paths) and frequency diversity (signals arriving at different frequencies) are considered in another part of this manual. This section will

be confined to the consideration of the methods of combining diversity

signals and the measurement of the performance of the combiners.

There are various ways in which diversity combining can be

accomplished. Most notable are combining either immediately before

or after detection, where the signals are either selected by switching

or they are added together.
-145-

COMMON COMBINERS (SIMPLIFIED DIAGRAMS)

SIGNAL I DEMODULATOR

SIGNAL 2 DEMODULATOR

OUTPUT

COMPARATOR

FOR MAX S/N

(Q) SELECTION COMBINER ( POST- DETECTION )

SIGNAL 1 — IF AMPLIFIER

AGC ADDER DETECTOR

SIGNAL 2 —

i ,

lr AMr lit iln

OUTPUT

(b) EQUAL GAIN COMBINER (PRE- DETECTION )

SIGNAL VARIABLE

GAIN AMPLIFIER

SIGNAL 2 VARIABLE

GAIN AMPLIFIER

AGC

VARIABLE

GAIN AMPLIFIER

BIAS

BIAS

VARIABLE

GAIN AMPLIFIER

DEMODULATOR

DEMODULATOR

OUTPUT

(C) MAXIMAL RATIO COMBINER (PRE-DETECTION)

Figure 44
-146

COMBINER PERFORMANCE CHARACTERISTICS

^i

CVJ So

cr. N

Ul

>

UJo

UJ

<r

N

N No

RECEIVER I

VZ N

Figure 45
-147-

11.1. Methods of Combining

Classified according to the method of combining, there are

three common types of combiners: the selection combiner, the equal

combiner, and the maximal ratio combiner. Figure 44 shows a simplified block diagram of each of the three methods in a typical receiving

system.

A selection combiner determines the larger input and connects

this to the output. The equal gain or linear adder combiner sums the

signals and applies the sum to the output. The maximal ratio or ratio

squarer combiner squares the signals before addition and applies the

sum of the squares to the output.

A comparison of the three methods of combining can be done

graphically in a manner described by Altman and Sichak [ 1956] and

illustrated in figure 45. For this comparison it must be assumed that

(l) Signals add linearly, noise adds in an rms fashion,

(Z) All receivers have equal gain,

(3) All receivers have equal noise outputs, and the

noise is random in character,

(4) The desired output signal-to-noise power ratio

S /N Q

is a constant.

a. The Selection Combiner

The selection combiner utilizes but one receiver at a time.

The output signal-to-noise ratio is equal to the input signal-tonoise ratio of the receiver in use at the time. This is illustrated by

curve (a) in figure 45.

b. The Equal Gain Combiner

The equal gain combiner merely adds the different inputs. If two receivers are in use,
-148-

S

l + S

2 1 S

l + S

2

S /N = _ -i= \T (61)

This is illustrated by curve (b) in figure 45.

c. The Maximal Ratio Combiner

The maximal ratio or ratio squarer combiner utilizes a relative

gain change between the output signals in use. For example, if the

stronger signal has unity output and the weaker signal has an output

proportional to G, then

S, + GS S, + GS

S /N = -J Z- = -i Z- (62) o o r p! 2 2~ I v/n

i + gn2 n|i + g

2

V

Maximizing the above expression by differentiating and equating

to zero yields

G = S

2 /S,

i.e., this signal gain is adjusted to be proportional to the ratio of the

input signals. Then

(S o /N

o

} max

= J Sj + S^ /N (63)

(S /N ) 2

= (S, /N)

2 + (S,/N)

2

(64) o o max 12

which is the equation of a circle. This is illustrated in figure 45 by

the curve (c).
-149-

SIGNAL-TO-NOISE IMPROVEMENT IN

DIVERSITY SYSTEM

A

10

^ 9

MAXIMAL GAIN COMEilNER

"^— EQUAL GAIN COME INER

-en JLL ECTOR CON1BINER

ORDER OF DIVERSITY

(NUMBER OF INDEPENDENT SIGNALS)

Figure 46
150-

COMPARISON OF THE TIME DISTRIBUTION OF THE OF THREE TYPES OF

COMBINERS USING DUAL DIVERSITY

20

> in

5 to

tr <

LU IJ- CO O

O _ 2 < 6 o

S -10

<t LlI 2 I

co o

.- -20 o 3

"30

-40

5 .2

1

1 d

1

b

8

<

2 d b :C^

MAXIIV AL R/ — EQIVTIO JAL GAIN SELECT ON

^—NO DIVE (RAYLE

RSITH GH Dl STRIBUTION)

0.010.1 I 5 10 20 30 40 50 60 70 80 85 90 95 98 99 99.5 99.9 99.95 PERCENT OF TIME THAT THE ORDINATE IS EXCEEDED

99.99

Figure 47
-151-

11.2. Comparison of Combiners

It can be seen that the maximal ratio combiner utilizes the best

features of the two previous combiners. When one signal is zero, the

combiner acts as a selector combiner; when both signals are equal,

the combiner acts as an equal gain combiner. It can also be seen that

the maximal ratio combiner yields the best output for any combination

of signal-to-noise ratios since the curve of operation indicates that the

optimum output occurs for lower values of input signal-to-noise ratios

as evidence by its proximity to the origin.

Another method of comparison as described by Brennan [ 1959]

is based on the difference in output to be expected from these three

methods as the number of independent signals increase. If each of

the signals are assumed to be Rayleigh distributed, then a statistical

analysis of the output from each of these combiners results in the comparison illustrated in figure 46. It can be seen that as the number of

independent signals increases, the superiority of the maximal ratio

combiner increases. Where quadruple diversity if used (four independent signals) the average signal-to-noise ratio of the output using

the selection combiner is only a little better than 3 db superior to no

diversity, whereas the equal gain combiner results in a 5.25-db

improvement with the maximal ratio combiner yielding a 6-db improvement.

If the operation of the combiners are compared, not on the

basis of average values but on the basis of a time distribution of the

output signal-to-noise ratio, the real significance of the combiner

becomes evident. A time distribution is merely the percentage of an

interval of time where the signal amplitude exceeds particular signal

levels. As can be seen from figure 47, the Rayleigh distribution has

a time distribution where the signal amplitude is approximately 5.2

db above the median value for 10% of the time intervals of the measurement, whereas, for 90% of that interval, the signal amplitude exceeded

a level that is 8. 2 db below the median. (This does not yield any information on how these time intervals are distributed over the measuring

intervals. The distribution is actually a summation of time increments

over the entire measuring intervals.) Where Rayleigh distributed

signals are combined according to the principles utilized in the above

three types of combiners, the output can be predicted as a function of

the types of combiners, the output can be predicted as a function of the
-152-

COMPARISON OF THE TIME DISTRIBUTION OF THE OF THREE TYPES OF

COMBINERS USING QUADRUPLE DIVERSITY

20

10

> </> 3 3

O w

< (75 cr <

LU Ll. CO O

O Z

2 < P ° S»<I LU 2 I O h- v) o

Il~

=3 LU Q. >

O Z

LU

cr

10

r: -20

30

40

^-—

V

AXIM*vL RATIO -—- EQUAL GAIN

i__ SELECTION

-NO DIVERSITY

(RAYLEIGH DISTRIBUTION)

0.01 0.1 I 5 10 20 30 40 50 60 70 80 85 90 95 98 99 9R5 99.9 99.95 PERCENT OF TIME THAT THE ORDINATE IS EXCEEDED

99.99

Figure 48
-153-

order of diversity and the type of combiner. This is illustrated in

figure 47 for dual diversity and in figure 48 for quadruple diversity.

It should be noted that although there is enhancement at the median

(50%), the real enhancement occurs at the high percentage (low level)

signal-to-noise ratios. The signal-to-noise ratio exceeded 99.9% of

the time is improved by at least 23 db when quadruple diversity is

employed.

Under conditions of Rayleigh fading there is but small improvement of the maximal ratio combiner over the equal gain combiner. The

best improvement will not be greater than 1.05 db. If the fading lacks

the depths characterizing the Rayleigh distribution, the equal-gain

combiner approaches the maximal ratio combiner. (The maximal

ratio combiner is independent of the type of distribution, whereas the

equal-gain combiner is not.) But, if the fading is such that exceptionally deep fading is experienced, the operation of the equal-gain

combiner, in the limit, can become inferior to the selection combiner.

Hence the equal-gain combiner should not be used if exceptionally deep

fading is expected.

This analysis of combining action is based on certain assumptions. It was assumed that independent signals were being combined,

and it was assumed that the noise is completely random. The assumption of independence requires that the signals received on the different

receivers are unrelated at least in an instantaneous sense; the variations in one will yield no information concerning the variations in any

other. The relationship between such signals can be expressed in

terms of a correlation coefficient, where a correlation coefficient of

one indicates total dependence or a one-to-one relationship at each

instant of time, and where a coefficient of zero indicates total independence. If the correlation coefficient is zero, the above applies;

if the correlation coefficient is one, no diversity occurs. If a degree

of correlation between the extremes occurs, diversity is possible but

degraded. About half the diversity efficiency is experienced for correlation coefficients of 0.8, whereas practically full efficiency is experienced for coefficients less than 0.3. This concept of diversity efficiency is considered by Florman and Tary [ 1962] . Of importance here

are the relative merits of the three types of combiners under these

conditions. As the correlation increases the selection combiner

approaches the nondiversity condition; the equal-gain combiner, although

degraded will approach the maximal ratio combiner which maintains

its original relationship to the selection combiner.
-154

COMBINER OUTPUT FOR RAYLEIGH DISTRIBUTED INPUTS

WHEN THE CORRELATION COEFFICIENT, />, IS EQUAL TO ONE

20

10

> en 2|

< CO

UJ U. en O

O 2

2 -10 P °

< LU 2 X

co o

Z> LU

Q. >^ -20

Ld

en

30

40

^v

^r^— EQUAL RAT

Q

. GAir

10 cc UADRl

1 OR MAXIMA

)MBINER PLE DIVERS

L

ITY

E 31W\L G Mr

F

J

Dl

R

10 JAl

MAX

COI

. Dl

IM

VE

4L- NERS

RTY

S ELE CT ION COME

FOR

D

1INERn-FOLC

IVERST

)

OfllO.I I 5 10 20 304050 60 70 80 85 90 95 98 99 99.5 99.9 99.95 PERCENT OF TIME THAT THE ORDINATE IS EXCEEDED

99.99

Figure 49
155-

COMPARISON OF COMBINER OUTPUT WHEN INPUT SIGNAL

HAS CORRELATION COEFFICIENTS,^) , OF UNITY AND ZERO

o

CO

O Q

I- UJX

I-o

IUJ>

or

"0.010.1 I 5 10 20 304050 60 70 80 85 90 95 98 99 99.5 999 99.95 PERCENT OF TIME THAT THE ORDINATE IS EXCEEDED

99.99

Figure 50
-156-

If the correlation coefficient is one, then the selection combiner

should have no effect upon the character of the signal. Since the

selection combiner utilizes only the strongest signal, the output will

be the same as the one signal from that input that happened to be active

at the starting time. The action of the equal-gain and maximal-ratio

combiners will be different. With a correlation coefficient of one, the

equal-gain combiner coincides with the maximal ratio combiner, and

either combiner will yield an improvement over a signal equal to the

average improvement (as illustrated for the maximal ratio combiner

in figure 46) for all percentage of time greater than the median. Then

for dual diversity the output will be Rayleigh distributed but displaced

by 3 db above the input signal; for quadruple diversity the replacement

will be 6 db (see figure 49). Hence, if the identical Rayleigh distributed signal is applied to the two inputs of a maximal ratio combiner

used in dual diversity, the time distribution of the output will follow

curve (b) in figure 50; whereas, if two independent Rayleigh distributed

signals having equal means are applied to the same inputs, then the

output will follow curve (g). Therefore, the improvement in the signal

level exceeded 99% of the time that occurs when the correlation coefficient changes from unity to zero is approximately 8. 7 db. It is also

well to note that when the correlation coefficient is zero, the output of

the maximal ratio combiner is approximately 11.7 db better than a

single input at the 99% point. If the same comparison were made in a system where a selection combiner was used, the results would be

a bit different. The output of the combiner would follow curve (c) in

figure 50 when the correlation coefficient is unity, and would follow

curve (i) when the correlation coefficient is zero. At the signal level

exceeded 99% of the time, lack of correlation improves the selection

combiner output by approximately 10 db. This concept of uncorrelated

signals is an important factor to be considered when determining the

separation distance between antennas in a diversity system.

Another assumption required in the consideration of combiner

action is that concerned with the character of the noise. It is assumed

that the noise is completely random and uncorrelated. Correlation

between the noise occurring in the individual inputs to the combiner

can exist especially when the noise includes effects from external interference. It can be shown that the presence of high correlation between

the noise voltages has unfortunate results with respect to combining.

Selection combining would be unaffected since but one signal is in use

at any one time. However, with both equal gain and maximal ratio
-157-

O

=3

LUC3

HYBRID

ADDING

CIRCUIT

' r

or

<=> z

m

enLU

Ll_

o_

«C

l—

CXI LU

u_

Q_

3E

*Cu_

t—

i 1

1 '

i ,

or

U_l X

cr: cz>

1

CO

1 **: CJ>

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oro

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•H
•158-

combiners, such is not the case. It is possible that the output signalto-noise ratio using either of these two combiners under such circumstances will be less than that utilizing a single signal. In addition, the

performance worsens as the order of diversity (number of independent

signals) increases. Therefore, where highly correlated noise inputs

are to be expected, the use of any combiner other than the selection

combiner will probably degrade rather than enhance a single signal

reception system. Since correlated noise is usually produced external

to the system, condition such as these can be foreseen, at least to a degree, especially when the noise is man-made.

11.3. Pre -Detection and Post-Detection Combining

Classified according to where in the reception process the combining takes place, combiners commonly used are pre-detection IF

combiners and post-detection baseband combiners. The former

accomplishes combining before demodulation at the intermediate frequency; the latter accomplishes combining after detection at the baseband frequencies.

If pre-detection combining is considered, phase control circuitry

is required to establish the coherency of the signals at the intermediate

frequency. This control is unnecessary in the case of selection combining since only one signal at a time is used; however, it is indispensable in the case of the other two combiners (see figure 51). At the

present time pre-detection combining is not used extensively because

of the difficulty of establishing this phase control. Although this is

difficult to achieve in practice, the principles are straightforward.

Figure 51 illustrates one method of achieving the phase control as described by Adams and Mindes [ 1958] .

Separate receiver front ends are used up to the IF amplifier

output. The relative signal phase is measured at this point by a balanced modulator (phase detector), and the phase is controlled by

supplying a corrective d-c voltage to one local oscillator, causing it to gain or lose phase with respect to the other local oscillator as

required to establish additive signal phase at the combining point.

The resulting amplitudes of the co-phased signals are added in a hybrid, and the combined signal is applied to the demodulator. In
159-

QD

cr o —

DD = 8 O

1- < o CD UJ III 1- CO

LU < U DD

h-coo

CL

>— or

-a: U_J i

H Li-J _v o or ^ —

\ 51 =: i

o

«c

—

^ -a: Q_ CC

cz>

CJ> C3

-a: 1

o= p= or UJ LfcJ o z: u_

CO

J u_i

C_3 c^ E<c di 1 I U_l i

U_l

U-J oo ,_

Q_

U_f

or

U_l lZ1 Q_

-a: C3

U-J dae: O

«a: 2z^CJCO

<^>

-a:

in

0)

60
160-

this system failure at any point in either receiver does not interfere

with normal operation of the remaining receiver; the phase control

circuit becomes inoperative at this time.

Where AM or SSB are concerned, the operation of combiners

is the same whether pre-detection or post-detection is used. There

is some advantage to pre-detection combining where selection diversity

is used in that the effect of the transients due to switching is reduced.

However, where FM is in use, some doubt exists as to the advisability

of post-detection. D. G. Brennan [ 1959] shows that the statistical

consideration of the combining of FM signals favors the pre-detection

method over the post-detection method. The argument favoring the

pre-detection combiner is based on the fact that the input and not the

output of an FM demodulator is Rayleigh distributed. Consequently,

the combining of several of these signals will not yield the results as

outlined above, and the comparison between the relative merits of the

various combiners will not apply. In post-detection, FM combining,

the equal gain combiner is not used, and the maximal ratio combiner

will yield performance little different from selection combining. (It

would appear that pre-detection combiners in FM service could provide

additional performance with respect to distortion, FM quieting, less

circuit complexity, and better reliability near the threshold level.)

11.4. General Considerations

Most present-day systems employ post-detection or baseband

combining, utilizing either maximal ratio or equal-gain combiners.

This equal gain of linear adder combiner is impractical as an FM postdetection combiner. This is because in deep fades the noise output of

the conventional FM receiver rises sharply to a level comparable to

full signal output. Therefore, if weak FM signals are to be combined

after detection, a close approximation to ratio squared combining must

be provided over a wide range of signal ratios if sufficient rejection of

the greatly increased noise is to be provided. Hence, maximal ratio

combiners are usually used in FM post-detection.

Figure 52 is a simplified block diagram of a typical FM receiver

using the baseband combiner [Adams and Mindes, 1958] . Referring to

the circuit diagram, each receiver selects the noise components above

the normal signal frequency, and these are amplified and detected to
-161

produce a control voltage that is applied to the corresponding combiner

tube to control the combining ratio. Differences in control voltage will

vary the combining ratio favoring the signal having the lower noise.

For protection against failure of either signal channel or a failure in the noise amplifier, a pilot tone is added at the transmitter

point. This pilot tone is received with the signal passed through the

noise amplifiers for protection against failure and finally used to

operate an alarm relay that disconnects a receiver when the pilot

tone is absent, thus permitting the remaining receiver to function

normally. In most cases, dual pilot tones and an alarm circuit at the

transmitter are used to prevent accidental loss of the receivers due

to failure of the pilot tone.

Additional work in this area has been performed by Hausman

[1954], Kahn[l954], Kelley [ 1957-1958], Long and Weeks [ 195 7]

and Mack [ 1955] .

12. POWER SUPPLIES

12.1. Unregulated Power Supplies

No circuitry is used in the unregulated supply to maintain a constant output voltage with varying input line or variation in load.

As input line voltage varies, the output voltage will vary the same

percentage and in the same direction. Also, as load is applied, the

internal voltage drop increases, and the output voltage will drop

accordingly. A load regulation of 10 to 25% is typical. The main

advantages of this type of supply are its simplicity, low cost, and high

reliability. However, in all but the most basic systems, variation

in power supply output may cause poor or erratic system performance.

12.2. Resonant Regulator Power Supplies

Constant voltage can be readily maintained despite input line

voltage variations by incorporating magnetic voltage regulating circuitry

ahead of the rectifiers and filters in the unregulated d-c supply. Since

no tubes or transistors are used, the unit is extremely rugged and

reliable. Load regulation is not good, although some load compensation
-162-

is accomplished by the magnetic circuitry so that it is better than an

equivalent unregulated supply. Load regulation for these types runs

between 5 and 10% .

Momentary or continuous output short circuits cannot damage

this type of supply, since the current is limited to approximately 125%

to 150% of maximum rating by the resonant circuitry. Since the

variable auto transformers used in these supplies increase internal

impedance, this tends to offset the advantage of low-cost regulation.

This type is suitable in systems requiring fixed output voltages.

Excellent line voltage regulation and transient response for

line and load pulse makes these units suitable for supplying power for

transistorized circuitry. Direct-current output voltage typically

remains within the regulation limits for line voltage surges up to

10%. An output voltage change of 1.5% for each 1% change in input

frequency will occur due to the frequency sensitive nature of this type

of unit.

12.3. Magnetic Amplifier and Saturable -Core -Reactor

Power Supplies

Precise regulation of output voltage for both line and load variations are obtained from these supplies, typically holding ± 0.21% regulation. A closed -loop circuit is incorporated in both types. They are

insensitive to frequency variation, although slight degradation in performance may be expected when they are continuously operated at some

frequency other than the nominal design frequency. When operated at

lower power-line frequencies, there will be an increase in ripple. No

derating of output of voltage or current is usually necessary for the

electronic type, but the tubeless type may have to be derated for continuous performance. Although line transients are somewhat attenuated, maximum excursions of 5% will be experienced for load transients

of 20%.

A smaller, lighter, and more reliable supply than the electronic

type is the tubeless magnetic amplifier power circuit and transistor

power reference type. This type has the advantage of the elimination

of vacuum tubes, and hence a corresponding associated reduction in
-163

maintenance. Other advantages are a wider range of output adjustments and somewhat better dynamic characteristic. The response

time of this type is faster than the electronic type but not fast enough

to prevent line transients from coming through. Maximum excursions

of 4% of output voltage may be experienced for load transients of 20%.

12.4. Transistorized d-c Power Supplies

Best performance such as regulation, response time, output

impedance, and ripple are obtained from the fully transistorized

supplies. For low and medium power units, these are substantially

smaller in size and lower in weight. Some of the other features of a transistorized supply are:

(1) Fast response time and reduced ripple

(2) Low output impedance

(3) Regulation of ± . 25% to ± 0. 05%

(4) Ripple 0.5 millivolts to 5 millivolts rms

(5) Unaffected in input frequency variations (can be

applicable for nominal 50, 60, or 80 c/s input)

Transistorized supplies have excellent dynamic performance,

and "transient free" output voltage can be obtained.

12.5. Series-Tube Regulated Power Supplies

The same excellent performance characteristics of transistorized supplies can be obtained from series -tube regulated power

supplies with voltage ranges from to 1000 volts. Vacuum tubes are

able to withstand higher voltages, and are therefore better utilized in

the 75- to 1000 -volt supplies. The maximum current from these

supplies is ordinarily of the order of 2 amperes.
164-

13. REPEATERS

Repeaters are used to transmit energy over relatively short

paths. In some cases the path is such that the scatter mode or diffraction mode is used; however, in general, repeaters are considered

to be a series of line -of -sight paths. It is this latter category that is

of interest here .

The simplest combination is that where the transmission path

can be divided into two free -space paths with the repeater joining the

two segments. In such a case the basic transmission loss of the repeater, within line of sight of both path terminals, is given as the

sum of two free -space basic transmission losses less the repeater

gain. The basic transmission loss is given by Norton [1953] . That

is, the transmission loss over the entire path is equal to the sum of

the transmission loss on each path individually decreased by the gain

contributed by the repeater. The expression for the free-space transmission loss over a path with a single repeater can be expressed as

follows:

L

b

= 64.89 + 20 log 10d + 20 log

10

d

2 + 20 log^f^

+ 2 ° 1OSl0fMc2 " G

l " G

2

" K

(65)

where d and d = the distances in kilometers from the repeater site

to each of the terminals of the path. (If dj and d£

are in miles, then the constant 64.89 is replaced

by 73.16.)

f, , , and f „ = the frequency in megacycles per second of the signals Mel MC2 n •, -. , r f n employed on the two legs of the path

G and G_ = the gains of the two repeater antenna in db relative

to an isotropic antenna

K = the repeater gain in db
-165-

N.B. This expression is independent of the gains of the transmitting

and receiving antennas. In the practical case, the gains of

these antennas must be subtracted from the transmission loss.

With active repeaters, K is normally positive; with passive

repeaters, K is normally negative or zero.

If more than one repeater is used, the above expression (65) is

changed by adding the path loss of each additional leg. The above

expression will have the following added to it for each additional leg:

32.45 + 20 log 10

d

3 + 20 log f Mc3 - G

3

- G

4

- K

£ (66)

13.1. Active Repeaters

The above expression is valid for both active and passive

repeater operation. It is especially useful in this form when active

repeaters are considered. To reduce interference effects on multiple

repeater paths and to reduce coupling between the transmitting and

receiving antennas at the repeater, the carrier may undergo a change

in frequency at each active repeater. The modulation information

arrives from the transmitting location on one carrier frequency, is

recovered, and superimposed upon a carrier of another frequency

which is radiated either to the receiving location or to the next repeater

location.

13.2. Passive Repeaters

Passive repeaters as described by Greenquist [1954] and Jakes

[1953] do not amplify the signal transmitted over the paths, but merely

reflect, scatter, or reradiate a portion of the original signal to the

desired receiving location. This can be done either by receiving the

signal on one antenna and reradiating it from another, or the signal

can be reflected or scattered one or more times by means of large

reflectors. The path loss formula (65) can be simplified slightly since

the frequency is a constant, and since in most cases identical antennas

are used at the repeater.
-166-

a. Back-to-Back Directional Antennas

When a back-to-back antenna system is used as the repeater,

power is received from the transmitting location on one antenna and

is fed through a short piece of transmission line to another antenna

which radiates the energy toward the receiver. Parabolic antennas

at the repeater are individually pointed to the transmitter and receiver,

respectively. Each path then (the path from the transmitter to the

repeater and the path from the repeater to the receiver) can be considered as independent line -of -sight paths.

Since the path can be dismembered into two or more segments,

the equipment requirements can be considered for each segment

individually. The above general statement implies that the actual gains

of the antennas are known. In a previous section it was pointed out

that the effective gain of the antenna is conditioned by such parameters

as the minimum distance between antennas and ground reflections.

Each segment of the path should be analyzed to determine whether or

not these two parameters are affecting the apparent gains realized

over the path.

The power requirements for the path are calculated for the

effective antenna heights and the gain of the antennas. Mechanical

alignment of the antennas or reflectors is necessary to utilize the

path to best advantage. This is accomplished by transmitting a signal

from the transmitter and adjusting the alignment in azimuth and elevation until a maximum signal is obtained. It may be necessary to adjust

the heights of the antennas relative to the ground to achieve the optimum

field resulting from the phase addition of the direct and ground-reflected

waves. In the case of the active repeater, this maximizing of the amplitude of the signal can be accomplished at the repeater receiver, usually

at the intermediate frequency. If the repeater is a passive repeater

and the signal is fed directly from one antenna to the other through a section of transmission line, then the signal at the repeater location

may be monitored on a field -intensity meter. (Note: It is assumed

that radio communications are available between the transmitter location and the repeater location.) After the transmitter-to-repeater leg

is adjusted, the repeater receiving antenna can be connected to the

transmitting antenna, and the same procedure can be followed on the

repeater-to-receiver leg where the signal is monitored at the receiver

location.
167-

b. Single Flat Reflectors

Where a single flat reflector is used as a passive reflector,

the aforementioned expression can be used where K is assumed to be

0, and G is the gain of the reflector. For a passive flat reflector,

the gain is proportional to the effective area of the reflector

G = 10 log

1() A + 20 log1() f Mc - 38.54 (67)

where A is the effective area in square meters of the reflecting sheet.

The effective area of the antenna is the projected area normal to the

transmission path in the direction of either the transmitter or the

receiver. Therefore, if the angle at which the signal from the transmitting antenna strikes the passive reflector is too great, the effective

area of the reflector becomes quite small. It can be seen that for a high-gain flat reflector, considerable area is necessary. This type

of repeater has the advantage of eliminating the line loss which is

found in the back-to-back repeater. The problem of contour tolerance

is more easily solved in the case of flat reflector in contrast to the

large parabolic antennas. A much better surface efficiency is possible

(The aperture efficiency of the parabolic antenna is taken to be 54%.)

c. Multiple Flat Reflectors

To reduce the incident angle that the energy from the transmitter

experiences when directed upon a passive flat reflector, two reflectors

can be used, and this incident angle can be maintained to less than 45°

If the projected areas along the transmission paths are assumed to be

square, and if the geometric mean of the areas of the two reflectors is

large with respect to "v 2d , where d is the separation between the

two reflectors, then (65) applies in a three -path determination.

L

b

= 97.34 + 20 log

1()

dj + 20 log

1() d£ + 20 log

1() d

3

+ 60 log.

n

f - 2G. - 2G_

10 mc 1 2

(68)

where G and G are determined from (67)
-168-

The disadvantage of using flat reflectors as passive repeaters

is in their size and the difficulty in adjusting them. Practical 7-Gc/s

systems using 10 -foot parabolic antennas for transmitting and receiving, and using antennas having acceptable gains at the repeater would

require reflectors in the neighborhood of 55 square meters. If it is

desired to maximize the gain on a path such as this, the difficulty of

moving the repeaters as suggested in the section on using back-toback parabolic antennas can be easily imagined. To maximize a system using multiple flat passive reflectors would require that signal be

transmitted from the transmitting location and be received at the

receiving location, and by radio communications between transmitter,

repeater, and receiving sites, the position of these large reflectors

could be adjusted until the signal is a maximum at the receiving location. Nevertheless, the practicality of a system using multiple flat

reflectors has been demonstrated in practice as described by

Cappuccini and Gasparini [ 1958] and Young [ 195 7] .

It is evident from the equations that the maximum transmission

loss occurs when the repeater is located midway between the transmitter and the receiver, and minimum transmission loss occurs when

the repeater is located close to one end of the path. This arises from

the fact that the transmission loss is a function of the product of d

and d „ .

ACKNOWLEDGMENTS

The authors are indebted to many members of the staff of

Central Radio Propagation Laboratory for the advice and assistance.

In particular, recognition is due J. W. Herbstreit for his continuous

help and advice during the preparation of the manuscript.

Acknowledgment is due J. C. Harman for the drafting of the

figures, C. M. Benedict for the photography, and Miss S. J. Bush who

typed the entire manuscript.
-169-

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-170-

Camies, B. S. , Principles of frequency modulation (John Rider and

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1948).

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Review 109, p. 603 (Jan. 1958).

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(John Wiley and Sons, New York, N. Y., 1956).

Florman, E. F. , and J. J. Tary, Required signal-to-noise ratios,

RF signal power and bandwidth to achieve a given performance of

multichannel radio communication systems, NBS Technical Note

100 (Jan. 1962).

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(July 1944).

Greenquist, R. E., An analysis of passive reflector antenna systems,

Proc. IRE 42, p. 1 1 73 (July 1954)

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Harris, F. S., The parametric amplifier, CQ 14, No. 11, p. 74 (Nov.

1958).
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Haus, H. A., and R. B. Adler, An extension of the noise figure

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Hausman, A. H. , An analysis of dual diversity receiving systems,

Proc. IRE 4_2, p. 944 (June 1954).

Herrmann, G. F., Low noise up-conversion from 500 mc to 10 kmc

using variable capacitance diodes, presented at the 16th Annual

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1958).

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ft U.S. GOVERNMENT PRINTING OFFICE : 1963 0—670950

S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged in technical work.

In general, each section carries out specialized research, development, and engineering in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside ofthe

front cover. WASHINGTON, U. C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. High Voltage.

Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering Metrology.

Mass and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Standard Refer- ence Materials. Applied Analytical Research. Crystal Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Polymers. Macromolecules: Synthesis and Structure. Polymer Chemistry. Polymer Physics. Polymer Characterisation. Polymer Evaluation and Testing. Applied Polymer Standards and Research. Dental Research.

Metallurgy. Engineering Metallurgy. Microscopy and Diffraction. Metal Reactions. Metal Physics. Electrolysis and Metal Deposition.

Inorganic Solids. Engineering Ceramics. Glass. Solid State Chemistry. Crystal Growth. Physical Properties.

Crystallography.

Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials. Codes and Safety Standards. Heat Transfer. Inorganic Building Materials. Metallic Building Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics. Operations Research. Data FYocessing Systems. Components and Techniques. Computer Technology. Measurements Automation.

Engineering Applications. Systems Analysis.

Atomic Physics. Spectroscopy. Infrared Spectroscopy. Far Ultraviolet Physics. Solid State Physics. Electron Physics. Atomic Physics. Plasma Spectroscopy.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation. Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy. Ele- mentary Processes. Mass Spectrometry. Photochemistry and Radiation Chemistry.

Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering Laboratory. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Cryogenic Technical Services. CENTRAL RADIO PROPAGATION LABORATORY

Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere Research. Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Services. Vertical Soundings Research.

Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements.

Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics.

Radio Systems. Applied Electromagnetic Theory. High Frequency and Very High Frequency Research. Fre- quency Utilization. Modulation Research. Antenna Research. Radiodetermination.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. High Latitude Ionosphere

Physics. Ionosphere and Exosphere Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.

RADIO STANDARDS LABORATORY

Radio Physics. Radio Broadcast Service. Radio and Microwave Materials. Atomic Frequency and Time-Interval

Standards. Radio Plasma. Millimeter-Wave Research.

Circuit Standards. High Frequency Electrical Standards. High Frequency Calibration Services. High Frequency

Impedance Standards. Microwave Calibration Services. Microwave Circuit Standards. Low Frequency Calibration

Services.
NBS
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