NASA Technical Reports Server (NTRS) 19740023597: Program on application of communications satellites to educational development: Design of a 12 channel FM microwave receiver. [color television from communication satellites

Survival, Water, Medical Field Manuals

Military Manuals

Nasa Technical Reports Server (Ntrs)

Document text

WASHINGTON UNIVERSITY 


Center for Development Technology 

COMMUNICATIONS GROUP 


Report No. R(T)-74/2 


July. 197^ 


DESIGN OF A 12 CHANNEL FH MICROWAVE RECEIVER 


(NASA-CR-139640) PROGRAM ON APPLICATION 
OF COMMUNICATIONS SATELLITES TO 
EDUCATIONAL- DEVELOPMENT: DESIGN OF A 12 


CHANNEL 
VUniv, ) 


FM MICROWAVE 
166 p HC 


receiver 


i 


(Washington 
CSCL 17B 


N74-31710 


Unclas 

G3/Q9 46880 


Craig 0. Risen 
Fred J. Rosenbaum 
Robert 0. Gregory 


R«p(odluccdrbv 

NATIONAL TECHNICAL 
INFORMATION SERVICE 

us 0«partnieDt of Commerco 
Springfield, VA. 22ISI 



WASHINGTON UNIVERSITY / ST. LOUIS 


PSICES SygiECT TO 

/ MISSOURI 6 313 0 


PROGRAM ON APPLICATION OF COMMUNICATIONS SATELLITES 
TO EDUCATIONAL DEVELOPMENT 

Center for Development Technology 
(Communications Group) 

Washington University 


Report No. R(T)-74/2 


July, 1974 


DESIGN OF A 12 CHANNEL FM MICROWAVE RECEIVER 


CRAIG 0. RiSCH 
FRED J. ROSENBAUM 
ROBERT 0. GREGORY 


This study was supported by the National Aeronautics and Space 
Administration under Grant No. NGR-26-008-054. The views 
expressed in this memorandum are those of the author and do 
not necessarily represent those of the Center for Development 
Technology, Washington University, or the sponsoring agency. 




ii 


DESIGN OF A 12 CHANNEL FM MICROWAVE RECEIVER 
Abstrac t 

The design, fabrication, and performance of elements of a low 
cost FM microwave satellite ground station receiver is described. 

It is capable of accepting 12 contiguous color television equivalent 
bandwidth channels in the 11,72 to 12.2 GHz band. Each channel 
is 40 MHz wide and incorporates a 4 MHz guard band. The modulation 
format is wideband FM and the channels are frequency division 
multiplexed. Twelve independent CATV compatible baseband outputs 
are provided. The overall system specifications are first discussed, 
then consideration is given to the receiver subsystems and the 
signal branching network. 



1i1 


TABLE OF CONTENTS 

No. Page 

1. Introduction 1 

1.1 Background 1 

1.2 Previous Results . ^ 

1.3 System Considerations ^ 

1.4 Scope • 

2. Mixer, IF Amplifier and Band-Pass Filters 13 

2.1 Introduction ..... 13 

2.2 Pre-Amplifier Design 14 

2.3 Power Amplifier Design • • 1^ 

2.4 First Band-Pass Filter 19 

2.4.1 Design and Analysis 1^ 

2-4.2 Performance 21 

2.5 Second Band-Pass Filter 21 

2.5.1 Design and Analysis 21 

2.5.2 Performance 22 

2.6 Mixer Description. . ..... 25 

2.7 Overall Performance of the IF Amplifier. ........ 25 

3. Demodulator and Output Amplifier 36 

3.1 Introduction - - 36 

3.2 Wideband Limiter 36 

3.2.1 Design and Analysis 36 

3.2.2 Single Stage Prototype. . . - • 

3.2.3 Construction of a Two Stage Limiter 42 

3.2.4 Performance .... ......... 44 

3.3 Low-Pass Filter 44 

3.3.1 Specifications 44 

3.3.2 Design and Analysis . 45 

3.3.3 Performance 49 



1v 

TABLE OF CONTENTS 
(continued) 

No. Page 

3.4 Wideband Discriminator 54 

3.4.1 Design and Analysis 54 

3.4.2 Performance 60 

3.4.3 Performance of 300Q Discriminator 60 

3.5 Overall Performance 61 

3.6 Base Band Output Amplifier 68 

3.6.1 Design and Analysis ....... 68 

3.6.2 Performance . 71 

4. Branching Network 76 

4.1 Introduction 76 

4.2 Channel Dropping Filter Design and Theoretical 

Performance . 77 

4.3 Prototype Filter Performance 88 

4.4 Manifold Design and Prototype Performance 89 

5. Conclusions ........... 99 

5.1 Principal. Results 99 

5.2 Future Work. 101 

6. Acknowledgement 108 

7. Appendices 109 

7.1 Filter Design 110 

7.1.1 Introduction HO 

7.1.2 Prototype Equations and Low- Pass Design 110 

7.1.3 Band-Pass Filter Design 119 

7.1.4 High-Pass Filter Design 127 

7.2 Voltage Controlled Oscillator 136 

7.3 Lumped Element Quarter Wavelength Transformer 141 

7.4 Fourier Analysis of a Trapezoidal Wave 143 

7.5 Measurement Techniques 146 



I 


V 

TABLE OF CONTENTS 
(continued) 


No. 


Page 


7.5.1 Measurement of Limiter Harmonics. ...... 

7.5.2 Measurement of Inductance with Hewlett-Packard 

Automatic Network Analyzer. .... 


7.6 Determination of Parallel Line x/4 Coupled Filter 
Dimensions Using a Fibonacci Search. 


149 


8 . 


Bibliography. 


153 



?! 


vi 

LIST OF TABLES 

No. Page 

1.1 Satellite Ground-Terminal Characteristics 3 

2.1 Element Values for First Band-Pass Filter .... 20 

2.2 Element Values for Second Band-Pass Filter 24 

2.3 Mixer Performance Specifications 

3.1 Power Levels of Harmonics in Limiter Output 

4.1 Dimensions of Parallel Strips Normalized to B - 1/8 inch. . . 82 

4.2 Line Lengths for Manifold 95 

5.1 Performance Specifications of Baseband Channel , 104 

5.2 Cost Estimate for One Baseband Channel 105 

5.3 Estimated Cost of the Branching Network 106 

5.4 Estimated Delivered Cost of the Entire Ground Station .... 107 



vn 

LIST OF FIGURES 

No. Page 

1.1 Constitution of the Baseband Signal . 6 

1.2 Block Diagram of 12 Channel Receiver • • • 9 

2.1 Schematic Diagram of MC1590G Package 

2.2 Schematic Diagram of Mixer and IF Amplifier 17 

2.3 Comparison of Amplitude Responses of Branching Network, 

First 8PF, and Second BPF and Resultant Response 23 

2.4 Basic Mixer Schematic 27 

2.5 Isolation Between LO and RF Port in dB as a Function of 

Frequency • • * 28 

2.6 Return Loss of Mixer Input as a Function of Frequency ... 29 

2.7 Input Impedance to Mixer Over the Frequency Range of 1 .0 

to 1.4 GHz Normalized to 50si . 30 

2.8 IF Amplifier Output Power as a Function of Input Power. . . 32 

2.9 Intermodulation Product Levels Relative to fmb as a Function 

of Frequency for Different Levels of fint ^mb • - • • • 33 

2.10 IF Amplifier Frequency Response and Response of Diode 

Detector 34 

3.1 Basic Limiter Configuration 37 

3.2 Limiter Input (Dotted Line) and Output (Solid Line) as a 

Function of 0 for One Period 39 

3.3 Change in Output Power as a Function of the Change in Input 

Power for Single Stage Limiter * ^1 

3.4 Limiter Amplifier Schematic . 43 

3.5 Change in Output Power as a Function of the Change in 

Input Power for a Two-Stage Limiter ...... 46 

3.6 Photograph of Limiter Output at 80 MHz 48 

3.7 Experimental and Theoretical Responses for Limiter Low-Pass 

Filter 51 



VI i 1 

LIST OF FIGURES 
(continued) 


No. 


Page 


3.8 Output Power as a Function of Input Power for 

Three Different Frequencies 

3.9 Frequency Response of Limiter 

3.10 Basic Discriminator Configuration 


3.11 Open Circuit and Short Circuit Transmission Line Equivalent 
Circuits 


52 

53 
55 

57 


3.12 Normalized Discriminator Output as a Function of Input 

Frequency . . . 

3.13 Prototype Discriminator Output as a Function of Input 

Frequency * 

3.14 Voltage Output as a Function of Input Frequency for the 

Open and Short Circuit Line Equivalents 

3.15 System Response at the Output of the Limi ter-Fil ter . . . , , 

3.16 System Response After Tuning Limiter-Fi Iter . . 

3.17 Discriminator Output as a Function of Frequency When 

Connected to Limiter Output .... . 

3.18 Discriminator Output for Various Input Levels 

3.19 Output Amplifier Schematic. 

3.20 Overall Schematic of Demodulator and Output Amplifier . . . . 

3.21 Output of Final Amplifier as a Function of Input Frequency 

Deviation 


58 

62 

63 

65 

66 

67 

69 

70 
72 

74 


3.22 Final Amplifier Output Voltage as a Function of Input 
Frequency Deviation for Differing Input Power Levels. 

4.1 Power Levels and Frequencies of LO Relative to 

the Signal Channels, Dotted Lines are LO Power Level 
Before Isolation, Solid Lines Indicate Level After 
Isolation . . 


78 



ix 


LIST OF FIGURES 
(continued) 


No. Page 

4.2 Five Resonator Parallel Coupled Resonator Filter. ..... 80 

4.3 Filter Amplifier Schematic 83 

4.4 Filter Amplifier Gain and Reverse Isolation Over the 

Range of 1.0 to 1.4 GHz 84 

4.5 Input and Output Return Loss Swept Over the Range of 

1.0 - 1.4 GHz with Upper Trace Showing 0 dB Reference ... 85 

4.6 Forward IsolationiFrequency Swept from 1.0 to 1.4 GHz 
with Top Trace or 0 dB Reference and Vertical Scale 

of 2 dB/cm 86 

4.7 Theoretical Prototype Channel Dropping Filter 

Performance ..... 87 

4.8 Experimental and Theoretical Responses for Prototype 

Channel Dropping Filter - • • • ^0 

4.9 Branching Network . . 93 

4.10 Branching Network Insertion Loss (Solid Line) and Return 

Loss (Dotted Line) as a function of Input Frequency .... 97 

4.11 Passband Response of a Typical Filter 98 

5.1 Baseband Channel Package. . 103 

Appendices: 

7.1.1 Focal Program for Determining the Number of Elements in 

a Low-Pass Filter. • 112 

7.1.2 Low- Pass Filter Configurations 113 

7.1.3 Low-Pass Filter Frequency Response 114 

7.1.4 FOCAL Program for Generating the g Values and Determining 

the Values of the Elements in a Low-Pass Filter 117 

7.1.5 Print Out of Low-Pass Filter Design Program . . . 118 

7.1.6 Low-Pass Limiter Filter. 120 

7.1.7 Frequency Response of a Band-Pass Filter ... 121 



X 


LIST OF FIGURES 
(continued) 

No. Page 

7.1.8 FOCAL Program to Determine the Number of Elements for a 

Band-Pass Filter 122 

7.1.9 Possible Band-Pass Filter Configurations 123 

7.1.10 Band-Pass Design Program. 126 

7.1.11 Print Out for Band-Pass Design Program 128 

7.1.12 Input Band-Pass Filter 129 

7.1.13 Frequency Response of a High-Pass Filter 131 

7.1.14 FOCAL Program for Determining the Number of Elements in a 

High-Pass Filter 1^2 

7.1.15 High-Pass Design Program 133 

7.1.16 Possible High Pass Configurations 134 

7.1.1? Print Out of High-Pass Design Program 135 

7.1.18 High-Pass Filter Design Example 137 

7.2.1 Voltage Controlled Oscillator ..... 138 

7.2.2 VCO Output Frequency as a Function of Input Voltage to 

the Varactor 139 

7.2.3 VCO Output Power as a Function of Output Frequency 140 

7.3.1 x/4 Transmission Line and Equivalent Circuit ... 142 

7.3.2 Magnitude of Reflection Coefficient as a Function of 

Frequency for a/4 Transformer 1^^ 

7.5.1 Experimental Set-Up Used to Measure Harmonic Content of 

the Limiter 1^7 

7.5.2 Set-Up for Inductance Measurement 1^3 

7.6.1 Part I of Search Program 131 

7.6.2 Part II of Search Program * 132 



DESIGN OF A 12 CHANNEL FM MICROWAVE RECEIVER 


1.1 BACKGROUND 

The communication satellite is being seen as an evermore viable 
means of providing an educational communication system. (1)* If a 
multi -carrier satellite transponder having a large number of TV- 
equivalent bandwidth channels were used in conjunction with a CATV 
system it would be possible to economically disseminate large amounts 
of information to many subscribers. In order to implement such a 
system with many points of reception, low cost terminal equipment 
is required. Newman et. al . (2) have suggested the use of multi- 
channel, multicarrier ground station receivers to provide the 
necessary satellite to CATV interconnection using one RF carrier 
per channel . 

Although it is intended for use in an educational satellite 
netv\fork, low cost ground receivers such as the one described here 
could be used for commercial purposes as well. 

This report is concerned with the implementation of a low cost 
microwave receiver. This receiver is designed to accept 12 contiguous 


*The numbers in parentheses in the text indicate references in the 
Bibliography. 



2 


color television equivalent bandwidth channels in the 11.72 to 12.2 
GHz band using a wideband FM format and frequency division multiplexing 
(FDM) of the channels. Each individual channel is to have a usable 
bandwidth of 36 MHz and a guard band of 4 MHz. The receiver provides 
an output for each channel compatible with standard video signals 
suitable for use with a CATV headend. 

As it is our intention thac these receivers find widespread 
usage, both in education and commercial systems, a low cost (less 
than $10,000) is a major design consideration. For example, a double 
conversion scheme is used which allows construction of the channel 
dropping filters at L-band, utilizing stripline techniques which 
are more economical than the use of wave guide or coaxial filters as 
required at higher frequencies. Beyond the channel separation 
filters, i.G, branching network, the design of each channel is iden- 


tical. Straightforward, yet innovative designs were attempted which 
use standard components. Identical components have been used as 
much as possible to obtain economies of scale. The use of tunable 
elements has been avoided wherever possible to eliminate the need 
for complicated testing and alignment procedures. 

The main emphasis of this report will be on the design of the 
branching network and baseband channels along with some discussion 
on the front-end design of the receiver. Theoretical performance 
characteristics based on overall system requirements are determined 
for each subsystem. The performance of each subsystem is evaluated to 
see how well the specifications are met. In order to lend some per- 
spective to the work reported here let us first examine some other 
work done in the area of ground station receiver design. 



3 


1.2 PREVIOUS RESULTS 

General Electric has reported a single conversion, single 
channel receiver (3) (4). Use of the appropriate converter on the 
front end allows for either 2.5 GHz or 12 GHz reception. The converter 
feeds a 7 stage transistor IF amplifier having a center frequency of 
120 MHz with a bandwidth of 40 MHz and an overall gain of 45 dB, 
Following the IF amplifier is the limiter which is a single stage 
differential amplifier with a low-pass filter at the output. The 
discriminator uses open and short circuited A/8 transmission lines 
with S-band Schottky diodes as the detectors. The baseband amplifier 
is DC coupled to the discriminator to produce the necessary video 
output of IVpp into 75f^. 

Lusignan, et. al. (5) report another single channel, single 
conversion system for use at 2.62 GHz. The front-end down converter 
for this system provides an IF of 120 MHz. The IF Amplifier has a 

25.2 MHz bandwidth and a gain of 60 dB. It is implemented by a 
cascade of four transistor stages with an FET input. All stages are 
transformer coupled. The limiter, which Is coupled to the output 

of the IF Amplifier through a 3-pole filter, is merely a two stage 
differential amplifier running in saturation. The limiter has a 
5 dB dynamic range. The discriminator which is directly coupled 
to the limiter uses a single 3x/8 short circuited transmission line 
and one detector diode. The resulting output suffers at most a Z% 
deviation from linearity over a 25 MHz bandwidth centered at 120 
MHz. 

Another single channel, single conversion system has been 
reported by NASA (6). The front-end converter is designed to work 



4 


at 845 to 875 MHz and to provide a 70 MHz IF. The IF amplifier 
consists of four cascaded transistor stages capacitively coupled. 

It has a voltage gain of 75 dB, provides a nomnal output of 0 dBm 
into 75^?, and must accept -60 to -30 dBm, 75fi inputs. The dynamic 
range is 20 dB and the 1 dB bandwidth is 30 MHz. The limiter is a 
three stage transistor amplifier employing signal biased back-to- 
back diodes at the output of the last two stages. Its operating 
input level is 0 dBm at 75 r. Tne dynamic range is 15 dB and the 
0.5 dB bandwidth 1s 30 MHz, Two transistors turn the single 
ended output of the limiter into a balanced output which drives a 
Foster-Seely type discriminator which has an output linearity of 
3% over the 30 MHz band. A three stage FET amplifier provides a 
standard video signal of 1 Vpp into 75fi. 

RCA (7) has reported the design of a 24 channel spaceborne 
transponder for operation at 5925 to 6425 MHz in the receiver mode 
and 3700 to 4200 MHz in the transmit mode. The bandwidth of each 
of the baseband channels is 36 MHz. 

1.3 SYSTEM CONSIDERATIONS 

Based on a report of the results of the 1971 World Administra- 
tive Radio Conference (8) and the existing usage of the various 
services discussed in that report, operation in the 12 GHz region 
is indicated for television broadcasting from satellites. The 
receiver we have designed is to be used in a multi carrier system 
where individual TV channels are Frequency Division Multiplexed (FDM) 
together in a 11.72 - 12.20 GHz band. Such a system has several 
important advantages over a single carrier system. First, it allows 
Individual TV channels to originate simultaneously from different 



5 


programming centers. It also permits channelization in the satellite 
transponder design so that one can limit certain failures in the 
transponder to individual channels. The need for tight phase and 
amplitude requirements over broad bandwidth in the various subsystems 
of the transponder and earth terminal is reduced by a multi carrier 
approach. 

The constitution of the baseband signal is shown in Figure 1.1. 

In addition to the standard video signal, the system must handle two 
15 KHz aural signals. The two aural channels are handled by FM 
modulating two subcarriers, one at 4.7 MHz and the other at 5.5 MHz, 
and then frequency division multiplexing them with the video baseband. 

In any satellite to earth communication system there is a optimum 
balance between the amount of Effective Radiated Power (ERP) produced 
by the satellite and the needed sensitivity or "Figure of Merit (G/T)" 
for the earth station receiver. In general, G/T is defined as the 
ratio of antenna gain to overall system noise temperature and is 
expressed in dB/^’K. The optimum G/T which produces the best overall 
system economy depends on the user, system requirements, launch vehicle 
constraints, etc. Computer aided satellite system analysis and 
utilization studies carried out by Stag! et. al . (9) at Washington 
University indicate 18*'22 dB/°K to be the optimum range for G/T for 
a community reception type satellite television broadcast system in 
the U.S. for near term educational program delivery via interconnection 
of institutional and commercial CATV headends. Based on satellite 
television broadcasting system optimization studies, (9) (10) we 
have opted for G/T of 17.5 dB/*^K for our receiver. This G/T is to 
be achieved with a 10 ft. parabolic antenna which has 49 dB gain at 



6 



Fig. 1.1 Constitution of the Baseband Signal 


7 


12 GHz and a receiving system noise temperature of 1400®K of which 
200° K is attributed to antenna noise and the remainder to the 
receiver. This 10 ft. disk should have limited steering capa- 
bilities and a 3 dB beamwidth of .55° - .60° which is adequate to 
accomodate wind caused deviations from the set axis and the satellite 
movements provided that the spacecraft has a ±0.1 East-West as well 
as North-South station keeping ability. 

With an ERP of 56 dBW per TV channel and a 36 MHz RF channel 
bandwidth, the proposed terminal with a G/T of 17.5 dB/°K will be able 
to deliver a peak video signal power to weighteo r.m.s. noise ratio 

[S/N] of 53 dB for 99.8 percent of time in a region with rain 
y j w 

statistics similar to that of New Jersey. {2) With the satellite 
uplink, downlink and the farthest route in the cable-television 
distribution plant peak weighted signal to noise ratio [S/N] being 

P ?w 

67 dBj 53 dB and 53 dB respecti vely» the user served by the farthest 
drop cable facility would have the potential of receiving a [S/N] 

p ,w 

of 49 dB or a TV picture equivalent to TASO Grade I. (2) 

The desired characteristics of the ground terminal are summarized 
in Table 1.1 and the resulting receiver block diagram is given in 
Figure 1.2. The expected input power level is -74 dBm per channel. 
Allowance is made for a 15 dB fade margin. In order to eliminate the 
need for a balanced mixer configuration at the input and to more 
easily facilitate separation of the channels, we have opted for a 
double conversion scheme. 

The front-end down converter which frequency shifts the informa- 
tion from 11.72 - 12.2 GHz to 1.02 - 1.5 GHz was built by Westinghouse 



8 


TABLE 1.1 


SATELLITE GROUND-TERMINAL CHARACTERISTI CS 


Ground Terminal lype 

Receive Only 

Antenna 

10-ft. parabolic dish 
Limited manual steering 

Antenna Gain 

48.98 dB at 12-GHz 
54 percent efficiency. 

Antenna Polarization 

Linear 

Antenna Noise Temperature [T^] 

200” K (Maximum) 

Low Noise Receiver 

Double Conversion - 
First IF at 1 GHz and 
the second at 80 MHz 
Channel Separation 
after 1st IF. 

Receiver Noise Temperature [T^] 

1,200”K (Maximum) 

Receiver Bandwidth 

11.700 - 12.200 GHz 

Individual RF Carrier Bandwidth 
(Per.TV Channel). . 

36 MHz 

Modulation 

Frequency Modulation 

Demodulator 

Discriminator (12 dB 
threshold) 

Receiving System Noise 

Temperature [T^=T^+Tp] 

1 ,400”K 

Receiving System [G/T] 

[Antenna Gain to System Noise 

17.52 dB/”K 


Temperature Ratio] 




Figure 1.2 Block Diagram of 12 Channel Receiver 





10 


(n). It consists of a single ended (single diode) mixer employing 
image and sum frequency enhancement techniques to achieve a midband 
insertion loss of 3.8 dB, and a three stage IF amplifier having a 
noise figure of 2.5 dB. The overall conversion results is a gain 
of 25 dB. 


The branching network used in the present effort consists of a 
set of 12 doubly terminated Tchebycheff filters appropriately spaced 
along a distribution network. To help make up for distributed losses 
and to allow for an additional measure of isolation against leakage 
from the second local oscillator (LO) into adjacent channels, a 
single transistor amplifier is implemented at the output of each 
fi 1 ter . 

After branching, the 12 individual channels are now available to 


the inputs of 12 identical 


■i n/ln rli 13 1 

tifVti f iviviMI 




a itidA i Ilf Jill 


level of -40 dBm. As seen in Figure 1.2, each baseband channel con- 
sists oT'a' mixer, ba^ filter (BPF), IF amplifier j group delay 
equalizers (G.D.E.), limiter^ discriminator and baseband amplifier. 

The mixer at the input to each of these channels converts to the second 
intermediate frequency of 80 MHz. Preliminary calculations showed 
that this frequency would most easily facilitate the synthesis of the 
required set of 12 local oscillator frequencies. An appropriate band- 
pass filter having a bandwidth of 36 MHz filters the output of the 
mixer and provides some additional channel selectivity. The IF 
amplifier should be able to provide a nominal 10 dBm level for a minimum 
input of -70 dBm, to drive the limiter and discriminator. The 
limiter must be wideband (40 MHz) and have a minimum 10 dB dynamic range. 
The discriminator must provide an extremely linear output {< 3 % deviation) 



11 


from linearity, based on previous work (5) (6), to prevent phase 
distortion of the signal. The final amplifier provides a 1 Vpp 
composite video signal into 75fi which is compatible with typical 
CATV remoduldtors for local distribution. Provision is made for 
group delay equalizers to adjust the channel’s delay characteristics. 

It is planned that the 12 local oscillator frequencies for’ the 
baseband channels plus the X-band LO for the front end will be * 
synthesized from one 10 MHz crystal used in conjunction with 
appropriate harmonic generators, mixers, and filters. 

1.4 SCOPE 

Chapter 2 is concerned with the design, construction, and 
performance of the IF amplifier. Included in this section is a 
discussion on the specification of the bandpass filters and their 
design. The performance of a commercially made mixer is also 
discussed. The section concludes with some data taken on the 
overall IF amplifier performance when driven by the mixer. 

Chapter 3 is devoted to the limiter and discriminator. The 
design of a simple limiter configuration and its performance are 
first considered. This is followed by a discussion on the design 
of a low-pass filter to remove the higher order harmonics in the 
limiter's output to the discriminator. The design of a modified 
transmission line discriminator then follows along with a discussion 
on the conversion from a distributed parameter to a lumped parameter 
system. This chapter concludes with performance results for the 
entire baseband channel from the input of the mixer to the output 
of the baseband amplifier. 



12 


Chapter 4 discusses the design criteria for the branching 
networks. Theoretical performance is considered along with the 
performance of a first cut prototype filter design. 

A final discussion and summarized results are given in 


Chapter 5. 



13 


2 . MIXER, IF AMPLIFIER AND BAND-PASS FILTERS 
2.1 INTRODUCTION 

This chapter describes the design, construction, and performance 
of the IF amplifier and its accompanying band-pass filters. Also dis- 
cussed is the performance of a small commercially produced flat pack 
mixer used to down convert from L-band to the 80 MHz IF. The specifi- 
cations for the amplifier are discussed first. These include deter- 
mining input and output power and impedance levels, overall gain require- 
ments, bandwidth, and selectivity. Then consideration is given to 
implementing a design and evaluation prototype performance. Finally, 
the overall performance of the IF amplifier with the mixer driving 
it is reported. 

The preliminary operating specifications for the IF amplifier are 
specified by Newman et. al . (2). Final specifications evolved during 
the design phase. Based on the input impedance level and power require- 
ments of the limiter, the IF amplifier should have an output impedance 
level of 300i^ and be able to provide about 6 Vpp. This corresponds to 
an output power of approximately 12 dBm. Its input impedance should 
match the mixer s output impedance of and it should be able to amplify 
a minimum signal of -70 dBm. Hence, the amplifier must have a maximum 
gain of 80 dB over the frequency range of 60 to 100 MHz. In order to 
eliminate the need for an AGC loop and to provide additional limiting 
we will consider operating the amplifier near or in saturation, provided 
that its intermodulation characteristics do not adversely affect the 
system performance. 

The band pass specifications and selectivity of each channel are 
now considered. The selectivity requirement chosen is based on that 



14 


used for the microwave receivers of the Bell System's TH-3 telephone 
communication system (12): at least 30 dB suppression of the adjacent 

channel band edges. Based on Carson's rule, at least 36 MHz is needed 
for the desired FM format. Allowing a 4 MHz guard band, 40 MHz of 
bandwidth per channel is available in our design. Therefore, the 
amplitude roll-off can start ar, 62 and 98 MHz, respectively, and be 
down 30 dB at 58 MHz and 102 MHz. Since the sharpest selecti vities 
with the fewest number of elements are obtained with the Tchebycheff 
response, such filters are used in the design. 

Before turning to the actual design, let us consider the configura- 
tion we intend to use for the amplifier. One can think of the IF 
amplifier as consisting of a pre-amplifier section and power amplifier 
section. The band pass filter is also implemented in two sections. 


One is at the input tn the first pre-ampl 1 ficr stage, the other foil 


uw- 


ing it. Although both filters serve the purpose of eliminating out- 
of-band signal components, the second band pass filter also helps 
eliminate high frequency noise in the amplifier. In addition, such 
an arrangement prevents the need for a multipole filter at the input 
to the IF Amplifier which might prove difficult to tune and have 
excessive insertion loss. 


2.2 PRE-AMPLIFIER DESIGN 


Most of the gain is to be developed in the pre-amplifier section . 
The easiest and most economical way of implementing this section is to 
use several high frequency, linear amplifier integrated circuits in 
cascade. The MC1590G integrated circuit presents acceptable charac- 
teristics for such use. According to its specifications, each package 
should be able to provide at least 20 dB of gain out to 100 MHz. 



15 


Figure 2.1 shows a schematic diagram of this package (13). By adjusting 
the size of the load resistors, Rj^, through which bias is supplied 
to pins 5, 6, and 7, one can control the gain and resulting band- 
width. For R|^ = 100 u, each package is able to develop a gain of 
between 20 and 25 dB. For this amount of gain however, the response 
starts to roll off above 80 MHz. By using inductive peaking on the 
output pins 5 and 6, it is possible to raise the response on the 
high end. To calculate the required inductance, one first determines 
the input and output impedance of the package. From the data sheet, 
it is found that the output capacitance and resistance are 2 pf 
and Rq ^ 2to, respectively. For the input there is a capacitance 
C. 8 pf and resistance R^. IKj^. Maximally flat response out to at 
least 100 MHz requires (l4): 



where - 100 U and C = + Cq = 10 pf. Solving equation 2:1, one 

finds that L = .04 ^h. 

’ The pre-amplifier stage was prototyped by cascading two packages 
in the same manner as I.C. 2 and 3 in Figure 2.2. For proper 
operation, DC bias must be applied to pins 5, 6, and 7. By supplying 
22 volts to the 120 resistor at the input to the biasing network it 
is possible to bias pins 5, 6, and 7 to their maximum rated level of 
18 volts. This level results in the most gain per package. From the 
32 volt level required to operate the limiter, the 22 volt level is 
obtained from the 2N2959 emitter follower and zener diode configuration 
indicated in Figure 2.2. For use in the prototype, pin 1 on the first 
package was terminated in 50 to match the signal generator. Also, 






Figure 2,2 Schematic Diagram of Mixer and I.F. Amplifier 



18 


pin 5 on the second package had the same R-L arrangement as pin 6. 
Point by point measurements showed that there was a 2 dB variation 
in gain over the range of 60 - 100 MHz and a gain of approximately 
23 dB per package with an input level of '-50 dBm, A cascade of three 
of these packages is needed to adequately drive che power amplifier 
for inputs at -70 dBm. 

2.3 POWER AMPLIFIER DESIGN 

Preliminary considerations for this stage suggested that a 
push-pull arrangement would be desirable since both outputs of the 
MC1590G could be used. However, subsequent prctotyping and testing 
of such an arrangement indicated that the necessary gain and required 
bandwidth could not be obtained. This was largely due to the problem 
of effectively fabricating transformers at these frequencies. 

Instead of the push-pull arrangement, only oin 6 is used to 
drive a feed-back pair of 2N918 transistors in the arrangement shown 
in Figure 2.2. The design of such a stage is reasonably straight- 
forward and can be easily developed experimental 1y as was done here. 
The 2.2Kfi resistor in the collector of the input transistor serves 
mainly as a bias resistor and Its value is not overly critical. The 
value of 330 in the collector of the output transistor v/as chosen 
to provide a 300 output level for the limiter and the value of 
180 Q in the base of the input transistor provided the best match to 
the pre-amplifier output. It was found that providing some series 
feedback in the emitter in addition to the shunt feedback of a 470 Q 
resistor provided the necessary power to drive the limiter over the 
frequency range of interest. It was found that this stage when 



19 


prototyped provided an additional 13 dB of gain to the signal 
appearing at the output of the preamplifier when biased at 22 volts 
as shown in Figure 2,2. 

2.4 FIRST BAND-PASS FILTER 
2.4.1 Design and Analysis 

In order to arrive at a suitable design for the first band-pass 
filter, the following parameters must first be specified: selectivity, 

center frequency, upper and lower cut-off frequencies, acceptable 
passband ripple and impedance level. The selectivity is first 
determined. In order not to have too many elements and a high pass- 
band insertion loss, a specification of 30 dB attenuation at 120 MHz 
was chosen. It will be seen later that this taper along with the 
tapers of the branching network and second band-pass filter are 
adequate to provide the necessary 30 dB attenuation at adjacent band 
edges. The center frequency is 80 MHz and the upper and lower cut-off 
frequencies are 98 MHz and 62 MHz respectively. The passband ripple 
should be .01 dB to provide a smooth passband response and the 
impedance level is SO Q to match the mixer. 

Applying the methods outlined in Appendix 7.1.3, it was determined 
that a filter having these specifications must have 4 resonators with 
the element values indicated in Table 2.1. This filter is shown 
schematically in Figure 7.1.12. It must be noted that a slight impedance 
transformation takes place, since the required terminating resistance 
is 55 Q. This terminating resistance is realized in a 56 resistor 
which is connected between pin 1 of IC number 1 and ground. 



20 


TABLE 2.1 Element Values for First 
’Band-Pass Filter 


Resonator 

L 

C 

No. 

Mh 

pf 

1 ■ 

.06614 

63.0316 

2 

.25634 

15.7118 

3 

.03568 

1 16. 827 

4 

.14316 

29.1212 



21 


2.4.2 Performance 

The filter was constructed using hand wound inductors and stock 
value silver mica capacitors. The inductors were fabricated with #30 
wire using 22 1/4 watt resistors as the form and applying the formu- 

las of Grover (15) to determine the number of turns. The completed 
inductors were then tested on a phase meter according to the method 
shown in Appendix 7.5.2 and the turns spacing was adjusted to provide 
the required inductance. For the required capacitance values, parallel 
combinations of not more than two fixed capacitors were used to attempt 
to realize as closely as possible the values indicated in Table 2.1. 

In practice these values can be realized to an accurancy of 5%. 

Subsequent swept measurements indicated that some trimming was 
needed to tune up the response. It was found that the best response 
was obtained using values shown in Figure 2.2. This arrangement 
gave a reasonably flat amplitude response with about a ± .5 dB ripple 
over the pass band. At 62 and 98 MHz the response was down 1 dB. Due to 
the lack of sensitivity of our equipment we were unable to effectively 
measure out-of-band response. Although this response is somewhat 
different from the calculated response, one must consider that these 
filter designs are based on loss free considerations (i.e, infinite Q 
inductors and capacitors). Also, we are not able to realize the 
precise values of required inductance and capacitance. Furthermore, 
there are parasitic effects which are hard to account for. 

2.5 SECOND BAND-PASS FILTER 
2.5.1 Design and Analysis 

The selectivity of this filter is specified by the performance of 
the branching network filters and first band pass filter. Together, 



22 


both of these filters provide 60 dB of attenuation at 120 MHz. A 
brief graphical analysis given in Figure 2.3 shows that if an 
attenuation of 30 dB at 110 MHz *^or the second band pass filter is 
specified, there will be a tota" of 30 dB of attenuation at 58 and 
102 MHz as desired. The center frequency is 80 MHz with upper and 
lower cut-off frequencies of 100 and 60 MHz. Tne pass band ripple 
again is to be .01 dB and the impedance level is 100 K to match 
the biasing resistance on pin 6 af the IC package.. 

Applying the methods of Appendix 7.1.3, the number of resonators 
required is found to be 7. The required values of inductance and 
capacitance are found as outlined in Appendix 7.1.3, also. Assuming a 
configuration of the form shown in Figure 7.1.9, the resonators 
should have values of L and C as indicated in Taole 2.2. On this 
structure, the input and output impedance are each 100 s). 

2. 5.2 Performance 

This filter, like the first band-pass filter, was constructed 
with hand wound inductors and stock capacitors. Initial swept 
measurements indicated that some trimming of component values was 
necessary to tune up the response. By altering capacitor values as 
shown on Figure 2.2, an equi -ripple response of ± .5 dB between 62 and 
98 MHz was obtained. Again, it was difficult to effectively measure 
the out-of-band response due to the lack of sensitivity of our 
equi pment. 

As before, the difference between the response predicted by the 
design equations and the actual response can be attributed to lossy 
elements, inability to obtain the exact required value for a given 
element and parasitic effects. 



Insertion Loss, dB 


23 



Input Frequency, MHz 


Figure 2.3 Comparison of Amplitude Responses of 
Branching Network, First BPF 
and Second BPF and Resultant Response 




24 


Table 2.2 Element Values for 
Band-Pass Filter 

Second 

Resonator L 

C 

" yh 

pf 

1 and 7 .13314 

31.7095 

2 and 6 .55403 

7.6200 

3 and 5 .06070 

69.5561 


4 


.64780 


6.4969 



25 


2.6 MIXER DESCRIPTION 

The mixer used to down convert from L-band to the 80 MHz 
IF is manufactured by Merrimac Research and Development Inc. 

It is their model DMF-2A-750 "Flat Pack" subminature mixer which has 
specifications as given in Table 2.3. The device measures .13 X .50 
X .38 inches and has 8 pins, three of which serve as connections for the 
LO, RF, and IF respectively. The rest are connected to ground. Figure 

2.4 shows the schematic diagram of this device as furnished by 
Merrimac. The hot carrier diodes are arranged in a monolithic IC 
quad. 

Subsequent testing showed that the mixer was within its advertised 
specifications. Figure 2.5 shows a plot of LO to RF port 
isolation as h function of frequency. 

2.7 OVERALL PERFORMANCE OF THE IF AMPLIFIER 

Driving the IF amplifier from the output of the mixer, measure- 
ments were made on the input impedance to the mixer* minimum detectable 
signal, linear dynamic range, two tone i.itermodulation products, 
and the frequency response. All of these measurements are referenced 
to the input of the mixer. At the output of the amplifier, a 300 
to 50 resistive L-pad was used to provide about 20 dB of attenuation 
and the appropriate impedance match to the 50 u measurement system. 

The RF port to the mixer was matched experimentally with a 1 pf 
capacitor to ground across the RF input line to the mixer. This 
resulted in a return loss of more than 15 dB over the range of 1.0 to 

1.4 GHz as shown in Figure 2.6, Figure 2.7 shows the Smith chart 
representation of the input impedance normalized to 50 a over the same 



26 


Table 2.3 Mixer Performance Specifications 


Frequency Range 


RF and LO 

50-1500 MHz 

I.F 

DC - 1000 MHz 

Isolation 

LO - RF 

25 dB 500-1500 MHz 

LO - IF 

20 dB 500-1500 MHz 

RF - IF 

15 dS 500-1000 MHz 

Conversion Loss 

9 dB 

Compression (1 dB) 

0 dBm 

Impedance (Nominal) 

50 n 

Local Oscillator Drive 

+10 dBm 

Max. Input Power 

+17 dBm 

N.F. 

9 dB ± 1 dB 

Wei ght 

2.8 grams 



27 



Figure 2.4 Basic Mixer Schematic 






Isolation, dB 


28 


40 ! - - __ j: 

|- . '' j 

30 : — ■ ^ j 

I 

20 ’ — ! 

10 - 111 ^ 
-ill 

. L....... 1 . . ! . L- I ! 

.9 1.0 !.l 1.2 1.3 1.4 

LO Frequency, GHz 


Figure 2.5 Isolation of Between LO and RF Port 
in dB as a Function of 
LO Frequency 




Upper Trace is 0 dB Reference 


Vertical Scale: 5 dB/cm 

Horizontal Scale: Trace Begins at 

1.0 GHz and Ends 
at 1.4 GHz 


Figure 2.6 Return Loss of Mixer Inout as a 
Function of Frequency 



30 



Figure 2.7 Input Impedance to Mixer Over the 
Frequency Range of 1.0 to 1.4 GHz 
Normalized to 50^2 



31 


frequency range. As can be seen, the input impedance is nominally 
between 50 ^ and 75 At 1 GHz, the input is about perfectly matched 

to 50 U- In a similar manner, the LO port is matched by slightly 
widening the input line to obtain a nominal return loss of 10 dB. 

The minimum detectable signal at the mixer's input was found 
to be approximately -86 dBm. A plot of output power as a function of 
input power as shown in Figure 2.8. Curve A is the measured response. 
The output wideband noise level is -2.67 dBm and affects the dynamic 
response at low levels. Curve B shows the equivalent linear dynamic 
range if no noise were present. From Curve A it is apparent that the 
range of linear operation is between -65 dBm and -52 dBm. Operation 
into the nonlinear range, as will be seen later, can result in 
higher intermodulation distortion than operation in the linear range. 

In order to study the effects of intermodulation distortion, 
two signals (tones) .were fed simultaneously into the RF port of 
the mixer. One tone, f^^^, at 1240 MHz, produces the desired 80 MHz 
IF while the other tone, f.^^, was varied between 1220 MHz and 1260 
MHz to produce interf erring signals in the 60 to 100 MHz IF band. 

A spectrum analyzer was then used to measure the resulting spurious 
signals. Figure 2.9 shows the power levels of the resulting spurious 
signals relative to the level of f^j^ plotted as a function of their 
frequency for three different levels of The desired signal 

f^b ^ level of -50 dBm, the point at which the amplifier begins 

to saturate. The level of f^j^ was then lowered to -55 dBm. It was 
found that spurious signals are not detectable if f.^^ were much 
below -55 dBm, as is shown in Figure 2.9. As can be seen, operation 



Output Power, dBm 






at "55 dBm 
1 nt 

f^b at -55 dBny^ 



f. . at -50 dBm 
- int 



Input Frequency, MHz 
nf f. . where f_u= -50 dBm Except as o 


34 



Vertical Scale: 1 dB/cm 

Horizontal Scale: MHz as Marked 


Figure 2.10 IF Amplifier Frequency Response and 
Response of Diode Detector 




35 


of the amplifier into the nonlinear region produces considerable 
intermodulation product levels. 

The overall frequency response from the input to the mixer to 
the output of the IF amplifier as measured on a network analyzer is 
shown in Figure 2.10. This response was obtained for an input level 
of “55 dBm. The trace below the response curve represents the network 
analyzer diode detector’s characteristic. As can be seen, there is a 
± .5 dB bandwidth of 36 MHz which meets the specifications for the 
IF amplifier. 



36 


3 . DEMODULATOR AND OUTPUT AMPLIFIER 


3.1 INTRODUCTION 

This section presents an analysis of and ?et of design criteria 
for an FM demodulator having a 40 MHz bandwidtf' operating over a 
range of 60 MHz to 100 MHz with center frequency of 80 MHz. Also 
presented is the design of a 5 MHz baseband output amplifier. The 
demodulator consists of three basic components; a wideband limiter* 
a low pass filter and a wideband discriminator. 

We shall first discuss the design of the wideband limiter 
which is to have an operating bandwidth of at least 40 MHz and a 
10 dB dynamic range. Next, a low pass filter which orovides 
suppression of the unwanted harmonic frequencies generated by the 
limiter is considered. Then an FM discriminator which has a virtually 
linear DC output characteristic over the operating frequency range 
is discussed. The last component considered is the baseband 
amplifier which is used to provide IVpp into 75fi from the discrimina- 
tor's output- The performance of the entire demodulator is also 
described. 

3.2 WIDEBAND LIMITER 
3.2.1 Design and Analysis 

For the receiver, a two stage limiter was chosen. Each stage 
has a configuration shown in Figure 3.1. For quiescent D-C 
conditions one can write: 




° ■ '^ D 2 ■ ^3 ^^3 ■ ^2 **2 


(3.1) 


(3.2) 



37 



<? 



Figure 3.1 Basic Limiter Configuration 



38 


where Vp^ and Vp^ the diode voltage drops, 
voltage appearing across R-j (and 

V. - V, 


The quiescent 


w - w - 'B ~/D1 
^2 


(3.3) 


+ 1 


Since V-j and represent the voltage at which the limiter clips the 
incoming signal, this voltage is called the limiting voltage and is 
denoted by V^. It should be noted that Equation (3.3) does not take 
into account the effects of an actual load on the output. To 
compensate for this effect, R 2 must be replaced by R 2 * in Equation 


(3.3) such that: 


R 


2 


^2 

\ * “^2 


(3.4) 


Where Rj^ is the load resistance. 

An AC signal is now applied to the input. The reactance of 
C-| and is neglected. The amplitude A of the input signal is 
always taken to be much greater than V^. In its positive half 
cycle, the input signal is clipped by the diode . Similarly, the 
negative half cycle is clipped by the diode D 2 - Hence, the output 
of the limiter will be a modified trapezoidal wave as shown in 
Figure 3.2. 

Since the diodes act as switches, the input and output 
impedances vary with time. Assuming a sinusoidal signal, of 
amplitude A, it is seen that when it is between ~V^ and both 
diodes are on and the input and output impedances are the 
parallel combination of R-j , R 2 and R^. The time during which the 
input signal exceeds V^, is off and D 2 is on. Here the input 






40 


impedance is R-j and the output impedance is R 2 in parallel with R^. 
When the input signal is below diode is off, but D 2 is on. 

Now, the input impedance is R-j in parallel with and the output 
impedance is R 2 - 

This rather complicated result is simplifed as follows. If 
A>>V^, as is intended, and if R 3 >>R-j R^>>R2’ input 

and output impedances are effectively R^ and R^, respecti vely. 

3.2.2 Single Stage Prototype 

To test the design concepts, a prototype single stage limiter 
for operation at 50fi was built and tested. The results indicated 
that such a configuration would make an effective limiter. A 
single stage limiter was then constructed to operate at an impedance 
of 300fi, the intended impedance level for a limiter suitable 
for use in the receiver. Applying the basic design equations, a 
single stage prototype is obtained with R-j = R 2 = 330fi, C-j = C 2 = 

.001 \if, = 1.2KU and = .01 yf. The limiting voltage was 
chosen to be .5 volt and the required value of Vg was 8.65 
volts. 

To evaluate the quality of operation of this limiter, measure- 
ments were made on the change in output power for a given reduction 
of input power at the channel center frequency (80 MHz). The results 
of this measureiTient are shown in Figure 3.3. The 0 dB level of the 
input corresponds to 13.6 Vp-p while 0 dB on the output is equivalent 
to .84 Vpp. 

As can be seen from Figure 3.3, there is about a ,2 dB change 
in the output for a 1 dB change in the input in the limiting region. 



Output Power, dB 


41 



r. 30 „ 20 - 10 ^ 0 

. Input Power, dB 


Figure 3.3 Change in Output Power as Function of the 
Change in Input Power for 
Single Stage Limiter 



42 


Based on the performance of existing systems, this is not sufficient 
limiting. For a system similar to this one it was decided that for 
an input variation of 1 dB the output should not change by more than 
.083 dB over an input range of 12 dB (6). Since this specification 
could not be met with only one stage of limiting, the use of a 
two stage limiter was indicated. 

3.2.3 Construction of a Two Stage Limiter 

The two stage limiter used in the receiver is actually two 
single stage limiters tied together by a single transistor 
amplifier. 

The second limiter stage is essentially the same as the 300 q 
prototype just discussed; the circuit element values are identical. 
However, V is now specified to be .8 V and Vg^ 22 VDC. 

A stage of amplification between the first and second stages is 
provided to produce hard limiting in the second stage. If the ampli- 
fier is driven hard enough it should also provide some additional 
limiting. A schematic of the amplifer is shown in Figure 3.4. Due 
to the wide variation of 3 for the 2H918 transistor, it is impossible 
to accurately predict the gain of this stage. Therefore the choice 
of bias voltage and resistors is determined experimentally. The 
following values were used: 

R-j = 1.8Kf2 V-, = 22 VDC 

= 1 .2K‘:^ = 22 VDC 

Rg = Z,ZK^ 

= 2.2KS^ 

The purpose of* R-, and is to limit the DC current while the gain is 
controlled by R 2 . Resistor is necessary to drain off charge on the 




44 


capacitor at the output of the first limiter to permit normal 

p 

transistor operation. Using the above values of bias voltage and 
resistance, the overall gain was found to be nominally 6 dB over 
the frequency range of interest. The amplifier was tested by driving 
it from the output of the first limiter and terminating it with the 
second limiter. 

In order to obtain a low source impedance to drive the amplifier, 
is chosen as 100^^ in the first limiter. At this level, the output 
imnedance is not so low that too much current will be drawn from the 
limiter. For a 300fi limiter input impedance level, R-j = 330^2. Since the 
amplifier has an input inpedance of about 400 j^, it is safe to assume 
that it does not load the output of the first limiter too badly. 

Hence, with = 1.2K$^ and Vg = 2 2V we have = .75V. 

3.2.4 Performance 

The complete two stage limiter's performance was tested as before. 

In Figure 3.5 the results of this measurement are shown. As can be seen, 
the linearity is within our requirements. The output changes by about 
.83 dB for a 10 dB change of the input. Figure 3.6 shov;s a photograph 
of the limiter's output at 80 MHz. Since the output specifications that 
we are most interested in are those obtained at the output of the low 
pass filter which follows the second limiter, we will defer further com- 
ment on limiter performance until the filter design is discussed. 

3.3 LOW-PASS FILTER 
3.3.1 Specifications 

Due to the adverse effects of the higher order harmonics on the 
performance of the discriminator, a low pass filter is needed at 
the output of the limiter. The out-of-band attenuation characteristics 



45 


of the filter will be specified by the harmonic content of the limiter 
output* Theoretical ly , if V^<<A, the output wave will be trapezoidal. 

In a Fourier analysis of such a wave, the coefficients represent 
the amplitudes of the fundamental , second harmonic, third harmonic, etc. 
In appendix 7.4, a Fourier analysis is performed on a trapezoidal 
wave. The coefficients are; 


Bt = - [2ujt - 1/2 sin 2wt 1 
1 TT L c cl 

(3.5) 

B = 0 (n even) 
n 

4V 

B = cos no)t^ (n odd) 

n niT . c 

/ 1 

(3.6) 

(3.7) 

(ot = sin”^ \ c/a) 

(3.8) 


Using the experimental techniques outlined in Appendix 7.5 the 
acuta! harmonic content of the limiter output was determined. The 
results are given in Table 3.1. Also given in this table are the 
theoretically predicted values as obtained from equations 3. 5-3. 8 with 
= -75V and A = 6 Vpp. The presense of second, third and fourth 
harmonic is not surprising considering the actual shape of the output 
waveform (see Figure 3.6). The presence of the even harmonics is 
probably due to the more pronounced effect of the junction capacitance 
of the diodes at this impedance level. The third harmonic is at a lower 
than predicted level largely due to parasitic reactions. 

From the results of the harmonic content, it is now possible to specify 
the amplitude taper of the harmonic suppression filter. From the data 
in Table 3.1 and the photograph of the limiter output, it was decided 
that 30 dB suppression of the second harmonic would be required. 

3.2.2 Design and Analysis 

Using the information presented in the section on harmonic 
analysis of the limiter (see Appendix 7.4) It is possible to specify 



46 



Figure 3»5 Change in Output Power as a Function of 
the Change in Input Power for 
a Two- Stage Limiter 




47 


Table 3.1 Power LeVels of Harmonics in Limiter Output 


i 

Freq . 1 

MHz j 

1 

1 

1 

Predicted 
Power 
Level (dB) 

1 Actual j 

1 Power j 

f Level (dB) 1 

f •. 

1 Fundamental 

60 

0 

- ° i 

1 

1 

|2nd Har. 

; 120 

-00 

i -20 ; 

3rd Har. 

1 

! ISO 

j 

' 

; 

-1 

i 

j -15 i 

;4th Har. 

1 

j 

i 

j 

i 240 

1 



j -28 



48 



Vertical Scale: 
Horizontal Scale: 


.5 V/cm 
5 nSec/cm 


Figure 3.6 Photograph of Limiter Output at 
‘ 80 MHz 



49 


the cut-off frequency and the amplitude taper of the low pass filter. 
Since the lowest frequency of interest is 60 MHz, the lowest second 
harmonic is at 120 MHz. From data given in Table 3.1, the second 
harmonic of 60 MHz is already down 20 dB from the fundamental. This 
means that the filter must provide an additional 10 dB of attenuation 
at 120 MHz. Also, we would like to have as small an amplitude ripple 
as possible so as not to defeat the purpose of the limiter. Therefore, 
a ripple of .01 dB was selected. Finally, the cut-off frequency 
should be somewhat greater than 100 MHz to insure that the amplitude 
stays flat out to 100 MHz and to eliminate the effects of phase 
distortion at the band edge. A value of 105 MHz is adequate for this 
purpose. 

Applying the methods outlined in Appendix 7.1 .1 we find that in 
order to have a ripple of .01 dB, an Impedance level of 300 j^, a cut- 
off frequency of 105 MHz, and an attenuation of 10 dB at 120 MHz we 
need a total of 9 elements having the following theoretical values: 

~ ^9 ~ .3705 yh 

C 2 = Cg = 7.2136 pf 

Lg == = .8209 yh 

C 4 = Cg = 8.658 pf 

Lg = .8671 yh 

The configuration of this filter is of the form shown in Figure 7.1.2 in 
Appendix 7.1 .1 
3.3.3 Performance 

The filter was built and tested using standard values of 7 pf for 
the 7.2136 pf value and 9 pf for the 8.658 pf value. The inductors 
were hand wound with number 30 wire using 22 Mfi 1/2 watt resistors 



50 


as forms. The number of turns required were computed from tables pro- 
vided by Grover (l5)* The response of this structure is shown in 
Figure 3.7 where the insertion loss is plotted as a function of 
input frequency. For purposes of comparison, theoretical plots of the 
same structure allowing .01 dB and .5 dB ripple are shown also. Further 
comment on this comparision is contained in Section 7.1.3. 

Several things must be recalled when looking at this data. First, 
the termination is a purely resistive value of 300u, the correct ter- 
mination for this filter. Secondly, where we have indicated 0 dB, 
there is in fact some insertion loss which is difficult to measure result- 
ing from the use of a pad to transform from ZOOo. to the measuring 
system. Finally, these characteristics will change somewhat when the 
filter is driven by the limiter and terminated by the discriminator. 

These effects will be studied more closely when the overall performance 
is considered. 

To evaluate limiter performance including the filter, two types 
of measurements were made. First, a set of measurements were made on 
the dynamic range at 60 MHz, 80 MHz, and 100 MHz. In Figure 
3.8 we have plotted the output power as a function of the 
input power for each of the three frequencies of interest. The other 
measurement was on the output linearity as a function of input frequency. 
The results of this measurement are shown in Figure 3.9. As can be 
seen, the output is virtually a straight line from 74 MHz on. However, 
at the low end the output starts to peak up. This effect is probably 
due to paras i t1 c reactances and impedance mismatches at the input and 
output to the filter. It will be shown later how this nonlinearity 


can be tuned out. 



Insertion Loss, dB 



60 70 80 90 100 110 120 


Input Frequency, MHz 

Figure 3.7 Experimental and Theoretical -Responses for Limiter 

Low-Pass Filter 



52 



Figure 3,8 Output Power as a Function 
of Input Power for Three 
Different Input Frequencies 



Output Voltage, Vpp 


1.4 


! 


"O'- 


1.2i— 


1.0 


60 






o -G ■ • ■ c. -o G- • G “'-'O- O G ■ ■ O - 


J 

70 


80 


Input Frequency, MHz 


90 


Figure 3.9 Frequency Response of Limiter 



cn 

u> 




54 


3.4 WIDE BAND DISCRIMINATOR 
3.4,1 Design and Analysis 

Having considered the limiter and filter in great detail, 
attention will now be given to the design and analysis of wideband 
discriminator based on a device described by Lee and Seo (16) (17), which 
consists of a bridge composed of two X/8 lengths of transmission line 
one open circuited, the other short circuited. The circuit diagram 
is shown in Figure 3.10. Assuming lossless lines, the input impedance 
of the open and short circuited lines are: 

^sh = j tan e (3.9) 

^oc “ ^0 ® (3.10) 

where: 

Zq = characteristic impedance of the line. 

0 = w»CC' - 2ir(^/x). 

X = wavelength of the input 
= length of the line, 

L = inductance per unit length. 

C = capacitance per unit length, 
w = angular frequency of the input. 

The output voltage of the discriminator can be expressed as 

Vo = ni(|V,l - IV 2 I) (3.11) 

Vo = ''iVlnt(’ + cot2 - (1 + tan^e)'^/^] (3.12) 

where: 

= constant related to the diode characteristic 
= amplitude of input signal 

|V^| = voltage at the output of the short circuited line. 

Iv^l = voltage at the output of the open circuited line. 

Y = input resistor constant 




56 


R = input resistor 

The sensitivity of the discriminator is expressed as dV^/de. We 
desire the value of y that gives the most sensitivity and greatest 
output linearity. From Lee and Seo(17),the greatest linearity is 
obtained with y - .833 and the greatest sensitivity for y = 2. Let 
us consider a choice of y = 1. Now equation 3.12 reduces to: 

Vq " '^in (|sino| - |cos0|) (3.13) 

Notice that the cross-over point (V^ = 0) occurs when e = 45*^ or 

£ = X/8. 


This transmission line discriminator is easily implemented at 
80 MHz by replacing the shorted and open circuited lines with their 
lumped element circuit equivalent. Assuming lossless lines, these 
lumped element equivalents are as shown in Figure 3.11. For the 
purposes of analysis, let us neglect the diodes. Then we can write 
the input impedance to the discriminator as: 


'in = 


(R + Z^) (R + Z^) 
2R + Z-| + ^2 


(3.14) 


where is the input impedance to the open circuit equivalent and 
the input impedance of the short circuit equivalent. Also: 


Zo - -j 


( ^L2 — 1 / ^ 


( 1 / C0C9 + 1 /oiCo ) j wC« 


(3.15) 


'j 2 


(3.16) 


C , - 1 


The theoretical discriminator characteristic appears as shown in 
Figure 3.12 where is the center frequency and is the cut-off 
frequency of the short circuit equivalent which is simply a low pass 
filter. Therefore, we can express as: 



57 



Open Circuit Line Equivalent 



Short Circuit Line Equivalent 


Figure 3.11 Open Circuit and Short Circuit Transmission Line 

Equivalent Circuits 




CO 





59 


(i) = 

c 


/L7C7 


(3.17) 


Furthermore at = 0 arui |Z-j| = [Z^j. Since Z-j and are 

pure imaginary we can write 
Z ^ = Z ^ 

For C = and L - = L 2 we have; 


(3.18) 




2 C - 1 


oIq LC - 2 


("o’-) 


(<./lc - 1)2 


(3.19) 


Multiplying through, this reduces to; 


4 2 2 2 

2o3^ L^C - 4(*)^^LC + 1-0 


(3.20) 


Solving for 


0 ’ 


^0 




.541 


/LC vie 

Finally, the characteristic impedance is given by. 


(3.21) 


(3.22) 


Using equation (3.21) and (3.22) it is possible to determine 
what the equivalent lumped values of L and C should be by specifying 


the center frequency and the impedance level Z ; 


L = (.541) -0 

03. 


C = (.541) 


Cl) T- 
0 0 


(3.23) 

(3.24) 


The correct values of and necessary on the output will be deter- 
mined by the desired basebandwidth. For a television baseband channel 
at least 4.5 MHz is needed. If f^ is the frequency at which the 
signal is down 3 dB than is determined by: 



60 


R 3 = l/27rf^ (3,25) 

3.4.2 Performance 

A prototype discriminator with a center frequency of 80 MHz and a 
characteristic impedance of 50S2 was built. The design values are L = 

.054 ph and C = 21.5 pf with R-j = R 2 = 47j 2. A theoretical plot of out- 
put voltage normalized to the input level was made with respect to input 
frequency for these values of L and C. The results indicated a virtually 
linear response from 60 to 100 MHz as shown in Figure 3.12. 

The prototype was breadboarded using 22 pf for C. The indicators 
were hand wound according to methods outlined in Grover (16). For the 
output low pass filter, = 220 kfi and = 300 pf. Performance of 
this prototype indicated that such a configuration would make a suitable 
discriminator, 

3.4.3 Performance of 300f^ Discriminator 

A 300s^ discriminator suitable for use in the receiver was then 
implemented. Using the design equations, the appropriate values of L 
and C for a discriminator with = 300i^ and f^ = 80 MHz are L = ,324 ph 
and C = 3.58 pf. To compensate for component tolerance, etc. it was de- 
cided to let C 3 be adjustable. In the actual circuit, values of L = 

.330 uh and C = 3 pf were used. Also, R^ " ^2 ~ input. To 

obtain the 5 MHz base bandwidth, = Z,2YSi and = 12 pf are used in 
the output circuit. 

Upon attempting to test this circuit, it was found that due to the 
parasitic capacitance of the circuit and the diode junction capacitance 
adequate performance could be obtained by removing the two fixed capaci- 
tors in the open and short circuit resonators and leaving only for 
the purpose of adjusting the center frequency to 80 MHz, 



61 


A constant amplitude signal of 1 Vpp was fed into the input and 
data was collected in the DC output as a function of input frequency 
giving us the characteristic which is shown in Figure 3.13. Data 
related to the performance of the open and shorted resonators is 
presented in Figure 3.14. If such curves are linear then the output 
characteristic must be linear also. Examination of each curve 
separately will tell the performance of each resonator and determine 
its effect on the overall performance. As is expected, both curves 
are fairly linear and the differences between them at each point 
compare closely with the results in Figure 3.13. In Figure 3.14, 
|V$ct is the magnitude of the voltage at the output of the short 
circuit resonator and (V^^| the output of the open circuit resonator. 
3.5 OVERALL PERFORMANCE 

Previous testing has indicated that we have a usable 
limiter and discriminator. The problem is to now make them function 
effectively together. Point by point measurements indicated a fairly 
linear output response from 60 to 82 MHz. Beyond 82 MHz, the slope 
of the discriminator output began to fall off. This indicated that 
the limiter output was more frequency dependent when driving the 
discriminator then when driving a purely resistive termination. 

With the demodulator connected to the IF amplifier and mixer, 
swept measurements were made of the linearity of the output of the 
discriminator. These too revealed that the output fell off slightly 
above 82 MHz. Observing the separate outputs of the short circuit 
resonator and open resonators yielded some interesting results. 

First, there was some ripple on the separate curves which tended to 
cancel when they were added together. Also, the output of the short 




Output Voltage mV 



Input Frequency, MHz 


Figure 3.14 Voltage Output as a Function of Input Frequency 
for the Open and Short Circuit Line Equivalents 



64 


circuit resonator was about 1/2 that of the open circuit resonator 
and considerably more non-linear. Further investigation revealed 
that the low pass filter at the output of the limiter had a nominal 
insertion loss of 2 dB. 

By replacing the inductor in the short circuit line equivalent and 
the L-C resonator in the open circuit line equivalent with 300n resis- 
tors and observing the separate outputs we have an indication of the 
overall response of the entire system. Figure 3.15 shows the 
response of our system when the resonating elements are replaced by 
300u resistors. The base line indicates the zero voltage reference. 

As can be seen, there is considerable ripple, and the output falls 
off above 85 MHz. 

By adjusting the values of fixed capacitance in the low-pass 
filter the response could be adjusted as shown in Figure 3.16, to 
reduce the insertion loss of the filter to a few tenths of a dB 
over the pass band. 

Having considerably improved the overall system response, the 
reactive elements were reconnected. As expected, the trimming of 
capacitors values in the filter greatly improved the output 
characteristic. By trimming the bias voltages on the limiter the 
output of the discriminator was linearized. The resulting output 
is shown by Figure 3.17 which is a plot of the discriminator output 
voltage as a function of input frequency. 

In order to study the effect of input level on the output 
characteristic, a set of measurements were made at various input levels 



65 



Vertical Scale: 50 mV/cm 

Horizontal Scale: MHz as Marked 


Figure 3.15 System Response at the Output 
of the Limiter-Filter 



66 



(1 


Vertical Scale: 50 mV/cm 

Horizontal Scale: MHz as Marked 


Figure 3.16 System Response After Tuning 
Li mi ter- Filter 


L-.r 

I • . 



’0 


80 


9' 


Figure 3. 


Input Frequency, MHz 


7 ^discriminator Output as a Function of 
Frequency When Connected to 
Limiter Output 




68 


as shown in Figure 3,18. As can be seen the output linearity starts 
to deteriorate below input levels of -55 dBm. This is well within 
design specifications, since the expected levels from the output of 
the branching networks are nominally -50 dBm. These results indicate 
that the entire system is working properly. We must now consider the 
design of an adequate baseband output amplifier. 

3.6 BASE BAND OUTPUT AMPLIFIER 
3.6.1 Design and Analysis 

Connected to the output of the discriminator is a differential 
amplifier which takes the double ended output of the discriminator 
and converts it to a single ended output at a level of IVpp into 7Sq, 
The circuit diagram of the amplifier is shown in Figure 3.19. In 
order to prevent video bounce, we must have a response that extends 
down to DC. Therefore, the amplifier must be directly coupled to the 
discriminator. This arrangement presented some problems for proper 
operation of the discriminator. 

Originally, and were not part of the circuit. At this 
point the output was found to be badly distorted. Examination of 
the individual discriminator outputs at the input to the amplifier 
revealed that they no longer crossed at the 80 MHz center frequency. 
The reason for this was due to the biasing on the bases of and 
Q 2 . It became apparent that some adjustment to the biasing of 
and was needed to return the outputs of the discriminator to the 
80 MHz crossover point. This was accomplished by the addition of 
the bias resistors and their values being determined experi- 
mentally. Adjustment of along with the bias voltages allowed us 
to center the output about 0 volts. 



Output, mV 




70 


+ 6.2 Volts 



Figure 3.19 Output Amplifier Schematic 


■o o' 


7] 


The Input impedance is controlled by R-j , and The overall 
gain of the circuit is approximately the ratio of Rg to Ry. To 
eliminate loading the discriminator outputs as much as possible we 
would like to have a fairly high impedance but not so high as to 
limit the basebandwidth to a value below 5 MHz. As can be seen from 
Figure 3.19, the input impedance isl.SKi^and the gain should be about 
10 . 

From quiescent analysis , it can be shown that, in general, for 
a configuration of this type R 5 = 2 R^. The actual values of these 
resistors are not critical. Values of 1 . 2 Kj 2 and 2.2KQ for and R^, 
respectively, were chosen. 

The value for is determined from the maximum negative level 
needed, -.5V in this case. At this level, the load draws about 
6.67 mA. A DC analysis shows that a value of about 680^^ is a good 
choice to allow this point to go to at least -.5V. 

The purpose of Rg is to prevent the immediate destruction of 
Qg in the event of a short circuit on the output. The diodes D1 
and D2 insure that will not be cut-off anywhere over the range of 
output voltage from -.5V to +.5V. 

The transistors used are 2N918 and the diodes are 1N914. 

An overall schematic diagram of the output amplifier and demodulator 
is given in Figure 3.20, As can be seen, Zener diodes are used to 
develop the different bias voltages from one ± 32 V supply. 

3.6.2 Performance 

In order to test the performance of this circuit we operated it 
as a pulse amplifier. All measurements were made with input grounded 
and input connected to a fast rise time pulse generator. Subsequent 





73 


testing revealed that the output had a 10 to 90% rise time of about 
45 nsec. Delay between input and output is about 5 ^sec and the 
single ended gain is approximately 7, Swept measurements of the 

output of this amplifier when driven by the discriminator showed that 
we could get about 1.2 Vpp into 75^^ with no loss of linearity as is 
shown in Figure 3.21. In Figure 3.22 a family of output curves is 

presented for differing power levels at the input to the 
mixer. 





74 



Figure 3.21 Output of Final Amplifier as a Function 
of Input Frequency Deviation 


Output Voltage tn Volts 


75 



Figure 3,22 Final Amplifier Output Voltage as a Function of 
Input Frequency Deviation for Differing 
Input Power Levels 




76 


4. BRANCHING NETWORK 

4.1 INTRODUCTION 

This chapter is devoted to the design and theoretical prototype 
performance of the branching network. This network must be able to 
accept the twelve 40 MHz wide contiguous channels which are available 
at the output of the front end converter and distribute them to the 
appropriate baseband receivers. Consideration is first given to 
the desired characteristics of the individual channels, including 
a discussion of the required selectivity, allowable passband ripple 
and the amount of reverse isolation needed. This is followed by a 
discussion of the appropriate design of the channel dropping filters 
themselves. A suitable method for manifolding the filters is deter- 
mined which will keep filter interactions to a minimum and provide 
an input which is compatible to the front end converter output. 

The band pass specifications, selectivity, and reverse isolation 
of each channel are now considered. In order to gain some perspective 
about the type of selectivity and passband specifications needed for 
our system, let us first consider the specifications for two systems 
with requirements similar to ours. As reported by Comsat (18), 
Intelsat IV has a twelve channel input branching network, each 
channel having a 3 dB bandwidth of 40 MHz and a .5 dB bandwidth of 
36 MHz with < .1 dB variation over a 32 MHz range. Leakage from 
adjacent channel centers ± 40 MHz away must be 50 dB below the level 
of the desired signal at the channel center frequency. RCA (7) 
describes a 24 channel system with quite similar requirements. 



77 


As described in Section 1.3 we have 12 channels each requirinq 
a minimum usable bandwidth of 36 MHz and a 3 dB bandwidth of 40 MHz 
with adjacent band centers 40 MHz apart. Since there is additional 
filtering after the second mixer, there is no need to place as 
strenuous a requirement as RCA or Comsat on our out-of-band taper. 
Hence, we have opted for 30 dB attenuation of adjacent bandcenters. 

As was shown in Section 2.4, this taper, coupled with the tapers of 
the two IF band-pass filters, was able to provide 30 dB of suppression 
at the adjacent channel band edges. It is desirable to minimize the 
pass band ripple but still have as few elements per filter as possible. 
We found the value of .1 dB to be the best compromise for passband 
response. 

Unfortunately the LO frequency for the mixer of each channel 
corresponds to the RF center frequency of the next-to-adjacent channel . 
In order to prevent interference between the LO leakage from the next- 
to-adjacent channel and the FM signal of interest for the given channel, 
the LO leakage level should be no more than the minimum detectable 
signal of the amplifier which is -86 dBm (see Section 2.7). Assuming 
that the LO level is +10 dBm, the leakage signal is at a level of -20 
dBm (see Figure 2.5), This means a minimum of 66 dB reverse isolation 
is required at the channel's LO frequency for each filter as shown in 

Figure 4.1. The means of implementing this isolation are discussed in 
Section 4.2. 

4.2 CHANNEL DROPPING FILTER DESIGN AND THEORETICAL PERFORMANCE 
Initial consideration had been given to using stagger tuned 
amplifiers to implement the channel dropping filters. This arrange- 
ment has several important advantages. First, instead of a net 



Power Level , dBm 


78 




Frequency 


Figure 4.1 Power Levels and Frequencies of LO Relative to 
the Signal Channels, Dotted Lines 
are LO Power Level Before 
Isolation, Solid Lines Indicate 
Level After Isolation 



79 


insertion loss as would be the case if passive elements were used, 

i 

a net insertion gain could be realized. Also, each transistor 
stage could provide a broadband reverse isolation of 20 dB. However, 
preliminary calculations showed that a minimum of 5 stages would be 
needed to obtain the desired response. In view of the cost of 
implementing such a structure, it was felt that a more conventional 
approach be tried. 

Subsequent investigations revealed that use of side coupled 
half-wavelength (x/2) resonators implemented in stripline presented 
the best solution based on overall economy and ease of implementation. 
An example of such a structure is shown in Figure 4.2. Matthaei 
et. al. (19) give step by step methods for determining the dimensions 
of the resonators and their spacing. For our purposes it was 
found that the nomograms supplied by Matthaei did not have sufficient 
accuracy for determining the dimensions. For this purpose, T. Monsees 
has implemented a FOCAL program using a Fibonacci search and 
polynomial representation of the elliptic integrals in Matthaei 's 
equations 5.05-1 and 5.05-4 to accurately determine the dimensions. 

Use of this program is explained in Appendix 7.6 of this report. 

By applying the methods outlined. in section 7.1.3, the number 
of resonators is first determined. For a passband ripple of .1 dB, 
bandwidth of 36 MHz and attenuation of 30 dB, 40 MHz from the band 
center, at least 5 resonators are needed for each filter. 

In order to get some idea as to the difficulties encountered 
when attempting to physically realize these filters, a prototype design 
for use at fQ = 1240 MHz, the bandcenter, is considered. This filter 



£ 





Figure 4.2 Five Resonator Parallel Coupled Resonator Filter 



81 


is to be fabricated on 3M* type GX-060-55 1/16" thick "Cu-Clad" 
board which has = 2.56. Applying the methods of Section 8.09 
of Matthaei et. al . (19) the values of even and odd mode impedance 
for each of the resonators are first computed. Then applying the 
methods of Section 5.05 of Matthaei and Appendix 7.6 of this report, 
the filter dimensions are obtained as shown in Table 4.1. 

All of these filters are symmetric devices. Hence, based on the 
forward characteristics of 40 dB attenuation 40 MHz away from band- 
centers, they should be able to provide at least 60 dB of isolation 
to the LO leakage from the baseband channel mixer. An additional 10 
dB of isolation can be obtained with a single transistor amplifier 
which has a nominal reverse isolation of 20 dB and a forward gain of 
10 dB. A standard amplifier for this is given in Figure 4.3. The 
operating characteristics for this amplifier are given in Figure 4.4 - 
4.6. It should be noted that the amplifier has a nominal gain of 10 
dB and reverse isolation is greater than 17 dB. Input and output 
return loss are > 10 dB and > 5 dB respectively. Forward isolation 
is nominally 8 dB. 

Using MICTPT (20) it is possible to simulate, on a computer, 
the filter itself to obtain its theoretical frequency response as 
shown in Figure 4.7. As can be seen this filter should provide .1 dB 
passband ripple with 35 dB of attenuation 40 MHz from bandcenter and 
an attenuation of 68 dB 80 MHz from bandcenter. It seems quite 
possible that the filter alone will be able to provide the necessary 


*Trade name Minnesota Mining and Manufacturing Company, Minneapolis, 
Minnesota. 



82 


j 

0 

1 

2 


Table 4.1 Dimensions of Parallel 
Normalized to b = 1/8 inch 

Stri ps 

"'j j+i 

,j+i 


.6500 ± .0003 

.1739 ± .0001 

.165 

.7143 ± .0001 

.6463 ± .0003 

.165 

.7155 ± .0001 

.7318 ± .0003 

.165 


The length ^ is a quarter wavelength at the center frequency f 



83 


O 


+ 18.2 V 


4.3K > 


RFC 


Zo - 38s^ 




o 

50s2 

9 


O 


0 “| f - - 

j--13/16"-*| 8.2 pf 


s 


7.68yh 

TYTu 

HP 35821 E 


10 pf 


1.2K< 




1.38nh ^ 200 

1 

— \ A 

^ ' 

i 

' : 100 pf 


t \ 






0 

1 

i 

-'7 


Figure 4.3 Filter Amplifier Schematic 



84 



Amplifier Gain (V: 2 dB/cm) 

(Lower Trace is 0 dB Reference) 



Reverse Isolation (V: 5 dB/cm) 

(Upper Trace 0 dB Reference) 

Figure 4.4 Filter Amplifier Gain and Reverse Isolation Over 
the Range of 1.0 to 1.4 GHz 




85 



Input Return Loss (V: 


10 dB/cm) 



Output Return Loss (V: 5 dB/cm) 


Figure 4.5 Input and Output Return Loss Swept Over the 
Range of 1.0-1. 4 GHz with Upper 
Trace Showing 0 dB Reference 




86 



Figure 4.6 Forward Isolation;Frequency Swept from 1.0 to 1.4 GHz 
with Top Trace or 0 dB Reference and 
Vertical Scale of 2 dB/cm 



Insertion Loss, dB 


V 


87 



Input Frequency, GHz 


Figure 4.7 Theoretical Prototype Channel Dropping 
Filter Performance 


CH 



88 


reverse isolation. However, these characteristics are based on 
ideal loss free considerations. Ultimately, the need for an 
amplifier stage will be determined by the experimentally measured 
characteristics of an actual filter. Even if the reverse isolation 
requirements are met, distributed losses in the filters and manifold 
may require the need for the extra gain afforded by the amplifier. 

4.3 PROTOTYPE FILTER PERFORmWCE 

When the prototype 5 resonator filter outlined in Section 4.2 
was built and tested subsequent measurements indicated a response 
of the form shown by the experimental curve given in Figure 4.8. 

As can be seen, there is no visible ripple; the response is somewhat 
rounded- The 4 dB bandwidth is 40 MHz and the midband insertion 
loss is approximately 4.2 dB. As will be seen, these results are 
the best that can be expected based on our present choice of materials. 

Applying methods outlined by Matthaei (19) the expected value 
of midband insertion loss is first calculated. The increase in 
midband insertion loss due to the finite Q's of the resonators is 
given by 


(aLft)g = 20 log (% + 1) 


= 8.686 


(4.1) 


where is obtained from Figure 4.13-2 of Matthaei (19) and 

^ (4.2) 

where w is the fractional bandwidth and Q^, is the unloaded Q of a 

single resonator. The Q's of each of the resonators are assumed the 
same. In general 


1 + Qc tan6 


(4.3) 



89 


where tan 6 is the dissipation factor and is the Q due to copper 
losses. is obtained from'Fig. 5,04-4 of Matthaei (19). Applying 
Equ. 4.1 - 4.3 to our particular filter, we find that = 251 and 
(aL^)q = 4 dB. Allowing .2 dB for connector losses, the measured 
value of 4.2 dB is not an unreasonable value of midband insertion 
loss. 


Since the resonator Q's are now known, it is possible to use 
MICTPT (20) to model the actual lossy structure on a computer. In 
this manner, the theoretical response shown in Figure 4.8 is 
obtained. Also, for comparison purposes, a point-by-point plot of 
the experimental response is shown. As can be seen, the shapes of 
both the experimental and theoretical lossy response are similar. 
However, the experimental response is shifted down 10 MHz. This 
corresponds to an error of about .8%. This error is not unreasonable 
when one considers the work of Cohn (21) who was able to achieve a 
minimum error of .6% after 3 attempts in building a similar structure 
This error is largely due to the inability to accurately determine 


the dimensions shown in Figure 4.2. It will be desirable 

in future designs to flatten out the response somewhat and insure 
that the 3 dB bandwidth is at least 40 MHz. However, the response 
shape is to a great degree limited by the resonator Q's. 


4.4 MANIFOLD DESIGN AND PROTOTYPE PERFORmNCE 

A suitable manifolding scheme must be realized to distribute the 
signals and keep filter interactions to a minimum while providing a 
low VSWR to the front end converter output. A straightforward 
approach to this problem would be to split the output of the front 
end using a 3 dB hybrid with all even and odd channels on separate 



Insertion Loss, dB 


9a 



Input Frequency, MHz 


Figure 4.8, Experimental and Theoretical Responses for 
Prototype Channel Dropping Filter 



center for 

DEVELOPMENT TECHNOLOGY 

Robert P, Morgan 
Director 


Box 1106 



WASHINGTON UNIVERSITY 

SAiisfT LOUIS. MISSOURI o;n:.io 


August 23 , 1974 


TO: Regular Receivers of Technical Reports Issued 

By Program on Application of Communications 
Satellites to Educational Development 
{NASA Grant No, NGR-'26-00 8-054) 

FROM: Robert P, Morgan iJ 

Principal Investig^or^ 


Enclosed you will find a copy of Report No. 
R(T)-74/2 entitled, "Design of a 12 Channel FM Microwave 
Receiver,” by C. Risch, F. Rosenbaum and R, Gregory 
issued by the above-mentioned program. This report 
is based upon an M.S. thesis by Mr. Craig 0. Risch 
in the Department of Electrical Engineering of Washington 
University, St. Louis. 

Any comments you may have on this report would 
be appreciated. 


RPM; esp 
Enclosure 



91 


lines. Circulators would be used at the inputs to each filter. In 
this way, the filters would be electrically isolated from each other 
and their interaction minimized. Also, a low VSWR is presented to 
the front end output. This approach, however, is undersirable since 
the use of circulators adds to the size, weight, and insertion loss 
of the structure and increases its cost. 

Edson and Wakabayaski (22) suggest the use of singly terminated 
filters appropriately spaced along one “feeder" transmission line. 

To provide a low input VSWR, adjacent channel band edges are to be down 
3 dB. The physical arrangement of the filter is such that the impedance 
of the center filter is pure real with all filters to the left of center 
providing a capacitive reactance and those to the right being inductive 
at the center frequency of the input. These susceptances modify the 
original transmission line into two separate regions having opposite 
impedance tapers. Although this method avoids the use of circulators, 
it does produce other problems. The spacing of the filters along the 
feeder line must be determined experimentally. The method is optimum 
for channels near the center and breaks down for channels at both ends. 

A more systematic approach to the design of multiplexers is 
described by Atia (23). Doubly terminated filters are appropriately 
spaced along a feeder transmission line. The correct spacing is ‘ 
determined by computer optimization to reduce loading effects of near- 
by filters, and there is no required cross-over points for adjacent 
bandedges. Optimum performance for all channels can be obtained 
with little filter interaction. Although this method was reported 
for a waveguide multiplexer design, the same approach can be applied 
to realize similar structures in stripline. 



92 


The arrangement of the branching network intended for use in our 
receiver is shown in Figure 4.9. The channel dropping filters are 
as described in Section 4.2. A 3 dB hybrid is used to separate the 
even and odd channels into two separate 50 n distribution lines in 
order to reduce the amount of adjacent channel interference. Two 
isolators are necessary to provide a low input VSWR for the front-end 
converter output and to provide isolation for the even (or odd) 
channels rejected by the filter manifold. It may be possible to use 
only one isolator at the input if the hybrid provides sufficient 
isolation between the two distribution lines. Since dielectric and 
copper losses are greater at the higher frequencies, it is desirable 
to locate the higher frequency filters nearer the source. 

Appropriate line lengths between the filters can be 

determined by computer techniques. Since the even and odd numbered 
filters are to be well isolated, the operation of the entire branching 
network is satisfactorily determined by considering either set of 
filters. Hence, for analysis purposes, only the odd numbered filters 
are considered. The spacings are adjusted such that at its center 
frequency each filter sees and open circuit looking away from the 
source. This process is initiated by first using MICTPT (20) to 
find the input impedance to BPFp at the center frequency for BPR^ 
(fs). A Smith Chart is then used to determine the length of 
line (s^^^ 3 ) required for BPF^ to see an open circuit at f^ when 
looking toward BPF^ . Then the input impedance for the parallel 
combination of BPF^ and BPF^ in series with ^ is computed at f^. 
Again, using a Smith Chart, the appropriate length of line ^) is 
determined as before. In this manner, the required line lengths are 



93 



Figure 4.9, Branching Netvyork 


6 



94 


determined. Initial calculations yielded line lengths which were too 
short to be physically realizable. By adding a half wavelenth (Xg/2) 
line to the originally calculated length for ^ and repeating the 
procedure, physically realizable line lengths are obtained as shown 
in Table 4,2, where the guided wavelength x. in inches corresponding 

to the center frequency of the jth filter (f.) is given by; 

J 

A. = in. 

^ fVl7(2.54) (^-4) 

when the relative permitivity of the substrate, is taken to be 
2.56 (see Section 4.2). The structure Is to be realized as a 50 
stripline with taps on the line for connection to the appropriate 
f i Iters, 

In order to test how well this branching network scheme should 
perform, MICTPT (20) is again used to examine the insertion loss of 
each filter and the return loss at the input to the manifold as a 
function of frequency. The results of this calculation are shown in 
Figure 4.10. The out-of-band attenuation characteristics closely 
resemble those for a typical filter operating without interaction 
with other filters (see Figure 4.7), The in-band return loss is 
reasonable with typical values > 15 dB. The worst case is for BPF-j , 
which is at the end of the line. Figure 4.11 shows a typical passband 
response of the filters used in this scheme. Although the response 
is not equi -ripple as shown in Figure 4.7, the maximum ripple 
variation is still only ''.1 dB. Hence, although there is some 
impedance interaction with the rest of the network, it does not 
appear to seriously degrade filter performance. 



95 


Table 4.2 Line Lengths for Manifold 

j *^ 3 , j+2 [inches] 

1 .0335a, .2208 

3 (.0145)A5 + Aj/2 3.1673 

5 (.4710) Xj 2.716 

7 (.4292) Ag 2.330 

9 (.3961) A,^ 2.030 



96 


The results of these calculations indicate that doubly terminated 
50 Q filters connected at appropriate points along a bO Q distri- 
bution line should provide an adequate means of implementing the 
branching network. It must be pointed out that the analysis of the 
performance does not take into account the discontinuities of the 
distribution line where the filters are tapped in. Also, the distri- 
bution line and the filters are considered to be loss free. However, 
in spite of these simplifications, the analysis does provide enough 
information for the synthesis of a first-cut prototype design. 
Furthermore, a more realistic model for the manifold could be 
implemented in a subsequent design effort. 




Return Loss, HR 





99 


5. CONCLUSIONS 

5.1 PRINCIPAL RESULTS 

As part of the low cost objective of the receiver, several inno- 
vative design approaches were used to implement various subsystems. 
Instead of using the conventional approach of cascading several transis- 
tor stages containing discrete components, the IF amplifier used in 
the present effort uses a cascade of 3 linear high frequency inte- 
grated circuits driving a single feedback pair of transistors. Such 
an arrangement is very economical since it is easy to design, uses 
few components and can be assembled in a short time. 

The 4-pole and 7-pole filters used in conjunction with the IF 
amplifier for shaping the channel passband used standard fixed 
capacitors and required a total of 4 tuning capacitors for alignment. 

The inductors had to be hand wound. However, if used in large 
quantities they could be custom manufactured quite economically. 

The measured passband ripple of these structures was greater than 
the theoretically predicted value due to the use of lossy elements 
having a 5 % tolerance. The passband response could have been 
smoothed had we opted for more adjustable elements. However, since 
the increased filter ripple did not seem to adversely affect the 
overall system performance, such measures were deemed unnecessary. 

In this manner we have attempted to keep the time for filter 
assembly and alignment to a minimum. 

For the limiter, we have used two identical back-to-back diode 
arrangements separated by a single transistor amplifier. A brief 
theoretical analyses of this circuit is given in Section 3.2 and a 



100 


set of design equations are formulated. Experimental results were 
found to correlate well with the theory. The measured dynamic 
range and frequency response of this structure indicated that it 
would perform quite well in the overall system. 

Since the discriminator will detect the higher order frequency 
components contained in the limiter's output, it was necessary to 
insert a 9-pole low-pass filter between the limiter and discriminator. 
This filter was constructed entirely with fixed elements and gave 
satisfactory performance. 

The approach used in the discriminator 's design is particularly 
unique. A modified transmission line discriminator which uses a 
lumped element equivalent for the transmission line networks has 
been implemented. This structure has an extremely linear output 
response. A complete analysis of the conversion from distributed 
to lumped parameter systems is given in Section 3.4. The results 
of this analysis were used to determine a set of design equations and 
predict the theoretical performance. The discriminator used in 
this receiver uses only two standard input resistors, two standard 
inductors and one variable capacitor for adjusting the center 
frequency. 

The baseband output amplifier is a relatively standard design. 

To convert from L-band to the 80 MHz IF a low-cost commercially made 
mixer has been used. 

The proper branching network design has been determined by 
computer simulation. The channel dropping filters utilize a side 
coupled resonator design implemented in stripline. To eliminate 
adjacent channel filter interaction two manifolds separated by a 3 dB 



101 


hybrid are employed with odd and even numbered channels on separate 
manifolds. The optimum spacing of the filters along the manifolds 
is determined by computer simulation. 

All of the baseband channel subsystems have been housed in a 
1 X 3 X 12 3/16 inch box supplied courtesy of Martin-Marietta, 
Aerospace, Communications and Electronics division. The complete 
package is shown in Figure 5.1. Its total weight is 1 2/3 lbs. To 
prevent oscillation, shielding was required between the first and 
second preamplifier stages and also between the IF amplifier output 
and limiter input. To prevent interference from spurious signals 
the box is made RF tight overall. Two DC feed through connectors 
are required for connection to a ± 32 volt power supply. The RF 
and 10 inputs use OSM connectors. The video output uses a BNC 
connector. Complete performance results for the subsystems considered 
in this report are given in Table 5.1, The estimated cost of 
components, assembly, alignment, etc. are given in Table 5.2. 

Table 5.3 shows the estimated cost of the branching network. It 
is anticipated that the lO chain could be built for about $3000 and 
the antenna cost should be no more than $2000. The estimated 
delivered cost of the entire receiver is given in Table 5.4. 

Based on the performance results of existing prototypes and the 
cost analysis it can be seen that a low cost multi-channel receiver 
can be realized. 

5,2 FUTURE WORK 

The work previously described in by no means complete. A 
number of important areas of interest have yet to be explored. 



102 


(1) The overall link performance characteristics of the 
baseband channel must be investigated. This would include 
determining the amount of AM to PM conversion, FM linearity 
of the overall system, and a measure of the overall 

group delay. The group delay measurements are of course 
required for determining the design of group delay 
equalizers, if they are in fact needed.. Ultimately 
this system will have to be tested by using an actual 
color TV FM signal applied to the input. 

(2) Now that a set of basic design criteria for the 
branching network has been developed a prototype model 
should be constructed and tested. 

(3) Consideration should be given to implementing circuitry 
for obtaining the 12 required LO frequencies. 







104 


Performance Specifications For 
Baseband Channel 


Table 5.1 

Input Level 

Minimum Detectable Signal 
Input Return Loss 

Output 

IF 

Overall Bandwidth 
Bandwidth per Channel 

Channel Selectivity 

DC Power Supply 

Dimensions 
Weight 
Mixer - 
LO Input Level 
LO Input Return Loss 

IF Amplifier - 
Output Level 
Output Noise Level 
Dynami c Range 

Limiter « 

Nominal Input Level 
Dynamic Range 
Input Impedance 

Discriminator 
Input Impedance 
Output Linearity 


-40 dBm Max into 50i^ 
-86 dBm 
>15 dB 

1 Vpp into 75 r 

80 MHz 
1.0 - 1.5 GHz 
36 MHz ± .5 dB 

30 dB Suppression of 
adjacent Channel 
Bandedges 

± 32 volts 10 watts 

1 X 3 X 12 3/16 inches 
1 2/3 lbs. 

+10 dBm 
>10 dB 


+ 16 dBm Max into 300^^ 
- 2.67 dBm 
15 dB 


+ 10 dBm 
10 dB 
300Q 

ZOOQ 

<1% Deviation from Linearity 



105 


Table 5.2 Cost Estimate for One Baseband Channel 

Price per Unit in Quantities of 1000 
Bill of Materials: 

Miscellaneous Resistors and Capacitors $ 4.30 


Miscellaneous Semiconductors 

22.00 

Mixer 

20.00 

OSM Connectors (2) 

2.25 

Aluminium for Housing 

2.00 

Miscellaneous Hardware 

2.00 


$52.55 

Labor (Estimated) 


Machining of Housing 

$35.00 

PC Board Processing 

2.00 

RF Assembly and Test 

75.00 


$ 112.00 


$164.55 


Total 



106 


Table 5.3 

Estimated Cost of the Branching Network 


Cfuan. 

Item 

Cost 

1 

3 dB Hybrid 

50.00 

2 

Circulators 

300,00 

3 

Loads for Hybrid and Circulators 

30.00 

12 

Channel Dropping Filters 

600.00 

2 

Man i folds 

200.00 


Miscellaneous Hardware 
(connectors, etc.) 

50.00 


Assembly and Test 

350.00 


TOTAL $1580.00 



107 


Table 5.4 

Estimated Delivered Cost of the 
Entire Ground Station 


Antenna 

$2000.00 

Westinghouse Front-End 

250.00 

Branching Network 

1580.00 

12 Baseband Channels 

3600.00 

LO Chain 

3000.00 

DC Power Supply 

200.00 

Alarm Circuits 

500.00 


$11,130.00 


Total Delivered Price 



6. ACKNOWLEDGEMENT 


This work was supported by the Center for Development Technology 
of Washington University through NASA Grant NGR-26-008^054. 



109 


7. APPENDICES 




no 


7.1 FILTER DESIGN 

7.1.1 Introduction 

The following sections will be concerned mainly with the techniques 
used to design the filters which were used in the if amplifier and 
limiter (see Chapters 2,4, 2.5, and 3.3). We will concentrate mainly 
on the design of the low pass, high pass, and band*-pass filters, 
doubly terminated and having a Tchebycheff response. We first describe 
a fundamental set of design equations based on the low pass prototype, 
then show how the band-pass and high pass structures can be realized 
from this basic prototype. We will then proceed to show how the 
design equations can be implemented with computer programs suitable for 
use on a small on-line computer to quickly and accurately design 
actual structures. 

7.1.2 Prototype Equations and Low-Pass Filter Design 

It can be shown from the work of Matthaei et. al. (19) that one can 
use the Tchebycheff polynomials to obtain an expression that relates 
the out of band insertion loss at a given frequency to the ripple, 
cut-off frequency, and the number of reactive elements in a low-pass 
filter; 

Lp(<oa) = 10 log^p |l + e cosh^ j^n cosh’^ ^1| (7.1.1) 

where: i_^ = insertion loss in dB 

n = number of elements . 
o)-] = cut-off frequency in rad/sec 

Wg = frequency in rad/sec beyond the cut-off frequency 
where we desire to have a loss of Lp. 

■ Wo Ct5)] 


and : 


e 


-1 


(7.1.2) 



Ill 


where is the ripple in dB, (see Figure 7.1.3). 

This equation was then written in a FOCAL program as shown in 
Figure 7,1.1, to solve for the number of elements required for a 
given ripple, Lp, cut-off frequency, W^, out-of-band attenuation, 

LF, and W, the frequency at which this out-of-band attenuation is 
specified. 

It will be shown later how equation 7.1.1 can be used to 
determine the number of elements for high-pass and band-pass filters 
through appropriate mappings - 

Structurely, the low-pass filter can exist in four different 
forms, each having the same response as illustrated in Figure 7.1.2 
The values g^ through g^ represent normalized values of series 
inductance and parallel capacitance. In Figure 7.1.2 a and b, g^ 
is the normalized generator resistance, In Figure 7.1.2 c and 
dj 9- is the normalized generator conductance G* , where 6* = 1 /r' . 

In Figure 7.1,2 b and c, is the normalized load resistance 
^'n+r Figure 7.1.2 a and d, is the normalized value of the 
load conductance where 

For all doubly terminated Tchebycheff filters with pass-band 
ripple, the gj^ values which are the values of series inductance and 
shunt capacitance normalized to the scale g^=l and w'-j = 1 may be 
computed 1n the following manner. We first find: 


B = In 



(7.1.3) 


T = sinh 



(7.1.4) 



112 


I.' 


0 1 . vM 
0 1 . 0/1 > 
0 1 S 

0!.’1H S 

■1 1 • ! s 

0 \ •]’> S 
(M • ] A S 
0 1 . 1 ''-. r 


! ! f "LF” LK> ! # ” W" » Vi * I > "LvC" # WC # ! ! 

AsrFFAf-’C . '^30‘0S0^L.F ) J S 0=^ ■* I 
C=FF\P( . 030 3S8 > } S l) = l"-l 

h: = FS'JTC 0/0 ) 

3 = FLJG( F+P’SO f ( F 1 ) ) 

X-W / WC J S ri sF L JG t X + F 3 J r C A t - ! ) ) 


Figure 7.1.1 FOCAL Program for Determing the Number of 
Elements in a Low-Pass Filter 





113 



Figure 7.1.2 Low-Pass Filter Configurations 



114 


dB 



Figure 7.1,3 Low-Pass Filter Frequency Response 




115 


ak = sii 


b. = + sii 


From the 3k and bk parameters we can then generate the 9k parameter: 


9] = 2a^ 


g, = iVlA 

>^k-l 9k-l 


k = 2,3, 


= T for n odd 


= coth‘^(3/4) n even . 

For any low-pass structure shown in Figure 7.1.2, one can then 
determine the actual values of series inductance and parallel 
capacitance by using the following equations; 


\%‘f \"i / \% ' ri / 

= /!l_\ 

'*^0 ' V} J ^ \G 'j Vl / 


^^n+l 9n+l 


where; w-j = cut-off frequency in rad/sec 
Rq = impedance level in ^ 

^n+1 ~ terminating resistance in , 



116 


All primed quanties are normalized quanties. In general we set 
w-j ' - ^ , and = 1 

In order to solve for the required g values and the actual L 
and C values it is possible to write a FOCAL program to solve 
equation 7.1.3 through 7.1.12 as shown in Figure 7,1.4. 

Here the ripple in dB, LR, number of elements, N, impedance level 
in ohms, RO, and the cut-off frequency in MHz, WC are to be specified. 
Upon execution, a print out of the normalized g values, G(K) and 
the corresponding values of series inductance, L(K), in yh, parallel 
capacitance, C(K), in pf, and the required value of terminating 
resistance, RT are obtained. These values are the possible values for 
all of the configurations shown in Figure 7.1.2. However, it is 
easy to see that for Figure 7.1.2 a and b, one must select the odd 
k subscripted values of C and the even k values for the inductors. 

For Figure 7.1.2 c and d, we find that this situation is reversed. 

In order to show how these filter programs can be used to realize 
actual structures consider the design of the low pass filter and 
between the output of the limiter and input to the discriminator 
(see Chapter 3.3) the filter must have the following specifications; 
uj^/2tt = 105 MHz, = .01 dB, = 50fi, Lp = 10 dB at 120 MHz. 

Setting LF = 10, LR = .01, W = 120, Wc = 105 in the program of Figure 
7.1.1, the required number of elements is found to be 9.13823. Of 
course the actual number of elements used is 9. With a knowledge of 
the number elements, the program in Figure 7.1.4 is used to determine 
the g values and the actual element values. Setting LR = ,01 * N = 9, 

RO = 300, and Wc = 105, the results shown in Figure 7,1.5 are obtained. 



117 




.11 .\ A A 
^ 1 . > 1 1 


• ' L a” ^ l- A , ” C :jn /[>)'’» :< 0 > ' • WC ( /L )" ^ < F 

I],** (:('<) L(K>t'JHJ 



• I T '> P 1 = .A • 1 1 '•» 9 A ; i ) = L-\ / 1 7 - i 7 ; S V. 1 = * P I + .<P" 1 K A 

(1 P> , •■> -1 s T = F i'.?;p < •) ) .J S S= FF. aP ( - .J ) ; 'j PA = FL JG C ( T + ^ f - .j ) J 

.) >, ‘\:A S PC- = ‘ -i '1 ’► A' » A r A = L F F P C G G ) “ F F, aP ( “ U Ci ) J / ■-* 

1 •> . A u'i s K = 1 ; ' > .p * i s ( \ . >j / c- A ; I J .3 • p 

F k=p>.'^;a A 

ii^.A'1 I ( ITK( A. 1 > A* 3 


1 A . I Gi ' ; A A ; A -i .j= R :M ; .s C- .J = (.'A- 

1 'It . > A S A = F S 1 t ( P ♦ .K “ I > + P I / P / A j ; S R A = G A + G A + C h' :i 1 \ ( R ^ P 1 / .vi ^ if P 

; ) R . P .1 S 1'\ J A iS' / R 0 + G O 

;!R./<-i R L = CiM^ iv.)/W 1 ? :S G = GiM /P J/ W 1 J 0 A . 


^ /4 . I <A 
A A . ">P 
.'I A , A A 
A /] , l 
A ♦ A 1 


5 I;,' = F |.; A )-■ ( . ( A / A ) i S yl = F -F a P ( - R A / A ) 

R GF = L ( P ) / C U - P ) J t p ; G a • 4 
•S GF = t 

r P . A » •<.»" •• , /? 4 • A , GF j M .» •’ < r - •* > % a . 5 » of * P J> ! ! ! ; ;) 

r P.P*G>.-<^'’ .R, >G,\>'’ ‘'^L^RFA^" ^ it: A. /|,0 I E r-V ! 


Figure 7.1.4 FOCAL Program for Generating the g Values 
and Determing the Values of 
the Elements in a Low-Pass Filter 



118 


; y 

,;oC OH.''iS ) : 




C ( K ) 


L C K ) C iJfi J 0 


l 

v) . 8 M -'J S 

,.1 . 3 73 3 6 


1 .9970S 

1 . 6-^10 9^ 

\ 

1 

>3 .><P.AA9 

A 

! .71 

.). 11'61A 

S 

\ .9>V>7 9 

.1 .V? SSS9 


1.71 ?S9 

■3.7 7874 

7 

1 . /» IS 

1.8 :?-.1 A9 

-< 

\ . /^c»79 S 

1 . S 4 89.3 

9 

1 . 1 /) /1 7 

.1 . 3 73 3 S 

,1 

1 . .IvV.lOS 



.^ y = ■ \ . V/i ♦ '1 ,'i 


A 


( r\ U H H" J 

. n SI ) 

.us s .') 

. SS^S9 

I. S9 91 ) 

. . SS-?S9 
. U S 9 
. 9 1 .{iP -i 


Figure 7.1.5 Print Out of Low-Pass Filter 
Design Program 



119 


One of the basic configurations shown in Figure 7.1.2 must now be 
chosen. Since the filter has an odd number of elements and should 
provide a high input impedance at frequencies beyond the 
prototype shown in Figure 7.1.2 d is selected. Thus the odd k 
subscripted values of L(k) and the ^ven k subscripted of C(k) are 
used. Hence, the circuit appears as shown in Figure 7.1.6. Also, 
the terminating resistance RT = 300fi. This circuit was built up and 
tested using hand wound inductors and fixed values of capacitance 
having a 5% tolerance. In Figure 3.7 one can compare the measured 
frequency response of the actual structure to the theoretically 
predicted response. 

The experimental response as indicated in Figure 3.7 has about .5 
dB pass band ripple and falls off much quicker than the theoretically 
predicted response for a .01 dB ripple filter. As expected from the 
theory, allowing a theoretical pass band ripple of .5 dB for the same 
structure results in a theoretical taper which is closer to the 
experimental results. It is then reasonable to assume that we could, 
if desired, trim the element values to smooth the passband ripple and 
provide less of a taper. 

7.1.3 Band-Pass Filter Design 

By making use of a suitable low-pass to band-pass mapping, one 
can use the basic low pass design equations to obtain the design 
parameters for a band-pass filter. The band-pass response is obtained 
by first folding the low-pass response to produce a symmetic curve 
about the frequency origin and then translating this response to the 
desired center frequency, to produce the band pass response as 
shown in Figure 7.1.7. The low-pass to band-pass mapping is; 



120 


.370 .820 .867 .820 ,370 



All Inductors in ph 
All Capacitors in pf 


Figure 7.1.6 Low-Pass Limiter Filter 



121 



1 .7 Frequency Response of a 
Band-Pass Filter 



)CAL -1 ? 


1 . :M A 

I 

1 . A/; A 
1 • '* A 
1 .A? 3 

1 - 1 :t S 
I • } ‘^ S 
1 . 1 A >; 

1*16 r 


? ! ^"Lr" ,LF, ! ^ ! > 

A-i =FS-]TC 'vAt.:,;! ) • c; u = (lv:^; -Iv I ) /W^ ; 
A ~7 XF C • ; V1 P S r, -if L I’"' ) 7 S = A - I 

C = ^ X Pi • A 1 A A '.1 1-; '¥ L !'J = 0 ” 1 

iA-F'S J rc A/D ) 

G=F L JD C F + F" SO T C F t A - 1 ) ) 

:i -F L or i A+~ S OT C X' t A - I ) ) 

0=G/-i 


” "01 

S X-C :.■:;;; t A- 


7. 2i wO , 


^ * -O 1 t 

i- 1 ?' ) / < 


Figure 7.1.8 FOCAL Program to Determine the Number of 
Elements for a Band-Pass Filter 



123 




Figure 7J>9 Possible Band-Pass Filter Configurations 



124 





(7.1.13) 


where w, the fractional bandwidth is 


w = 



^1 


(7.1.14) 


0)^ - /co-j '^ 2 ^ (7.1.15) 

and and lo-j ’ refer to the low pass response as indicated in 


Figure 7.1.3 while a>, Wp refer to the band pass response as 
shown in Figure 7.1.7. Hence, equation 7.1.1 can be modified as; 



This can be solved to give the required number of L - C resonators, n. 
As was done for the low pass case, the equation can be implemented in 
a FOCAL program that solves for n if the ripple, LR, the upper and 
lower cut-off frequencies, W1 and W2, the out-of-band attenuation LF, 
and W, the frequency at which LF dB of attenuation is desired are 
specified. This program is shown in Figure 7.1.8. 

Like the low-pass filter, the band-pass filter can have four 
different realizations, each one having the same response. These forms 
are shown in Figure 7.1.9. The parameters g^ and g^^-j are defined in 
exactly the same manner as for the low pass filter. The values 
represent the normalized impedance of each series resonator and 
normalized susceptance of the shunt resonators. Again, these are the 

I 

same g parameters as generated in the low-pass design. “ 1 sind 

I 

co-| =1, the series impedance is; 



125 




, _ 1 

= fT- 

0 s u) C 
0 s 


R. 


-2. n 

W 9k 


(7.1.17) 


and the shunt susceptance is; 


B = 
P 


w-C = 
0 p 


(0 L 

0 p 


WRo 


(7.1.18) 


where Vl = Vl >^0 

The k subscript on the g parameters is changed to j in equation 
7.1.18 to differentiate between those g values which pertain to the 
series resonators and those which refer to the shunt resonators as 
shown in Figure 7.1.9. 

Once again it is possible to generate the g values as in the 
low -pass case. For this case, equations 7.1 .17, 7.1.18 and 7.1.19 are 
used to determine the actual L and C values and the required 
terminating resistance. To use this program, one must specify LR, 
the pass-band ripple in dB, N, the number of resonators, RO, the 
input impedance level, LF, the lower frequency limit of the pass- 
band, and UF, the upper limit of the passband. This program is 
shown in Figure 7.1.10. 

Upon execution, the values of series inductance in uh, LS(K)[UH] 
and series capacitance in pf, CS(K)[PF] are obtained, as well as the 
parallel values of inductance in yh, LP(K)[UH] and capacitance 
CP(K)[PF] in pf. In addition, the terminating resistance RT is 
obtained in The set of values to be used depends on which 
configuration in Figure 7.1.9 is chosen. In Figure 7.1.9 a and b, 
for even values of k, one uses the series values of L and C while 
the odd values of k give the required parallel L and C. The situation 
is reversed in Figure 7.1,9 c and d. 



126 



S PI =3 . 1 S9:^.;S = 7.:175S ‘-;L = P <^1^ 1 ^ Lr ^ 1 »' A 

• 1 '•> ,S = <^P I IF* I '';'.l - FS'JT C V‘'J* '.vD i S ?. = (■ '-- J^ WL ) /'/■•'' 

■■>.^'1 :•; r = FFXP ( ') ) ? ') S =FFaP < “ ‘J ) » -S PA = FL-JGC CT+3> /( r- 3 

S GG = PA S GA = CFFXPCGG>-FFaP( -GG) J /G. 
p . /n) '3 K = 1 ; ! ) 3 • ? ; S G:M=3 * A:Vf /GA J i) 3 . A ; i) 3 . 

o, t,,,! p k=3>X5I1 3 

- A 1 I ( ,\i / 3 - ~ I T P ( / 3 > “ * 3 3 ) ^1 • 1 > • 3 > A • 3 


3*13 S AJ=A:NJ;S 3J = 3i\llS GU=GN 

3,33 S 3.\=FS 1 :N!C C 3 + K- I ) *P 1 /'?/iV J 5 3 3:V=GAt-GA+ C F >iXC 1 /tM> ^ t..> 

3 . 3 ■. i S G = -'I * A 0 + A i\ / ■'i O^G 0 

3 . 43 S L3= C r.i\':}- ■iO) /( A^V.A) ; S G3=X /( + J) 

3 • /i3 S LP= ( X ^ !\' J ) / ( G iM * v*.'i ) ) 5 3 C'j * - n N / ( ‘■;v) * /v + -J 0 > > 0 4*5 

/, ,p 3 3 ‘v-: = FFXPC AA//I > J S V' = Fr:AP( -3A/4 ) 

A • • I S GF = C ( W + ' / ) / ( “ '7 > J f 3 5 S R F = A 0+ G F 5 G 4 • 4 

4 * 3 !') i I T ” i 'i 0 

4 .44 r ! ! > ’• A r ~ •• j A . 5 > a' r > ! 5 J 

4.5-;’ T 'S AA./J, LS^i' I F A>" *' ^ G 1 F 1 •> J i) 4* A 

4. AH T “ "LG* I FA,” ” , CP * I F 1 3^ ! 


Figure 7.1.10 Band-Pass Design Program 



]Z7 


As an example of the application of there techniques consider 
the problem of designing the band pass filter located between the 
I.F. output of the mixer and the input to the IF amplifier (see 
Chapter 2.4). According to the specifications described there, the 
filter requires a SOU input impedance, .01 dB pass-band ripple, 
upper and lov^r cut-off frequencies of 98 MHz and 62 MHz respeHively 
and an attenuation of at least 30 dB at 40 MHz. First, using the 
program shown in Figure 7.1.8 to determine the number of resonators, 
we set LF = 30, LR = .01, W = 40, W2 = 98 and W1 = 62 and find that 
n = 3,990. Thus>n = 4 is used. Now the second program (Figure 7.1.10) 
is applied to obtain the actual values of L and C. Setting LR = .01, 

N = 4, RO = 50, LF = 62 and UF = 98 we obtain the result shown in 
Figure 7.1.11. 

Since there is an even number of resonators, either configura- 
tion a or c in Figure 7.1.9, can be used. If one chooses Figure 
7.1.9 a, the odd values of k give the parallel L's and C's while 
the even k values give the series l's and c's. The resulting 
configuration was shown in Figure 7.1.12. The value of the terminating 
resistance for this structure is 55.0374 ohms. 

7.1.4 High Pass Filter Design 

The basic design equations for the low-pass filter can again 
be used for high-pass design by making the frequency transformation; 

aj-| 0), ' 

(7.1.20) 

where w' and w-j ' are the angular frequency variables related to the 
low-pass response shown in Figure 7.1,8 while w-j and w are the angular 
frequency variables related to the corresponding high pass response 



0 

I...:: ; .'11 
\i : /i 

M ( OH/iS ) : ‘'v i 
LFC MHZ) : 

‘ \F ( MH.Z ) :9-^ 


:< 

K) CUH) 

S ( K) C H h" J 

LP ( ;< ) C iJK 3 

CP ( A ) i: 

1 

1 . 1 S 7S M 


vl . A A A 1 /! 

A3. i'U A 


. 3AS3-'i 

15.7113 


1 !'1 A . 1 3 A 

3 

;.'i . •^9 3 17 

1 ^.•'^733 

i.;;35A3 

1 1 A. 3? 7 


1 . 1 /| 31 M 

v? 9 . 1 1 '3 

3 .3 7?B(3 

A " . AP ^ 


MS .0 3 7^J 


Figure 7.1.11 Print Out for Band-Pass Design Program 






130 


shown in Figure 7*1.13, In effect, this transformation interchanges 
the origin with the point at infinity and the positive frequency 
axis with the negative axis. 

The effect of this transformation is to change the inductive 
reactance id'l' in the low-pass prototype to a capacitive reactance 
in the high pass filter: 

-a)l03^ L /w = “1 /u)C (7.1.21) 

1 t 

and any capacitive susceptance w C in the low pass filter is then 
transformed to an inductive susceptance: 

C/w = -1/toL (7.1-22) 

Hence the same values used for the low-pass prototype can be used 
to obtain element values for a high-pass design. 

If this transformation is applied to the standard low-pass 
design programs we can obtain programs to design high-pass filters. 

For example see Figure 7.1.14. To determine n, one specifies LR, 
the ripple in dB, WC, the cut-off frequency, LF, the out-of-band 
attenuation', at the frequency W. To determine the required element 
values we c|n use the FOCAL low-pass program which solves equations 
7.1.3 thru 7.1.12 and apply equations 7.1.2 and 7.1.22 to obtain the 
high-pass filter design program shown in Figure 7.1.15. 

Thus, to determine the element values one must specify LR, N, 

RO, and WC. Like the low-pass and band-pass filters, the high-pass 
can also exist in four equivalent forms as illustrated in Figure 
7.1.16. As in the case of the low pass filter, the design program 
gives values which are applicable to all four forms. To determine 



131 



Figure 7.1.13 Frequency Response of a High-Pass Filter 



132 


C FOCAL - 1 ?? 


0 1.01 A ! ! #**LF‘NLF# ! 'S LI > 

:.) 1 , ..•; /| s A =F KXP ( . ^ 3 0 bo * LF ) 5 S 3 =A - 1 
n.06 S C=FFXP( .:^r30'P5f'i S 0 = 01 

■11.00 S F = FS-3TC -3/1)) 

0 1 , 1 .1 G =FLOC ( F + F.A- JT CF T2 - 1 ) > 

rO.11 3 V!='P-i‘l''C“01 

oi.r-’ :•> x=v'/i\Co s h = flog< x+fsot< a > ) 
A 1.1.'! s 0 = C/H 
= ^1 1 . 1 A T .'i 



Figure 7.1.14 FOCAL Program for Determining the Number 
of Eleinents in a High -Pass Filter 



133 


i": 

T R Q <■'■<'> LOO CUM 3 C(K)I:PF3'S 


^•^.1 i S RI=3* M! '59 :oS U^LA/17.3 75S L 1 =3 tp M L A 

■;A,93 S T"FLXP(A);S S=FFXP(-Q)JS OA^FLOGi: < T + R ) /C T-: 
;s GG= A /R ? 55 GA = C FRXi^ C GG ) -FEaPC - CG ) 3 /P 


)2 • 

A-') 

S 

:'=1 

;o 3 • 3 05 

G 


P-icAA/GA 

i = 

3 p . 

5 A 

iT 

<=p 

J lA J ••) 3 





1 r» . 


J 

CG/ 

4-Fl TPC X/P ) - 

.05)4. 1 


3 * 

1 i 

s 

AO- 

A'SiJG 20= 

i i 

OS 

GO- OS 


•)A . 

44 

4 

Ai\' = 

E55I sAi: ( 

K- 

1 ) 

/P/N3 

' 3 • 

3 5 

3 

GG = 

4t4A0^'A(N}/ 

00 

;^G 

0 


■; 3 . 

4 A 

S 

L = P 

0/in 

S 

: ] :t 

1 /G1 A GX 

'I' 

ZA . 

\ A 

s 

!■'= 'f 

FXP03A/ 

)5 


V=FFaP< 

- 

’ ^1 . 

A J 

r ‘ 

QiV ~ 

r C ■-'+ 10 /( W~ 

V)3tP;G 4 

9 


3 1 

s 

r:G = 

1 





3 4* 

44 

T 

A 4 . 

' .. <0’ 

M 

7.6 

.5^GF, ! 

J 

G • 

A3 

T 

?A , 


•o 

7.6 

.5> 

4 t 


’S L*1 E6^ 




Figure 7.1.15 High-Pass Design Program 


r f 

; ) 3 


/,\j) 3 ip 


hZl2 



134 



Figure 7.1,16 Possible High Pass Configurations 


135 


L ^ 

.\i : • > 

r?0( Oni'^iS > : 
'c% ( MH zy : \ 


K 

G( K ) 

L ( K > t 0H J 

0 C K ) L r'G J 

1 

J 

0 * 0^16 63 

16.66 0 ? 

o 

1 . -^'" 9^1 

0 • jt) 6^ 7 ^ 

0 6.6 6 7 61 


o » >-) 

0 .001 30 

1 ^ . -107 6 

/j 

1 - .'^'^9 61 

0 . 0 60 70 

0 6 . 3 (') 7 :■} 

3 

1 • Virl 

0 • i/ } 0 6 66 

13.66/) '3 





= 

^0 




Figure 7.1.17 Print Out of Hligh-Pass Design Program 



136 


which values apply to a given configuration, note that for Figure 
7.1.16 a and b the odd k subscripted values of inductance and the 
even k subscripted values of capacitance are to be used. For 
Figure 7.1.16 c and d, the situation is reversed. 

As a design example, consider a high-pass filter with a cut-off 
frequency of 100 MHz, impedance level of 50fi, pass-band ripple of 
.5 dB and an attenuation of 10 dB at 85 MHz. Using first the program 
for determining the number of elements (Figure 7.1.14) set LR = .5, 

WC - 100, LF = 10, and W = 85 and find that N = 5.248* choose n = 5. 
Having a knowledge of the number of elements one can now apply the 
second program (Figure 7.1.15) to determine the required values of 
L and C. Setting LR = .5, N = 5, RO = 50, and WC = 100 we obtain 
the result shown in Figure 7.1.17. Since the filter has an odd 
number of elements and assuming it is desirable for the input to 
the filter to present an open circuit impedance above 03^, con- 
figuration d of Figure 7.1,16 is chosen. Hence, the circuit shown 
in Figure 7.1.18 is obtained. Note that the terminating resistance 
is 50n for the structure. 

7.2 VOLTAGE CONTROLLED OSCILLATOR 

For the purpose of making swept measurements in the performance 
of the amplifier of Chapter 2, a voltage controlled oscillator (VCO) 
was constructed that could be frequency modulated in a linear manner 
over the range of 60 - 100 MHz and which provided a fairly constant 
power output over that range. 

As is shown in Figure 7.2.1, the circuit is a series tuned 
Hartley Oscillator with a varactor diode in the resonator circuit. 



18.66 pf 12.53 pf 18.66 pf 



Figure 7.1.18 High-Pass Filter Design Example 




138 


+ 20 V 



form 

D: 5-10 pf Varactor 


Figure 7.2.1 Voltage Controlled Oscillator 


Input Voltage, Volts 



to 


Figure 7.2,2 VCO Output Frequency as a Function of 
Input Voltage to the Varactor 



Output Power 




Output Frequency, MHz 


Figure 7,2.3 VCO Output Power as a Function of Output Frequency 



141 


Hence, by changing the bias to the varactor, the frequency of 
oscillation is changed. Figure 7.2.2 shows the tuning curve which 
is linear to 1%. The power output over the same frequency range is 
shown in Figure 7.2.3. The output is reasonably constant, exhibiting 
only 1.3 dB of variation over the tuning range. These measurements 
were made with the output loaded to 50fi. In order to have the VCO 
perform to specifications indicated here, it is recommended that 
it always be loaded with 50 ft. 

7.3 LUMPED ELEMENT QUARTER WAVELENGTH TRANSFORMER 

Quarter wavelength sections of transmission line are routinely 
used as impedance transformers. At frequencies below 1 GHz, the use 
of a transmission line for this purpose is impractical due to the length 
of line required. However, from the methods outlined in Everitt and 
Anner (24)one can replace the line by a lumped element equivalent 
circuit as shown in Figure 7.3.1. For this quarter wavelength (x/4) 
transformer, the characteristic impedance required to provide a match 

between two different load resistances, (Z^ and Z ) is; 

'0 r 



= Z 
0 r 


For the lumped element equivalent: 


(7.3.1) 


^o’ = l’<ll = = 1^1 

where and X 2 are inductive and Xj is capacitive. If f is 
the center frequency at which a perfect match is obtained, one finds 
the following lumped element values for the x/4 transformer: 



(7.3.4)' 







143 


As an example, consider the lumped element equivalent A/4 trans- 

I 

former which matches 300« to SQn at 80 MHz. From equation 7.3.1, 

= 121.5fi and from equations 7.3.2 and 7.3.3 one obtains L-j = = .242 

ph and = 16.45 pf. Figure 7.3.2 shows the theoretical magnitude 
of the reflection coefficient, }pt plotted as a function of input 
frequency for this structure. 

It is possible to effectively cascade these A/4 transformers to 
obtain a match over a wider frequency range if so desired. Matthaei ,{25) 
provides a detailed analysis and a set of design equations for making 
such broad-band impedance matching structures. 


7.4 FOURIER ANALYSIS OF A TRAPEZOIDAL WAVE 

To good approximation, the output of the limiter described in 
Chapter 3 is represented by the waveform shown in Figure 3.2. 
Hence, 

/ 

A sine 0<e<a)t 
c 

0)t^ < 0 < 7T - <i)t 

c c — — c 


V(e) = 


A sine it - tut < 0 < tt + wt 
c — c 

-V TT + U)t < 0 < ZtT - Wt 

C ^ — Q 


A sine 2tt - wt < o < 2 tt 

c — — 


(7.4.1) 


is the limiter's output over one period. It is possible to represent 
V(o) as a Fourier series of the form: 


00 


n=l 


sin n 0 


(7.4.2) 


since V(e) is an odd function. The Fourier coefficients correspond 
to the amplitudes of the higher order harmonics contained by V{e). 



144 



Figure 7.3.2 Magnitude of Reflection Coefficient 
as a Function of Frequency for 
A/4 Transformer 



145 


These are given by; 


B - 2 

T 


r 

/ 


V( 0 ) sin ne de 


(7.4.3.) 


Therefore, for the limiter output, the amplitudes of the harmonics 
will be given by: 


Bn f ^ 


<ut 


0 sin ne de + V 


/ 7T-0)t 

. ^ 
Sin r 


c 

ne de 


+A 


ir+(ut 

f ■ 

I sin 

TT“Wt 


e sin ne de - 


iT+a)t. 


2ir-wt 


sin ne de 


/ 


2it 


+A / sin e sin ne de I n > 2 

27r-o)t 


(7.4.4) 


Solving these integrals and substituting wt^ = 0 we have 
2V 

^ (7.4.5) 

" “mr n ^ 2 

To solve for B-| , the fundamental equation 7.4,4 is used with n=l : 

B, = ^ |2a.t^ - 1 sin2oit^ j (7.4.6) 

Also it should be noted that 


o.tc = si 


n"’(v^/Aj (7.4.7) 

Further, as can be seen from equation 7.4.5, all. even coefficients 
are zero. The theoretical and experimental amplitudes are compared 
in Table 3.1, 



146 


7.5 MEASUREMENT TECHNIQUES 

7.5.1 Measurement of Limiter Harmonics 

An experimental set-up like the one shown in Figure 7.5.1 was 
used to measure the harmonic content of the limiter's output. A 
100 MHz low pass filter at the output of the generator was used to 
eliminate its harmonics. The 100 MHz high pass filter is necessary 
to eliminate the fundamental component of the limiter output so that 
the limiter hamionics can be measured without overdriving the spectrum 
analyzer. 

The procedure used for measuring the harmonic content is quite 
simple. First, without the high pass filter in place, a reference 
level of 0 dB is set on the spectrum analyzer. Next, the high pass 
filter is reinserted and the spectrum analyzer is set to the second 
harmonic frequency. Attention is then decreased in the variable 
attenuators to bring the level of the second harmonic up to that 
previously set for the fundamental. The attenuation removed is 
noted and a correction is made for the insertion loss of the high 
pass filter at this frequency. This yields directly the level by 
which the harmonic is down from the fundamental. By using a 

procedure such as this, we are able to obtain the experimental results 
shown in Table 3. 1 . 

7.5.2 Measurement of Inductance with Hewlett-Packard Automatic 
Network Analyzer. 

In order to accurately determine the inductance of the hand-wound 
inductors used in the filter designs described in Chapter 2.4, 2.5, 3.3, 
they were measured using the experimental set-up shown in Figure 7.5.2. 
The oscillator is set to 100 MHz and the attenuators are adjusted to 
provide sufficient power to operate the analyzer. To calibrate the 




148 



Figure 7.5.2 Set-Up for Inductance Measurement 




149 


phase meter the inductor is temporarily shorted out and the cable 
lengths in the reference and test channels are adjusted to give a 
180® indication on the phase meter. The short is then removed and 
the meter should return to 0®. If the meter doesn't return to 
exactly 0° it can be triirened by use of the vennier control on the 
phase meter. The inductance can now be measured by placing the 
inductor into the mount and noting the value of the phase angle 
0 . To compute the inductance, L, substitute 0 into the following 
formula: 


1 1 + /I + tan 9 

tan 0 


yh 


(7.5.1) 


If one wants to adjust the value of inductance, it is convenient 
to know the resulting phase for a given inductance. For L in yh 
and 0 in degrees we have: 

e = cos"^ ( 5^ . 1- . )^ - 1 (7.5.2) 
(41x1)“^ +1 


In making these measurements care should be taken to keep the 

inductor leads as short as possible. Also, the output frequency of 

oscillator should be monitored and kept constant. In this manner, 

it is possible to measure inductance to an accuracy of 5%. 

7.6 DETERMINATION OF PARALLEL LINE 4 COUPLED FILTER DIMENSIONS 
USING A FIBONACCI SEARCH ’ 

From the even and odd mode characteristic impedances of each 
parallel set of coupled resonators in the parallel coupled strip- 
line resonator filter (see Figure 4,2), Matthaei et. al. (19) 
supply equations for determining the strip dimensions using elliptic 



integrals of the first kind. Based on these equations, Matthaei (19) 
presents a set of design nomograms. It was found that the accuracy 
of these nomograms was insufficient for our purposes. By employing 
a Fibonacci search and polynomial representation of the elliptic 
integrals, T. Monsees has developed the FOCAL program shown in 
Figure 7.6.1 and 7.6.2 which solve for the normalized dimensions 
w/b and s/b, (see Matthaei, p. 175) to whatever desired accuracy. 

The use of these programs is rather straight forward. The 
appropriate values for the even and odd mode characteristic line 
impedances are calculated in the usual manner (19)- The nomograms (ig) 
are then used to first determine the maximum and minimum values of 
the range over which one would expect to find the correct values of 
w/b and s/b (see Figure 4.2). Initial values of s/b and w/b are 
also determined in this manner. The program shown in Figure 7.6.1 
is applied first. Setting S/B MIN, S/B MAX, W/B (the initial value), 
ACC'CY (required accuracy expressed in parts per 10'^)^ ZO ODD and 
ZO EVEN to their appropriate values, a print out of two possible values 
of S/B are found. These are averaged and the result used in the 
second program, along with the appropriate nomogram values for W/B MAX 
and W/B MIN. This program gives two possible values of W/B. The 
first program is run again using the average the two print out values 
from the second program for W/B. Now the S/B MAX and S/B MIN used 
are the two values from the first run of this program. One then 
proceeds to iterate in this manner until the final values of s/b and 
w/b are within the required accuracy. 



01.01 A "W/3 «IN”XL,*'W/8 MAX’*Xl) #”ACC *CY'*OA> ’* S/B“C 1 
0 1.02 A •’Z0>ODO“ZO*”Z0*£VEN'VE 

0 i .03 S PA=0 

02.01 S L=2^FITR((XU-XL)/DX) + US S(2)=liS SC3^=2 

02.03 S SU)=S(2)JS S<2)=3(3)iS S ( 3 ) =S< 1 ) +S ( 2) ; 1 (S(3)-L)2.03 
02.05 S LX=XL5S UX=XU 

02.07 S XU ) = (S< 1)/S<3>)*<UX-LX)+LX5S XN=XU)JD 3lS YU) = Y«viiS A8 = 2 

02.09 S X( AB J =< S( AB ) /SC 3) ) *( UX-LX ) +LX ; S XN=X(A6>it> 3iS Y(A8) = YN 

02.11 I (FABSC Y(2))-FA8S( Y( 1 )))2.13iS JX = XC2)JS YU = Y(2>;S XC2)=:X(1) 

02.12 S Y(2)=YU)>S AB = U6 2.15 

02.13 S LX = XCI)IS YL-Y(l)iS X(1)=X(2>J3 Y<1>=:Y<2);S AB=2 
02.15 S S(3)=S(2)JS SC2>=S<l);S 3 U > =S( 3 ) -SC 2 ) J I (2-SC3)>2.09 
02.17 S XiM = X(A9)ll (FABSCAN-XL)-0X)2.25i I < FABSCXN-XU) -0A>2.25 

02.19 I < -FA3SC FSGNC YU> -FSGNC YL) ) )2.235I U*'EX. MlN 
02.23 T ! >XN# ! ;G 7. I 

02.25 T t 1 

03.20 S 0=CI+XN*1 .57085S M=THiO 6 
03.30 I CPA)2.25>3.32>S M=M/Trt;6 3.35 
03.32 S M=M*TH 

03.35 S Ml -1 -MjD 4 
03.42 0 5 

03.50 S YN=ZE-94.2478*Kl /I . 6*Ki R 

04.10 S K1 =1 .3863-*“ . 1 11 97*Ml +.07253»M1 r2 

04.20 S K1 =K1 +C .5+ . I 21 35*M! + .028873*M! T2 3*FL0G( I /Ml ) IR 

05.10 S K=K1SS Ml =1 -FS^TC 1 -Mt2) 5D 4 

05.20 R 

06.10 S TH = CFEXPCD)-FEXPC-0)3/J:FEXP(D) + FEXP(-D) 3iR 

07.10 1 CPA)2.25> 7.25^J 

07.20 S PA«i;S ^E-ZO)G 2.01 

Figure 7.6.1 Part I of Search Program 



01.01 A 
01*02 A 
01 .03 S 


’♦S/B MlN**XL<"S/8 rtAA"XLJ^ ”ACC *CV'*DA#”VJ/B"C1 

••Z0>ODD‘*iO>"Z0»EVEN^*ZE 

C1=C1*1 *570815 HA=0 


S L=2»FITR<(XU-XL)/DX)-H1S S(2)=llS 5<3)=2 
S 3<1)=S(2>1S S(2>=S(3)lS S ( 3 ) =S< 1 > +St 2 ) 1 I ( S< 3> “L)2*03 

Q I iCsjXL. * ^ L1X*»XU 

S X( l > = C S< l > 3 > > ♦ < UX-LX ) +LX 1 S XN=X<l)lO 3lS lfCI>»VN#S A3-2 
S X(AB)=<$( A8)/St3) >*CUX-LX>‘»'LX;S XN»X(AB)5D 3lS 
I (FABSf Y( 2 > >-FABS< 1 > > 12* 1 31 S JX=X(2)lS yU»V(2)lS X<2>**A<1 
S Y( 2) =Y( 1 ) IS ABs^l 16 2*15 

S LX=X(l)lS YL=Y<1)1S X(l>=X(2)lS Y(l)=Y(2)lS A0a2 
S SC3)=S<2)lS SC2)ssSCl>lS 5<1>®5C3)**S<2>1I <2*S<3) >2*09 

S XN=X< A8 > 1 1 < FAB SC Xi^-XL) ‘•OX > 2 • 25 1 I C FABSC XN-XU> -OX >2 • 25 
02.19 I C-FA8SCFSGN<YU)-FSG4M(YL)))2.23iT I *ӣX. 

02.23 T ! *XM> J IG 7.1 
02.25 T ! >‘*NR’S ! iO 


02^ 

02 « 

02 . 

02 . 

02 . 

02 . 

02 . 

02 

02 

02 


01 
03 
05 
07 
09 
1 1 
12 
13 
15 
.17 


03*20 S 0=C I +XN^ I . 57081 S M=TH1D 6 
03.30 I CPA)2*25>3.32lS M=M/THI6 3*35 
03.32 S M=M+TK 
03.35 3 Ml=l-rtiO 4 
03.42 D 5 

03.50 S YN=ZE-94.2478*Kl/l .6*K1R 

04.10 5 Kl-1 .3863 + . 1 1 I 97*M1 ‘►.07253^Ml t2 

04.20 S K1 =K1 + C .5+ .1 21 35*M1 + *028873*M1 t2 3*FLOGU /Ml )1R 

05.10 S K = KliS Ml=l-FStiTCl-MT2)lD 4 

05.20 R 

06.10 S TH = CFEXP(D) -FEXPC -0) i/tFEXP(D)+FEXPC -D) 31 R 


07.10 I (PA)2.25>7.21‘oi 
07.20 S PA = llS ZE = Z01G 2.01 

Figure 7.6.2 Part II of Search Prograin 


cn 

ro 



153 


8. BIBLIOGRAPHY 


1. J. P. Singh, R. P. Morgan and F. J. Rosenbaum, "Satellite Networks 
for Education," Proceedings of the International Telem etering 
C onferenc e, Vol . ' 7., pp." 429-439, Los Angeled, Calif. December 


2» B. A. Newman, J. P. Singh, and F. J. Rosenbaum, "Design of a 12 
GHz Multi carrier Earth Terminal for Satellite - CATV Interconnec- 
tion," Memorandum No. 71/7, Center for Development Technology, 
Washington University, St. Louis, Mo., November 1971. 

3. "Ground Signal Processing Systems, Summary Reports on Analysis, 
Design and Cost Estimating," NASA CR-727(39, Contract NAS 3-11520. 
General Electric, Space Systems Organization, Valley Forge Space 
Center, Philadelphia, Pa., June 1970. 

4. J. P. Messier, Y, C. Hwang, J. J. Zampini, "Low Cost Ground 
Receiving Systems for Television Signals from High-Powered 
Communications Satellites," Vols. I and II, NASA CR -20933, Final 
Report. General Electric Company, Electronics Laboratory, 

Syracuse, N. Y* 

5. B. B. Lusignan, P. Z. Bulkeley, J. M. Janky, and R. B. Taggert, Jr., 

"The Design and Development of Low-Cost Microwave Adaptor Suitable 
for Television Reception from. High -Power Communications Satellites," 
NASA CR-72773, Center for Radar Astronoiny, Stanford University, 
Stanford California, October 31, 1970. See Also: K. Ohkubo, 

C. C. Han, J. Abernaz, J. M. Janky, and B. B. Lusignan, "Optimi- 
zation in the Design of a 12 Gigahertz Low Cost Ground Receiving 
System for Broadcast Satellites," Vol. I and II, NASA CR-121185, 
October 15, 1972. 

6. A. Whalen (Trust Experiment Mgr.) "Breadboard Design and System 
Analysis for the ATS-F Trust Experiment Small Ground Station," 

NASA, Goddard Space Flight Center, Greenbelt, Maryland, 

September , 1 971 . 

7. M. V. O'Donovan, C. M. Kudsia, L. A. Keyes, "Design of a 
Light-Weight Microwave Repeater for a 24-Channel Domestic 

.Satellite System," RCA Review , Vol. 34, pp. 506-528, September 
1973. 

8. J. D. Parker, "Report on the Geneva Space Telecommunications 
Conference-Broadcasting Aspects," IE EE Transactions on Aerospace 
a nd Electronic Syste ms, AES- 8, No. 4, pp. 505-509, JuTy 1972. 

9. J. B. McCuller and J. P. Singh, "A Computer Program for Small 
Terminal .Fixed/Broadcast Satellite System Parameter Optimiza- 
tion," Report R(T)-74/l, Center for Development Technology, 
Washington University, St. Louis , Missouri , October 1973. 



154 


10. T, W. Stagi, N. H, Morgan, and J. P. Singh, "Computer-Aided 
Communication Satellite System Analysis and Optimization," 

Report R(T)“73/2, Center for Development Technology, 

Washington University, St. Louis, Missouri, October 1973. 

n. J. E. Degenford and B, A. Newman, "12 GHz Image and Sum 
Enhanced Mixer Diode Converter," Westinghouse Defense and 
Electronic Systems Center, Baltimore, Maryland, October 1973. 

12. E. J. Drazy, R. E. Sheckey, and H. C. Wang, "TH-3 Microwave Radio 

System: Network," The Bell System Technical Journal , Vol. 50, 

No. 7, pp. 2137-2153, September 1 . 

13. Motorola Inc., Linear Integrated Circuits Data Book , November 
1973. 

14. J. Millman, H. Taub, Pulse, Digital, and Switching Waveforms , 
McGraw-Hill, New York, 19^5, pp. 147-150. 

15. F. W. Grover, Inductance Calculations: Formulas and 

Tables , Dover PubTication^ Inc. , NevT York, 1^62. 

16. C. W. Lee and W. Y. Seo, "Super Wide-band FM Line Discriminator," 
P roceed i ngs of the IEEE (Letters), Vol. 51, pp. 1675-1676, 

NoVember T96^3. 

17. C. W. Lee, “An Analysis of a Super Wideband FM Line Discriminator," 
P roceedings of the IEEE , Vol. 52, pp. 1034-1038, September 1964. 

18. E. T. Jilig, "The Intelsat IV Spacecraft," COMSAT Technical Review, 
Vol. 2, No, 2, Fall 1972. 

19. G. L. Matthaei , L. Young, and E. M. T. Jones, Microwave Filters 

Impedance Matching Networks and Coupling Structures, McGraw-Hill, 
ITew York,' 1964. 

20. D. H. Olsen and F, J. Rosenbaum, “MICTPT-A Minicomputer General 
Purpose Microwave Two- Port Analysis Program," IEEE Transactions 
on Microwave Theory and Techniques (Letters), MTT-22, No. 3, 
pp, 340-34T, March 1974. 

21. S. B, Cohn, "Parallel-Coupled Transmission Line Resonator Filters," 
IRE Tran sactions on Microwave Theory and Techniques , Vol- MTT-6, 
pp. 223-227, April 1958. 

22. W. A. Edson and J. Wakabayaski, "Input Manifolds for Microwave 
Channelizing Filters," IEEE Transactions on Microwave Theory 
a nd Technique s, MTT-18, No. T, pp. 270-726, May 1970. 

23. A. E. Atia, "Computer Aided Design of Waveguide Multiplexers," 

I EEE Transactions on Microwave Theory and techniques , MTT-24, 

No. 3, pp. 332-336, March 1974. 



155 


24. W. L, Eventt and G. E. Anner, Communication Engineering, McGraw^ 
Hill, New York. 1956. 

25. 6. L. Matthaei, "Impedance Matching Structures Having a 
Tchebsycheff Characteristic," Proceedings of the IEEE , Vol . 52, 
pp. 939-963, August, 1964.