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
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