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Li. bbOy
AFCS TECHNICAL REPORT
FM QUIETING CURVES
and Related Topics
SYSTEM TECHNICAL APPLICATIONS FACILITIES
1842 ELECTRONICS ENGINEERING GROUP (AFCS)
RICHARDS-GEBAUR AIR FORCE BASE, MISSOURI
30 SEPTEMBER 1977
1842 ELECTRONICS ENGINEERING GROUP
MISSION
The 1842 Electronics Engineering Group (EEC) is
organized as an independent group reporting
directly to the Commander , Air Force Communica-
tions Service (AFCS) with the mission to provide,
communi cati ons -el ectronl cs -meteorol og i cal ( CEM)
systems engineering and consultive engineering
for AFCS.. In this respect, 1842 EEG responsi-
bilities include: Qeye.l oping engineering apd
installation standards for use in planning,
programming, procuring, engineering* ins tailing
and testing CEM systems, facilities and equip-
ment; performance of systems engineering of CEM
requirements that must operate as a system or ,
in a system environment; operation of a special-
ized Digital Network System Facility to analyze
and evaluate new digital, technology for applica-
tion to the Defense Communications System (DCS)
and other special purpose systems; operation of
a facility to prototype systems and equipment
configurations to check out and validate ehgi- .
neerlng-i nstall ati on standards and new 1 nstalla-
tion techniques; providing consultive CEM
engineering assistance to HQ AFCS, AFCS Areas,
MAJCOMS, POD and other government agencies »
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t REPORT NUMBER
TR 77-18
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/ FM Quieting Curves
& and Related Topics ,
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• a. supplementary notes
1*. KEY WORDS (Cnntlnu a on rororao *ld* II neceeeary and Idtnllly by block number)
Frequency Modulation radio performance
Phase Modulation radio parameters
Noise FM
Quieting Curves PM
ABSTRACT (Continue on rovr too oldo II nacaooary and Identity by block number )
his report describes the relation between readily measured frequency modulation
radio transmitter and receiver parameters and the basic baseland signal and
noise performance of the radio transmitter/receiver combination. Equations,
graphs, and charts are provided to facilitate application.
DD 1 JANM7I 1473 EDITION OF 1 NOV SI IS OBSOLETE
APPROVAL PAGE
This report has been reviewed and approved for publication and distri-
bution.
1' J Lpdt
ZYGMUND J. BARA
1842 EEG/EET (AFCS)
Chief, Command, Control
Division
Defense Communication Systems Engineering
WILLIAM R. P?'OV7N’~M«ior, U?Tf ~
1842 EEG/EE1E
Chief, Engi/.oering Services i ranch
George M. Kizer
GEORGE mV KIZER
1842 EHG/EETET
Electronics Engineer, Author
TABLE OF CONTENTS
Para No Page
1 Introduction 1
2 Basic Modulation Theory 4
3 Wideband FM Receiver Baseband Signal and Noise
Characteristics 21
*4 Experimental Verification 47
5 Predicting FM M/W Terminal Thermal Noise Performance 109
6 Baseband Signal and Slot Noise Versus RSL Using
Generalized Charts 119
7 FM Microwave Radio Terminal Equipment Parameters 150
8 A Digital FM System 214
9 Conclusions 220
10 Recommendations 223
1 1 Bibliography 224
Distribution List 77Q
LIST OF ILLUSTRATIONS
Figure No. Page
I FM RF Spectrum, Sinewave Modulation, Integer Betas 6
? FM RF Spectrum, Sinewave Modulation, Carrier Dropouts 7
3 FM RF Spectrum, Sinewave Modulation, Sideband Dropouts 8
^ Slot Noise Versus Received Signal Level 22
5 Typical Microwave Oscillator Induced Baseband Noise 38
6 M/W Transmitter Voltage Controlled Oscillator Noise 39
7 M/W Receiver Easeband Noise Versus Received Signal
Level 40
8 Baseband Noise Versus Carrier to Thermal Noise for
Hard and No Limiting 44
9 LOS M/W Receiver Simplified Diagram 48
10 LOS M/W Receiver IF Response 50
II TROPO M/W Receiver Simplified Diagram 51
IP TROPO M/W Receiver IF Response 53
13 LOS M/W Receiver Baseband Noise Versus Received
Signal Level 54
1M LOS M/W Receiver Baseband Noise Versus Received
Signal Level 55
15 TROPO M/W Receiver Baseband Noise Versus Received
Signal Level 55
LIST OF ILLUSTRATIONS (CONT.)
Figure
No.
Page
15.1
Baseband Slot Noise,
No Carrier Present
58
16
TROPO Quieting Curve
, Normal Configuration
59
.17
TROPO Quieting Curve
, 20 dB PrelF Attenuat ?n
60
18
TROPO Quieting Curve
, <40 dB PrelF Attenuation
61
19
TROPO Quieting Curve
, 60 dB PrelF Attenuation
62
20
LOS Quieting Curve,
Normal Configuration
63
21
LOS Quieting Curve,
10 dB PrelF Attenuation
64
22
LOS Quieting Curve,
20 dB PrelF Attenuation
65
23
TROPO Quieting Curve
, 20 dB PrelF Attenuation
66
2*1
TROPO Quieting Curve
, 40 dB PrelF Attenuation
67
25
TROPO Quieting Curve
, 60 dB PrelF Attenuation
68
26
LOS Quieting Curve,
10 dB PrelF Attenuation
69
27
LOS Quieting Curve,
20 dB PrelF Attenuation
70
28
LOS Quieting Curve,
30 dB PrelF Gain
71
29
Measured Slot Noise
Near FM Threshold Due to
White Noise Baseband Modulation
76
30
Quieting Curves, Two Quieting Sources
79
31
Quieting Curves, Three Quieting Sources
80
32
Wide Slot Quieting Curves
82
33
Wide/Narrow Slot Quieting Curve Comparison
83
34
TROPO Baseband Signal Suppression
86
35
LOS Baseband Signal Suppression
87
36
Quieting Curve, Quieting Source Frequency Offset
88
37
Quieting Curve, Unmodulated RFI
91
38
Quieting Curve, Unmodulated RFI
92
table OF CONTENTS (CONT.)
Figure No.
39 Quieting Curve, Unmodulated RFI 93
40 Quieting Curve, Unmodulated RFI 94
41 Quieting Curve, Unmodulated RFI 95
4? Quieting Curve, Unmodulated RFI 96
43 Baseband Slot Noise Versus Interferring Carrier
Frequency and Power 97
44 LOS Quieting Curve, LC-8 98
45 LOS Baseband Noise Versus Received Signal Level,
LC-8 99
46 LOS Baseband Signal Suppression Versus Received
Signal Level , LC-3 100
47 Sample Quieting Curve 101
48 Sample Quieting Curve 102
49 Sample Quieting Curve 103
50 Sample Quieting Curve 104
51 Sample Quieting Curve 105
52 Sample Quieting Curve 1°6
53 Sample Quieting Curve 1°7
54 Sample Quieting Curve 108
115-
54.1 Noise Equations Factors 116
54.2 Noise Equations Error Analysis 117
55 Theoretical Quieting Curve, Rectangular
IF Response
56 Theoretical Quieting Curve, Gaussian IF Response 12i
iv
LIST OF ILLUSTRATIONS (CCNT.)
Figure No. Page
57 Theoretical Quieting Curve, Average IF Response 122
58 Theoretical Quieting Curve Example 126
59 Theoretical Baseband Signal Suppression Curve 127
60 Combiner Improvement Curves 134
61 Power Addition/Subtraction Curves 136
6? LOS M/W Receiver Quieting Curve, No De-emphasis 140
63 TROPO M/W Receiver Quieting Curve, CCIP De-emphasis 144
6R TROPO M/W Receiver Quieting Curve, No De-emphasis 145
65 LOS M/W Receiver Theoretical Quieting Curve 146
66 TROPO M/W Receiver Theoretical Quieting Curve 147
67 Generalized M/W Transmitter and Receiver 151
68 Example Transmitter Configurations 156
159-
69 FM RF Spectrum, Sinewave Modulation, Various Dropouts 163
70 FM RF Spectrum, Distorted Sinewave Modulation, First
Carrier Dropout 165
71 FM RF Spectrum, Distorted Sinewave Modulation, First
First Sideband Dropout 166
’!? FM RF Spectrum, Square Wave Modulation, First Carrier
DroDOut 167
73 FM RF Spectrum, Square Wave Modulation 168
7R CCIR/EIA Emphasis Curves 170
7^.1 REL Emphasis Curves 171
75 Baseband Noise Spectrum Versus Received Signal Level,
No De-emphasis and CCIR De-emphasis 172
76 CCIR/Time Constant Emphasis Networks 175
V
LIST OF ILLUSTRATIONS (CCNT.)
Figure No.
77 Serrasoid Baseband Circuitry 185
7s Simplified Serrasoid Baseband Circuitry 186
78. 1 Gaus3ian/Rectangular IF Power Response
79 Peak/RMS Voltage Ratios 195
80 FM RF Spectrum, Heavy White Noise Modulation 189
81 FM RF Spectrum, Light White Noise Modulation 2no
8? Idealized Thermal Noise Power transfer 203
83 Idealized Amplifier
84 Noise Figure of Caseaded Devices 206
85 Noise Figure of Lossy Network and Amplifier 206
86 Simplified Noise Figure Meter 209
87 Theoretical BER Curves, Various Noise Sources 215
88 Theoretical and Measured BER Curves, Gaus3iar. White
Noise 216
89 Theoretical and Measured BER Curves, LOS M/W Receiver 219
90 Typical Areas of Quieting Curves Degradation 221
LIST OF TABLES
Table No. Page
I FM RF Spectrum, Sinewave Modulation, Voltage Ratios 9
? FM RF Spectrum, Sinewave Modulation, Decibels 10
3 FM RF Spectrum, Square Wave Modulation, Voltage Ratios 11
f) FM RF Spectrum, Square Wave Modulation, Decibels 12
5 Normalized Slot Noise, Rectangular and Gaussian IF
23-
Responses 27
28-
6 Normalized Slot Noise, Averaged IF Response 32
7 Theoretical Narrow Slot 20/30 dB Noise Quieting 34
8 Theoretical Narrow Slot FM Threshold 35
9 Theoretical Wide Slot FM Threshold 36
10 Theoretical Baseband Signal Suppression 42
II Theoretical Baseband Slot Noise for Hard and No Limiting 45
12 LOS M/W Receiver Characteristics 49
13 TR0P0 M/W Receiver Characteristics 52
l1! Measured FM Thresholds 72
15 Measured 20 dB Noise Quieting 73
16 Baseband Slot Noise Near FM Threshold Due to White
Noise Baseband Modulation 75
17 Narrow Slot Impulse Noise Versus Received Signal Level 79
18 Measured Baseband Signal Suppression
19 Slot Noise Measurement Conversion Factors 123
vii
LIST OF TABLES (CQNT.)
Table No. Page
20 Recommended Quieting Curve Slot Frequencies 225
2) CCIR/EIA Emphasis Values 130
21.1 REL Emphasis Values 131
22 Sample Quieting Curve Data 137
2 3 Sample Quieting Curve Data 138
2*4 Sample Quieting Curve Data 139
2^ Measured De-emphasis Values 141
26 Sample Quieting Curve Data 142
27 Sample Quieting Curve Data 143
28 Betas and Dropouts for Sinewave Frequency Modulation 153
29 Dropout Power Levels, Sinewave Frequency Modulation 158
30 Pivot Frequencies 182
31 Emphasis Approximation Error Analysis 183
32 Rectangular/Gaussian IF Responses(deleted-see Figure 78.1)
33 RF Bandwidth Factors 197
31) RF Bandwidths for CCIR Deviation Recommendations 198
viii
1. Introduction.
1.1 With all the articles, reports, and books written about frequency
modulation, transmittsrs and receivers, why write another report? Despite
the volumes written about frequency modulation equipment, several important
features have been neglected. Other significant features have been
described, but are spread over so many different sources or buried
in so much extraneous material that it has been difficult to get the
important information and put it in perspective. The principle interest
in writing this report has been to give engineers and technicians the
information necessary to understand and predict the basic performance
of frequency modulation microwave radio terminals. A thorough knowledge
of the performance of communication systems is required to adequately
specify, develop, test, engineer, install, and verify proper operation
of an item of communication equipment. For frequency modulation microwave
radio terminals, this includes a knowledge of the baseband signal and
noise properties of the terminal transmitter and receiver configuration.
The noise at the baseband of an analog microwave receiver is a complex
mixture of noise from such sources as radio terminal thermal and inter-
modulation noise, crosstalk, and frequency division multiplexer noise.
This noise can generally be divided into two broad categories. The
first category is noise which is independent of the signal applied to
the terminal baseband. This noise includes the effect of thermal noise
generated within the receiver, the phase noise of the transmitter, cable
crosstalk from other baseband signals, radio frequency interference,
and multiplexer tone leakage, power supply ripple, and miscellaneous
sources. Since this noise has no relationship to the baseband signal,
it can be measured with the baseband signal removed from the transmission
equipment. It is called idle noise. The other main noise category
includes the noise which is directly related to the frequency and power
level of baseband signal. Although this noise includes such effects
as baseband cable and radio terminal crosstalk, this type of noise is
loosely termed intermodulation noise. This noise can only be measured
with a signal applied to the transmission equipment oaseband. The
primary tool for predicting and evaluating idle radio noise is the
frequency moduiation (FM) slot noise quieting curve. The primary tool
for evaluating radio intermodulation noise is the noise power ratio
(NPR) bucket curve. Bucket curves can be used to predict and analyze
such noise factors as waveguide and free space multipath effects and
microwave terminal differential gain and phase. Utilization of bucket
curves requires a full understanding of quieting curves. Unfortunately,
present job duties preclude the investigation necessary to write a
report on bucket curves. This report will only cover FM aspects of
noise quieting curves and related topics. Nevertheless, quieting
curves are quite important and deserve considerable attention. Idle
noise sets the lower limits on the noise performance of an analog
digital microwave radio terminal. The thermal noise component of a
microwave receiver is the dominant factor in baseband signal and noise
performance of the radio terminal for low power level radio signals.
1
Therefore, thermal noise of the terminal directly effects fade margin
and radio link reliability as well as terminal noise performance.
Although the present report is directed toward convencional frequency
division multiplexed analog baseband transmission, the information is
directly applicable with minor modification to the transmission of wide-
band video or digital quasi-analog signals over analog microwave equipment.
An example will be given using quieting curve concepts to determine
bit error rate performance of the three level partial response quasi-
digital FM radio terminals currently being installed in the Digital
European Backbone (DEB) digital wideband communications upgrade.
1.2 In the communications business, the object is to get information
from one place to another with the least degradation in quality. Infor-
mation that must be transmitted quickly over a long diatance usually
takes the form of a telephone call or a data circuit processed for trans-
mission on a telephone circuit. These signals are routed over cables
and controlled with various types of processing, monitoring, and routing.
If the signals are transmitted very far, they almost invariably make
their way to a microwave (M/W) transmission system for long distance
bulk transmission. Prior to transmission, as many as several hundred
separate telephone channels are combined (frequency division multiplexed
or FDMed to produce a wide frequency range (wideband) baseband signal)
for efficient processing. The M/W transmission system generally consists
of several separate M/W links, each consisting of a radio path and two
M/W radio terminals. At one terminal, the combined telephone circuits
(baseband) are converted into a modulated radio signal with frequency
as high as 11 gigahertz (GHz).
1.3 The modulated radio frequency (RF) signal passes through nonlinear
transducers, imperfect transmission lines, and i3 transmitted through
the air where it is susceptible to multipath, interference, and fading
degradations. After transmission over several radio links, the baseband
signal is reconverted (demultiplexed) into individual telephone circuits.
While the telephone circuits exist as individual channels, they are
processed by individual amplifiers and cables. They are susceptible
to noise and other forms of distortion. The failure or degradation
of a single telephone circuit, while undesirable, is not immediately
hazardous to many customers. Failure or degradation of a single radio
terminal, however, since it carries many telephone circuits, can have
serious consequences. For this reason, considerable attention is given
to M/W radio terminal performance.
1.4 As a radio terminal transmits a baseband signal from one location
to another, the signal is easily influenced by nonideal characteristics
of the overall transmission medium. The effect of these imperfections
is to Introduce noise into the reconstituted (demodulated) baseband
at the last M/W terminal. The processing of baseband signals at a
frequency modulation (FM) M/W radio terminal is complex. The noise
degradation of the baseband signal can be grouped roughly into two
2
categories. The first type is noise which is primarily independent
of the baseband signal itself. This noise can be introduced by M/W
transmitter phase /frequency noise (phase jitter), various forms of
interference and crosstalk, and internally generated ("front end")
receiver thermal noise. For simplicity, these types of noise will be
called simply "idle noise." The second type is noise which is directly
related, among other factors, to characteristics of the baseband signal
itself. Sources of this type of noise include waveguide echo and moding,
multipath, differential gain and phase, amplitude modulation to phase
modulation (AM to PM) conversion, as well as other forms of intermodu-
lation distortion. For simplicity, this type of noise will simply be
called intermodulation noise.
1.5 The primary method ol characterizing the thermal noise performance
of a M/W radio is through the use of what is called an FM slot noise
quieting curve or simply quieting curve. The quieting curve is a plot
of noise in the baseband of a M/W FM receiver as various levels of
unmodulated RF signals are applied to the receiver. The baseband noise
is measured with a frequency selective voltmeter (FSV) with a measurement
bandwidth of 3.) kilohertz (KHz), the nominal frequency width of a single
telephone circuit. The FSV is tuned to different frequencies in the
baseband of the receiver while the received signal level (RSL) applied
to the receiver is varied. By plotting these noise measurements as
a function of baseband frequency and RSL, it is possible, given an
actual operational RSL of the receiver, to predict the thermal noise
due to the M/W terminal which will be added to a particular multiplexed
telephone circuit. Of course, after the noise at the various baseband
locations (slot noise) is demultiplexed, the various slot noises will
appear in various individual telephone circuits.
1.6 This report deals with the FM noise quieting curve, the various
factors which affect it, and the parameters necessary to predict it.
The elementary baseband signal characteristics as a function * RSL
are also discussed briefly. Due to the wide range of topics covered,
this report is limited primarily to formulas and results. Derivations
have been limited to those which directly aid the understanding of a
concept. Theoretical aspects will not be covered in any depth. This
report will briefly cover the important thermal noise characteristics
of an FM radio and provide the necessary tools to put that knowledge
to use .
3
2. Basic Modulation Theory
2.1 The purpose of a wideband microwave radio transmission system is
to transfer a wide frequency baseband signal. from one location to another.
Invariably, a sinusoidal radio frequency wave (RF sine wave) is modulated
to transfer a baseband signal from one radio terminal to another. Ampli-
tude modulation is a simple modulation process to visualize. A baseband
signal is merely transferred to radio frequency. At radio frequency,
it may appear with its normal low to high frequency orientation (higher
frequency baseband signal producing a higher frequency RF component
than a lower frequency baseband signal). In this case, an upper sideband
has been produced. If the frequency orientation of the baseband is
reversed at RF, then a lower sideband has been produced. Sometimes
both sidebands are produced (double sideband), sometimes only one (single
sideband). A sinewave (carrier) is used in the modulation process.
Sometimes the carrier is eliminated prior to transmission of the RF
signal (suppressed carrier). A1 though there are several forms of ampli-
tude modulation, the processes are similar. Each baseband frequency
component produces one or two discrete frequency components in the modu-
lated RF signal. These components are equal in amplitude (except in
vestigial sideband modulation) and are separated from the carrier frequency
by a frequency difference equal to the frequency of the baseband component.
The nature of the modulation is such that the frequency of the RF modulated
signal depends only on the carrier frequency and the frequency of the
corresponding baseband component. The amplitude of the RF spectral
components depend only on the amplitude of the corresponding baseband
spectral component's amplitude. The frequency of the modulated signal's
spectral components are independent of baseband signal amplitude and
vice versa.
2.2 Instead of modulating the amplitude of the transmitted signal,
it is possible to transmit baseband signal by changing the angle of
the transmitted sinewave relative to its unmodulated condition. The
properties of this angle modulation are considerably different than
amplitude modulation. Two common methods of achieving angle modulation
are called phase modulation (PM) and frequency modulation (FM). The
United States Electronic Industry Association (EIA) Standard RS-252-
A defines frequency modulation (para 2.1) as "... that process of angle
modulation in which the instantaneous frequency deviation of the sinusoidal
carrier is proportional to the instantaneous voltage of the modulating
signal." The standard defines phase modulation (para 2.2) as "...that
process of angle modulation in which the instantaneous phase deviation
of the sinusoidal carrier is proportional to the instantaneous voltage
of the modulating signal." It should be mentioned that the phase and
frequency of a sine wave are related to each other. As Van der Pol
has pointed out, the definitions of phase and frequency are not unique.
Using Stumper's "zero crossing" definition of frequency has analytical
and heuristic advantages and leads to the frequency counter FM demodulators
such as those described by Latin. The most common definitions, however,
imply that phase is the time integral of frequency and that frequency
4
is the time derivative of phase. When a carrier is phase modulated,
the frequency of the carrier is also modulated. When we specify phase
modulation, we are defining a specific relationship between phase changes
and the modulating waveform. The frequency will also change, but the
relationship between frequency change and the modulation waveform is
not explicitly stated. Likewise, when frequency modulation is used,
the phase of the carrier is also modulated. All that has been directly
defined is a particular relationship between the carrier frequency and
the modulating waveform. Using integral and differential calculus
relationships, the definition of an equivalent PM (or FM) could be
derived for each of the above definitions of FM (or PM). The advantage
of the proceeding definitions, however, is their simplicity.
2.3 There are several forms of practical angle modulators and demodulators.
Most frequency modulators are voltage controlled oscillators (diode
reactance, reactance tube, or klystron type) or zero crossing type
(saturable reactor). The diode reactance and klystron type are the
most popular for wideband microwave use. Phase modulators are the pulse
position type. A popular wideband modulator of this type is the serrasoid.
There are no practical wideband phase demodulators. Types of frequency
demodulators include the ratio, Foster-Seeley, and Travis detectors,
line discriminators, cycle counters, and various forms of phase locked
loops and frequency feedback demodulation methods. The Travis discriminator
is the most popular type in current high performance wideband terrestrial
communication systems.
2.4 Unlike amplitude modulation, the spectrum of the modulated signal
(as viewed on a spectrum analyzer, for example) is a complex function
of both the frequency and amplitude of the baseband signal. The next
page shows the transmit spectrum of an angle modulator for a sine wave
baseband signal of different amplitudes. The only difference between
the different pictures is the level of the modulating sinewave, yet
the spectruma are different. When a single sinewave is used to angle
modulate a carrier, a definite relationship exists (as defined by Bessel
functions of the first kind of integer order) between the modulation
index (beta) of the modulator and the amplitudes of the various sideband
components. FM is a complex modulation process. It is not easy to
determine frou; the signal Into the modulator what the spectrum of the
output will be. In the previously mentioned pictures, the modulated
RF spectrum changed considerably, although the input signal did not
change its waveform. Certain levels of sine wave modulation cause
disappearance of certain RF modulated signal spectral components.
Examples of this are given on the next two pages. The rolati .nship
between modulator input sine wave level and spectral component disappearance
(drop out) will be used later. The voltage and power (dB) amplitude
of the spectral components for a sinewave modulated carrier have been
tabulated on the next two pages. For comparison, the various spectral
components for a square wave frequency modulated carrier are shown on
the following two pages. When a single sinewave is the baseband signal
c
6
First
Carrier
Dropout
f
Second
Carrier
Dropout
Eighth
Carrier
Dropout
FM RF Spectrum
Sinewave Modulation
Figure 2
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0,0/60
-0.31 /</
-0.1066
0.1082
0.3829
0.3446
0.00
0.1 b06
-0.2/6/
-0,2429
0.1146
0.3576
0.3621
0.2b
0.2131
-0.2207
-0.2037
0.0391
0.3213
0.3721
6. bO
0.26/» 1
-0.1 b3H
-0.3074
-0.0353
0.2748
0.3736
0. /V
0.209b
-0.0003
-0.3133
-0.1053
0.2196
0.3656
/.00
0,3/101
-0.004/
-0.3014
-0,1676
0.1578
0.3479
7.2b
0.2V20
0.0606
-0.2731
-0.2192
0.0916
0.3204
/ , bO
0.2663
0 . 1 3b 2
-0.2303
-0.2581
0.0238
0.2035
/. lb
0. 22b2
0.1916
-0.1750
-0,2023
-0.0428
0.2382
0.00
0.1/1/
0.2346
-0. 1130
-0,29! 1
-0.1054
0.1850
II . 2b
0. 1092
0.2622
-0,0456
-0.2043
-0. 161 1
0.1281
B.bO
0./14I9
0.2731
0.0223
-0.2626
-0.2077
0.0671
0. /b
-0.02b >
0.26/2
0.0070
-0.2274
-0.2430
0.0053
v.oo
-0,/)V/)3
0.24b 3
0.1440
-0.1009
-0.2655
-0.0550
V, 2b
-0.1474
0.2091
0.1926
-0.1258
-0.2743
-0.1114
V.bO
-0, 1939
0.1613
0.2279
-0.0653
-0.2691
-0,1613
V. /b
-0.2273
0. 1048
0.2480
-0.0020
-0.2506
-0.2028
10,00
-0.24bV
0.043b
0.2546
0.0584
-0.2196
-0.2341
10.2b
-0.2490
-0.0190
0.2453
0. 1147
-0.1781
-0.2537
io. bo
-0.2366
-0.0789
0,2216
0.1633
-0.1283
-0,26 1 1
1 0 • 7 b
-0.2101
-0.1325
0.1854
0.2015
-0.0730
—0,2550
ii.oo
-0,1/12
-0.1/6H
0.1390
0.2274
-0.0150
-0,2383
j j ,2b
-0.1226
-0.2093
O.OH54
0.2397
0.0424
-0.2096
1 1 . bO
-0.0676
-0,2284
0.0279
0.2301
0.0963
-0. 1711
1 1 • 75
-0.0096
-0.2331
-0.0300
0.2229
0 # 1 438
-0,1250
1 2. 00
0,0477
•0.2235
-0.0849
0.1951
0.1025
-0.0735
12.2b
0. 1010
-0.2004
-0.1337
0.1567
0.2104
^7.0193
FREQUENCY MODULATED RF SPECTRUM/SINE RAVE MODULATION INPUT
(levels «• voltage radios)
Table 1
9
btTA
CARRIER
SIDEBAND
SIDEBAND
SIDEBAND
SIDEBAND
SIDEBAND
1
2
3
4
5
0.
0.
-200.00
-200.00
-200. 00
-200.00
-200.00
0.2b
-0.14
-18.13
-42.19
-69.78
-99.88
-131 .92
0-*0
-0.55
-12.3!
-30.28
-51 .82
-75.88
-101 .88
J. /5
-1 .27
-9.14
-23.47
-41.43
-61 .93
-84.38
1 .00
-2.32
-7.13
-18.79
-34.17
-52.12
-72.05
1 . 2d
-3.80
-5.34
-15.34
-28.6?
-44.62
-62.56
1 ,bO
-b .82
-5.07
-12.69
-24.30
-38.59
-54.90
1 . /d
-6.66
-4.73
-10.63
-20.74
-33.59
-48.50
2.00
-13.00
-4.78
-9.05
-17.79
-29.37
-43.05
2.2b
-21.64
-5.22
-7.86
-15.34
-25.76
-38.33
2.50.
-26.31
-o.07
-7.0!
-13.29
-22.64
-34.20
2. Yd
-15.70
-7.41
-6.49
-II .59
-19.94
-30 .,56
3. CO
-11.70
-V.39
-6.27
-10.20
-17.59
' -27.32
j.2b
-9.56
-12.36
-6.35
-9.09
‘-15.55
-24.45
3.50
-8.40
-17.24
-6 . 77
-8.25
-13.79
-21 .89
3. Yd
-7.93
-29.57
-7.55
-7.66
-12.29
-19.61
4.00
-8.02
-23.60
-6.77
-7.33
-11 .02
-17.58
4. 2d
-8.65
-16.16
-1^.57
-7.25
-9.98
-15.79
4.50
-9.bB
-12.73
-13.24
-7.44
-9.16
-14.21
4. Yd
-II .d 7
-10.78
-17.50
-7.93
-8.55
-12.64
b.00
-15.01
-9.69
-26.64
-8.76
-8.15
- 1 1 . 66
b. 2b
-20.62
-9.24
-28.32
- i 0 . 0 1
-7.97
-10.67
b.bO
-43.29
-9.33
-18.61
-11.83
-8.03
-9.87
b. Yd
-22.39
-9.05
-14.58
-14.51
-8.34
-9.25
o . 00
-16.44
- 1 1 . 1 0
-12.29
-18.80
-8.93
-8.82
0.2b
-13.43
-13.12
-10.94
-28.15
-9.86
-8.59
6.50
-11.70
-16.26
-10.25
-29.03
- 1 1 . 22
-8.55
6. Yd
-10. Y 7
-21.90
-IO.OR
-19.55
-13.17
-8.74
/. (X)
-10.40
-46.59
-10.42
-15.52
-16.04
-9.17
/ . 2d
-10.69
-23,28
-II .27
-13.18
-20.76
-9.89
/. 50
-11,49
-1 7.38
-12.76
-11.77
-32.46
-10.95
Y. /D
-12.95
-14.35
-15.10
-10.98
-27.37
-12.46
b.00
-15.31
-12.59
-18. 94
-10.72
-19.55
-14.62
6. 2d
-1 9.23
-1 1 .03
-26.8!
-10.92
-15.86
-17.85
b.50
-27.55
-II .27
-33.0?
-11.61
-13.65
-23.46
a. Yd
-31 .72
-11.46
-21 .21
-12.86
-12.29
-45.55
9.00
-20.88
-12.21
-16.78
-14.85
-11.52
-25.19
y.25
-16.63
-13.59
-14.31
-18.00
-11 .24
-19.07
9.50
-14.25
-15.85
-12.85
-23.70
-II .40
-15.85
9. Yd
-I2.b7
-19.59
-12.08
-51.21
-12.02
-13.86
10.00
-12.18
-27.24
- 1 1 . 88
-24.68
-13.17
-12.61
! 0.2b
-12.0b
-34.42
-12.21
-18.8!
-14.99
-II .91
10.50
-12.52
-22.06
-13.09
-15.74
-17.83
-11 .67
10. Yb
-13.55
-1 /.50
-14.64
-13.92
-22.74
-II .84
1 1 .00
-15.33
-15. 05
-17.14
-12.87
-36.46
-12.46
1 1 .25
-IH. 23
-13.58
-21 .37
-12.41
-27.45
-13.57
11.50
-23,40
-12.83
-31 .08
-12.47
-20.33
-15.33
11.75
-40.34
-12.65
-30.45
-13.04
-16.84
-18.06
12.00
-26.42
-13.02
-2! .42
-14.19
-14.77
-22.68
12.25
-19.92
-13.96
-17.48
-16.10
-13.54
-34.29
FREQUENCY M0UULA1EI) HF SPECTRUM/SINE WAVE MODULATION INPUT
(levels in dB)
Table 2
10
BETA
CARRIER
SIDEBAND
SIDEBAND
SIDEBAND
SIDEBAND
SIDEBAND
1
2
3
4
5
0.
1 .0000
0.
0.
0.
0.
0.
0.25
0. 9745
0. 1 f 68
0.0155
-0.0165
-0.0038
0.0069
0.50
0.9003
0.3001
0.0600
-0.0257
-0.0743
0.0091
0.75
0.7842
0.4176
. 0.1283
-0.0217
-0.0286
0.0075
1.00
0.6366
0.5000
0.2122
0,0000
-0.0424
-0.0000
1.25
0.4705
0.5414
0.3016
0.6409
-0.0509
-0.0130
1.50
0.3001
0.5402
0.3858
O'. 1000
-0.0491
-0.0297
1.75
0. 1392
0.4990
0.4548
0.1734
-0.0330
-0.0469
2.00
0.0000
0.4244
0.5000
0.2546
0.0000
-0.0606
2.25
-0. 1083
0.3258
0.5159
0.3361
0.0501
-0.0664
2.50
-0.1801
0.2144
0.5002
0.4092
0. 1154
-0.0600
2.75
-0.2139
0.1021
0.4540
0.4661
0.1917
-0.0384
3.00
-0.2122
0.0000
0.3820
0.5000
0.2728
0.0000
3.25
-0. 1810
-0.0828
0.291 3
0.5067
0.3515
0.0548
3.50
-0.1286
-0.1400
0.1910
0.4848
0.4201
0.1236
3.75
-0.0650
-0.1688
0.0908
0.4357
0.4715
0.2017
4.00
-0.0000
-0.1698
0.0000
0.3638
0.5000
0.2829
4,25
0.0573
-0. 1 465
-0.0736
0.2756
0.5020
0.3603
4.50
0. 1 000
-0.1052
-0.1247
0.1801
0.4766
0.4265
4.75
0.1238
-0.0537
-0.1505
0.0853
0.4257
0.4748
5.00
0.1273
-0.0000
-0.15*6
0.0000
0.3537
0.5000
5.25
0.1120
0.0482
-0.1310
-0.0689
0.2671
0.4991
5.50
0.0818
0.0846
-0.0943
-0. 1165
0.1737
0.4716
5.75
0.0424
0.1055
-0.0482
-0.1405
0.0821
0.4195
6.00
0.0000
0.1091
-0.0000
-0.1415
0.0000
0.3472
6.25
-0.0390
0.0966
0.0434
-0. 1223
-0.6660
0.2614
0.50
-0.0693
0.0709
0."765
-0.0880
-0. 1 115
0.1696
6.75
-0.0871
0.0369
0.0955
-0.0450
-0.1343
0.0800
7.00
-0.0909
0.0000
0 ,0 99n
-n ,0000
-0. 1 350
0.0000
7.25
-0.0811
-0.0343
0.0878
0.0405
-0.1166
-0.0641
7.50
-0.0600
-0.06 1 1
0 .0646
0.0715
-0.0839
-0.1080
7.75
-0.0314
-0.0 112
0.0337
0.0893
-0.0429
-0 . 1 300
8.00
-0.0000
-0.0808
0.0000
0.0926
-0.0000
-0.1306
8.25
0.0295
-0.0724
-0.031 4
0.0822
0.0386
-0. 1127
8.50
0.0530
-0.0537
-0.0561
0.0605
0.0680
-0.0810
8.75
0.0672
-0.0282
-0.0709
0.0316
0.0850
-0.0413
9.00
0.0707
-0.0000
-0.0744
0.0000
0.0881
-0.0000
9.25
0.0636
0.0266
-0.0667
-0.0294
0.0782
0.0372
9.50
0.0474
0.0479
-0.0496
-0.0526
0.0576
0.0655
9,75
0.0250
0.0610
-0.0261
-0.0666
0.0300
0.0818
10.00
0.0000
0.0643
-0.0000
-0.0700
0.0000
0.0849
10.25
-0.0238
0.0579
0.0247
-0.0628
-0.0280
0.0753
10.50
-0.0429
0.0433
0.0445
-0.0467
-0.0502
0.0554
10.75
-0.0547
0.0229
0.0567
-0.0246
-0.0635
0.0289
1 1 .00
-0.0579
0.0000
0.0599
-0.0000
-0.0667
0.0000
1 1 .25
-0.0523
-0.0218
0.0540
0.0233
-0.0598
-0.0270
1 1 .50
-0.0391
-0.0394
0.0404
0.0420
-0.0445
-0.0483
1 1 .75
-0.0207
-0.0504
0.021 4
0.0535
-0.0235
-0,061 1
12.00
-0.0000
-0.0534
0.0000
0.0566
-0.0000
-0.Q642
12.25
0.01 99
-0.0483
-0.0204
0.051 1
0.0223
-0.0576
FREQUENCY MODULATED RF SPECTRUM/SQUARE WAVE MODULATION INPUT
(levels as voltage ratios)
Table 3
11
BETA
CARRIER
SIDEBAND
SIDEBAND
SIDEBAND
SIDEBAND
SIDEBAND
1
2
3
4
5
0.
0.
-200.00
-200.00
-200.00
-200.00
-200.00
0.2b
-0.22
-16.09
-36.21
-35.68
-48.36
-44.59
O.bO
-0.9'.
-10.45
-24.43
-3! .79
-36.90
-40.82
0.7b
-2.11
-7.58
-17.83
-33.29
-30.88
-42.53
1 .00
-3.92
-6.02
-13.46
-166.19
-27.44
-169.72
1 .25
-6.55
-5.33
-10.41
-27.76
-25.86
-37.73
I .bO
-10.45
-5.35
-8.27
-20.00
-26.18
-30.55
1 .75
-17.13
-6.04
-6.84
-15.22
-29. 6«
-26.57
2.00
-154.15
-7.44
-6.02
-11.88
-163.70
-24.35
2.25
-19.31
-9.74
-5.75
-9.47
-26.00
-23.56
2.50
-14.89
-13.38
-6.02
-7.76
-18.75
i24.43
2.75
-13.40
-19.82
-6.86
-6.63
-14.35
-28.31
3.00
-13.46
-1 56.65
-8.36
-6.02
-11.28
-162.67
3. 2d
-14.85
-21 .64
' -10.71
-5.90
-9,08
-25.22
3.50
-17.81
-17.07
-14.38
-6.29
-7.53
-18.16
3.7b
-23.75
-15.45
-20.84
-7.22
-6.53
-13.91
4.00
-154.15
-15.40
-157.67
-8.78
-6.02
-10.97
4.2b
-24.83
- 10.68
-22.66
-11.19
-5.99
-8.87
4.50
-20.00
-1 9.56
-18.09
-14.89
-6.44
-7.40
4.7b
-18.14
-25.41
-16.45
-21.38
-7.42
-6.47
5.00
-17. 90
-1 55. 74
-10.39
-158.24
-9.03
-6.02
5.25
-19.01
-26.35
-17.65
-23.24
-II .47
-6.04
b .50
-21 . / 4
-21.45
-20.51
-18.67
-15.20
-6.53
5.7d
-27.46
- 1 y.'_>4
-26.34
-17.04
-21 .71
-7.55
6.00
-152.85
-19.24
-156.65
-10.99
-158.59
-9.19
6.25
-28.18
-20.30
-27.24
-18.25
-23.61
-1 1 .65
6.50
-23.19
-22.98
-22.33
-21.H
-19.06
-15.41
6.7b
-21 .20
-28.06
-20.40
-20.94
-17.44
-21.94
1.00
-20.82
-1 54.01
-20.08
-157.25
-17.39
-158.83
7.2b
-21 .82
-29.31
-21.13
-27.84
-18.66
-23.87
7.50
-24.43
-24.28
-23.79
-22.92
-21 .53
-19.33
7.75
-30.05
-22.25
-29.45
-20.99
-27.36
-17.72
8.00
-154.15
-21 .85
-154.79'
-20.67
-157.67
-17.68
8. 2d
-30.59
-22.81
-30 XI
-21.71
-28,27
-i8.96
8.50
-25.52
-25,40
-25.03
-24.37
-23.35
-21 .83
8.7d
-23.45
-30.99
-22.98
-30.02
-21 .41
-27.67
9.00
-23.01
-1 55.0/
-22.57
-1 55.35
-21.10
-157.99
9.25
-23. 9j
-31.49
-23.52
-30 ,o2
-22.1 3
•:28.59
9.50
-26.49
-26.39
-26.09
-25.57
-24.79
-23.67
9.75
-32.05
-24.30
-31 .67
-23.53
-30.44
-21.74
1 0.00
-155.04
-23.84
-155.74
-23.10
-155.78
-21 .42
10.25
-32.48
-24.74
-32.14
-24.05
-31 .05
-22.46
10.50
-27.36
-27.28
-27.04
-26.62
-25.99
-25.12
10.75
-25.24
-32.82
-24.93
-32.19
-23.94
-30.78
1 1 .00
-24.75
-155.79
-24.46
-156.25
-23.52
-156.11
1 1 .25
-25.63
-33.22
-25.35
-32.65
-24.46
-31 .38
1 I .50
-28.15
-28.08
-27.88
-27.53
-27.03
-26.33
1 1 .75
-33.67
-25,95
-33.41
-25.43
-32.60
-24.28
12.00
-152.85
-25.45
-156.38
-24.95
-156.65
-23.85
12.25
-34.03
-26.31
-33.79
-25.84
-33.05
-24.79
FRfcOUENCY MODULATED RF SPECTRUM/SQUARE HAVE MODULATION INPUT
(levels in dB)
Table 4
12
to a modulator, the frequency separation between the various spectral
components of the modulated signal is always equal to the sinewave
frequency. When two or more sinewave baseband signals are used simultan-
eously, the frequencies of the sideband components are separated from
the carrier by all possible combinations of frequencies which oan be
obtained from sum and differences of all harmonics of the modulating
slnewaves. For many possible wideband baseband signals, an exact deter-
mination of the transmit signal spectrum is not practical. About the
only practical method of analysis of the baseband/transrait signal relation-
ship is on a statistical basis. There is, however, a general relationship
between the modulating signal and the modulated waveform. This generalization
is mentioned by both Middleton and Giacoletto. Middleton calls it the
"Principle of Adiabatic Frequency Sweeps". The principle simply states
that for any general modulation waveform producing frequency modulation,
the transmitted radio frequency (RF) spectrum will be symmetric about
the unmodulated carrier frequency if the modulating signal has voltages
which, when viewed in time, are symmetric about zero volts. Conversely,
unsymmetrical modulating signals produce unsymmetrical FM modulated
RF spectrums. This is a useful principle. It indicates that if an
FM modulator is driven by a sinewave, the RF spectrum will be symmetric.
If it is not, the modulated wave has unquestionably been distorted.
The FM receiver requires a symmetric received RF spectrum to produce
a symmetric baseband signal like a sinewave. It receives an unsymmetric
RF spectrum, it can only produce an unsymmetric voltage waveform at the
baseband demodulator output. If a sinewave (a symmetric waveform) is
transmitted and an unsymmetric waveform is received, the baseband signal
has been distorted.
2.5 There are several ways that RF spectrum can be made unsymmetric.
At high baseband modulator input levels, nonlinearity of the baseband
amplifiers and the modulator itself are distinct possibilities. However,
even at low drive levels, it is possible to make the RF spectrum unsymmetric.
As Middleton and Panter have mentioned, simultaneous (correlated) amplitude
modulation and frequency modulation invariably produce an unsymmetric
RF spectrum. It is possible to have this take place right at the FM
modulator. Most FM modulators are immediately followed by hard limiters
to avoid this possibility. If the RF circuitry has nonuniform amplitude
frequency response, or a uniform but unsymmetric (about the carrier
frequency) frequency response, correlated AM and PM will be introduced
into the signal. In severe cases, either of these can cause distortion
of the normal sideband amplitudes and, therefore, distortion in the
demodulated signal.
2.6 The modulation index of an angle modulated signal is a factor which
relates the modulating waveform to the phase deviation of the modulated
signal. This factor is called beta (B) and has the units radians per
millivolt. For most baseband signals, a beta is difficult or impossible
to define. However, for a sinewave baseband input, tne determination
of beta is straightforward. For a phase modulation system, the beta
is just the specified phase sensitivity of the modulator. For a frequency
13
modulation system, beta is the specified frequency deviation sensitivity
of the modulator (kilohertz per millivolt) divided by the frequency
(kilohertz) of the modulating sinewave. The division of frequency deviation
by frequency is a direct result of having to integrate the sinusoidal
frequency deviation to obtain equivalent phase deviation. As mentioned
earlier, knowing the sinewave beta of the angle modulation transmitter
allows us to predict exactly (using Bessel functions) the RF transmit
spectrum for sinewave modulation.
2.7 Like amplitude modulation, there are many possible variations of
angle modulation. As mentioned previously, however, there are two basic
angle modulation types. With amplitude modulation, it is possible,
with suitable processing of the signals, to turn one type of modulation
into another (for example, suppress the carrier, filter one sideband,
etc.). As with amplitude modulation, (see, for example, Black and Taub
and Schilling.) with suitable processing a phase modulation system can
be converted into a frequency modulation system and vice versa. Specifically,
if the baseband input of a phase modulator is preceeded by a time integrating
circuit, the combination will have all the properties of a frequency
modulator. Likewise, if the baseband output of a phase demodulator
is coupled to a time differentiation circuit, the combination will have
all the properties of a frequency demodulator. A similar procedure
holds for frequency modulation. A frequency modulator with baseband
input preceeded by a time differentiation circuit has exactly the same
properties as a phase modulator. A frequency demodulator whose baseband
output is followed by a time integration network has exactly the same
properties as a phase demodulator. Therefore, it is theoretically
possible to mix and match various modulators and demodulators to achieve
a desired microwave radio system. These properties are not theoretical
abstractions. The Radio Equipment Laboratories (REL) military tropospheric
scatter (TROPO) microwave radio system AN/FRC-39(V) is basically a phase
modulation, frequency demodulation system. The baseband circuitry of
the modulator and demodulator is such that overall the modulator and
demodulator are completely compatible. In fact, the serrisoid phase
modulator u3ed in the AN/FRC-39(V) , when preceeded by the baseband
corrector networx, produoes a transmit RF signal which is completely
indistinguishable from a comparable FM modulator preceeding by the
appropriate pre-emphasis network.
2.8 Frequency and phase demodulators have different noise properties.
A strong unmodulated carrier centered in the symetrir (if) passband
of a phase demodulator produces a flat (white) spectrum of thermal noise
over the entire output baseband if the only noise generated in the
receiver is white thermal noise. In frequency division multiplexing
(FDM) used to produce an analog baseband to apply to an angle modulator,
different 3.1 kilohertz wide telephone channels appear at different
3.1 kilohertz frequency positions (slots) in the radio baseband. There-
fore, for strong received signal levels, a phase demodulator will introduce
the same noise in ail telephone slots. When the telephone channels
are demultiplexed, the radio noise will be the same for all channels.
14
With a frequency demodulator under the same conditions, the thermal
noise voltage in the receive baseband increases linearly with frequency
(hence, it is often called triangular noise). Since power is proportional
to the voltage squared, the noise power increases with the square of
the baseband (slot) frequency. Therefore, the noise power increases
at a rate of 6 dB per octave or 20 dB per decade. When there is no
carrier present at the receiver, the noise spectrum (as Crosby and
Downing note, for example) is essentially the same (flat) for all baseband
frequencies (so called rectangular noi3e). Under the same conditions,
(as noted by Taub and Schilling, for example) the noise voltage in the
baseband of the phase demodulator decreases inversely with baseband
slot frequency. Therefore, the noise power is reduced 6 dB per octave
(20 dB per decade). Due to the flat noise spectrum in the baseband
of a phase demodulator under strong received signal conditions, it is
a highly desirable type of angle modulation receiver. High performance
wideband phase demodulators are difficult to construct. At the trans-
mitter, the problems are more difficult. Most phase modulators can
only produce low modulation index modulation. To obtain the necessary
modulation index with a phase modulator, multiplication of the modulator
output is generally required. Using a multiplier puts some severe require-
ments on the basic phase noise performance of the modulator's oscillator.
Every time the oscillator output is doubled, the noise it produces at
the baseband of a receiver with a strong RSL (receiver in saturated
region) i3 increased 6 dB. From a practical point of view, it is much
easier to use a voltage controlled oscillator as the modulation source.
With such modulators, wide linear frequency shifts directly proportional
to input voltage can be obtained. Little or no multiplication is required,
and the modulated signal can often be produced directly at RF without
the need of an up converter. Using frequency modulators, high performance
wideband microwave systems are readily achievable.
2.9 If we wish to use a phase demodulator, we must turn the frequency
modulator into a phase modulator to be compatible with a phase demodulator.
To turn a frequency modulator into a phase modulator, the baseband input
to the modulator must be preceded by a differentiation network. Taking
advantage of the elementary properties of Fourier transforms, if a device
causes differentiation in the time domain, it will cause an additional
term directly proportional to frequency in the voltage versus frequency
response of tne overall system. Since power is proportional to voltage
squared, the power frequency response of a baseba d circuit with a different-
iator in it will have a frequency response which increases with the
square of frequency. Again, this is 6 dB per octave. This is not an
undesirable feature for the telephone channels in the high end of the
baseband; their level is boosted through the differentiation network.
However, relative to the high end of the baseband, the telephone channels
at the low end of the baseband will be suppressed. For a 600 telephone
channel radio baseband extending from 60 kilohertz to 2660 kilohertz,
for example, out of the differentiation network the highest telephone
IS
channel would be 33 dB greater in level than the lowest telephone channel.
To recover the baseband at the receive end, the integrator network at
the frequency derrodulator must boost the lowest channel 33 dB relative
to the highest telephone channel so that uniform frequency response
is maintained in and out of the radio terminal. In a noiseless transmission
system, attenuating the low end of the baseband 33 dB and then boosting
it 33 dB at the receive baseband would be no problem. Unfortunately,
all transmitters use oscillators which have significant phase jitter.
This Jitter causes a roughly flat noise spectrum to be produced at the
baseband of a companion frequency demodulator (if the received signal
level is sufficiently high that thermal noise is negligible compared
to the transmit phase noise). Because of the significant amount of
transmit phase noi3e (Strictly speaking, the noise is equivalent frequency
noise produced by phase noise.) that will appear at the baseband of
the FM receiver, attenuating this level of the low frequency telephone
channels by many dB is out of the question. The signal to noise ratio
of the low frequency channels will have been excessively degraded at
the receiver by the transmitters phase noise. Because of these consider-
ations, actual differentiation and integration networks are never used
with frequency modulation modulators and demodulators. Instead, dev ?es
called pre-emphasis and de-emphasis networks are used. These networks
have essentially the frequency response of differentiators and integrators
over about the top octave of the radio baseband. Over the rest of the
baseband, the networks have essentially constant frequency response.
Frequency modulation radio terminals with pre-emphasis and de-emphasis
are actually a hybrid of frequency and phase modulation systems. Over
about the top octave of the rad.o baseband, they have noise characteristics
of phase modulation systems. Over the rest of the baseband, however,
they have the noise characteristics of a frequency modulation system.
During the rest of this report, frequency modulation (FM) systems will
be considered exclusively. However, it should be kept in mind that
when FM «ystems use pre-emphasis and de-emphasis networks, they achieve
some of the thermal noise properties of phase modulation systems. The
effect of de-emphasis networks on thermal noise performance of FM receivers
will be included in that report.
2.10 At this point, the character of baseband noise has only been inferred
for high carrier to thermal noise ratios and for the case where there
is no received signal. As the carrier level of the received microwave
signal is reduced from a strong RSL, the noise power in the baseband
of the receiver increases. As the carrier level at the receiver is
reduced 1 d3, the noise at the baseband output of the receiver increases
1 dB. The frequency distribution (shape) of the noise remains the same.
If viewed on an osciiliscope, the noise would appear as the usual relatively
smooth looking background thermal noise. As the received signal level
approaches low levels, the character of the noise starts to change.
In addition to the smooth noise, noise spikes (impulses^ begin to appear.
As the received signal gets lower and lower, the individual noise spikes
or clicks occur more and more often. With continued reduction in received
signal, the clicks rapidly merge into a crackling or sputtering noise.
16
Finally, the clicks murge to produce a continuous high level of noise
out of the baseband of the receiver. As the noise impulses appear more
and more often, the noise in the various baseband slots starts to increase
faster than 1 dB for 1 dB decrease in received signal level. The received
signal level at which the noise in a narrow measurement slot in the
baseband increases 2 dB for a 1 dB reduction in carrier level is generally
called FM noise threshold. Since the impulse noise is essentially flat
in power spectrum, the noise increase is first seen in the low baseband
frequencies where the normal thermal noise is quite low. The difference
in FM threshold between the highest and lowest 3lot in a wideband receiver
can be several dB. For standardization, FM noise threshold is normally
measured in one of the highest baseband slots. For those interested
in why impulses occur for low received signal levels, Taub and Schilling's
text is highly recommended. In addition to the basic thermal noise
properties of FM systems, there are several other properties of interest.
2.11 Because FM signals carry no information in the amplitude of the
transmitted signal, it is possible to use a limiter in the receiver
to suppress any residual amplitude modulation in the received signal
before it is demodulated. The use of a limiter in an FM receiver can
introduce additional intermodulation when receive signals have passed
through certain types of amplitude nonlinearitie3. Middleton has pointed
out that not using a limiter, however, leaves the signal prone to another
type of intermodulation distortion. In general limiters are used for
a couple of very good reasons. The received signal and thermal noise
performance of the receiver is significantly improved near FM noise
threshold when the limiter is used. For large received signal to
thermal noise (large carrier to noise ratio) conditions (i.e., well
above FM noise threshold), the use of heavy limiting gives the FM receiver
its ability to reject unwanted signals lower in power than the desired
signal. This ability is often expressed as capture ratio. This ability
is very important to high quality microwave communication since it is
directly responsible for the ability of the receiver to reject other
signals on its frequency (co-channel interference), signals on frequencies
slightly different than its own (adjacent channel interference), and
its own signal reflected from stray sources (multipath). Since all
wideband microwave receivers use hard limiters (heavy limiting), many
authors have stated or implied that FM receivers have an inherent ability
to reject other signals of lower received power level. This simply
is not true. Without hard limiting action, the FM receiver loses much,
if not all, of its ability to reject unwanted signals.. Downing
specifically mentions that the ability of an FM receiver to reject impulse
noise and coherent interference i3 directly attributable to the receivers
amplitude limiter. Corrington mentions an interesting example. During
some propagation tests he was conducting, he observed two distant FM
stations. Both stations were on the same frequency and of nearly equal
receive signal strength. However, each signal was randomly fading up
and down in received signal level. His receiver was such that it achieved
limiting for strong received signals, but did not limit for weak received
signals. When both signals were strong, the limiter was saturated and
17
only the stronger signal's program was heard. When the other signal
became stronger, there would be a short burst of noise and the program
would abruptly change to that of the stronger signal. For many minutes,
conditions were such that the programs changed back and forth about
once every fifteen seconds. Occasionally, both signal levels fell below
the level at which the receiver limited. During those periods of time,
both programs could be heard simultaneously.
?. 12 There are two important considerations to insure hard limiting.
Panter mentions that in order to achieve high suppression of unwanted
interference, the limiter and the stages preceding the first limiter
stage must have essentially flat frequency response over the frequency
range cf the desired signal. Ruthroff mentions the other important
consideration. It is well understood that in limiter circuits, a minimum
level ir.to the limiter is necessary to achieve limiting. Contrary to
common belief, however, merely increasing the drive level does not
necessarily improve limiting. Strangely enough, overdriving a practical
limiter circuit can seriously degrade it. For circuits of finite frequency
bandwidth and utilizing limiter diodes with finite back resistance,
there is some unique input level at which limiting is best. The purpose
of Automatic Gain Control (AGC) in an FM receiver is to keep the carrier
input level near the value for best limiting.
One other factor in good interference rejection is the bandwidth
and symmetry of the FM demodulator (discriminator). As Panter mentions,
for best capture ratio the discriminator must be able to accommodate
the necessary amplitude and frequency excursions which occur in an
interference situation. Leentvaar and Flint have shown that it is
possible to reduce or eliminate the capture effect of an FM reoeiver
by reducing the bandwidth of an FM demodulator.
2.14 Due to the nonlinear demodulation action of an FM receiver, limiters
and the general nonlinear process of FM generation and detection, the
noise produced in an FM receiver due to an arbitrary interfering signal
is difficult to predict with any degree of precision. The articles
listed in the bibliography are available for information on specific
interference situations. A few generalizations, however, are available.
Corrington suggests some effects due to a single unmodulated interfering
signal. Introducing an unwanted carrier into an FM receiver increases
the overall noise demodulated at the baseband of the receiver. At a
low level relative to the desired signal (high carrier to interference
ratio) the increased noise in the baseband of the FM receiver is primarily
at low baseband frequencies. As the interfering signal gets stronger,
the noise at higher baseband frequencies increases faster than the noise
at lower frequencies. When the desired signal and the interference
are about the same level (C/I= OdB), the baseband noise is quite high
and essentially the same at all baseband frequencies.
18
2.15 If both the desired and the interfering signal are unmodulated
or only lightly modulated (loaded) FDMed FM signals, a high ' . jnsity,
very narrow noise spike is produced in the receiver baseband. This
spike is a crossmodulation (beat) product caused by the modulation of
the desired signal by the interference. The baseband frequency of the
noise spike is the difference between the frequency of the unmodulated
signal and the desired signal. If the interfering signal or the main
signal is highly loaded but the other is lightly loaded, noise is produced
in the baseband and is concentrated around the baseband frequency corresponding
to the difference between the center (carrier; frequency of the desired
and the interfering signals. If both signals are highly modulated,
broadband interference can be expected. Unlike the case when the signals
are unmodulated or only lightly modulated, the noi3e appears as broadband
intermodulation noise.
2.16 In addition to interference considerations, Taub and Schilling
and Panter mention that if the received signal is not centered in the
center of the IF of the .•eceiver or if the IF frequency response is not
symmetric with respect to the normal center frequency, the noise out
of the baseband will be greater than normal. Rice, Sundie, and Taub
and Schilling indicate that the FM threshold of an FM receiver will
be degraded due to the production of additional baseband noise if the
received signal is modulated. Middleton indicates if an FM modulator
is wideband white noise modulated and the signal is demodulated by a
receiver with no limiter, the receive baseband will experience considerable
essentially flat noise even for strong received signal levels.
2.17 One other noise characteristic of FM receivers is the noise out
of the receive.- at received signal levels at FM threshold and less.
As Middleton has shown, the character of the noise out of the baseband
of an FM receiver changes dramatically as the limiting in an FM receiver
is changed from hard to soft to no limiting. If limiting action is
reduced or lost in the region of FM threshold, the noise in the baseband
increases dramatically. The baseband noise is basically wide frequency
range flat spectrum noise which can significantly degrade FM threshold.
It is interesting, however, that with no carrier present at the receiver
and no receiver limiting, the noise out of the baseband receiver is
invariably less than the noise that would occur with heavy limiting.
The noise out of the baseband of the radio with no carrier present is
a direct function of the amount of limiting in the receiver. The relation
between amount of limiting and baseband noise is highly nonlinear, however.
Several dB of baseband noise is lost as limiting transitions from hard
to soft.
2.18 To this point, no mention has been made as to how the baseband
signal is affected as the received carrier i3 reduced into the region
near FM threshold. With hard receiver limiting, the baseband signal
remains constant. However, as the carrier falls below the FM threshold
level, the baseband signal is suppressed rather abruptly. Below FM
19
threshold, the demodulated baseband signal is reduced 2 dB for every
dB of reduced signal level. As with baseband noise near FM threshold,
the limiter affects the suppression of the baseband signal. The best
performance is obtained with hard limiting. As limiting goes soft,
the signal suppression starts earlier. Middleton has shown that the
effect with soft limiting is to ca' a the baseband signal level to start
being lost at a much stronger received signal level. The baseband signal
level is lost more gradually. With soft limiting, the received baseband
signal level eventually drops ofr at the same 2 dB per 1 dB of received
signal reduction as occurred for hard limiting. However, with soft
limiting, a given amount of signal suppression will occur at a stronger
received signal level.
20
3. Wideband FM Receiver Baseband Signal and Noise Characteristics
i.l If the noise in a single baseband noise slot were plotted as a
function of RF Received Signal Level (RSL), the plot would appear as
shown on the next page.
1.? Region A is the region of the quieting curve where the RF signal
has essentially been lost and the slot noise is dependent on the thermal
noise generated within the front end of the receiver, the receiver IF
response, and the amount of receiver limiting. Region B is the non-
linear region of the quieting curve. This region is a complex function
of the signal introduced into the receiver, the thermal noise generated,
the receiver IF response, and degree of signal limiting. Region C „'s
the linear region of the receiver. Here the noise decreases in direct
proportion to the increase in signal introduced into the receiver.
Region D is the so-called saturated region of tha receiver. Here, the
slot noise at the baseband of the radio is independent of the received
signal level and receiver generated noise.
3.3 Describing the noise in regions A, and B is a complex problem.
Fortunately, the problem has been solved by several people (e.g. Middleton,
Rice, Stumpers, and Wang). Most of the solutions are quite complicated.
The solutions involve multiple infinite series and cros.s products of
confluent hypergeometric functions or multiple indefinite integrals
of complicated infinite series. Taking advantage of the previous solutions
to the problem, it is possible to tabulate the slot noise for various
carrier to thermal noise (C/N) ratios (assuming hard limiting). The
tabulated results on the next few pages have been normalized. To convert
the tabulated noise values to dBm0 noise in a 3-1 kHz baseband slot,
add the following factor:
No (dBm0) = +29.8 - 20 log Af/ch rm3 + 10 log B - P
where
Af . , = per channel r-ms deviation in KHz
/ch rms
B = receiver IF bandwidth in MHz
P = baseband pre-emphasis in dB relative to baseband pivot frequency
(formulas for this are given later in this report)
To convert the C/N values to RSL, use the following formula:
RSL(dBm) = C/N(dB) - 114.0 + NF + 10 log B
where
NF = receiver overall noise figure in dB measured at the same point
at which RSL is to be measured
21
(0uiap) J9moj asiON }0|$
Slot Noise Versus Received Signal Level (RSL)
Figure ^
22
Received Signal Level (RSL, dBm)
‘t
C/N
C/N
Diff.
Rect.
Gaus •
(dB)
(PR;
(dB)
Noise
Noise
(dB)
(dB)
F/B-0.2
5.
3.162
0.6
-11.7
-II. 1
4.
2.512
1.2
-10.8
-9.5
3.
1 .995
1.6
-9.6
-8.0
2.
1.585
1.8
-8.4
-6 .7
1.
1 .259
1.9
-7.3
-5.5
0.
1.000
1.9
-6.4
-4.5
-1 .
0.794
1.9
-5.5
-3.6
-2.
0.631
1.9
-4.8
-2.9
-3.
0.501
1.9
-4.2
-2.4
-4.
0.398
1 .8
-3.7
-1.9
-5.
0.316
1.8
-3.3
-1.5
-6.
0.251
1.8
-3.0
-1.2
i
-7.
0.200
1.8
-2.8
-1.0
-8.
0.158
1.7
-2.5
-0.8
-9.
0.126
1.7
-2.4
-0.6
-10.
0.100
1.7
-2.2
-0.5
F/B»0. 1
5.
3. 162
1.2
-14.5
-13.3
4.
2.512
1 .8
-13.0
-11 .2
1
3.
1.995
2.0
-11.3
“9 » 3
1
2.
1.585
2.1
-9.7
-7.6
1 .
1.259
2.0
-8.2
-6.2
0.
1.000
1.9
-6.9
-5.0
i
-1 .
0.794
1.7
-5.8
-4.0
-2.
0.631
1.6
-4.9
-3 • 3
-3.
0.50!
1.5
-4.1
-2.6
•
-4.
0.398
1 .4
-3.5
-2.1
-5.
0.316
1.3
-3.0
•1*7
-6.
0.251
1 .2
-2.6
* 1 » j
-7.
0.200
1.2
-2.2
-i.t
-8.
0.158
1 .1
-2.0
-0.8
-9.
0.126
1 . 1
-1.7
-0.7
i
-10.
0.100
1 .0
-1.0
-0.5
t
h/b=o.o
5.
3.162
1 .6
-16.0
-14.4
4.
2.512
2.0
-14.0
-12.0
3.
1.995
2. 1
-11 .9
-9.8
[
2.
1 .585
2.0
-10.0
-3.0
1 .
1.259
1 .8
-8.3
-6.5
0.
1.000
1 .6
-6.0
-5.2
1
-1 .
0.794
1.3
-5.6
-4.2
-2.
0.631
1.1
-4.5
-3.4
-3.
0.501
1 .0
-3.7
-2.7
-4.
0.398
0.8
-3.0
-2.2
-5.
0.316
0.7
-2.4
— 1.7
-6.
0.251
0.6
-1.9
-1.4
-7.
0.200
0.5
-1.6
— l.l
-8.
0.158
0.4
-1.3
-0.9
1 i
-9.
0.126
0.4
-l.l
—0. 7
■ 1
1
1
-10.
0. IQO
0.3
-0.9
-0.5
Slot Noiee
RtctACguiar and G«u»»ian RK/IF R«»poo«a
Table 5
i
i
23
C/N
F/B-0.2 <«**>
20.00
19.00
18.00
17.00
16.00
lb. 00
14.00
i3.ro
12.00
11.00
10.00
9.00
8.00
7.00
6.00
b.00
F/b*0. I
20.00
19.00
16.00
17.00
16.00
16.00
14.00
13.00
12.00
1 1 ,00
10.00
V , 00
6.00
/ .00
6.00
5 . On
I
i F/u*o.ob
■ 20.00
I V.00
18.00
I 1.00
1 0 . 00
lb. 00
14.00
13.00
12.00
II .00
10.00
9.00
6.00
/.00
6.00
b .00
C/N
Diff.
Rect .
Gdus .
(PR)
(dB)
Noise
(dB)
Noise
(dB)
100.00
0.34
-28.31
-28.65
79.43
0.34
-27.86
-28.20
03.10
0.34
-26.86
-27.20
50. !2
0.34
-25.86
-26.20
39.81
0.34
-24.86
-25.20
31 .62
0.34
-23.86
-24.20
25.12
0.34
-22.86
-23.20
1 9.9b
0.34
-21.86
-22.20
15.8b
0.34
-20.86
-21 .20
12.59
0.34
-19.86
-20.20
10.00
0.34
-1 c .86
-19.19
7.94
0.32
-17.83
-18. 15
6.31
0.25
-16.70
-16.96
5.01
0.08
-15.36
-15.44
3.98
0.20
-13. 7i
-13.51
3. 1 6
0.51
-11.78
-11.28
1 00.00
o. 07
-34.33
-34.26
79.43
0.07
-33.88
-33.81
63.10
0.07
-32.88
-32.81
50.12
0.07
-31.88
-31.81
39.81
O.o?
-30.08
-30.81
31 .62
0.07
-29.86
-29.81
25.12
0.07
-26.88
-28.81
19.95
0.07
-27.08
-27.81
15.05
0.07
-26.88
-26.81
12.59
0,07
-25.88
-25.81
10.00
o.OO
-24.86
-24.78
7.94
0.13
-23. / 4
-23.62
0.31
0.30
-22.28
-2 1 . 98
5.01
0.o3
-20.16
-19.53
3.98
0.98
-17.43
-16.45
3 . 1 o
1.22
-14.50
-13.28
1 00.00
0.17
-40.35
-40.
, 18
79.43
0. 1 7
-39.90
-39.
.73
C3. to
0.17
-36.90
-38.
,73
50.12
0.17
-37.90
-37.
,73
39.01
0.17
-30.90
-3o.
,73
31 .62
0.17
-35.90
-35.
,73
25. 12
0.17
-34.90
-34.
.73
1 9. 95
0.17
-33.90
-33.
,73
15.85
0.17
-32.90
-32.
,73
12.59
0.17
-31 .89
-31.
,72
10.00
0.20
-30.82
-30.
62
7.94
0.36
-29.37
-29.
,01
6.31
0.77
-26.87
-26.
, II
5.01
1.17
-23.2!
-22.
,04
3.98
1 .40
-19.23
-17.
83
3.16
1 .50
-15.56
-1 4.
07
Sloe Noise
Rectangular and Gauaaian RF/IF Response
Table 5
(cont. )
24
C/N
(dB)
C/N
(PR)
Diff.
(dB)
Rect.
Noise
Gaua .
Noise
(dB)
(dB)
20.no
1 00.00
0.20
-46.37
-46.17
19.00
79.43
0.20
-45.92
-45.73
18.00
63.10
0.20
-44.92
-44.73
17.00
50.12
0.20
-43.92
-43.73
I0.00
39.81
0.20
-42.92
-42.73
lb. 00
31 .62
0.20
-41.92
-41.73
14.00
25.12
0.20
-40.92
-40.73
13.00
1 9.95
0.20
-39.92
-39.73
12.00
15.85
0.20
-38.92
-38.72
II .00
12.59
0.21
-37.89
-37.69
10.00
10.00
0.31
-36.61
-36.30
9.00
7.94
0.73
-34.10
- 37
8.00
6.31
1 .24
-29.63
-28.39
7.00
5.01
1 .47
-24.49
-23.02
6.00
3.96
1 .55
-10.82
-18.27
5.00
3.16
1 .58
-15.88
-14.30
tyb*o.oi
20.00
100.00
0.20
-54 . 33
-54.12
19.00
79.43
0.20
-53.88
-53.68
18.00
63. 10
0.20
-52.88
-52.68
17.00
50.12
0.20
-51.88
-51.68
to. 00
39.61
0.20
-50.88
-50.68
15.00
31 .62
0.20
-49.88
-49.68
14.00
25.12
0.20
-48.88
-48.68
13.00
19.95
o.2o
-47.88
-47.68
12.00
15.85
0.21
-46.87
-46.67
1 1 .00
12,59
0.27
-45.71
-45.45
10.00
10,00
0.70
-43.21
-42.51
9.00
7.94
1.32
-37.59
-36.27
8.00
6.31
1.53
-30.87
-29.34
!.()<)
5.01
1 .59
-24.93
-23.34
6.00
3.98
1 .60
-20.01
-18.41
8.00
3.16
1 .61
-15.97
-1 4.36
H/b-'O.OOb
20.00
1 00.00
0.20
-60.35
-60.14
19.00
79.43
0.20
-59.90
-59.70
18.00
63.10
0.20
-58.90
-58.70
17.00
50.12
0.20
-57.90
-57.70
16.00
39.81
0.20
-56.90
-56.70
15.00
31 .62
0.20
-55.90
-55.70
14.00
25.12
0.20
-54.90
-54.70
13.00
19.95
0.20
-53.90
-53.70
12.00
15.85
0.22
-52.87
-52.66
11 .00
i 2 ,59
0.42
-51,27
-50.84
10.00
10.00
1.17
-46.32
-45.15
9.00
7.94
1.52
-38.43
-36.90
8.00
6.31
1 .59
-31 .08
-29.49
7.00
5.01
! .60
-25.00
-23.39
6.00
3.98
1 .61
-20.03
-18.43
5.00
3.16
1 .61
-15.98
-14.37
Slot Noise
Rectangular and Gaussian RF/IF Response
Table 5
(cont . )
2«;
I
C/H
C/N
Diff.
Rect.
Gaus.
F/B-0.0025 <«»>
(PR)
(dB)
Noise
(dB)
Noise
(dB)
20.00
100.00
0.20
-66.37
-66. id
19.00
79.43
0.20
-65.92
-65.72
13.00
63.10
0.20
-64.92
-64.72
17.00
50.12
0.20
-63.92
-63.72
16.00
39.81
0.20
-62.92
-62.72
15.00
31 .62
0.20*
-61 .92
-61.72
14,00
25.12
0.20
-60.92
-60.72
13.00
19.95
0.21
-59.92
-59.71
12.00
15.85
0.25
-53.81
-58.56
II .00
12.59
0.80
-55.30
-55.00
10.00
10.00
1.47
-47.64
-46.17
9.00
7.94
1.59
-38.67
-37.08
8.00
6.31
1 .60
-31 .14
-29.53
7.00
5.0|
1.61
-25.01
-23.40
6.00
3.98
1 .61
-20.04
-18.43
5.00
3.16
1 .61
-15.98
-14.38
F/a-o.oci
20.00
100.00
0.20
-74.33
-74.12
19.00
79.43
0.20
-73.38
-73.68
18.00
63.10
0.20
-72.88
-72.68
17.00
50.12
0.20
-71 .88
-71 .68
10. 00
3V.8I
0.20
-70.88
-70.68
16.00
31 .62
0.20
-09.88
-69.68
14.00
25.12
0.21
-03.88
-68.68
13.00
1 9. 95
0.21
-67.87
-67.66
12.00
15.65
0.44
-66.20
-65.76
II .00
12.59
1.36
-58. y4
-57.58
10.00
10. on
1 .58
-48.09
-46.51
9.00
7 . 94
1 .61
-38.74
-37.13
8.00
6.31
1 .61
-31 .15
-29.54
7.00
5.01
1 .61
-25.02
-23.41
6.00
3.98
1 .61
-20.04
-18.43
6.00
3.16
1 .61
-15. ;
-14.38
F/8-0.0005
20.00
100.00
0.20
-80.35
-80.14
19.00
79.43
0.20
-79.90
-79.70
18.00
63.10
0.20
-78.90
-78.70
17.00
50.12
0.20
-77.90 ,
-77.70
16.00
39.81
0.20
-76.90
76.70
15.00
31 .62
0.20
-75. 9'"'
-/ 5.70
14.00
25 . 1 2
0.21
-;h.9o
-74.70
13.00
19.95
0.23
-73.85
-73.62
12.00
15.85
0.83
-70.65
-69.82
II .00
12,59
1,54
-59.66
-58.12
10.00
10.00
1 .60
-48.16
-46.55
9.00
7.94
I .61
-38.75
-37.14
8.00
6.31
1 .61
-31.15
-29.54
7.00
5,01
1.61
-25.02
-23.41
o.OO
3.98
1 .61
-20.04
-18.43
5.00
3.16
1 .61
-15.99
-14.38
Slot Noise
Rectangular and Gauaaian RF/1F Response
Table 5
(cont. )
26
C/N
C/N
Dlff.
Ract.
Gaua.
F/B-0.000 25 (dB)
(PR)
(dB)
Noise
(dB)
Noise
(dB)
20.00
100.00
0.20
-86.37
-86.16
>9.00
79.43
0.20
-85.92
-85.72
18.00
63.10
0.20
-84.92
-84.72
17.00
50.12
0.20
-83.92
-83.72
>6.00
39.81
0.20
-82.92
-82.72
15.00
31 .62
0.20
-81.92
-81.72
14.00
25.12
0.21
-80.92
-80.72
13.00
19.95
0.28
-79.71
-79.43
>2.00
15.85
1 .27
-73.22
-71.95
II .00
12.59
1 .59
-59.86
-58.27
10.00
>0.00
1.61
-48.18
-46.57
9.00
7.94
1 .61
-38.75
-37.14
8.00
6.31
1 .61
-31 .J 5
-29.54
7.00
5.01
1.61
-25.02
-23.41
6.00
3.98
1.61
-20.04
-18.43
5.00
3.16
1 .61
-15.99
-14.38
F/8-0.0001
20.00
100.00
0.20
-94 . 33
-94. 12
19.00
79.43
0.20
-93.88
-93.68
18.00
63.10
0.20
-92.88
-92.68
17.00
50.12
0.20
-91 .88
-91 .68
16.00
39.81
0.20
-90.88
-90.68
15.00
31 .62
0.21
-89.88
-89.68
14.00
25. 12
0.21
-88.07
-88.66
13.00
1 9.95
0.58
-86.69
-86. 1 1
12.00
15.85
1.54
-74.33
-72.79
1 1 .00
12.59
1.61
-59.92
-58.31
10.00
10.00
1.61
-48.18
-46.57
9.00
7.94
1.61
-38.75
-37.14
8.00
6.31
1 .61
-31.15
-29.54
7.00
5.01
1 .61
-25.02
-23.41
6.00
3.98
1.61
-20.04
-18.43
5.00
3.16
1.61
-15.99
-14.38
F/B-0.0
20.00
100.00
1.61
-358.50
-356.89
19.00
79.43
1 .61
-354.22
-352.61
18.00
63.10
1 .61
-282.77
-281,16
17.00
50.12
1.61
-225.92
-224.31
16.00
39.81
1.61
-180.65
-179.04
15.00
31 .62
1 .61
-1 44.59
-142.98
14.00
25.12
1 .61
-115.84
-114.23
13.00
19.95
1.61
-92.91
-91.30
12.00
15.85
1.61
-74.58
-72.97
II .00
12.59
1.61
-59.93
-58.32
10.00
10.00
1.61
-48.18
-46.57
9,00
7.94
1.61
-38.75
-37.14
• 8.00
6.31
1 .61
-31.15
-29.54
7.00
5.01
1.61
-25.02
-23.41
6.00
3.98
1 .61
-20.04
-18.43
5.00
3.16
1.61
-15.99
-14.38
Slot Nolaa
Rectangular end Causal an IF/IF Kaapooat
Table 5
(cont. )
33.
F/B-0.2
F/B-O. I
F/B-0.0
C/N
C/N
Diff.
Avg.
CdB)
(PR)
CdB)
Noise
CdB)
5.
3. 162
0.3
-11.4
4.
2.512
0.6
-10.2
3.
t .995
0.8
-8.8
2.
1.585
0.9
-7.6
1.
1.259
0.9
-6.4
0.
1.000
1 .0
-5.4
-1 .
0.794
1.0
-4.6
-2.
0.631
1 .0
-3.9
-3.
0.501
0.9
-3.3
-4.
0.398
0.9
-2.8
-5.
0.316
0.9
-2.4
-6.
0.251
0.9
-2.1
-7.
0.200
0.9
-1.9
-8.
0.158
0.9
-1.7
-9.
0. 126
0.9
-1.5
-10.
0. 100
0.9
-1.4
5.
3.162
0.6
-13,9
4.
2.512
0.9
-12.1
3.
1.995
1.0
-10.3
2.
1 .585
1.0
-8,6
1.
1 .259
1 .0
-7.2
0.
1 . 000
0.9
-6.0
-1.
0.794
0.9
-4.9
-2.
0.631
0.8
-4. 1
-3.
0.501
0.8
-3.3
-4.
0.39B
0.7
-2.8
-5.
0.316
0.7
-2.3
-6.
0.251
0.6
-1.9
-7.
0.200
0.6
-1.6
-8.
0.158
0.6
-1.4
-V.
0.126.
0.5
-1.2
•10.
0.100
O.S
-1.0
0.
3. 1 o2
0.8
-15.2
4.
2.512
: -o
-13.0
3.
1 .995
1.0
-10.9
2.
'.585
1.0
-9.0
1.
1.259
0.9
-7.4
0.
1.000
0.8
-6.0
-1.
0.794
0.7
-4.9
-2.
0.631
O.o
-3.9
-3.
0.501
0.5
-3.2
-4.
0.390
0.4
-2.6
-5.
0.316
0.3
-2. 1
-6.
0.251
0.3
-1.7
-7.
0.200
0.3
-1.3
-8.
0.158
0.2
-1.1
-9.
0.126
0.2
-0.9
■10.
0.100
0.2
-0.7
Averaged Slot Nolae
Table 6
F/B«0.2 (dB)
20.n0
19.00
18.00
17.00
16.00
lb. 00
14.00
13.00
12.00
II .00
10.00
9.00
8.00
7.00
6.00
5.00
F/B-0.1
C/N
Diff.
(PR)
(dB)
100.00
0.27
79.43
0.27
63.10
0.27
50.12
0.27
39.81
0.27
31 .62
0.27
25.12
0.27
1 9.95
0.27
15.85
0.27
12.59
0.27
10.00
0.27
7.94
0.26
6.31
' 0.23
5.01
0.14
3.98
0.00
3.16
0.15
20.00
19.00
18.00
17.00
16.00
15.00
14.00
13.00
12.00
II .00
10.00
9.00
8.00
7.00
6.00
5.00
F/B-0.05
100.00
0.07
79.43
0.07
63.10
0.07
50.12
0.07
39.81
0.07
31.62
0.07
25.12
0.07
1 9.95
0.07
15.85
0.07
12,59
0.07
10.00
0.06
7.94
0.04
6.31
0.05
5.01
0.21
3.98
0.39
3.16
0.51
20.00
19.00
18.00
17.00
10.00
15.00
14.00
13.00
12.00
I I .00
10.00
9.00
8.00
7.00
6.00
5.00
100.00
79.43
63.10
50.12
39.81
31 .62
25.12
I 9. 95
15.85
12.59
10,00
7.94
6.31
5.01
3.98
3.16
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
C.02
o.oo
0.08
0.28
0.48
0.60
0.65
Averaged Slot Noise
Table 6
(cont . )
Avg.
Noise
(dB)
-29.03
-28.03
-27.03
-26.03
-25.03
-24.03
-23.03
-22.03
-21.03
-20.03
-19.02
-17.99
-16.83
-15.40
-13.61
-II .53
-34.85
-33.85
-32.85
-31.85
-30.85
-29.85
-28.85
-27.85
-26.85
-25.84
-24.82
-23.68
-22.13
-19.84
-16.94
-13.89
-40.82
-39.82
-38.82
-37.82
-36.82
-35.82
-34.82
-33.82
-32.82
-31 .81
-30.72
-29.1 9
-26.49
-22.63
-18.53
-U.62
29
f-/B°0.02b
F/B*O.OI
F/B=0.005
C/N
C/N
Diff.
Avg.
Nolae
(dB)
(PR)
(dB)
(dB)
20.00
100.00
0.00
-46.82
i 9.00
79.43
0.00
-45.82
18.00
63.10
0.00
-44.82
1 7.00
50.12
0.00
-43.82
16.00
39.81
0.00
-42.82
lb. 00
31 .62
0.00
-41 .82
14.00
2b. 12
0.00
-40.82
Id. 00
19.95
0.00
-39.82
12.00
15.85
0.00
-38.82
11.00
12.59
0.00
-37.79
10.00
10.00
0.05
-36.45
9.00
7.94
0.26
-33.73
8.00
6.31
0.52
-29.01
7.00
5.01
0.63
-23.76
6.00
3.98
0.67
-19.05
b.00
3.16
0.69
-15.09
20.00
100.00
0.00
-54.78
19.00
79.43
0.00
-53.78
18.00
63.10
0.00
-52.78
17.00
bO. 1 2
0.00
-51 .78
10. 00
39.81
0.00
-bO.78
lb. 00
31 .62
0.00
-49.78
14.00
2b . 1 2
n.00
-48.78
13.00
1 9.9b
0.00
-47.78
12.00
lb. 8b
0.00
-46.77
1 1 .on
12.59
0.03
-45.58
10. oo
10.00
0.2b
-42.86
9.00
7.94
0.b6
-36.93
8.00
6.31
0.66
-30.11
7.00
5.01
0.69
-24.14
6,00
3.98
0.70
-19.21
b .00
3,16
0.70
-15.17
20.00
100.00
0.00
-60.80
19.00
79.43
0.00
-59.80
18.00
63. 'O
0.00
-58.80
17.00
50.12
0.00
r57 ,80
16.00
39.81
0.00
-56.80
lb. 00
31 .62
0.00
-55.80
14.00
25.12
0.00
-54 ,80
13.00
19.95
0.00
-53.80
12. HO
lb. 8b
0.01
-52.76
1 1 .00
12.59
0. 1 1
-51 .05
10.00
9.00
10.00
7.94
0.48
0.66
-45.74
-37.67
8.00
6.31
0.69
-30.29
7.00
b.Ol
0.70
-24.19
6.00
3.98
0.70
-19.23
5.00
3.16
0.70
-i5. 18
Averaged Slot
Nolae
Table 6
(cont. )
30
F/B-0.0025
C/N
C/N
Dlff.
Avg.
Noiaa
(dB)
(PR)
(dB)
(dB)
20.00
100.00
0.00
-66.82
19.00
79.43
0.00
-65.82
IS. 00
63.10
0.00
-64.82
17.00
50.12
0.00
-63.82
16.00
39.81
0.00
-62.82
lb. 00
31 .62
0.00
-61 .82
14.00
25. 12
0.00
-60.82
I 3.00
19.95
0.00
-59.82
12.00
15.85
0.02
-58.68
1 1 .00
12.59
0.30
-55.40
10.00
10.00
0.63
-46.90
9.00
1.94
0.69
-37.87
0,00
6.31
0.70
-30.33
7.00
5.01
0.70
-24.21
6. 00
3.98
0.70
-19.23
b.00
3.16
0.70
-15.18
F/B-O.OOI
20.00
100.00
0.00
-74.78
IV. 00
79.43
0.00
-73.78
18.00
63.10
0.00
-72.78
17.00
50.12
0,00
-71.78
16.00
3v,3l
0.00
-70.78
15.00
31 .62
0.00
-69.78
14.00
25 . 1 2
O.no
-68.78
1 3.00
1 9. yb
O.oo
-67.76
12.00
lb. 85
0.12
-65.98
1 1 .00
12.59
0.58
-58.26
10.00
10.00
0.69
-47.30
9.00
7.94
0.70
-37.93
8.00
6,31
0.70 •
-30.35
7.00
5.01
0.70
-24.21
o , 00
3.98
0.70
-19.24
5.00
3.16
0.70
-15.18
F/b«0.0005
20.00
100.00
o.oo
-80.80
1 9.00
79.43
0.00
-79.80
18.00
03.10
0.00
-78.80
1 1.00
50.12
0.00
-77.80
16.00
39.81
0.00
-76.80
15.00
31 .02
0.00
-75.80
14.00
25.12
0.00
-74.80
13.00
19.95
0.01
-73.73
12.00
15.85
o.3l
-70.24
1 1 .00
12.59
0.67
-58.89
10.00
10.00
0.70
-47.36
9.00
7.94
0.70
-37.94
8.00
6.31
0.70
-30.35
7.00
5.0!
0.70
-24.21
6.00
3.98
0.70
-19.24
5.00
3.16
0.70
-15.18
Averaged Slot
Noise
Table 6
(cont . )
31
C/N
C/N
Dlff.
Avg.
Noise
<dB)
(PR)
(dB)
(dB)
20.00
100.00
0.00
-H6.R2
19.00
79.43
0.00
-85.82
18.00
63.10
0.00
-84.82
17.00
50. 1 2
0.00
-83.82
16.00
39. HI
0.00
-82.82
1 1> . 00
31 .62
•0.
-81 .82
14.00
2b. 12
0.00
-80.82
13.00
19.9b
0.04
-79.57
12.00
15.85
0.53
-72.58
1 1 .00
12.59
0.69
-59.06
10.00
10.00
0.70
-47.37
9.00
7.94
0.70
-37.94
8.00
6.31
0.70
-30.35
7.00
b .01
0.70
-24.21
0.00
3.98
0.70
-19.24
b.oc
3.16
0.70
-15.18
8/8=0.0001
20.00
1 00.00
1 9.00
/ 9.43
18.00
63.10
17.00
50. I 2
10. 00
39.81
lb. 00
31 .02
14.00
25.12
13.00
19.95
12.00
lb. Ho
1 1 .00
12.59
10. 00
10. 00
9. no
/ . 94
H.00
0.31
/ .00
5.01
O.00
3.VH
b . no
3.10
0.
-94.78
0.
-93.78
0.
-92.78
0.
-PI. 78
0.
-90.78
n.oo
-89.78
n.no
-88.77
n , | 9
-86.40
0.0/
-73.56
0.70
-59. 1 1
n.70
-47.38
0.70
-37.94
0.70
-30.35
0.70
-24.21
O./o
-19.24
0.70
-15.18
8/H-0.0
20.00
1 00 . 00
0.70
-557.70
19. on
/9.43
0.70
-353.42
18.00
03.10
0.70
-281 .97
17.00
50.12
0.70
-225. 11
lo.OO
39.81
0.70
-1 79.84
15.00
31 .02
0.70
-143.78
14.00
25.12
0.70
-115.04
13.00
1 9.9b
0.70
-92.10
12.00
15.85
0.70
-73.78
1 1 .on
12.59
0,70
-59.12
10.00
10.00
0.70
-47.38
9.00
/ . 94
0.70
-37.94
8.00
0.31
0.70
-30.35
/,00
5. 01
0.70
-24.21
6.00
3.98
0.70
-19.24
5.00
3.16
0.70
-15.18
Averaged Slot Noise
Table 6
(cont . )
52
3.4 The formulas used to generate the slot noise tables are given later
in this report. In some cases, there is a slight error associated with
the equation approximations. The error limits are noted later. In
the tabulated results, F is the baseband frequency of the center of
the noise slot; B is the IF bandwidth C/N i3 carrier to (thermal) noise
ratio. PR indicates power ratio. DIFF is the difference between the
two slot noise values. This gives a good check on the dependency of
the slot noise on IF response. Gaussian and rectangular IF responses
form reasonable limiting cases which limit the realistic range of IF
response shapes encountered in practice. All slot noise values have
been normalized to the value of slot noise at F/B = 0 and C/N = -dB for
he respective IF response.
3.5 Following this set of values, the averaged values have been computed.
These values are the algebraic average of the values for the Gaussian
and the rectangular IF bandwidth responses. The DIFF column indicates
the difference between the averaged IF response and either of the Gaussian
and rectangular IF responses. This column gives an estimate of the
variation to be expected between averaged theoretical quieting curve
characteristics and actual quieting curve measurements. The averaged
noise values have been normalized to the averaged slot noise for F/B
= 0 and C/N = - (dB).
3.6 There are a couple of common FM receiver specifications related
to the slot noise performance of the receiver in the A, B, and upper
C regions. One of the specifications is 20 dE (and occasionally 30
dB) noise quieting. The 20 dB (or 30 dB) quieting specification is
the RSL at which the noise in a specified baseband slot is 20 dB (or
30 dB) lower than the noise in the slot with no RSL present at the
receiver input. Theoretical, 20 dB and 30 dB C/N ratios are listed
on the next page. The C/N values can be converted to RSL using receiver
parameters and the previous formulas.
•j.7 The other specification is FM slot noise threshold or simply FM
threshold. There is not complete agreement by sources as to the defi-
nition of FM threshold. The most common definition, however, is the
RSL at which the receiver baseband slot noise has increased 2 dB for
a 1 dB reduction in RSL. Thi3 is often determined graphically with
quieting curves by extending the straight line of region C into region
B and defining FM tnreshold as the RSL at which slot noise is one dB
above the straight line extension. Generally, FM threshold is measured
in a narrow (nominal 3.1 KHz wide) noise slot. Theoretical narrow slot
FM threshold values are listed on the following page. Occasionally,
however, it is desirable to measure FM threshold in a relatively wide
slot. For example, if the FM receiver baseband contains a wideband
video or digital circuit, the FM noise threshold over the entire bandwidth
of the baseband signal would be appropriate. The theoretical wide noise
slot FM thresholds are tabulated on the next page. For the FM threshold
charts, (f/B) is the narrow slot baseband frequency divided by the IF
33
C/N(dB)
f/B
Rect.
IF
Gaut.
IF
Avg.
IF
0.2
12.6
10.9
11.8
0.1
7.2
7.2
7.2
0.05
6.3
6.5
6.4
0.025
6.1
6.4
6.3
0.01
6.0
6.3
6.2
0.001
6.0
6.3
6.2
0.0001
6.0
6.3
6.2
0.0
6.0
6.3
6.2
Theoretical 20 dB Noise Quieting
(narrow slots)
C/N(dB)
f/B
Rect.
IF
Gaus.
IF
Avg.
IF
0.2
22.6
20.9
21.8
0.1
15.8
15.2
15.5
0.05
9.6
9.6
9.6
0.025
8.1
8.3
8.2
0.01
7.9
8.1
8.0
0.001
7.8
8.1
8.0
0.0001
7.8
8.1
8.0
0.0
7.8
8.1
8.0
Theoretical 30 dB Noise Quieting
(narrow slots)
Table 7
34
f/B
Rectangular RF/IF
C/N (dB)
Gauasien RF/IF
C/N (dB)
Averaged Reaponse
C/N (dB)
0.2
6.19
6.69
6.4*1
0.1
7.56
7.85
7.71
0.05
8.58
8.79
8.65
0.025
9.39
9.56
9.48
0.0158
9.85
10.00
9.93
0.01*17
9.92
10.07
10.0
0.013**
10.00
10.15
10.08
0.01
10.26
10. *40
10.33
0.005
10.8*<
10.9*4
10.89
O.0025
11.31
11. *41
11.36
0.001
11.88
11.97
11.93
0.0005
12.26
12.35
12.31
0.00025
12.62
12.70
12.66
0.0001
13-0*4
13-11
13.08
0.0
Undefined
Undefined
Undefined
s
1 Theoretical FM Noise Thresholds
| (.narrow slots)
i
I
* Table 8
35
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36
(wide noise slots)
bandwidth, (f/B) max is the highest baseband slot frequency divided
by IF bandwidth, and (f/B) min is the lowest baseband slot frequency
divided by IF bandwidth. Note that a wide slot FM threshold always
occurs within 1 dB of the FM threshold for a narrow slot which has
baseband frequency equal to the maximum frequency of the wide slot.
3.8 The last region of interest is D. By conventional linearized
methods, (e.g., see Rowe |nd Panter) it can be shown that in the D region,
the noise is the normal f (6 dB per octave) thermal noise plus the
time derivative of any phase noise associated with the received carrier.
The differentiated phase n^ise is called frequency noi3e. It is distinctly
different noise than the f receiver thermal noise. For information
regarding phase and frequency noise, see references listed in bibliography.
In the D region, the f noise is negligible and the dominate noise source
is the frequency noise of the received carrier. At a sufficiently high,
stable carrier to thermal noise ratio with no multipath and the carrier
tuned to the center of a symetric IF, the only significant frequency
noise sources are the various oscillators in the transmitter and receiver.
3.# The frequency noise of an oscillator is a complex phenomenon.
In general, the phase noise of an oscillator varies in power roughly
2
as 1 / f where f is tht frequency of the measurement slot away from
the carrier frequency. The noise at the baseband of an FM demodulator,
however, is the time de 'ivative of the phase noise (for high carrier
to noise ratios). Sinct. the power response of a differentiator is
2
proportional to f , the 'requency noise appearing at the baseband of
the radio 13 essentially Hat (independent of baseband frequency).
After review of information regarding fundamental frequency (unmultiplied)
free running microwave oscillators from various vendors, it appears
that this is, in fact, the case for baseband frequencies greater than
roughly 100 kHz. Below this frequency, the noise gradually increases.
The frequency noise within the first few kilohertz of the baseband can
be several times the noise in the mid region of the baseband. As Baprawski
et al mention, use of properly optimized phase-locked loops can be used
to reduce the noise near the low end of the baseband. Duo to feedback
loop frequency response requirements, present phase-locked frequency
sources can only be used to reduce noise in roughly the first one half
megahertz of the radio baseband. Often the output of an oscillator
is multiplied to derive a higher frequency. As Payne points out, multi-
plying the output of the oscillator increases the effective deviation
of the frequency noise. Specifically, noise increase is 20 log M where
M is composite oscillator multiplication. For example, doubling the
oscillator frequency causes a 6 dB increase in frequency noise due to
doubling the effective deviation of the frequency noise components.
Payne also mentions that in the gigahertz region, the noise figure of
the multiplier diodes can be a significant factor. Up or down converter
mixer diodes can have the same effect. The noise figure of the diodes
can cause a significant increase in slot noise abovj roughly one megahertz
in the radio baseband. The following page graphs typical FM receiver
baseband slot noise due to a free running unmodulated M/W oscillator.
37
i
(8P) J3M0J asjojj wj
; Typical Microwave Oscillator Noise
Figure 5
38
Baseband Slot Frequency
I — -t — h— t +
i — t.
!
!
!
I
I
Figure 6
Horizontal: 1 kHz/Div.
Measurement Bandwidth:
100 Hz
Horizontal: 5 kHz/Div.
Meaourement Bandwidth:
100 Hz
Horizontal: 20 kHz/Div.
Measurement Bandwidth:
300 Hz
TROPO M/W Transmitter
VCO Spectrum
39
Vertical: 10 dB/Div.
Horizontal: 20 kHz/Div
(0 to 200 kHz)
Note: This LOS M/W
receiver Is not the
one used In the rest
of this report.
Vertical: 10 dB/Div.
Horizontal: 50 kHz/Div,
(0 to 500 kHz)
RSLs(dBm) - -100, -90,
-80, -70, -60, -50,
-40, -30, -20
Measurement Bandwidth:
3 kHz
Vertical: 10 dB/Div.
Horizontal: 1 MHz/Dlv.
(0 to 10 MHz)
LOS M/W Receiver
no de-emphasis
Baseband Noise Spectrum
for Various RSLs
Figure 7
0
3.10 There are several oscillators in a microwave system. The primary
oscillators of interest are the local oscillators for up and down frequency
conversion and the frequency modulated oscillator at the transmitter
(voltage controlled oscillator-VCO) . The up and down converter local
oscillators can be phase-locked to reduce low frequency noise. As Lawson
and Uhlenbeck have noted, certain hybrid configurations allow the noise
sidebands of the oscillator to be suppressed. These methods can not
be used on the modulated oscillator, however, 3ince any method used
to suppress the inherent noise of the oscillator will also suppress
the modulation. Therefore, the oscillator to be modulated must have
inherently low noise. If the output of this oscillator is multiplied,
a much quieter oscillator is required. It should be mentioned that
the transmit oscillators are usually frequency stablized by phase locked
loops. The loop bandwidths of these systems are quite narrow (often
less than a Hertz). These loops will not suppress noise in the radio
baseband greater than a few Hertz above zero frequency. It can be antici-
pated that the baseband noise of a voltage controlled M/W oscillator
used for FM will be similar to the noise of a free running M/W oscillator.
3.11 To point out the complex nature of oscillator noise, spectrum noise
plots of the sideband noise spectrum of a microwave voltage controlled
oscillator (with Automatic Frequency Control circuitry disabled) were
taken. The plots are on the next page. The sideband frequency distribution
is a combination cf both amplitude modulation noise (in phase noise)
as well as phase/frequency noise (quadrature noise). Therefore, a direct
relation between the frequency spectrum and noise in the baseband is
not possible. However, the noise process is obviously complex in the
near carrier region.
3.12 To illustrate the thermal and phase noise in a typical microwave
receiver, the baseband noise spectrum was plotted for various received
signal levels us.ing a spectrum analyzer. The pxots are on the next
page. Note the oscillator noise at the low baseband frequencies at
high C/Ns and the crossing of the noise slots for low C/Ns.
3.13 Having determined the basic slot noise as a function of RSL, the
next item of immediate interest is the performance of the baseband
signal versus RSL. As long as the received signal is hard limited by
the limiter prior to demodulation and as long as the carrier to noise
ratio (C/N) is large, the received signal at the baseband will vary
directly as the transmitted baseband signal and will be completely
independent of RSL. Part of an FM demodulator is an envelope detector.
All Incoherent detectors, including envelope detectors, exhibit a baseband
signal threshold. That is to say, for low C/Ns, the baseband signal
will be suppressed. Several people (e.g., Middleton, Rice, and Stumpers)
have derived equations relating FM demodulator input modulated signal
to noise ratio and output baseband signal suppression for a sine wave
baseband signal. Schwartz shows that the same equation for baseband
41
t
C/N
C/N
Signal
(dB)
(PR)
Laval
(dB)
10.
10.0000
0.0
9.
7.9433
0.0
0.
6,3096
0.0
7.
5.0119
-0.1
6.
3.9811
-0.2
5.
3.1623
-0.4
4.
2.5119
-0.7
3.
1 .9953
-1.3
2.
1.5849
-2.0
1 .
1 .2589
-2.9
0.
1 .00 00
-4.0
-1 .
0.7943
-5.2
-2.
0.6310
-6.6
-3.
0.5012
-8.1
-4.
0.3901
-9.7
-5.
0.3162
-II .3
-6.
0.2512
-13.1
-7.
0. 1 995
-14.9
-r.
0.1585
-16.7
-9.
0.1259
-18.5
-1C.
0. 1000
-20.4
-It.
0.0/94
-22.3
-12,
0.0631
-24.3
-13.
0.0501
••26.2
-14.
0.0399
-23.2
-1b.
0.0316
-30. 1
-16.
0.0251
-32.1
-17.
0.0200
-34.1
-lb.
0.0158
-36. 1
-19,
0.0126
-33.1
-20.
0.0100
-40.0
-21 .
0, 0u'79
-42.0
-22.
0,0063
-44.0
-23.
0.0050
-46.0
-24.
0.0040
-43.0
-2b.
0.0032
-50.0
-26.
0.0025
- 52 , 0
-27.
0.0020
-54.0
-28.
0.0016
-56.0
-29.
0,0013
-58.0
-30.
0.0010
-60.0
-31 .
0,0008
-62.0
-32.
0.0006
-64.0
-33.
0.0005
-66.0
-34.
0. 0004
-68.0
-35.
0.0003
-70.0
-36.
0.0003
-72.0
-37.
0.0002
-74.0
-38,
0.0002
-76.0
-39,
0.0001
-78.0
-40.
0.0001
-30.0
Baseband Signal Suppression
Table 10
42
signal suppression holds for any arbitrary baseband signal. The equation
for baseband signal suppression will be given later in this report.
The relation between baseband signal suppression and receiver input
carrier to noise ratio is listed on the next page. The dB factor listed
is (algebraicly) added to the normal baseband dBm or dBm0 power level.
Receiver carrier to noise ratio can be converted to received signal
level (RSL) based on FM receiver parameters using formulas listed later
in this report.
3.14 One of the assumptions so far has been that the microwave receiver
was hard limiting the received signal prior to demodulation. This
assumption requires us to believe that all microwave receiver limiters
are driven to saturation with Just the thermal noise from the front
end of the receiver. This is a highly questionable assumption. Loss
of hard limiting effects both the baseband signal and noise properties
of an FM receiver.
3.15 Like the problem of FM noise for low C/N, the problem of demodulated
FM signals and nol3e with arbitrary or no limiting is complex. Middleton
has solved this problem for an FM receiver with Gaussian IF frequency
response. His results indicate that as limiter action transitious from
hard limiting to soft (partial) limiting to no limiting, the slot noise
with no carrier present transitions to less and less noise. Also, the
baseband noise spectrum changes dramatically as limiting is lost. Middleton's
results for the two extreme cases of limiting were used to determine
the following normalized baseband noise spectrum charts. In absolute
power the noise associated with "1.0 milliwatt" on the "hard limiting"
curve is greater than the absolute power associated with "1.0 milliwatt"
on the "no limiting" chart. The most obvious differences between the
two curves is the change in shape. This is interesting, but the curves
also indicate a more important consideration. For a given slot frequency
and given C/N greater than 0 dB, the slot noi3e is much greater with
no limiting than it is with full limiting. We can anticipate that if
a receiver limiter action starts going soft for low C/Ns, the slot noise
will increase more than usual. At very low C/Ns however, we can expect
slot noise to be lower than it would be witi hard limiting. The slot
noise in the baseband of a M/W receiver varies depending on the amount
of limiter action. The baseband noise spectrum for an FM receiver with
rectangular IF and no limiting has not, to th° author's knowledge, been
derived. However, Stumpers and Wang have derived the baseband noise
spectrum for a rectangular IF FM receiver with hard limiting. Their
results indicate that, when compared with the Gaussian IF results for
low carrier to noise ratios, baseband noise falls off more quickly with
increasing baseband frequency and, for the intermediate carrier to noise
ratios, the baseband noise peaks occur at lower baseband frequencies.
The overall shapes of the baseband noise spectra c~e similar.
3.16 Using the results of Middleton, Rice and Stumper's, the slot noise
for hard limiting and no limiting were derived. These results are summarized
on the next page. These values are derived from truncated infinite
43
RELATIVE SLOT MOISt fOWER (MILLIWATTS) _ IELATIVE SLOT NOISE POWER (MILLIWATTS)
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4S
series summation of terms related to the IF characteristic. It is
interesting that for the hard limiting case, the series converged very
slowly. The values given represent 250,000 terms in the series. This
many terms were needed to get the answer accurate to within a couple
of units in the fourth place. These results agree well with the calculated
values of Rice and Stumpers. Although the attempt was made, the slot
noise distribution for no limiting and no carrier present could not
be verified experimentally.
3,17Limiter action also affects the demodulated baseband signal. It
appears that the solution for an arbitrary baseband signal in the presence
of arbitrary limiting has not been solved. Middleton has determined
the effect of soft limiting on the suppression of a baseband test tone.
His results indicate that as limiter action goes soft, a given amount
of signal suppression occurs earlier than it would be with hard limiting.
Another effect he shows is that, as limiting is lost, minor signal sup-
pression occurs at relatively strong RSLs.
46
^ . Experimental Verification
4.1 Having established the basic theoretical characteristics of PM
receivers, a series of experiments were conducted to verify the theory
and investigate effects not easily determined theoretically. In the
experiments, two types of PM receiver were used. One receiver was a
typical state-of-the-art LOS M/W receiver. This receiver was designed
for normal operation with typical RSLs of -30 dBm and little fading.
The characteristics of this receiver are listed on the next two pages.
The IF response data was courtesy of J.R. Hammer, G.L. Cook, and R.J.
Girvin. Unless otherwise mentioned, all data in this report captioned
"LOS M/W Receiver" was taken using this receiver. The other receiver
used was a typical TR0P0 M/W receiver. This receiver was designed to
operate with a nominal RSL of -60 dBm. Due to the fading characteristics
of TROPO RSL, the receiver was designed to operate satisfactorily with
RSLs approaching FM threshold. The characteristics of this receiver
are listed on the following pages. All data in this report captioned
"TROPO M/W Receiver" was taken with this receiver.
4.2 The first experiment was to see if the previous baseband noise
spectrum curves for hard and no limiting could be used to determine
whether or not the limiter in a M/W receiver is limiting. Using a
spectrum analyzer attached to the baseband of the M/W receiver, various
levels of unmodulated RF carrier were applied to the receivers. The
baseband noise spectrum as a function of input carrier to (thermal)
noise (C/N) was photographed for both the LOS and the TROPO M/W receivers.
The photographs (with image color reversed to facilitate reproduction)
are on the next three pages. The noise spectrum was plotted in millivolts
rather than milliwatts. However, since power is just voltage squared,
the millivolt display is just compressed in vertical dimension relative
to a milliwatt display. The shapes of either type of display is identical.
Comparing the photographs with the "Hard Limiting" and "No Limiting"
curves leave little doubt that the LOS M/W receiver has soft limiting
for low C/Ns. However, both receivers have hard limiting for high C/Ns.
4.3 Next, the theoretical quieting curves were compared with actual
quieting curves. This was done by measuring baseband noise with a frequency
selective voltmeter while different unmodulated RF signals were applied
to the M/W receiver. Baseband test tone suppression was also measured
by applying a test tone (of frequency 0.05 times the IF bandwidth) to
the M/W transmitter. The output of the transmitter was applied to the
M/W receiver through an attenuator. Varying the amount of attenuation
allowed various RSLs to be simulated.
4.4 The agreement between theory and experiment was excellent except
for very low C/Ns. As mentioned in the theory section, with no carrier
present at the receiver, the slot noise will be a direct function of
IF limiting. Clearly neither the TROPO nor the LOS receiver is fully
limiting at a -10 dB C/N. However, the TROPO receiver limiting is more
47
4&
Channel Capacity: 600 VF Circuits
Baseband (BB) Range: 60 to 2660 kHz
Receive Carrier Frequency: 5 GHz
De-emphasis: None
Per Channel Deviation: 140 kHz (rms)
Noise Figure: 8.1 dB (overall)
RF to IF Amplification:
Overall Gain: +19 dB
Linear Amplification Range:
- oo to -17 dBm RF Input
1/2 dB Gain Compression:
-16 dBm RF Input
1 dB Gain Compression:
-15 dBm RF Input
IF Amplification:
Maximum Gain: +40 dB
3 dB Bandwidth: 25 MHz
LOS M/W Receiver Characteristics
Table 12
49
-0.5 0.0 +0.5
A
LOS M/W Receiver IF Response
Figure 10
50
Frequency (MHz)
Relative to IF Center Frequency
Channel Capacity: 60 VF Circuits
Baseband (BB) Range: 12 to 252 kHz
Receive Carrier Frequency: 400 MHz
De-emphasis: CCIR
Per Channel Deviation: 100 kHz (rms)
Noise Figure: 1.5 dB (overall)
RF to IF Amplification:
Overall Gain: +40 dB
Linear Amplification Range:
- oo to -50 dBm RF Input
1/M dB Gain Compression:
-40 aBm RF Input
1 dB Gain Compression:
-37 dBm RF Input
5 dB Gain Compression:
-30 dBm RF Input
15 dB Gain Compression:
-20 dB RF Input
IF Amplification:
Maximum Gain: +26 dB
3 dB Bandwidth: 3-09 MHz
TROPO M/W Receiver Characteristics
Table 13
52
IF Noise BW: 3.286 MHz
IF 3 dB BW: 3,087 MHz
\ '
curve - Actual IF Response
Q - Ideal Gaussian Response
I
Vertical: 10 dB/Div.
| Horizontal: 2 MHz/Div.
(
I
I
TROPO M/W Receiver IF Response
Figure 12
€
53
effective (less soft) in the low C/N region. This is indicated by the
TROPO slot noise values being closer to the theoretical curves than
are the LOS noise measurements. This condition was also indicated by
the previous experiment. Slot noise measurements were also taken with
no signal into the M/W receivers. The results are plotted versus theoretical
results on the next page.
4.5 In addition to the quieting curves of the normal receivers, the
experiment was repeated with varying degrees of limiter action. To
reduce the limiting action in the receivers, various degrees of attenuation
(attenuator pads) were placed between the receiver mixer (down converter)
and the input to the IF amplifier. The IF amplifier is a variable gain
amplifier which tries to keep the input level to the limiter section
constant. Placing the attenuation (pad) in front of the IF amplifier
causes the amplifier to increase its gain to compensate for the pad
loss. As attenuation is increased, due to limited gain, the IF amplifier
will be less effective in holding the signal constant into the limiter
section. As the level into the limiter section is reduced, limiting
action is reduced (goes soft). When the pad is placed in the receiver,
not only is limiter action affected but noise figure is also increased.
Compensation was made for changes in noise figure in the graphed data.
Also, the TROPO receiver data has been corrected to delete the frequency
response of the CCIR de-emphasis network.
4.6 Notice in the following curves that as limiter action goes soft,
the noise for very low C/Ns is reduced. However, the noise in the low
frequency baseband slots start to experience additional noise near FM
threshold (approximately +10 dB C/N). For moderate amounts of limiter
degradation, about the only effect on noise in the FM threshold region
is to cause the low slot noise to increase more rapidly than normal.
In extreme cases, however, even high frequency noise slots are affected.
Also, note that the LOS receiver is significantly more sensitive to
pre-IF signal attenuation than is the TROPO receiver. The previous
data has also been plotted relative to the normal configuration data.
This shows the effect of both limiter and overall noise figure degradation.
4.7 Since the data indicated that the limiter of the LOS M/W receiver
was soft at low C/N ratios, a wideband amplifier was placed at the input
to the IF amplifier (the same place the pads had been placed) to drive
the limiter harder for the low C/Ns. The quieting curve was reaccomplished
and, as expected, FM threshold moved to the left and slot noise with
no carrier present was increased. The following two pages compare theoretical
and measured 1 dB FM noise thresholds and 20 dB noise quieting valves.
4.8 Several eourc#» h«v« indicated that if a received FM signal is modulated,
slot noise will increase (relative to slot noise produced by an unmodulated
carrier) near FM threshold. Middleton indicated that the slot noise
would be even greater without limiting. These effects were investigated
by white noise loading the LOS M/W transmitter with a Noise Power Ratio
transmitter connected to the baseband input to the transmitter. The
57
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2 dB io slot noise dB
obtain slot noise in dBm0
TROPO M/W Receiver
f/B
Gaus. normal
IF
0.1
7.9 7.5
0.05
8.8 8.5
0.025
9.6 9.5
0.01
10.4 ,9.5
r Theoretical^
C/N
(dB)
20 dB
pad
40 dB
pad
60 dB
pad
7.5
14.5
12
9.5
15.5
16
9.5
18.5
20
12.5
22.5
22,
Measured
LOS M/W Receiver
C/N
(clB)
f/B
Avg.
IF
30 dB
gain
normal
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pad
20 dB
pad
0.1
7.7
8
7
7.5
11.5
0.05
8 . 7
9
8
10.5
14.5
0.025
9.5
11
10
12.5
15.5
0.01
10,3
,13 __
13
13.5
22.5 i
^Theoretical Measured
FM Noise Threshold
Table 14
72
TROPO M/W Receiver
C/N
(dB)
f/B
Gaus .
IF
normal
20 dB
pad
40 dB
pad
60 dB
pad
0.1
7.2
8.5
9.5
15.5
16
0.05
6.5
9.5
11
18
19
0.025
6. A
9.5
11.5
18.5
19.5
0.01
6.3
t9.5. .
11.5
18.5
19.5 |
I " 1
1 Theoretical
V
Measured
LOS
M/W Receiver
C/N
(dB)
f/B
Avg.
IF
30 dB
gain
normal
10 dB
pad
20 dB
pad
0.1
7.2
10
12.5
18.5
22.5
0.05
6.4
12.5
16.5
24.5
28.5
0.025
6.3
12.5
1?
26.5
31
0.01
6.2
. 13
17
26.5
31.5 ,
Theoretical1 Measured
20 dB Noise Quieting
Table 15
73
modulated RF signal was applied to the LOS receiver using a variable
attenuator. Basic Intrinsic Noise Ratio (BINR) and Noise Power Ratio
(NPR) measurements were taken using a Noise Power Ratio receiver connected
to the baseband of the M/W receiver (See Tant's book for an explanation
of this measurement.). The BINR and NPR measurements were converted
t-o slot noise measurements. Theoretical results were determined by
using Rice's results for white Gaussian noise loading and the Anuff/Lou
formula for required IF bandwidth. The results were calculated for
CCIR loading and a baseband to IF bandwidth ratio of 0.1. The additional
assumption was made that the additional noise due to Gaussian baseband
noise loading was essentially flat spectrum over the radio baseband
and equal to the noise spectral density at zero frequency. The results
are tabulated and graphed on the next pages. The increased slot noise
due to lack of limiting can be observed.
4tg From a theoretical point of view, it has been shown by many sources
that as FM threshold is approached, the baseband noise becomes impulsive
in nharaoter. It is not at all obvious whether or not this would cause
a change in the impulse noise in a narrow baseband slot. In other words,
does the impulse noise in an FDM channel become higher (relative to
the idle channel noise) as FM threshold is approached. This question
was approach<_d experimentally by using a frequency selective voltmeter
to convert the baseband slot noise to a 3-1 kHz channel. To avoid clipping
the noise peaks, the FSV amplifiers were operated at a very low level.
However, the demodulated baseband noise was always held well above the
residual noise In the frequency selective voltmeter The results were
spot checked running the frequency selective voltmeter amplifiers with
10dB more gain. The results were also checked using a differnt type
of frequency selective volumeter as well as an actual frequency division
multiplexer (AN/UCC-iJ). The results were essentially the same in all
cases. The impulse noise was measured using a conventional impulse
noise measuring set. Demodulated slot noise wa3 measured using a noise
measuring .set with no noise weighting. Both devices had IdB bandwidths
wider than 5 kHz. Therefore, the noise measurement bandwidth was always
the 3-1 kHz of the FSV.
4.10 The peak value of an impulse is difficult to define; it is theoreti-
cally infinite. Impulse noise is characterized by excursions of the
total noise instantaneous voltage waveform which are much greater than
the rm3 voltage (average power) level of the noise. The definition
of peak level was defined for purposes of this report as the minimum
dB voltage level above the average power level in the 3-1 kHz noise
slot (for the given C/N) which would yield no indication on the impulse
level measuring set when observed for a period of thirty seconds. The
choice of peak level was arbitrary. If the level had been chosen as
the minimum level which would cause no more than one level indication
every 5 seconds, the peak level measured would have been about 2 dB
lower than the level measured using the above definition. The level
indications were essentially continuous at a level dB lower than the
level measured using the above definition. Reference levels on the
74
C/N
(dB)
0.0
Theoretical
f/B
0.0028 0.05
0.1
Measured
f/B
0.0028 0.05 0.1
“CO
0
0
0
0
0
0
0
0
0.2
0.2
0.2
0.2
0
1
0
+2
0.2
0.2
0.2
0.2
1
1
0
+4
0.4
0.4
0.4
0.3
2
1
1
♦5
0.5
0.5
0.5
0.4
1
1
1
+6
0.6
0.6
0.5
0.4
1
1
0
♦7
0.7
0.7
0.5
0.3
3
2
1
+8
0.8
0.8
0.4
0.1
3
0
0
+9
1.0
1.0
0.2
0
3
0
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♦ 10
1.2
1.1
0
0
3
0
0
♦ 11
1.4
0.7
0
0
3
0
0
♦ 12
1.7
0.1
0
0
4
0
0
+13
1.9
0
0
0
-
-
-
♦ 14
2.3
0
0
0
-
-
-
♦ 15
2.6
0
0
0
-
-
-
Baseband Slot Noise Increase (dB)
due to CCIR Gaussian White Noise
Baseband Loading
Table 16
75
76
Note: Add 1 dB to slot noise dB
value to obtain slot noise in dBm0.
impulse measuring equipment had a minimum step size of 2 dB. This led
to some granularity in the measured results. The experimental results
indicate that impulse noise peak to rms voltage levels in narrow slots
are completely independent of RSL or C/N.
4.11 It will be noticed that the impulse noise peaks were higher in
the lowest frequency slots than in the others. After taking the measure-
ments, the frequency stability of the generator used to simulate the
RSL was checked on a frequency counter. The signal was observed to
Jump around the nominal center frequency as much as 50 KHz. The signal
generator was replaced by the actual microwave transmitter. The actual
microwave transmitter was frequency stabilized and showed no frequency
jitter at a1!. Tne results were checked in the two low frequency base-
band slots. Under these conditions the results were identical to those
of the other slots. It is believed that the unusually high peak noise
readings in the low slots were caused by the frequency jitter of the
CW generator producing occasional high level low frequency noise spikes
(beat products) in the radio baseband.
4.12 The next experiment was to investigate how closely a quieting curve
taken with a typical continuous wave (CW) M/W signal generator compares
with a quieting curve taken with an actual M/W transmitter. The following
page shows the comparison. The M/W transmitter used to make the comparison
had a low power (J watt) output and a high power (5 watts) output.
The high power output was just the low power output amplified by a Traveling
Wave Tube (TWT ) amplifier. The quieting curve was taken separately
using each output as the quieting source. There was no difference in
the quieting curves. This was interesting (but predictable) since TWTs
operating in the frequency range of the LOS receiver ( 5 gHz) have noise
figures of typically 25 dB. When the quieting curves are compared,
it will be noticed that the only significant difference is in the high
C/N region. This is indicative of the frequency noise characteristics
of the two quieting sources.
4.13 Sweeping generators (even in the CW mode) are notorious for their
poor phase/frequency noise performance. Quieting curves were taken
using two different sweeping microwave oscillators (data courtesy of
H.L. Bennetts). Notice the wide range of possible values for slot noise
in the high C/N region when different sources are used. Sweeping generator
B (the up convertor for the HP microwave link analyzer) gave the best
performance of any of the generators tested. In the high C/N region,
its noise performance was as much as 5 dB better than the noise performance
for comparable conditions with the actual microwave transmitter. The
quieting curves illustrate the futility in using a quieting signal gene-
rator of unknown frequency noise performance to evaluate the high C/N
slot noise performance of a M/W receiver. The inherent noise of the
receiver is sometimes less than the noise of the quieting source.
4 . 14 Next , quieting curves were taken using wide slots. The two relatively
narrow bandwidth slots were formed using NPR test set filters. The
77
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Table 17
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Figure 30
Figure 29
Figure 31
80
Figure 29
wide bandwidth slot was formed using the baseband low pass filter in
the M/W receiver itself. The noise was measured using a wide bandwidth
true rms meter. The various slot measurements are plotted by themselves
and also versus the normal narrow slot quieting curves. For comparison
with the quieting curve data, 10 log (filter bandwidth (kHz) / 3>1kHz)
was subtracted from the wide slot data. FM threshold can be determined
for the wide slots by integrating the narrow slot noise formula over
the frequency range of the wide slot. As noted earlier, this leads
to a result which indicates an FM threshold for the widest slot should
occur about one dB earlier than FM threshold for the 2438 kHz narrow
slot. The experimental evidence shows reasonable agreement with that
result.
4.15 After observing the noise characteristics of the M/W receiver,
the next set of experiments observed the baseband signal suppression
characteristics of the M/W receiver. The modulated RF signal was then
applied to the LOS M/W receiver through a variable attenuator. The
test tone suppression as a function of C/N (RSL) was observed using
a frequency selective voltmeter (FSV) at the baseband of the receiver.
Since the noise power in the FSV slot was significant at low C/N ratios,
the actual FSV measurement was test tone plus noise power rather than
just test tone power. To correct for this, a FSV measurement was taken
with the test tone applied to the transmit baseband. Another measurement
(of noise) was made with the test tone removed from the baseband. By
subtracting the noise power (in milliwatts) from the test tone plus
noise (in milliwatts) the FSV measurements were corrected for the effects
of noise. The test tone levels used were less than normal CCXR loading
to avoid introducing significant increases in receiver slot noise due
to the modulation of the received signal.
4.16 The first experiment was to observe signal suppression at three
baseband frequencies. The three frequencies were 0.0028, 0.05, and
0.1 times the IF bandwidth. The 0.05 frequency had the least suppression
of any of the baseband test tone frequencies. The performance of the
other test tones relative to the performance of the 0.05 test tone has
been tabulated on the next page.
4.17 The next experiment was to observe signal suppression as a function
of baseband loading. Using an NPR test set white noise generator, CCIR
recommended values of white noise loading were applied to the transmitter
baseband to simulate normal baseband loading. Using the NPR test set
bandstop filters, noise was suppressed at three different frequencies.
Test ton** were placed in the transmitter baseband at those frequencies.
The test tone suppression was measured with no white noise loading and
was then measured with full noise loading. The difference in the baseband
suppression for the two conditions is shown in Tsbls 18*
4.18 Next, the baseband test tone suppression values obtained during
the previous experiments is plotted on an expanded vertical scale.
81
♦80
o
to
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o
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o
e
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TJ
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Figure 33
83
See note. Figure 28
C/N
(dB) f/B
0.0028 0.1
-3 -0.5 -0.6
-2 -0.9 -0.7
-1 -0.5 -0.9
0 -0.8 -1.0
♦ 1 0.0 -0.6
+ 2 -0.8 -0.8
♦3 -0.3 -0.6
Baseband Signal Suppression (dB) at High
and Low Baseband Frequencies Relative to
Signal Suppression at the Middle
Baseband (reference test tone at
ized baseband frequency of f/B «
of the
normal -
0.05)
C/N
(dB)
f/B
0.0028
0.05
0.1
-3
0.0
0.0
0.0
-2
0.0
0.0
0.0
-1
0.0
-0.5
0.0
0
0.0
-0.4
0.0
♦ 1
0.0
-1.0
0.0
♦ 7
0.0
0.0
0.0
♦ 3
0.0
0.0
0.0
Baseband Signal Suppression (dB) with
CCIR Gaussian White Noise Baseband
Loading Relative to Signal Suppression
with no Baseband Noise Loading
Table 18
84
The graphs on the next two pages show the effect of changes in limiter
action. The C/N values have been corrected to compensate for changes
in receiver noise figure due to the introduction of prelF attenuation.
Note that as limiter action goes soft, baseband suppression starts at
earlier C/N values. Also, notice that the LOS receiver is much more
sensitive to prelF signal loss than is the TROPO receiver.
4.19 In elementary developments of the theoretical noise of FM receivers,
one of the assumptions is that the received signal is centered in the
passband of the receiver. The frequency response of the passband is
also assumed to be symmetric about the carrier frequency. The unmodulated
receive carrier signal was deliberately tuned to one side of the receiver's
IF response and quieting curves were accomplished. Data was taken in
the 2438, 1248, and 70 kHz slots and is graphed on the next page. The
data reflects an extreme violation of the previous assumptions. It
can be anticipated that receiver idle noise performance will be degraded
if the received signal is not centered in the receiver's (IF) passband
response or if the receiver's (IF) passband frequency response is unsymmetric
relative to center frequency.
4.20 Most theoretical developments of receiver signal and noise performance
assume that the noise in the receiver is strictly thermal. The noise
power is assumed to be spread equally across the bandpass response of
the receiver. This is not always the case in practice. The most elementary
form of nonthermal noise is sine wave interference.
4.21 The next few graphs show the signal and noise characteristics of
an FM M/W receiv' ' for different levels and frequencies of unmodulated
carrier interfei ence . The baseband test tone signal frequency was 0.05
times the receiver IF bandwidth. The tests were run by mixing the outputs
of the unmodulated M/W transmitter and a CW signal generator. The composite
signal was applied to the input of the M/W receiver. Separate attenuators
allowed the outputs of the two signal sources to be varied independently,,.
The output of the M/W transmitter was considered the carrier and the
output of the CW generator was called the interference. The carrier
source was tuned to the center frequency of the receiver. Results were
obtained with the interference tuned to two different frequencies.
For one set of data, the interfering signal was tuned to a frequency
differing by i MHz from the receiver center frequency. This frequency
offset was chosen so that the interfering signal would be near the carrier
frequency, but none of the beat products caused by crossmodulation products
(beat products) in the receive baseband (due to the two RF input signals)
would fall into the noise measurement slot skirts. Also, the large
increase in baseband noise when two RF carriers have essentially the
same frequency, but randomly varying relative phase was avoided. The
other set of data was taken with the Interfering signal offset 10 mHz
from the receiver center frequency. This put the interfering signal
at the edge of the receiver's IF passband. Although the interfering
signal with the larger frequency offset caused more baseband noise,
a spectrum analyzer sweep of the radio baseband would not have shown
85
86
sc <u
■H i-l
C/5
Figure 35
87
08+ OL+ 09* OS* Ofr* 0£* 8P OZ* N/D 01* 0 01- Oi- 0£*
FM NOISE QUIETING CURVES
LOS M/W Receiver
88
See note, Figure 28
the beat product since it would appear at a frequency much higher than
the cutoff frequency of the receiver baseband low pass filter.
4.22 The first set of graphs were taken by holding the interfering signal
power at -60 dBm. When the C/I ratio approaches +10 dB, the signal
and noise properties become noticeably affected. Of course, if baseband
slot noise had been observed at integer multiples of the frequency difference
between the carrier and interference, the noise increase would have
been more distinct and would have been noticed at much larger C/I ratios.
The capture effect of the receiver is dramatic as it starts to quiet
on the interference rather than the carrier. The second set of graphs
were taken with the interfering signal level held at -90 dBm. The third
set of graphs were taken with the interference level varied with carrier
level variation so that the interference was always 10 dB less than
the carrier level. Notice that in all cases the slot noise was noticeably
higher and baseband signal suppression earlier for signals farther away
from the center of the receiver IF response.
4.23 The last set of interference data was taken by holding the interfering
signal power constant but varying its frequency relative to receiver
center frequency. The receiver had an RF filter as well as an IF filter.
The RF filter frequency response was broad enough that, for the interfering
signal frequencies used for this test, the frequency selectivity charac-
teristics of the receiver can be assumed to be entirely due to the IF
frequency response of the receiver. Clearly the noise process is complex
and a function not only of C/1 and interference frequency offset but
also baseband noise slot frequency.
4.24 It should not be assumed that the performance of all FM receivers
is the same. To constrast the previous results, tests were performed
on another LOS M/W receiver. It's nominal equipment characteristics
were quite similar to the characteristics of the LOS M/W receiver used
to perform the previous experiments. A quieting curve for the receiver
is given on the following page. Note the abnormally high noise in the
low frequency noise slots. Also, note the kink in the curves near the
-80 dBm RSL. During the experiment it was noted that the noise measure-
ments in this region were unusually erratic. Although it is difficult
to see on the quieting curve, two of the low frequency noise slots
actually cross each other, a theoretical impossibility.
4.25 The next page shows spectrum analyzer photographs of the baseband
noise spectrum for various RSLs. A comparison with the corresponding
photos for the other LOS receiver shows considerable difference. The
center photograph highlights the noise instability for RSLs near the
kinks in the quieting curve. Notice the crisscrossing of the baseband
spectrum. When this photo was taken, the noise measurements were so
unstable that the same picture could never be reproduced. Every trace
of the spectrum analyzer prruuced a radically different picture. This
was considerably different tnan the case for the LOS receiver used in
89
the rest of the test for this report. Results taken with the AN/FRC- '
157 receiver were repeatable day after day. The results taken on the
other receiver changed from moment to moment. Not even the baseband
suppression characteristics remained constant for the other LOS receiver.
The results of tests conducted at two different tiroes are shown on the
following page.
4.26 The FM quieting curve is a sensitive indicator of noise performance
of an FM M/W terminal. The following quieting curves were taken of
FM M/W receivers in actual operational environments. Although it is
not always clear what the problem is, the quieting curves do show that
there obviously undesirable conditions at the radio terminal. Occasionally
the quieting curves also shows measurement error and measurement equipment
problems.
90
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Figure 38
92
Figure 28
Figure 39
93
Figure 28
94
See note. Figure 28
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4
Slot Frequency
f/B-0.1
02.5 MHz)
Slot Frequency
f/B-0.05
(f-1.25 MHz)
C/1 - + 10
C/1- 0
C/I - -10
C/1 - -20
C/1 - -30
C/I - -40
i C/I - -50
I — , — ^ — T I , — j— ( 1 \ 1 — — I 1
\ T j 0 dB noise reference \. /
V Ji / is slot noise with
I no interfering carrier. 11^
Vertical Scale : Slot Noise Horizontal Scale : ’ Tiffset
(10 dB/div., + above line) (10 MHz/Plv./
Intersection of lines is zero on both scales.
LOS M/W Receiver
Quitting Carrier Power (C) -60 dBm
Interfering Carrier Power (I) Variable
(Beat products neglected on right hand plots.)
Baseband Slot Noise Va Interfering Carrier Frequency and Power
Figure 43
97
LOS M/W Receiver
no de-emphasis
Vertical: mV
Horizontal: 5 MHz/Div.
(0 to 50 MHz)
Vertical: mV
Horizontal: 200 kHz/Div
(0 to 2 MHz)
Note: This LOS M/W
receiver is not the
one used i; ;he rest
of this report.
Vertical: mV
Horizontal: 500 kHz/Div.
C 0 to 5 MHz)
Baseband Noise Spectrum
for Various RSLs
100
-30 -20 -10 0 +10 RSI +20 dB +30 +40 +50 +60 +70 +80
FM RECEIVER NOISE Of iETING AGO OR I GNAL.
AND IF LIMITING DATA
RECEIVER INPUT RF SIGNAL LEVEL (RSL) - dBm
Sample Noise Quieting Curve
Figure 48
102
SIGNAL LEVEL (RSL) ( - dbm )
Sample Noise Quieting Curve
Figure 49
103
Sample Noise Quieting Curve
Figure 50
104
SIGNAL LEVEL (RSL) (-dbm)
DATA SHEET B . fk ACC & FM C .INC CURVES **cc
Sample Noise Quieting Curve
Figure 51
105
dtu)
Sample Noise Quieting Curve
Figure 53
107
DATA SHEET t-*V ACC • FM QUIETING CUEVES
Sample Noise Quieting Curve
Figure 54
108
'HWT Vf Sjc.ka irv‘i .
5. Predicting FM M/W Terminal Thermal Noise Performance
Symbols Used on the Following Pages:
RSL = reoelved signal level (dBm) into receiver
NF= overall noise figure of receiver (dB) measured at the same place
at which RSL is measured
BTt?= 3 dB bandwidth of the receiver IF
lr
f = baseband frequency of the center of the narrow slot used (by a frequency
selective voltmeter) to measure receiver baseband noise
f/B = f/BT[? (with f and BTI? converted to same units (e.g., kHz or MHz))
lr lr
= baseband slot frequency compared (normalized or ratioed) to the
receiver IF bandwidth
H = IF frequency response (dB) at IF center frequency plus or minus
baseband slot frequency (f) minus IF frequency response (dB) at
IF center frequency
= normalized IF response of the receiver which shapes the receiver
thermal noise
= normalized thermal noise in a narrow slot at output of IF
h = normalized IF response of receiver (PR)
= antilog (H/ 10) = 10 H/1°
ftnax = maximum baseband frequency (excluding baseband pilots)
C/N = carrier to noise ratio (dB)
=power level of received signal compared to total noise power of
receiver’s internally generated thermal noise which appears at
the discriminator
p = carrier to noise ratio (PR)
= antilog ( (C/N)/ 10) = 10
(C/N)/ 10
f = baseband pivot frequency for the emphasis network
S = baseband test tone signal power level (dBm0) at the receiver
S = baseband test tone signal power level (dBm0) at the transmitter
Xj
109
N = noise power (dBm0) in a 3.1 kHz slot located at a center frequency
f in the receiver baseband
No = noise power (dBm0) in a 3-1 KHz slot located at a very low (approxi-
mately DC) receiver baseband frequency when no carrier is applied
to the input of the receiver
P = baseband pre-emphasis (dB) relative to baseband pivot frequency
Pp = baseband pre-emphasis (dB) at baseband pivot frequency relative
to baseband gain (dB) at pivot frequency with pre-emphasis strapped
out of the baseband circuitry
X = emphasis fime constant
Af, , = per channel rms deviation (kHz)
/ch rms
= rms deviation caused by a 0 dBm0 sine wave test tone (at
baseband pivot frequency jf emphasis is used)
PR = power ratio (e.g., milliwatts/milliwatts)
dB = 10 log (PR)
dBm0 = see next page
dBm = 10 log (power in milliwatts)
TLP = see next page
log (x) = common (Bragg's or base 10) logarithm of the number x
ir = pi « 3. 1416
e = base of natural (Naperian) logarithms = 2.7183
Noise Power Normalization:
5,1 In the pages which follow, all power levels will be given in arti-
ficial dBm0 values. The desirability of the dBm0 values is that they
allow direct comparison of different equipment. In communication systems,
power is often measured in absolute power referenced to one milliwatt.
This unit is the dBm. To convert from dBm0 to dBm values and vice versa,
use the following formulas:
dBra0 = dBm - TLP(dB)
dBm = dBra0 + TLP(dB)
no
where TLP is the Transmission Level Point in dB associated with the
test point at which the measurement is made.
Receiver Baseband Signal Level:
S(dBm0) = St(dBm0) + 20 log (1.0 - e'P)
C/N(dB) = RSL(dBm) + 114.0 - NF(dB) - 10 log BIp(MHz)
P(PR) = antilog ( ( C/N )/ 10) = 10
( C/N ) / 1 0
Receiver Baseband Noise in 3*1 KHz slot:
For C/N less than -10 dB:
N(dBm0) = No + (IF) - 4.34p
where the "IF" factor is obtained from the graph on the following page.
The formula is listed below for certain values of f/B. The value of
No is obtained using the appropriate formula listed below.
Rectangular IF
f/B - 0.0
N(dBm0)
=
No
- 4.34p
max.
error
= 0.23dB
f/B = 0.1
N(dBm0)
=
No
- 0.71 -
4.34p
max.
error
= 0.17dB
f/B = 0.2
N(dBm0)
=
No
- 1.43 -
4.34p
max.
error
= 0.06dB
f/B = 0.3
N(dBm0)
=
No
- 2.15 -
4.34p
max.
error
= 0. 12dB
f/B = 0.4
N(dBm0)
=
No
- 2.86 -
4.34p
max.
error
= 0. 39dB
f/B = 0.5
N(dBm0)
=
No
- 3.54 -
4 . 34o
max.
error
= 0.74dB
No(dBm0) = +29
.76 - 20
l0® Af7ch rms
(kHz) + 10 log Bjf(MHz)
Gaussian IF:
f/B = 0.0
N(dBm0)
=
No
- 4 . 34 p
max error =
0. 12dB
f/B = 0.1
N(dBm0)
=
No
- 0.03 -
4.34p
max.
error
= 0.1 IdB
f/B = 0.2
N(dBm0)
=
No
- 0.14 -
4.34p
max .
error
= 0.06dB
f/B = 0.3
N(dBra0)
=
No
- 0.31 -
4 . p4p
max.
error
= O.OOdB
f/B =0.4
N(dBm0)
=
No
- 0.54 -
4.34p
max .
error
= 0.07dB
111
f/B = 0.5
N(dBm0) = No - 0.83 - 4.34p max. error = 0.l8dB
No(dBm0) = +29.51 - 20 log Af. . (kHz) + 10 log BTt,(MHz)
/ch rms Ir
Averaged IF:
f/3 = 0.0 N(dBm0) = No - 4.34p max. error = 0.l8dB
f/B = 0.1 N(dBm0) = No - 0.37 - 4.34p max. error = 0.l4dB
f/B = 0.2 N(dBm0) = No - 0.79 - 4.34p max. error = 0.06dB
f/B = 0.3 N(dBm0) - No - 1.23 - 4.34p max. error = 0.06dB
f/B = 0.4 N(dBm0) = No - 1.70 - 4.34p max. error = 0.23dB
f/B = 0.5 N(dBm0) = No - 2.19 - 4.34p max. error = 0.46dB
No(dBm0) = +29.64 - 20 log Af/ch rmg(kHz) + 10 log BIp(MHz)
Note: The appropriate pre-emphasis value must be subtracted from the
above values If the terminal uses emphasis.
For C/N between -10 dB and +5 dB:
N(dBm0) = No + (A) + (D)p r (C)p2
where the ''A", "B", and "C" factors are obtained from the graphs on
the following pages. The value of No is obtained using the appropriate
formula listed below.
I Rectangular- IF:
f/B = 0.0 N(dBm0) = No - 0.22 - 7.284p + 0.722p2 max. error = 0.35 dB
f/B = 0.1 N(dBra0) = No - 1.03 - 6.600p + 0.738p2 max. error = 0.37dB
f/B = 0.2 N(dBm0) = No - 1.91 - 5.036p + 0.606p2 max. error = 0.48dB
f/B = 0.3 N(dBra0) = No - 2.65 - 3-326p + 0.390p2 max. error = 0.52dB
f/B = 0.4 N(dBm0) = No - 3-26 - 1.287o + 0.01 Ip2 max. error = 0.49dB
f/B = 0.5 N(dBra0) = No - 3-63 + 0.399p - 0.319p2 max. error = 0.50dB
J No(dBm0)= +29.76 - 20 log Af/(jh rmg(kHz) + 10 log BIp(MHz)
112
Gaussian IF:
f/B =0.0 N(dBm0)
f/B = 0.1 N(dBm0;
f/B = 0.2 N(dBra0)
f/B = 0.3 N(dBm0)
f/B = 0.4 N(dBm0)
f/B = 0.5 N(dBra0)
No(dBm0) = +29.51 - 20
Averaged IF:
f/B = 0.0 N(dBm0)
f/B = 0.1 N(dBra0)
f/B = 0.2 N(dBm0)
f/B =0.3 N(dBm0)
f/B = 0.4 N(dBm0)
f/B = 0.5 N(dBm0)
No(dBm0) = +29.64 - 20
= No + 0.03 - 5.588p
= No - 0.01 - 5. 440p
= No - 0.13 - 4.91 Ip
= No - 0.33 - 4.l63p
= No - 0.57 - 3.478p
= No - 0.83 - 2.973P
log Af , . (kHz) +
6 /oh rms
+ 0.326p2
+ 0.392p2
+ 0.438p2
+ 0. 391p2
+ 0.307p2
+ 0.227p2
10 log Bip
max. error
max. error
max. error
max . error
max. error
max . error
(MHz)
0.04dB
0 04dB
0.03dB
0.05dB
0.05dB
0.06dB
= No - 0.10 - 6.426p
= No - 0.52 - 6.01 4p
= No - 1.02- 4.969P
= No - 1.49 - 3.743P
= No - 1.92 - 2. 379p
= No - 2.24 - 1.282p
log Af , . (kHz) +
/on rms
+ 0.521p2
+ 0.564p2
+ 0.521p2
+ 0. 390p2
+ 0. 1 58p2
- 0.047p2
10 leg BIp
max . error
max . error
max . error
max . error
max. error
max. error
(MHz)
0.17dB
0. l8dB
0.23dB
0.26dB
0.26dB
0.26dB
Note: The appropriate pre-emphasis va)ue must be subtracted from the
above values if the terminal uses emphasis.
i.' Due to the computational difficulties involved in obtaining exact
results for low C/Ns, the preceeding results were obtained by fitting
polynomial curves to the results of Stumpers and Rice. The maximum
error in the preceeding results is graphed on the following page.
For C/N greater than + 5dB:
Rectangular IF:
N(dBm0) = -139.0
20 log Af/ch rms(kHz) - RSL(dBm) + NF(dB)
PUB)
+ 10 log/r(kHz) + (0.32575)|VF
(kHz)
113
Gaussian IF:
N(dBm0) = -139.2 - 20 log Af, . (kHz) - RSL(dBm) + NF(dB) - P(dB)
2 /ch rms
+ 10 logf4-7r(f/B) f2(kHz) + (0.450.’ 9)f” " 2/
4P BIpT (kHz)
Averaged IF:
N(dBm0) = -139.1 - 20 log Af
/ch rms
(kHz) - RSL(dBm) + NF(dB) - P(db)
+10 log/h f (kHz) + (0.38797)
V? BIp2(kHz)
for the above formulas
C/N(dB) = RSL(dBm) + 114.0 - NF(dB) - 10 log BIp(MHz)
p = antilog ( (C/NJ/10)
Note: The above formulas do not include baseband phase/frequency noise
associated with the transmitted carrier. This noise will dominate at
very high C/N ratios.
The following special cases apply when the FM receiver is operating
above FM (1 dB noise) threshold (C/N +13 dB) but with a low enough
RSL that transmit phase/frequency noise is not significant.
Noise in 3-1 kHz noise slot:
N(dBm0) = -139.1 + 20 log f(kHz) + NF(dB) - P(dB)
-20 log Af/(jh rms(kHz) - RSL (dBm)
Noise in arbitrary width 3lot (no de-emphasis, sharp cutoff bandpass filter)
N(dBm0) = -148.7 + 10 log (ffllax(kHz) - ffllin(kHz))
+ NF(dB) - 20 log Af. . (kHz) - RSL(dBm)
/ch rms
Noise in entire baseband (no de-emphasis, sharp cutoff low pass baseband
filter) :
N(dlim0) = -148.7 + 30 log fmax(kHz) + NF(dB)
-20 log Af/ch rms(kHz) - RSL (dBm)
114
B" Factor
Noise Equations Factors
Figure 54.1
:ont. )
16
-10 dB®* c/n*z +5dB
Nolt* Equation* Error Analysis
Figure 54.2
117
Note that although noise in a narrow noise slot increases with the square
of the slot frequency, total baseband noise increases with the cube
of the upper baseband limit.
FM One dB Noise Threshold:
Narrow Noise Slots:
Rectangular IF:
eG/n (f/B)2 = (1.2580) (c/n)*
Gaussian IF:
ec/n (f/B)2 = (1.7386) e+1T(f/B) (e/n)*
Wide Noise Slots:
Rectangular IF:
eC/n ( ( f/B) 3max - (f/B)3min) = (3.7741) (c/n)* ((f/B)max - (f/B)min)
Gaussian IF:
eG/n(((f/B)3max - (f/B)nlin) - (1.8849) ( (f/B)Sax - (f/B)Sin)
+ (2.1149) ( (f/B)Zax - (f/B)iin) - (1.7225) ( (f/B)Jax - (f/B)9min)
+ (1.1069) ( (f/B)1max-(f/B)1min)) = (5.2158) (c/n)* ( (f/B)max - (f/B)min)
Where the symbols are as previously defined with
c/n = carrier to noi3e power ratio = antilog ( (C/N)/10)
f/B = baseband slot frequency/IF bandwidth
(f/B)max = highest slot frequency/IF bandwidth
(f/B)min = lowest slot frequency/IF bandwidth
Of the last four formulas, the first three are essentially exact. The
fourth is based on a truncated MacLaurin series expansion of e . Maximum
error due to this approximation is 0.5J at f/B = 0.5. The error is con-
siderably less for smaller f/B values.
118
6. Baseband Signal and Slot Noisr Versus RSL Using Generalized Charts
6.1 Although quieting curves can be predicted using the preceeding
formulas, the process is cumbersome. To facilitate quieting curve
prediction normalized charts have seen produced based on various FM
receiver IF characteristics. To predict the FM noise quieting curve
for an FM receiver, a normalized quieting curve can be chosen based
on the FM receiver's IF characteristic. If the FM receiver's IF response
is unknown, the averaged IF response curve is suggested as a choice.
The normalized dB values for slot noise and carrier to noise ratio (C/N)
can be converted to dBm0 and dBm values respectively using the following
procedures.
6.2 The slot noise measured by the frequency selective voltmeter (FSV)
is plotted on the vertical scale. The noise corresponding to 0 dB on
the slot noise scale is determined from the following formulas:
N(dBm0) = +29.6 - 20 log £f . . (kHz) + 10 log BT_(MHz) + CF(dB)
i ch rms ir
CF(dB) = 10 log f 3dB bandwidth of FSV(kHz) \
\ 3.1 kHz /
= correction factor to allow for actual noise measurement
bandwidth (tabulated on next page).
6.3 Use of the correction factor CF produces the dBm0 noise values
whicn will be read by the FSV.
6.4 The actual RSL is plotted on the horizontal scale. The RSL corresponding
to 0 dB on the C/N scale is found from the following formulas:
RSL (dBm) = -114.0 + NF(dB) + 10 log BIp(MHz)
6.5 The slot noise is obtained for a given RSL by going up vertically
from the RSL to the appropriate (f/B) line. From this line, go to the
left horizontally and read noise from dBm0 scale.
6.6 The appropriate (f/B) valve is found by dividing the baseband slot
frequency (frequency to which FSV is tuned) f (in kHz) by the receiver
IF bandwidth (in kHz).
(f/B) = Baseband slot frequency (kHz)
IF bandwidth (kHz)
6.7 If the desired (f/B) valve is between the (f/B) valves listed on
the curves, read the slot noise N for the (f/B) value which is closer
to the desired (f/B) value and add the following correction factor to
the noise valve read from the graph. Theoretical FM noise threshold
has been indicated on the graphs by short vertical lines.
119
I
Theoretical FM Noise Quieting Curves
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Table 19
123
(Uniformly distributed noise power assumed)
N = 20 log/ (f/B) desired \
c v (f/B) from graph )
6.8 To evaluate wideband FM receiver performance, it is desirable to
measure receiver noise quieting in at least three noise slots. To
facilitate later comparison with Basic Intrinsic Noise Ratio (BINR)
and Noise Power Ratio (NPR) measurements taken with the same receiver,
it is recommended that quieting curves be taken at the same slot frequencies
as those used for BINR/NPR measurements. Recommended frequencies are
listed on the following page. The listed frequencies were chosen to
conform to current CCIR recommendations and the recommendations of Ta.it.
If there war* a conflict, the CCIR value* war* chosen.
6tq As an example, consider finding slot noise for an RSL corresponding
to a +35 dB C/N. Refer to the following graph. Assume the (f/B) desired
value is (0.0706) .
N(f/B = 0.1) = - 50.0dB
N( f/B = 0.0706) = N(f/B = 0.1) + 20 log 0.0706
0.1
= -50.0 + (-3.0) = - 53-OdB
Alternately
N( f/B = 0.05) = - 56 . OdB
N( f/B = 0.0705) = N( f/B = 0.05) + 20 log 0-C706
0.05
= -56.0 + (3.0) = - 53.0 dB
6.10 The baseband signal level is a function of RSL near FM threshold.
The signal level is found by reading the correction factor from
the slot noise (dB) scale on the graph on the next page. The level
(disregarding noise) of the received baseband signal S is found by using
the following formula:
S(dBra0) = St(dBm0) + Scp(dB)
6.11 For example, at an RSi. corresponding to OdB C/N, the signal level
will have dropped 4 dB (S= S^-4 dB).
6.12 If the receiver being tested has de-emphasj.3, the slot noise power
read from the graphs must be modified by the effect of the de-emphasis
networks. To determine the actual noise measured by the FSV after the
noise has passed through the de-emphasis networks, subtract (algebraicly)
124
Number of
Channels
12
Baseband
Frequencies
(kHz)
12-60
Slot Frequencies
(kHz)
27 40 56
24
12-108
40
70
105
36
12-156
40
70
105
48
12-204
40
105
185
•60-252
70
185
245*
60
12-252
40
185
245
60-300
70
185
270
72
*12-300
40
185
270*
120
60-552
70
270
534
132
•12-552
4 o'
270
534*
240
60-1052
70
534
1002
300
60-1300
70
534
1248
420
*60-1796
70
534
1248*
600
60-2660
70
1248
2438
900
316-4188
534
2438
3886
960
60-4028
70
2438
3886
O
o
316-5564
534
3886
5340
1260
*60-5564
70
3886
5340*
*60-5636
70
3886
5340*
1800
316-8204
534
3886
7600
2400
•316-11404
534
3886
7600*
2700
316-12388
534
3886
11700
Recommendations conform to CCIR NPR/BINR slot frequencies.
* No CCIR recommendations available for these basebands. *
Recommended Quieting Curve Slot Frequencies
Table 20
125
the pre-emphasis effect (dB) for the slot frequency of interest f relative
to the baseband pivot frequency. The formulas for the pre-emphasis
effect valves for the various types of pre-emphasis networks are listed
on the following pages. For CCIR and EIA emphasis networks, the pre-
emphasis valve may be read directly from the following table.
General Pre-emphasis Networks:
CCIR:
P(dB) = 10 log (+0.400 + 1.20 (f/fmax)2 + 0.801 (f/fmax)14
+ 1.03 (f/frnax)6 - 0.913 (f/fmax)8)
Pp(dB) = 0.0 dB
fp = (0.608) fmax
EIA:
P(dB) = 10 log (0.250 + 2.25 (f/fmax)2)
Pp(dB) = 0.0 dB
fp= (0.577) fmax
Time Constant:
P(dP) = 10 log (1.0 + 39.48 T2f2) - 10 log (1.0 + 13.16 X2fmax2)
Pp(dB) s 10 log (1.0 + 13.l6t2fmax2)
fp = (0.577) fmax
T = time constant (yusec)
f = baseband frequency (kHz)
fmax = maximum baseband frequency (kHz)
REL Pre-emphasis Networks:
72 channel system:
(12 to 300 KHz baseband)
P(dB) = 10 log (0.1743 + 2.477 (f/fmax) 2)
Pp(dB) = +7.58
128
fp = (0.577) fmax = 173 kHz
132 channel system:
(12 to 552 kHz baseband)
P(dB) = 10 log (0.1456 + 2.563 (f/fmax)2)
Pp(dB) = +8.37
fp = (0.577 fmax) = 319 kHz
252 channel system
(12 to 1052 KHz baseband)
P(dB) = 10 log (0. 160 + 2.520 (f/fmax)2)
Pp(dB) = +7.95
fp = (0.577) fmax = 607 kHz
Limitations
6.13 The previous sections have indicated the slot noise produced at
the baseband of an FM receiver due to the FM demodulation noise process.
The implicit assumption was that the demodulator output was only proportional,
regardless of C/N, to the time derivative of the phase of the composite
received signal plus noise waveform. It was also assumed that the total
noise power N (producing the C/N) is due to the thermal noise passing
through the IF amplifier and will be applied, without further bandlimiting,
to the FM demodulator. These assumptions are quite reasonable for conven-
tional FM demodulator with hard limiting. However, the assumptions
do not hold for FM demodulators with feedback (FMFB) and phase-locked
loop (PLL) demodulators.
6. 14 Receivers employing FMFB or PLL FM demodulators have exactly the
same noise characteristics in regions C and D as any comparable conven-
tional FM receiver. However, the FMFB and PLL receivers have improved
FM noise threshold performance. The C/N at which FM threshold occurs
can not be readily generalized. However, Schwartz suggests a simplification
for wideband FMFB receivers which implies a maximum attainable FM threshold
improvement of 7 dB for a receiver with maximum baseband frequency to
IF bandwidth ratio of 0.1 (f/B = 0.1) relative to conventional FM demodulation.
6.15 The noise performance of an FMFB or PLL receiver in regions A and
B is difficult to analyze. It involves not only analysis of the FM
noise process, but also analysis of the loop dynamico of the FMFB or
PLL demodulators under nonlinear conditions. This problem is formidable.
Enloe mentions that as of 1962 the problem had not been solved.
129
f/f
max
0.
0.025
0.050
0.075
0.100
0.125
0.150
0. 1 75
0.200
0.225
0.250
0.275
0.300
0.325
0.350
0.375
0.400
0.425
0.450
0.475
0.500
0.525
0.550
0.575
0.600
0.625
0.650
0.675
0.700
0.725
0.750
0.775
0.800
0.825
0.850
0.875
0.900
0.925
0.950
0.975
1.000
CCIR
(dB)
-3.98
-3.98
-3.95
-3.9!
-3.86
-3.78
-3.70
-3.60
-3.48
-3.35
-3.2!
-3.05
-2.89
-2.7 i
-2.52
-2.32
-2. I 1
-1 .89
-I .66
-! .43
-1 .19
-0.93
-0.68
-0.42
-0.15
0.12
0.40
0.68
0.96
! .24
1 .52
! .79
2.07
2.34
2.6!
2.86
3.12
3.36
3.59
3.80
4.01
EIA
(dB)
-6.00
-5.98
-5.9!
-5.79
-5.63
-5.43
-5.20
-4.95
-4.67
-4.37
-4.06
-3.75
-3.43
-3.10
-2.77
-2.45
-2.13
-I .81
-I .50
-1.19
-0.88
-0.59
-0.29
-0.01
0.27
0.55
0.81
1 .07
1 .33
1 .58
1 .82
2.06
2.30
2.53
2.75
2.97
3.18
3.39
3.60
3.80
4.00
CCIR/EIA Pre-emphasis Values
(change dB sign for de-emphasis value)
Table 21
130
1
f/f
72 Ch.
132 Ch.
252 Ch
max
(dB)
(dB)
(dB)
0.
-7.59
-8.37
-7.96
0.025
-7.55
-8.32
-7.92
0.050
-7.44
-8.18
-7.79
0.075
-7.25
-7.96
-7.59
0.100
-7.0!
-7.66
-7.32
0.125
-6.72
-7.31
-7.00
0.150
-6.38
-6.92
-6.64
0.175
-6.02
-6.50
-6.25
0.200
-5.63
-6.05
-5.84
0.225
-5.23
-5.60
-5.41
0.250
-4.83
-5.15
-4.98
0.275
-4.42
-4.69
-4.55
0.300
-4.01
-4.25
-4. 1 3
0.325
-3.61
-3.81
-3.70
0.350
-3.21
-3.38
-3.29
0.375
-2.82
-2.96
-2.89
0.400
-2.44
-2.55
-2.49
0.425
-2.06
-2.16
-2. 1 1
0.450
-1.70
-1.77
-1.74
0.475
-1.35
-1 .40
-1 .38
0.500
-1.00
-1 .04
-1 .02
0.525
-0.67
-0.70
-0,68
0.550
-0.35
-0.36
-0,35
0.575
-0.03
-0.03
-0.03
0.600
0.28
0.29
0.28
0.625
0.58
0.59
0.59
0.650
0.87
0.89
0.88
0.675
1.15
1.18
1.17
0.700
1 .42
1 .47
1 .45
0.725
1 .69
1 .74
1.72
0.750
1.95
2.01
1 .98
0.775
2.2 1
2.27
2.24
0.800
2.45
2.52
2.49
0.825
2.70
2.76
2.73
0.850
2.93
3.00
2.97
0.875
3.1 6
3.24
3.20
O.VOO
3.39
3.47
3.43
0.925
3.6!
3.69
3.65
0.950
3.82
3.91
3.86
0.975
4.03
4.12
4.07
1 .000
4.23
4.33
4.28
REL Pre-emphasis Values
(change dB sign for de-emphasis value)
Table 21.1
131
6. 16 In general, the analysis developed in the previous sections of
this report will describe the noise performance of FMFB and PLL demodu-
lators in regions C and D. The theoretical FM threshold C/N values
will be pessimistic and the theoretical slot noise for regions A and
B do not apply for FMFB or PLL demodulator receivers.
Combiner Improvement
6. 17 To this point, microwave receiver noise performance has only been
considered for a single receiver. An actual microwave terminal normally
will have two or more receivers with the capability to contribute to
the baseband output of the terminal. The outputs of the various individual
receivers are added (combined) to produce a baseband signal which, if
the combiner functions properly, will have superior signal to noise
performance when compared to the performance of a single receiver.
If the combiners do not function properly, baseband signal level sta-
bility and impulse noise performance can be seriously degraded. In
general, three types of combining are used: switching (selection),
equal gain, and maximal ratio (ratio squared) gain. The effect of
combiners is a complicated subject. As Brennan mentions, the relative
performance of combiners depends on the type of RSL fading the microwave
terminal experiences. There are, however, two cases of special interest.
The idealized situation for a LOS terminal is for all receivers to see
a constant, unfading RSL which is the same power level at all receivers.
For post-detection (baseband) combining, the selection combiner will
give no improvement over a single receiver. The equal gain and variable
gain combiners will have exactly the same signal to noise improvement.
In either case, the improvement will be ten tiu.es the common logarithm
of the number of receivers used for combining. Unfortunately, this
Idealized situation is seldom realized in practice. Diversity engineering
sometimes Intentionally makes the RSL of one receiver different than
that of the other receiver. Also, different waveguide run lengths and
waveguide hybrid losses can also invalidate the idealization. On the
other end of the scale, the TROPO receivers generally experience randomly
fading receive signals. If the receivers all have the same average
RSL and if the RSL are all Rayleigh amplitude distributed, then the
combiner signal to noise improvement will be, on the average, the values
that Brennan has predicted. Unfortunately, in real life, for various
reasons, the average RSLs of the various receivers is often different
by a few dB. Average combiner noise performance under practical conditions
is difficult to predict accurately without sophisticated parameter measure-
ment of the actual radio path.
6.18 Combiners serve to improve the baseband signal to noise performance
of a microwave terminal. Since the signal out of the combined baseband
must be the same level a3 the signal that was applied to the transmit
baseband, the combiner will reduce the noise at the combined baseband
when compared to the noise out of a single receiver. As a rough estimate
of the actual slot noise that will appear at the combined baseband of
132
a microwave terminal, the curves Brennan developed can be used. If
the terminal is LOS and the RSLs are stable and equal, the following
conditions are approximately correct. For selection combining, the
noise at the combined baseband will be exactly the same as for a single
receiver. The baseband noise can be read directly from the quieting
curve of a single receiver. If the terminal uses equal gain or ratio
squared combining, the noise at the combined baseband will be less than
for a single receiver by the amount shown on the following chart for
variable gain combining. The slot noise at combined baseband will be
the slot noise read from the quieting curve minus the dB valve read
from the Brennan chart. For a TROPO terminal, if the RSLs are the same
and all are randomly fading, then the noise improvement will be found
by using the curve on the Brennon chart which applies to the type of
combining appropriate. The slot noise at the combined baseband will
be the slot noise value read from the quieting curve minus the dB noise
improvement factor determined from the Brennan curve.
Noise weighting
6.19 When noise measurements are made on telephone circuits, various
weighting filters ire used to measure the noise. If a 3 kHz flat filter
is used to measure the noise, the slot noise previously determined from
the quieting curve can be used directly. If a C-Message or Psophometric
(CCITT) filter is used, a correction factor must be algebraicly subtracted
from the previously determined noise. This subtraction accounts for
the noise power lost by the frequency characteristic of the filter.
As Tant. mentions, the theoretical factor for C-Message is 1.5 dB and
is 2.5 for Psophometric weighting. The use of 2.0 dB as the factor
for either weighting characteristic is recommended.
Cable Noise
6.20 Cables connect the wideband M/W terminal with multiplexers. The
cables generally are located near other signal and power cables. The
other cables may induce crosstalk noise. The cables may have noise
induced by radio frequency interference. Occasionally, baseband noise
will be introduced by the M/W terminal itself. Cable induced noise
is difficult to determine without direct measurement. With LOS M/W
systems, however, the combined M/W terminal noise and cable induced
noise can be measured by terminating the transmit cable at the multi-
plexer and measuring the cable noise at the multiplexer end of the
receive baseband cable using a frequency selective voltmeter. Noise
measurements can then be taken with the transmitter baseband amplifier
input terminated and the frequency selective voltmeter located directly
at the combined terminal receive baseband. Using the two noise measure-
ments and the noise addition/subtraction curves, the cable noi3e can
be obtained.
133
Number of Independent Receivers
(after Brennan)
Combiner Improvement Curves
Figure 60
134
Examples
6.21 To show a method of comparing theoretical quieting curves with
actual quieting curve data, two examples will be shown.
LOS M/W Receiver (without de-emphasis):
6.22 The following page lists various slot noise values for various
RSLs. The values were taken in dBm at a -15 TLP. The receiver had
no de-emphasis. Therefore, to convert the measured valves to dBm0
values, +15 dB must be added to each value. These valves are listed
on the following page.
6.23 Following the noise slot measurements, a page is given which lists
baseband test tone power level versus various RSLs. The test tone level
was measured using a 3*1 kHz wide frequency selective voltmeter (FSV).
At low RSLs the noise in the FSV slot was significant. Therefore, what
the FSV measured was test tone level plus noise. To compensate for
the noise, after measuring the test tone plus noise (TTL + N), the test
tone was removed from the baseband of the transmitter and the slot noise
(N) was measured at the same RSL. Using the dB subtraction curve of
the power addition/subtraction curves the slot noise was subtracted
from the test tone level plus noise measurement. This value was listed
as the test tone level (TTL). The proceeding values have been plotted
on the following graph.
TROPO M/W Receiver (with CCIR de-emphasis):
6.24 The following page lists various receiver baseband slot noise values
for various RSLs. The values were taken at a -10 dB TLP. The receiver
had CCIR de-emphasis. To convert the measured valves to dBm0, +10 dB
plus the pre-emphasis value (or minus the de-emphasis value) must be
added to each valve to arrive at a dBm0 slot noise corrected for de-
emphasis .
Slot Frequency
TLP
De-emphasis
Correction
(kHz)
(dB)
(dB)
Factor
(dB)
308.7
-10
-4.7
+ 14.7
154.4
-10
+0.8
+ 9.2
77.2
-10
+3-5
+ 6.5
30.9
-10
+4.3
+ 5.7
De-emphasis values taken from actual measurement of the receiver are
listed on the next page. The values were taken by running transmitter
to receiver baseband frequency response with pre-amphasis strapped out.
135
i
[ Pot*r Addition, dB difference between two powers
I Power Subtraction
Com 1: dB to bo suotrtctod fro* larger power
Com 2: dB difference between two powers
]
Power Addition/Subtraction Curves
j Figure 61
!
136
FM RECEIVER NOISE uUlETIMG
| UMINAHV DAI A
[^) PINAL data
Sample Quieting Curve Data
Table 22
137
FM RECEIVER NOISE QUITTING
MMfLIMlNAWY Dm A
DATA
IF SvO
2 S M Hz.
I T A T lOf«
LOS
A* A 4 » * V TONI,
-1 5.
V f v I l
oiCCVAh
AV/FRC-157
AGC/i'
HONAL VOLTS
<t)L)
HO'Sf POHfi IM BAifHAM'jSLOT (— J g ^
oascbano Slot rnr' ituc v
/ i r>
so
ISO
iz5
12.5
os
ekes
0 o l
o oo 5
0.0015
4.5
V I 7
6, 5 I 6. S
10.5
1 0
u. S
1 1
31.5
33. 5
27. S JJ
a 8. S 0.S
a $
<3.5 I 13.5
14,5 I (5
17 I )7. 5 j |0 j 17. S
<<1,5
/2-
U. 5 13. S
?2.
36
43.5
45.5
41
41 i S», 5 51, S
-6 1
1 S
4 7' ~!
5
5 3,5 I 56.5 ! Si
/i.Z>
75.5
I ->4 5
60
54
63.5
et.s
jo jii gu.e t inc mil
KOI PMCQt.MHCf
*50 KHt
- 8? S ....
5(
6 1.5
65 5
7
tenai
nn
70
‘bos
BO
EEKi
00 70
NT HfttlhOl l) MSL
-85
Sample Quieting Curve De
Table 23
138
I 3. -j O xh.
- 8
i S) O Kill
-1*\
Sample Quieting Cirve Data
Table 24
139
Figure 62
140
f (kHz)
De-emphasis (dB)
f /fmax
Measured
Theoretical
252
1.0
-3.7
-4.01
227
0.9
-2.6
-3.12
202
0.8
-1.5
-2.07
176
0.7
-0.3
-0.96
151
0.6
+0.2
+0.15
126
0.5
+2.0
+1.19
101
0.4
+2.0
+2.11
75.6
0.3
+3.5
+2.89
50.4
0.2
+4.0
+3.48
25.2
0.1
+4.2
+3.86
f (kHz)
f/B
Measured
Theoretic)
309
0.1
-4.7
-4.99
154
0.05
+0.8
+0.01
1
77.2
0.025
+3-5
+2.85
30.9
0.01
+4.3
+3.79
t
Tropo M/W Receiver De-emphasis Performance
I
! Table 25
141
FM R[ CtIVFK NOISf Quit HUG
'00 Jn„, -100
-1 00 ^
3 0.°[ m.
-°ld _
Sample Quieting Curve Data
Table 26
142
Sample Quieting Curve Data
Table 27
ft
144
-130
Figure 64
145
08* 0L+ 09«
6.25 Notice that the measured values are significantly different than
the theoretical values. This shows the necessity of checking FM receiver
de-emphasis characteristics if accurate comparisons are to be made between
actual and theoretical quieting curves.
6.26 Following the noise slot page is a page listing baseband test tone
levels versus RSL. Using the same procedure as mentioned for the LOS
receiver, values for test tone level were determined from the test tone
plus noise measurements. The results have been plotted on the following
pages. The first graph shows the quieting curve witr.out de-emphasis
correction. The second graph shows the quieting curve after correction
for de-emphasis.
6.27 Calculations for using the Averaged RF/IF response chart with the
LOS receiver (excluding effects of de-emphasis) follow:
Receiver Specifications:
IF bandwidth: 25 MHz
per channel deviation:: 140 kHz rms
(for 0 dBm0 test tone)
noise figure: 8 dB
Noise Slot Measurement (FSV) Bandwidth: 3-1 kHz
Noise value corresponding to 0 dB slot noise on chart:
N = .29.6 - 20 log Af/(jh rmg + 10 log BJp ♦ CF
= +29.6 - 20 log (140) + 10 log (25) + 0
= +29.6 - 42.9 + 14.0 + 0 = +0.7 dB = +0.5 dB
RSL value corresponding to 0 dB C/N:
RSL = -114.0 + NF + 10 log BT„
lr
= -114.0 + 8.0 + 10 log (25)
= -114.0 + 8.0 + 14.0 = -92.0 dBm
The above data is noted on the following page.
Calculations for using the Gaussian RF/IF response chart with the TR0P0
receiver (excluding effects of de-emphasis) follow:
148
Receiver Specifications:
IF bandwidth: 3-09 MHz
per channel deviation: 100 kHz rras
(for OdBm0 test tone)
noise figure: 1.5 dB
Noise Slot Measurement (FSV) Bandwidth: 3.1 kHz
Noise valve corresponding to 0 dB slot noise on chart:
N = +29.6 - 20 log Af/Qh rms + 10 log BIp + CF
= +29.6 - 20 log (100) + 10 log (3-09) + 0
= +29.6 - 40.0 + 4.9 = -5.5 dBm0
RSL value corresponding to OdB C/N:
RSL = -114.0 + NF + 10 log B
= -114.0 + 1.5 + 10 log (3-09)
= -114.0 + 1.5 + 4.9 = -107.6 = -107.5 dBm
The above data is noted or. the following page.
Note: For ease in comparison with actual quieting curves, it is suggested
that the above calculated valves be rounded to the nearest J dB.
149
7. KM Microwave Radio Terminal E' prent Parameters
7.1 In ord'-?r to predict M/W terminal performance, it is necessary to
determine a few characteristics of the terminal transmitter and receiver.
The determination of these parameters will be discussed
…[truncated]