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AD-A063 798 OHIO UNIV ATHENS DEPT OF ELECTRICAL ENGINEERING F/6 17/7
ANALYTICAL determination OF THE interference OF COMMERCIAL FM S— ETC<U>
MAR 78 J E ESSMAN. T LOOS D0T-FA77WA-3932
UNCLASSIFIED EER-32-1 FAA-R-6050-1 NL
1 OF 2
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MICROCOPY RESOLUTION TEST CHARI
NAIIONAl BUM All Of ! ANDARDS ]9( • A
AD AO 63 798
ANALYTICAL DETERMINATION OF THE INTERFERENCE OF COMMERCIAL
FM STATIONS WITH AIRBORNE COMMUNICATION AND NAVIGATION
RECEIVERS AND EXPERIMENTAL VERIFICATIONS
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MARCH 1978
FINAL REPORT
D D C
@f?nnoia
JAN 29 1979
K^Einnsl
er b
~ DISTRIBUTION STATEMENT A
Approved tor public rclcoMj
Distribution Unlimited
U.S. DEPARTMENT OF TRANSPORTATION
FEDERAL AVIATION ADMINISTRATION
Airway Facilities Service
Washington, D.C. ?0590
kmMiiMantiai
Terhnicul Report Documentation Page
Apaiauauta Canvaraiaaa fits Manic Maaiata
TABLE OF CONTENTS
SUMMARY
INTRODUCTION
RECEIVER MODEL
MEASUREMENTS OF MODEL PARAMETERS AND
APPLICATIONS
A. Input Filter Characteristics.
B. Determination of Model Parameters.
ELT (EMERGENCY LOCATOR TRANSMITTER) MODEL
PAGE
APPLICATION
Calculation Signal Strengths.
Calculation of Intermodulation Contribution.
Cross- Modulation Considerations.
Combined Effects of Intermod and "Brute-Force"
Interference .
EXTENSIONS OF THE TECHNIQUES
CDI MODEL
A. Analytical Model.
B. Modeling Receiver Filters.
C. Effects of High Level Modulation on CDI Reading.
COMPUTER PROGRAM
CONCLUSIONS AND RECOMMENDATIONS
A. Statistical Model.
B. Model Improvement.
C. Standard Test Procedure .
D. Interference Profile Mapping of Potential
Airport Faci lities .
63
65 fa
66 White Section
Cuff Section □
66 □
3H
67 —
jisRM|wrjrco3Es_
On'. AV.V.l frua^.v SPiClST
XI
ACKNOWLEDGMENTS
PAGE
XII
XIII
XIV
REFERENCES
BIBLIOGRAPHY
APPENDICES
A. Theoretical and Experimental Measurements Using
Model and an FM-Interfering Signal.
B. Fi Iter Characteristics .
C. Interference Due to ELT.
D. Measurement of RMS Modulation Due to Intermod .
E. Noise Equivalent Bandwidth.
F. CDI Interference.
G. User Manual.
H. Subroutine Descriptions.
I. Computer Program Listing.
LIST OF FIGURES
PAGE
Figure 1. (a) Simplified Block Diagram of Receiver, (b) RF-Amplifier
Model, (c) Overall Model from RF-Input to IF Output.
Figure 2. RF Input Fi Iter Characteristics.
Figure 3. Relative IF and Detector Response.
Figure 4a. Variation of 3 K^/2 Kj as a Function of Intermod Generating
Frequencies.
Figure 4b. Plots of Effective 3K^/K^ as a Function of Interfering Signal Level.
Figure 5. Typical Applications.
Figure 6. IF Characteristics.
Figure 7. Signal Levels for No Interference.
Figure 8. Regions of Interference.
Figure 9.
’Skirt" Characteristics.
Figure 10. Signal Spectrum.
Figure 11. Birmingham, Alabama Area Airport.
Figure 12. Location of FM Broadcast Stations in Birmingham Area.
Figure 13. Map Showing Locations of FM Stations and Locations at Which
the FM Station Interference is Analyzed.
Figure 14. Block Diagram of Audio Processing Circuit of NAV 11 .
Figure 15. Simplified Schematic of Comparator Circuitry of
NAV 1 1 Receiver.
Figure 16 . 90/150 Filter Responses.
Figure 17. Normalized Detector Filter Characteristics.
v
PAGE
f
Figure 18. Audio Filter Characteristic*. 58
Figure A-l . Interfering Signal Spectrum; Modulation Index 6;
Bandwidth '200 KHz. 69
Figure A-2 . Spectrum of Desired Signal (108.5 MHz) at RF-Amplifier
Output. Signal - 17 dBm 70
Figure A-3 . Spectrum of Desired Signal (108.5 MHz) at RF-Amplifier
Output. Signal -47 dBm 71
Figure A-4. Detector Output with No Interference. 71
Figure A-5. Detector Output with Interfering FM-Signal (0 dBm) at
105.5 MHz. 72
Figure A-6. Detector Output Using Input Signals Described in
Figure A-2 , with 10% Modulation on Desired Signal. 72
Figure A -7. Detector Output Desired Signal Level =-70 dBm, No
Interfering Signal. 73
Figure A-8. Detector Output. 73
Figure B-l . Measurement Procedure for Obtaining a(u). 74
Figure B-2 . Simplified Schematic of RF Front End of NAV 11 Receiver. 74
Figure B-3 . Test Procedure for Determining a(u) Using Cross-
Compression Methods. 75
Figure C-l . Spectra of the Reradiated Signals at the Output of ELT. 78
Figure C-2 . Test Procedure for Spectral Measurements for Figure C-l . 83
Figure C-3. ELT Model. 84
Figure C-4 . Experimental Procedures. 85
Figure C-5. IM Effects of Two Closely Aligned Frequencies. 88
Figure C-6 . ELT Output Voltage as a Function of Input Frequency. 90
Figure C-7. k^ as a Function of Intermod Frequency for Varying FM
Band Generating Frequencies. 91
Figure C-8 . Variation of k^ for Different Signal Levels. 92
VI
PAGE
93
\
Figure C-9. Antenna Coupling Measurement.
Figure C-10. Antenna Locations.
Figure C-l 1 . ELT-Communi cation Antenna Coupling.
Figure C-12. Interference Model.
Figure C-13. Coupling Between ELT Antenna and Communication
Antenna as a Function of Frequency 22" ELT Antenna
Length.
Figure C-14. Normalized (50 ohms) Self Impedance at Various
Frequencies of the ELT Antenna (22") on Board
N1200U.
Figure C-l 5. Normalized Self-Impedance of ELT Antenna (16"
Modified Antenna) on Board N900U.
Figure C-16. Normalized (50 ohms) Self Impedance at Various
Frequencies of the Communications Antenna on
Board N1200U.
Figure E-l . Noise Equivalent Bandwidth of a Filter.
Figure G-l . Flow-Chart of FM Interference Program.
Figure H-l . Subroutinesand Functions Called by the Main Program.
Figure H-2 . Assumed Attenuation Characteristics.
Figure H-3 . Flow Chart of Subroutine CONVOL, Section Where AXB
is Convolved with Station " K" .
94
95
98
101
102
103
104
110
115
120
123
LIST OF TABLES
PAGE
Table 1 .
Possible Intermod Components (IM).
4
Table 2.
3K /2K Determined by Cross-Modulation Measurements
wifn 10 KHz AM Tone Modulation on Interfering Signal.
15
Table 3.
Parameters of Model Determined by Intermodulation
Technique.
16
Table 4.
Parameters of Model Determined by Cross- Compression
Measurements.
17
Table 5.
Summary of Results.
17
Table 6.
2
Coefficients of the FM signals e^ (t) and ec (t) for
R] =2.4, f] = 10.42 KHz, p2 = 2*4 and f2 = ,2‘5 KHz.
24
Table 7.
IM Spectrum.
25
Table 8.
IM Components Out of IF.
27
Table 9.
Summary of Measured and Calculated Results.
32
Table 10.
FM Broadcast Stations in the Birmingham Area.
40
Table 1 1 .
Airport Facilities.
40
Table 12.
Distance of FM Broadcast Stations from Localizer.
40
Table 13.
Printout of Signal Level Computations.
41
Table 14.
Signal Levels at Location (1).
44
Table 1 5.
Cross-Modulation Due to Interfering Signals. Location (1).
44
Table 16.
Intermodulation Interference. Receiver at Point (1) location.
45
Table 17.
Signal Levels at LOM Location.
45
Table 18.
Cross-Modulation Due to Interfering Signals. LOM Location.
46
Table 19.
Intermodulation Interference. Receiver at LOM Location 2.
46
Table 20.
Table 21 .
Table 22.
Table 23.
Table 24.
Table 25.
Table 26.
Table 27.
Table 28.
Table B-l
Table B-2 .
Table E-l .
Table F-l
Table F-2 ,
Table F-3.
Table F-4 .
Table H-l .
Table FI-2 .
Table FI-3 .
Signal Levels at Location (2) in Figure 13.
Cross- Modulation Due to Interfering Signals. Location (2).
Intermodulation Interference. Receiver at Location (2).
Signal Levels at Location (3).
Cross-Modulation Due to Interfering Signal. Location (3).
Intermodulation Interference. Receiver at Location (3).
Measurements of CDI Voltages.
Reference Notes Relative to Measurements in Table 26s
Summary of RMS Modulation Measurements and
Calculations.
Comparison of Results Obtained Using Cross-Compression
and RF Measurements.
Variations in a (u) as a Function of Receiver Frequency.
Comparison of Theoretical Modulation Factor Ratios
from Computer Program.
Effects of Detector Clipping on CDI (Normal Reading of
CDI = 60 pA).
Effects of Detector Clipping on CDI (Normal Reading of
CDI = 30 pA) .
Effects of Detector Clipping on CDI (Normal Reading of
CDI = 0 pA) .
Effects of Interfering Signal Frequency on CDI (Normal Reading of
CDI = 60 pA).
Variable Names and Their Meaning.
Edit Mode Commands.
Variable Names for Subroutine XMOD.
IX
PAGE
4~
47
47
49
49
49
53
54
59
75
76
111
112
112
113
113
121
122
126
Jl
I
SUMMARY
This paper summarizes the work performed under Contract FA77WA-3932 sponsored 1
by the Federal Aviation Administration (FAA), Airway Facilities Service. The primary
objective of the research sponsored here is the determination of an analytical model
capable of predicting the effects of strong interfering FM broadcast stations on airborne
navigational (specifically the lo.jlizer receiver) and communication receivers.
An analytical model of the RF-amplifier stage, using a third-order nonlinearity,
of airborne communication and navigation receivers capable of predicting the effects of
multiple interfering FM stations is developed. The effects of receiver input filters and
IF filtering are modeled. Measurement techniques useful in determining the various
parameters of the model are described and evaluated. The effects of different signal
powers and different signal frequencies on the parameters are investigated. Limits are
postulated on the accuracy of the model and regions of validity defined.
"Brute-force" interference due to strong interfering FM stations which saturates the
front end and intermodulation distortion due to the interaction of two or more FM stations
are considered.
Various signal characteristics are considered for evaluating the degree of distortion
introduced by interfering FM stations. The effects of filtering due to the receiver are
considered and the resulting FM-to-AM conversion analytically described. Signal char-
acteristics considered for evaluating distortion include peak (cross-) modulation indices
and RMS output of an envelope detector. The effects of receiver desensitation due to
saturation of the front end by the interfering signals are considered. A substantial amount
of time and effort was expended in experimental testing, on the bench, and the models
were developed. Although all the experimental results are not reported here, the most
important results are documented here.
A computer program was developed and is described here which theoretically
predicts the effects of multiple interfering FM stations. Input data include FM station
frequencies, powers, location, and other signal parameters, and calculations are made
of the RMS AM modulation at the receiver filter outputs. Examples are presented which
illustrate the use of the techniques developed. Tradeoff studies indicating the effects of
the creation of additional FM stations end/or the results to be expected when one or more
stations change their power levels, location, antenna patterns, etc. are illustrated by
example. The number of FM stations that can be considered is limited only by the com-
puting facilities available to the user.
Decision criteria that can be reliably used in predicting potential interfering
sources are considered.
The results of the interference on the Course Deviation Meter (CDI) of a localizer
receiver are investigated using single tone FM modulation of the carriers. Due to the
aasasss
9
narrow bandwidths of the 90 and 150 Hz filters the CD! response due to interference would
be extremely dependent on the modulation tone being assumed. To alleviate this and make
the observations more general, "white noise" with a constant spectral density is used to
evaluate the /~DI response.
The results are applied to specific airports where interference problems have
occurred and the results obtained by the theoretical model are analyzed.
II INTRODUCTION
Interference has always been an important problem area in communications systems.
With increased power levels of many transmitters and the solid state design of modern
receivers, interference due to high power stations driving receivers into nonlinear operation
is an increasing problem. This has been the case recently where there have been many
reported cases of commercial FM broadcasting station interference with airborne commun-
ication and navigational receivers. The Federal Aviation Administration (FAA) has
become concerned with the increased number of reports of interference with airborne
receivers. The research described in this report summarizes the efforts in developing a
useful analytical model of a localizer receiver having the following two properties:
(1) The parameters required to specify the model should be easily measured
or otherwise capable of being determined from manufacturers'specifications .
(2) The analytical model should be as simple as possible; however, it should
be useful in predicting potential interference problems due to multiple interfering sources.
In essence the objective is to develop an analytical model capable of predicting possible
interference problems due to existing FM stations, additional sources beyond those
currently in existence, changes in existing sources, etc.
Techniques for describing nonlinear distortion characteristics were emphasized
in the early 1950's when cable television (CATV) engineering had its beginning. Further
emphasis in this difficult-to-handle area were spawned by the increased use of satellite
communications systems, low cost solid state receiver circuitry, etc. Many investigations
have represented the nonlinear elements as having zero memory; - however, recently
interestiias been revived in the volterra series which was introduced by Wiener around
1942.
For the particular investigation described here, it was decided to use a simple
power series for the transfer characteristic for the active device in the RF amplifier, i .e
K. e. + K0 e. + K0 e.
i £■ i o I
( 1 )
where e- is the instantaneous input voltage to the active device, eQ is the output
voltage of1 the nonlinear element, Kj , and are complex numbers describing the gain,
-2-
phase shift and distortion characteristics of the device. Although, in general, any phase
angle can be specified by a proper choice of the constants Kj , and K^, for this work
we assume the phase angle on and to be 0° and the phase angle on to be either
0° or 180°. These assumptions give a simple worst case model in which the parameters of
the model are easily determined by measurements. Procedures are described which can
easily be applied to most receivers for determining the needed parameters. This simplified
model was deemed to be adequate in view of the wide variations in receivers from manu-
facturer to manufacturer and even from receiver to receiver of the same type. In addition
characteristics of a particular receiver will change significantly with age, temperature,
AGC, etc. Measurements indicate that even with all these possible variations the results
can be accurately reproduced within approximately 3 dB which is assumed to be of suffi-
cient accuracy in practice.
The terms generated which are of concern can be identified by considering the
first-and third-order terms given in (1), i.e.,
(1 ) Linear gain term
e . = K, e.
ol 1
(2 )
(2)
Third-order term
3
'o3
K3 e.
(3 )
The distortion terms can be illustrated by assuming the input to be a desired signal
(e. = A cos a t ) with angular frequency a and two interfering signals of angular frequencies
b and c respectively (e^ - B cos b t and e.^ = C cos c t), i.e..
e. (t) ~ A cos a t + B cos (b t + <t> ) + C cos (c t + <t> )
i I l
( 4a )
Using the inputs given in(4q) each of the signals can be assumed amplitude frequency or
phase modulated by letting the amplitudes A,B,C, the frequencies a,b,c or the phases
and functions of time respectively. Whichever happens to be the case, we can
assume the bandwidths of the signals to be B , B,, and B respectively.
a b c
Using (4a) the possible intermodulation terms of interest are listed in Table 1 . For
this table, the maximum FM station bandwidth is assumed to be 240 KHz. In addition to
the distortion terms listed in this table, the third-order nonlinearity will contribute self-
compression or self-expansion terms at the desired frequency (a) depending on whether
is negative or positive, i.e.,
3/4 K3 A~
cos at
(4b)
-3-
Similarly cross-compression or cross-expansion terms generated at the desired frequency
occur from the following terms:
3/2 AB2K cosat t3/2AC2K cos at ( 4c )
O j
All other terms are assumed filtered out by the receiver. It should be noted rhat even
if no intermodulation components generated are within the passband of the receiver as given
in Table 1 , there still existsa possibility of interference due to "brute-force" interference as
indicated by (4b) and (4c) . This type of interference shows up as cross-modulation which
is a phenomenon where the modulation of an interfering carrier is impressed upon another
carrier. This "brute-force" type of interference can be important when the receiver is in
the presence of strong interfering signals.
Interference of the types discussed above can also have the effect of desensitizing
the receiver. This is the result of the AGC reacting to the self-and/or cross-compression
of the carrier .
Ill RECEIVER MODEL
In general it is the RF amplifier stage where most of the nonlinear distortion is
generated; however, it is possible and in the presence of extremely strong interfering signals
it would be expected that the mixer stage would contribute to the nonlinear distortion. In
this investigation we assume the RF-amplifier to be the significant source of nonlinear
distortion; therefore, an adequate model of this stage is necessary and sufficient for our
purposes. Figure la indicates a block diagram of a typical receiver and Figure lb the model
of the RF-amplifier used in this work, where the nonlinear device input-output is specified
by the transfer characteristic given in (1). The input filter block is assumed to represent
the effects of the input circuitry, while the output filter block represents the effects of the
output circuitry of the RF-amplifier. In the frequency domain input and output attenuations
are represented by a(u) andp (u») respectively. If one assumes all the nonlinear terms to be
generated in the RF-amplifier, then the model shown in Figure lc can be assumed. Using
this model the input is assumed to be the RF-amplifier input (voltage at the output of the
receiver antenna) and the output is the IF-amplifier voltage output. In this case the output
filter will include the attenuation properties of the RF-amplifier output circuitry, the mixer
and the IF-amplifiers. Since no distortion terms are assumed generated with the mixer
stage, the effects of this stage is assumed to be a linear frequency translation and all
calculations and modeling can be done at either the IF or RF frequency, whichever is
convenient. This representation has significant advantages in practice in determining the
parameters experimentally. Methods were developed which allow the overall parameters
specified in Figure lc to be determined by simply monitoring the AGC voltage with an
interfering and desired signal present.
-5-
RF INPUT
RF INPUT
RF
MIXER
IF
AMr
INPUT
FILTER
a(u)
4
L
<
. i
V ..
N N
_RF_-_AMP
(b)
NON LINEAR
DEVICE
«!, K3
INPUT
Li: ;E \R
DEV
OUTPUT
FILTER
a(u)
Kr ' 3
FILTER
P(u)
RF OUTPUT
OUTPUT
FILTER
P(«)
IF OUTPUT
Figure 1. (a) Simplified Block Diagram of Receiver.
(b) RF-Amplifier Model, (c) Overall Model
from RF-Input to IF Output.
Using the model specified by Figure lb requires measurements of the RF-amplifiers
output, which in general are very sensitive measurements due primarily to loading effects.
Both methods were investigated.
IV MEASUREMENTS OF MODEL PARAMETERS AND APPLICATIONS
Application of the receiver model requires that the signal level at the receiver
input be known. In addition the following information regarding the receiver characteristics
is needed:
( 1 ) Input-filter characteristics a(u).
( 2 ) Kj and
( 3 ) Output filter characteristics from the RF to the output of the IF-
amplifier stages. With this information one can calculate the resulting distortion terms at
the output of IF-amplifier stages.
With this information the model can be used to predict the output from the IF-
amplifier and the output of the envelope detector. In a later section of this report an
analytical model of the CDI circuitry is described and developed. Since the interest in
this research was primarily concerned with the interference of commercial FM broadcasting
stations with aircraft localizer receivers, the examples and applications are in this area.
The receiver used for experimental work was Navll localizer receiver manufactured by
NARCO Corporation. The frequency range of the localizer receiver is 108 MHz to 118
MHz, while the commercial FM broadcasting band is from 88 to 108 MHz. As a result of
the adjacent location of these two frequency bands, both intermodulation distortion and
"brute force" type interference must be considered.
A. Input Filter Characteristics. Figure 2 indicates a plot of the receiver RF-
amplifier input filter function.* TFe" receiver is tuned to 108.5 MHz. The effects of the
output circuitry of RF-amplifier can be combined with the IF-amplifier and detector
characteristics so that one overall attenuation function is all that is required and since most
of the band limiting is done in the IF-amplifier, these characteristics are the most important.
These characteristics are normally available from manufacturers' data; however, if not,
they are easily measured.
Figure 3 i llustrates the overall attenuation characteristics of the NAV 1 1 localizer
receiver from the IF input to the detector output. Some discrepancies were observed between
*The measurement techniques used to obtain these results are described in
Appendix B.
-7-
Relative Response
in dB
to
m
m
m
in
in
in
in
O'
O
o
o
o
8
CO
o
s
m
o
o
o
I I I I l I I I
Receiver Tuned
to 108.5 MHz
(A
/ 0S
/ \
,® BW = 4 MHz ©
-10 -
Characteristics taken using Vector
Voltmeter. Assuming constant
incident voltage and measuring voltage
at RF AMP input at Mosfet Gate input
as function of frequency.
Figure 2. RF Input Filter Characteristics.
-8-
cfor Response.
measured values and theoretical values using an Ideal Bandpass Charcteristic . To
alleviate this a higher order approximation of the IF characteristics was used. In par-
ticular a triangular approximation was developed and is shown in Figure 3.
Since the interest in this research was primarily with regard to commercial FM
broadcast station interference with navigational receivers and due to the fact that the
navigational information is conveyed via AM techniques, the attenuation characteristics
of the receiver are important. This is due to the fact that the effect of bandlimiting the
FM interfering signal is to introduce AM modulation on it which causes significant
interference at the output of the AM detector. A considerable amount of experimental
data was collected during the execution of this project. Appendix A gives representa-
tive spectral plots illustrating these effects.
B. Determination of Model Parameters. Using the analytical model requires that
the parameters and 1C be determined. Actually it is only necessary to determine the
ratio Kg/K^ • Three methods were used to determine these parameters.
(1) Gain Compression Technique (two-carrier method) - in this scheme two
sinusoids are applied, one at the desired receiver frequency (a) and the other an inter-
fering signal .
Using (1) and (4c) (with c = 0) the third-order term predicts a cross-modulation
term at the desired frequency which is proportional to the product Kg AB^a (b ) where.
Kg = parameter of the third-order model
A - amplitude of the desired signal
B = amplitude of the interfering signal
c{u) = input filter characteristic
2
The desired signal amplitude A is assumed small compared with AB so that the
contribution due to the AJ term in (4b) can be neglected. The measurement of the ratio
using this technique was performed as follows:
(a) Measure the AGC voltage with only a desired signal input,
e. = \/~2 A cos at (A is RMS Voltage) ( 5 )
Neglecting the self- compress ion term in (4b), the output is approximately
e = ^7 AK. cos at ( 6 )
o I
(b) Applying an interfering signal along with the desired signal. The
result of the interfering signal is to compress the desired signal or expand the desired signal
depending on whether Kg is negative or positive.
J
Using (4c) and choosing those terms of interest at the receiver frequency we have,
e. v/2 A cos a t i- v 2 B cos b t ( 7 )
i
e v/2 AK, 0 i 3B?a2(b) K_/K,) cosat ( 8 )
(c) Increase the desired signal level until the AGC voltage is the same
as in step (a). The amount of dB increase in desired signal required to bring the AGC voltage
back to the value in step (a) is the amount of gain change of the desired signal level due to
the interfering signal. Hence, using (6) and (8) the ratio is easily determined.
(2) Two-carrier method with modulation - this method uses an interfering
AM-modulated signal along with a desired CW signal as the input. By measurement of
the cross-modulation obtained the ratio of K^/Kj can be determined. The steps in the
procedure are as follows:
(a) With a desired signal and no interfering signal applied, measure
the AGC voltage.
(b) Applying a combination of a desired signal and an interfering
signal with a known percent modulation, observe the AGC voltage.
(c) Increase or decrease, whichever is required, the desired signal
level until the AGC voltage is the same as in step (a).
(d) Measure at the IF-amplifier output the AM sidebands due to the
cross-modulation of the interfering signal on the desired signal. This gives the amount of
cross-modulation obtained which can be used to determine K^/Kj (note that cross-
compression of the carrier must be taken into account).
Mathematically the procedure can be described as follows: Let the input be
e. = v/5 A cos a t + v/5 B (t) cos b t ( 9 )
where B (t) = B, |1 + m cos u t| ( 10 )
1 m
m = percent modulation
w = frequency of modulation
m
2 2
Considering the third-order term and neglecting the terms containing m and B
the result is
K3 o 2 K3 2 2
e = AK. (1 + 3f^T o (b) B. + 6-ir-a (b) B. m cos <j t) cos at (11)
o I I I 1 ' 1 I m
(3) Intermod Method - this method is based on simply measuring the level
of an intermodulation component generated by two interfering signals of frequencies such
-11-
that they produce an intermod component at the desired frequency. These measurements
can be accomplished as follows:
(a) Apply a desired signal of known amplitude and measure the AGC
voltage .
(b) Without a desired signal apply the two interfering signals and
adjust the amplitudes such that the AGC voltage is the same as in step (a).
(c) The desired signal level in (a) is then equal to the intermod level.
The three methods above can also be modified such that the AGC voltage is held
constant and the levels at the IF-amplifier output are measured using a spectrum analyzer.
Specifying a receiver by such a model brings up the question of how much variation
in ratio K^/Kj is there. Most past work has been concerned with the modeling of wideband
amplifiers where problems with variations in the AGC characteristics are not present. In
addition, the ratio K3/K] could be a function of input signal levels and input signal
frequencies, etc. A considerable number of experimental measurements were obtained
using the NAVll localizer receiver to investigate these characteristics. Figure 4a shows
the results obtained using the intermod method. These results give an indication of the
variations in 3 K^/ (expressed in dB) as a function of the intermod generating frequencies.
Indicated on this figure are the signal levels of the two interfering signals. Figure 4b
indicates the results obtained as a function of interfering signal level.
If the model is consistent all three measurement techniques should give relatively
the same results for K^/Kj . Comparison of the results obtained using the three different
measurement techniques are given in Tables 2, 3 and 4. These results again indicate that
the ratio K_/Kj can be assumed essentially constant in regions where the third-order
model can be assumed valid.
Although the amount of data given in these tables is limited, some important
observations and conclusions can be made and are given in Table 5.
The measurements seem to indicate that there are variations which can probably be
attributed to the following:
(a) The sensitivity of the measurements.
(b) The receiver characteristics changing.
(c) The order of the model not being sufficient.
Signal levels required to give the data 3. Filter function used to calculate 31^/2 Kj
points are given in parentheses. The first is shown in Figure 2 .
is the b frequency signal level in dBm
incident, the second is the c signal level.
Figure 4a. Variation of 3K^/2K| As a Function of Interi. Generating Frequencies.
□DK
Desired Signal
Interfering Signal Gain Chang
Level (-dBm) B GC(-dB)
105.5 MHz
AGC
(Volts)
Comments
1 .2 1 .727
1.1 1 .498
0.9 1 .376
1 .0 1 .299
1 .218
-1.8 1 .198
-1.2 1.177
None measured by
this method .
Gain expansion-
model not valid
Same as above
3/2 K3/K] = 20 log (1 - GC') - 2BdBm - 2a (b)dB - 6dB
d B
where GC’ = 10GCdB/20
Localizer signals of these levels would be unusual.
Table 4. Parameters of Model Determined by Cross-Compression
Measurements .
Gain
Compression
Technique
Cross -
Modulation
Technique
Inter-
Modulation
Technique
Average Value
3K3/2K j (dB)
Maximum deviation
from the mean (dB)
Table 5. Summary of Results
The following conclusions can be drawn from the data obtained:
(a) The model is useful for localizer signal levels at -30 dBm or lower.
(b) The model is useful for "brute-force” interfering FM signal levels
of - 10 dBm or lower.
(c) The model is useful for interfering signals of the appropriate
frequencies such that an intermod is generated with strength of -30 dBm or less. From
Table 3 it is observed that this requires input signal levels less than -7.5 and -10 dBm
(referenced at the receiver input terminals).
(d) The value of K^/K^ can be assumed essentially constant for the
regions specified by (a), (b), and (c).
V ELT (EMERGENCY LOCATOR TRANSMITTER ) MODEL
During the course of this investigation, it was found that a considerable interference
problem was encountered on aircraft carrying certain ELT's. Substantial effort and time was
expended investigating these effects and in the modeling of this device. The results of these
investigations are documented in Appendix C.
VI APPLICATION
To illustrate the procedures involved in determining possible interference problems
using the model proposed, consider the simple case where there exist only two interfering
FM stations. The geometry of the problem is assumed to be that shown in Figure 5.
The analysis of the problem can be separated into three specific topics, i.e.,
(a) Calculation of signal strengths at the receiver input terminals.
(b) Calculation of "brute-force" interference contributions.
(c) Calculations of intermodulation distortion.
A. Calculation of Signal Strengths. The free space attenuation between lossless
isotropic antennas is given by
a (dB) = 36.3 + 20 log1()f + 20 log1()d (12)
-18-
r
where f is the frequency in MHz and d is the distance in miles. Using (12) the
path attenuations can be calculated as:
(a) Path attenuation for station 1: a^ 100 dB
(b) Path attenuation for station 2: ~ 91 dB
(c) Path attenuation for station 3: a ^ ' 91 dB
The maximum power available at receiver antenna is given by
P = (ERP). - (Attenuation). (13)
ai i i
where (ERP). is the effective radiated power from station 1 and (Attenuation),
is the attenuation ot the i signal. For the example here, we have,
P = 80 - 100 = - 20 dBm (power available from station 1)
al
P =80 - 91 = - 11 dBm (power available from station 2)
a2
P .=42 - 91 = - 49 dBm (power available from station 3)
a3
Applying the model requires a knowledge of the voltage input at the receiver
input terminals. Therefore, the power input to the receiver from signal i is given by
P. = P . - L.
i ai i
(14)
where
L. = A. + C. - D. (total loss due to antenna cabling system on
board the aircraft. (15)
A. = loss due to aircraft antenna.
C. = loss due to cabling, etc.
D. = directive gain of antenna.
In general A. and C. would have to be estimated or measured for a particular
application. For our example we use measured values obtained using a VOIVNAV
antenna on a Cessna 150 aircraft, i.e..
A, + C1 = 9 dB (102.5 MHz)
A2 + C2 = 7 dB (105.5 MHz)
A3+C3=3dB (108.5 MHz)
(16a)
(16b)
(16c)
The directive gain of the dipole antennas are assumed to be 6 dB; therefore, the
signal levels at the input to the receiver are:
j
-20-
(17a)
(17b)
07c)
FM1: Pj - 20 - 9 +-6 =- 23 dBm (17a)
FM2: P2 = - 11 - 7 +-6 = - 12 dBm (17b)
Localizer : P^ = - 49 - 3 + 6 = - 46 dBm (17c)
With this information the next step is to calculate the effects of these signals in
the receiver.
B. Calculation of Intermodulation Contribution . For the example here, assume
the FM signal characteristics given below:
FM 1 (Signal B)
Tone modulation 10.42 KHz
P| - 2 .4 (Modulation Index)
FM 2 (Signal C)
Tone modulation 12.5 KHz
=2.4 (Modulation Index)
Mathematically the interfering signals can be described by either the time domain
or frequency domain descriptbns. For example for the B signal (FM 1) the expressions are:
e^ (t) = B cos [ b t + pj sin u^t) (18a)
uj = 2tt (10,420)
N
e,(t) = BE J (B,) cos fb t + moj. t| (spectral representation
m _N of the FM signal)
(18b)
After passing through the input filter the results are,
e/ (t) = B i n (b + mu,) J ( p, ) cos fb t + mu, t|
b I m i I
m= -N
where N spectral components are assumed adequate for the representation and the
input filter is assumed to have an attenuation of a (u) at frequency u and no phase shift.
Si mi lari ly for FM 2:
ec (t) = C cos [ c t + p^ sin u^t 1 0 9a)
where =2w (12,500)
M
e'c (t) = Cj a (c t-k^) (P2) cos lc f +l<U2tl (19b)
k = -M
Using the Table 1 the term of interest in this example is (the RF filter removes
the rest of the terms):
-21-
*
.1
t
3/4 BC2 cos [ (2 c-b) M- 2<t>2 - ^ | (20)
(2 c-b)/2ir = 2 (105.5) - 102.5 - 108.5 MHz
Using (18b) and (19b) the intermodulation term in (20) can be written:
N MM
IM = (3/4) K„ BC7 Z I I a (b + mu,)
m= -N k=-M I = -M
a (c + ku2) a(c + 1^) (P2) J| (f*2) Jm (Pj)
cos f (2 c-b) t + (k + I) ~ mu^t| (21a)
where K3 is a parameter of the model and a (u) is the input filter attenuation.
The IF frequency characteristics are assumed given byy (u); hence, the output of the IF is
N M M
IM=3/4K BC2I I Z a(b + mu.) a(c + kuJ
J m= -N k= -M 1= -M
a( c + l2 ) y | 2 c-b + (k + |) - mu^| (21b)
Jk (P2 ) J| (P2 ) Jm (P]) cos( (2 c-b) t + (k + I) ujt-mu^l
In this equation the number of terms that must be considered in each summation
depends on the modulation index and the AM detector output depends on the number of
terms passed by the IF-amplifier, which depends on the bandwidth. The method used to
specify the number of terms considered is the "rule of thumb" quite often used in practice
to specify the bandwidth of an FM signal/ . e . ,
Bandwidth = 2 f (1 +p)
m
where f is the modulation frequency and p is the modulation index. The number
of terms in the series expansion for the FM signal that must be considered is
No. of terms = 2 fm (1 + P) / 2 fm = 1 + P
In particular, for the case being considered, i.e., P^ =2.4, f^ =10.42 KHz
(?2 = 2 .4 and f 2 - 12.5 KHz, the number of terms that should be retained is
N ~ 3-4 and M = 3-4
Further modifications of the spectral components will occur due to the RF and
IF characteristics of the receiver.
-22-
The results given in (21a) can be simplified by assuming the input filter a (u)
a constant. This will have very little effect on the results, since most of the AM
distortion (due to FM-to-AM conversion) results from the band limiting through the
IF-amplifier. With this assumption the squared term (e ^ (t) ) can be written in the
time domain as
e ^ (t) = C^f cos ( c t + p sin u,t | | 2
c z
e ^ (t) = / 2 f 1 + cos [ 2 c t + 2 p2 sin t| 1 (c)
where a (c) has been assumed constant over the bandwidth of the signal. The
term in (22) which contributes to the intermodulation distortion is
( / 2) cos [ 2 c t + 2 p^ sin (c)
(23 )
Note the term in (23) is simply an FM signal with a carrier frequency and
modulation index twice that of the original waveform.
Using (23), the intermodulation components contained in the term
3 e, e ^ k„ are:
b c 3
IM= 3 a (c) a (b) lc„ BC^ I 1 J (P.) J. (2P0) cos | (2 c-b) t + ku0t - mu tl
o . m I k z z
k m
Table 6 lists the coefficients of the FM signals e, (t) and e (t) which are above
.01 in magnitude for the specific case of p. =2.4, f = 10.42 Kfiz, R„ =2.4 and
f2 = 12.5 KHz. 1
Table 7 lists the various intermodulation terms along with the components of the
original FM signal which generates them. Only terms with amplitudes above .01 are
listed to show how each term is generated .
For example, the first listing in Table 7 is generated from the interaction of
7th order term of the squared signal e£ (t) and the 1st order term of the e^ (t), ? .e. ,
k = -7 of e (t): J 7 (2-2.4) cos |2ct - 7-2tt (12,500) t|;
m = 1 of e^ (t): (2 .4) cos [ b t + 2ir (10,420) t |
Amplitude of IM relative to unmodulated IM = (J y (4.8) )
I
-23-
J M .8) • J (2 .4) (.0429)(.520) = .00223
Spectral frequency = (-7) (12.5) - 10.42 = - 97.92 KHz
For this example, the signal levels are
B - signal power = -23 dBm
B =15.8 mv
rms
C - signal power = - 12 dBm
C =56.3 mv
rms
Order
n
J (p.)=J (2.4)
n 1 n
Amplitude Coeff.
of e^ (t)
J (2pJ = J (4.8)
n rZ n
Amplitude Coeff.
of e ^ (t)
c
0
0.00251
-0.24043
1
0.52019
- 0.29850
2
0.43098
0.11605
3
0.19811
0.39521
4
0.06431
0.37796
5
0.01624
0.23473
6
0.00337
0.11105
7
0.00059
0.04290
8
0.00009
0.01408
Table 6. Coefficients of the FM signals e, (t) and e (t)
b c
for |3j = 2 .4, f^ =10.42 KHz, =2.4 and
f2 = 12.5 KHz.
Considering the effects of the intermod only and assuming that the intermodulation
center frequency is the same as the receiver frequency, i .e. , 2 c-b = a, the effects can easily
be evaluated. Combining (24) with the desired signal the output can be written
v. (t) = A K cos at+3a(b)a (c) k,, BC^ I Z J (B.) •
i — , — o i n
4 k n
(2Bj) cos f a t + k u>2 f ~ "XJj f|
(25)
-24-
Output Intermod
Freq. in KHz
(Relative to Intermod.
Center Frequency)
-97.92
-85.42
-95.84
-72.92
-83.34
-93.76
-60.42
-70.84
-81 .26
-91.68
-47.92
-58.34
-68.76
-79.18
-35.42
-45.84
-56.26
-22.92
-33.34
-43.76
-54.18
-10.42
-20.84
-31.26
-41.68
2.08
• 3.34
-18.76
-29.18
14.58
4.16
-6.26
Output Intermod.
Level (Relative
to Unmodu lated
Intermod . )
-0.0223
0.0578
0.0479
-0.1221
-0.1012
-0.0465
0.1966
0.1629
0.0749
0.0243
-0.2056
-0.1703
-0.0783
-0.0254
0.0604
0.0500
0.0230
0.1553
0.1286
0.0591
0.0192
-0.1251
-0.1036
-0.0476
-0.0155
-0. 1 553
-0. 1286
-0.0591
-0.0192
0.0604
0.0500
0.0230
Order of Used
to Generate
Intermod.
Order of B
to Generate
Intermod.
Table 7. IM Spectrum.
-25-
Output Intermod.
Freq. in KHz
(Relative to Intermod.
Center Frequency)
27.08
16.66
6.24
-4.18
39.58
29.16
13.74
8.32
52.08
41.66
31.24
20.82
64.58
54.16
43.74
77.08
66.66
Output Intermod.
Level (Relative
to Unmodulated
Intermod. )
Order of Used
to Generate
Intermod.
0.1629
0.0749
0.0243
0.1221
0.1012
0.0465
0.0)51
0.0578
0.0479
0.0220
0.0223
0.0185
Order of B
to Generate
Intermod.
Table 7. IM Spectrum (Continued).
•- • ■
This signal is further filtered by the output stage of the RF-amplifier and the
IF -amplifier stages. For simplicity assume the filtering due to the IF to be ideal with
characteristics shown in Figure 6.
Figure 6. IF Characteristics.
The IF-bandwidth is assumed to be 50 KHz i .e . , Au = ( 2ir) ' ( 25 ) • (10).
With this assumption only those components within 25 KHz of the carrier will be passed by
the IF-amplifier . These are listed in Table 8.
IM Component
Frequency Relative
to Carrier
Amplitude Relative
to Unmodulated IM
2.08
0.16
4.16
.05
4.18
.03
6.24
.08
6.26
.02
8.32
.02
8.34
.13
10.42
.13
14.58
.06
16.66
.17
18.74
.07
18.76
.06
20.82
.02
20.84
.10
22.92
.16
Table 8. IM Components Out of IF. Only Those Components
Above the Carrier Frequency are Listed. Those
Below are the Same .
23MM
The effects of the IF-amplifier are represented by selecting the terms in the
summation given in 25) which are within the receiver bandwidth, i.e..
v 2 (t) - Kj A cos a t i-
P. t 1 2P t 1
2, J I
Terms in 3 BC K a (b) a (c) , _ , .» _ n
IF Bandpass | ^ * ’> &S '>
J (P.) J. (2P0) | cos | at •- nu0t - ku t
m I k Z Z
(26 )
Rewriting (26) in terms of an amplitude and a phase the results of passing this
signal through an envelope detector can easily be determined, i.e..
Kj A [ 1 t- d1 (t) ICj/ A Kj|
where d. (t) = Terms within f (3/4a(b) c>2(c) B C2 I I J (P,)
IF passband k n
(2p2) cos | (ku2- ncj| ) t| |
For the example being illustrated here we have the following:
(27)
a (b) - a (102.5) = - 9 dB
a (c) = a (105.5)= - 4.5 dB
(.36 linear magnitude)
(.6 linear magnitude)
A = 1 . 123 m volts
rms
Max ! d. (t) | =3 BC2 c(b) a2 (c) F =2N/5 (4.87X 10~6 ) F
1 4
where F is a factor introduced that accounts for the IF filtering and the phase
differences between the spectral components. The maximum value of the ratio d^ (t)/A
is,
K.d (t) -
Max|^-i ) = 20 (8.67X 10 F) = .173F
where = 20 (linear). This value would indicate a significant interference
potential.
This model can be used in several other ways. For example, the following
question might be asked: What minimum distance must be maintained between the localizer
receiver and two 100 kw FM stations, operating at frequencies such that an intermod at
the localizer frequency is produced, to avoid IM distortion. The distortion criteria is based
arbitrarily on the following:
1
-28-
If Max | (d, (t)/A)~rr— F| N .1 distortion potential
1 K,
■s
If Max | (d, (t) / A)—p — F| < .1 no distortion
1 "S
The arbitrary decision criterion listed above assumes that the receiver would
capture the stronger localizer signal; however, there would be notable output when
there is no desired signal present at interference signal levels below these values.
Note here we have arbitrarily taken the Max| d^ (t) F/A Kj| as the statistic.
Whether or not this is a good statistic needs further investigation.
For the example calculation we have
Max d1 (t) «3 3 BC2 F^a (b) a (c)
( B and C are peak values). If a decision boundary of 0.1 is used and the specific
values for this example are used the equality in (28) holds .
B (dBM) <-2 C (dBm) + A (dBm) -20 log F -20 log IC/K - 5.5
J ( 28 )
We have used the attenuations a (c) = -4 .5 dB and c^b) = -9 dB.
The region of allowable combinations of signal levels B and C which would pose
no interference potential under our criterion is illustrated in Figure 7.
B (dBm)
C (dBm)
-5.5 -20 log F -20 log
/ 1^1 + A (dBm)
No Interference
Figure 7. Signal Levels for No Interference.
-29-
The developed equations can be combined to place restrictions on the minimum
allowable distance from the localizer receiver for the commercial FM antenna. The
power input to the receiver in dBm (assuming (ERP). expressed in dBm) is
P; = (ERP). -36.3 -20 I °g ] 0 f " 20 l°910 d - L (29)
Using this relation the signal level in dBm available at the input to the receiver
is (using the B signal as example)
B (dBm) = (ERP)b -36.3 -20 log1Q b-20 log1Q db -l_b ( 30 )
Putting in the specific values for this example the result is
-20 log d <-42.4 -K./K (dB) - 20 log d +40 log d (31)
D u q q
The value of 3 K /2K has been given in the previous section for the NAV 1 1
receiver as approximately 4 dfe; hence ^/Kj = .5 dB. Assuming F = I, (31) becomes,
20 log db > 42 .9 + 20 log dy'd^ or db d ^ >140 d ( 32 )
Assuming a critical distance of 5 miles from the localizer (32) indicates there
would be a potential interference if the distances are such that
2
db dc > 698 ( 33 )
Using (33) the regions of interference can be identified as illustrated in
Figure 8 .
d
c
26 1 5
18.7 2 5
15.2 3 5
13.2 4 5
11.8 5 5
8.3 10 5
5.9 20 5
Figure 8. Regions of Interference.
Assuming F to be unity gives a pessimistic result in general. Another statistic
which has been used is the RMS output of the detector which is very simple to calculate
and measure. Experimental and theoretical results using this as the statistic have been
shown to agree very well and since it is easier to specify, is probably the better statistic.
Using the RMS value at the output of the detector we define the modulation factor (MF)
as,
Mp _ RMS Detector Output with FM Modulated Signal ^ ^4 )
RMS Detector Output with FM Carrier Only
Experimental and analytical results obtained are given in Table 9.* In order to
obtain the experimental results a true RMS reading meter and a full wave rectifying
averaging AC digital voltmeter were used to measure the detector output. It is seen
that the experimental and calculated results agree very well.
C. Cross-Modulation Considerations. As indicated earlier, the terms contributing
to cross-modulation effects result from:
3
( 1 ) e (generally small, so this term can be neglected)
a
2 2
( 2 ) 3e e, and 3e e
a b a c
It is easy to show that there would be no cross-modulation distortion produced
other than a change in carrier level if all frequency components are passed with the same
attenuation a. Since the frequencies of the interfering FM stations are located in the
"skirts" of the localizer receiver characteristics, each frequency component will be
attenuated differently. The different attenuation of each of the frequency components
results in AM modulation which appears as cross-modulation on the localizer signal.
To account for these effects, it is necessary to have available the receiver
selectivity characteristics. A very simple compact expression can be used to calculate
these effects. Considering one interfering signal, i.e.,
e^ (t) = B cos | bt + pi sin om^t ]
The equivalent Fourier series representation is
ao
e, (t) = B I J (fO cos f bt + mu.t] ( 35 )
b ml
m = -00
Assuming the "skirt" characteristics of the input filter of the RF-amplifier can
be approximated by a linear amplitude-frequency characteristic and zerophase shift as
* Details of the measurement procedures and results are given in Appendix D.
-31 -
shown In Figure 9, the attenuation characteristics can be written
a (b + kuj) = a (b) [ 1 + kuj6 | ( 36 )
where 6 ~(a(b 1_Au>)-a(b))/A<j
and is the slope of the input filter characteristics. Assuming an FM signal input to a
filter such as described above, the output can be shown to be
v = a (b) (1 t- B 5u, cos u.t) B cos (b t + B sin u,t) ( 37 )
o II I
Figure 9. "Skirt" Characteristics.
Figure 10. Signal Spectrum.
It is seen that the Frequency modulation of the output is the same as the input,
but in addition there is amplitude modulation which is the same as the original modulating
signal. The percent AM modulation produced by this attenuation function is
% modulation = pS Uj X 100 ( 38 )
The cross-modulation effects are given by
3 AB^ a (b) I 1 + pj cos t| ^ cos (at) ( 39 )
2
and
3 AC^ a (c) [ 1 + p„ 6<j0 cos t ] ^ cos (at)
(40)
Assuming
p 6 small, then equations (39) and (40) become.
3 KgAB^ a (b) | 1 + 2 p^5*co | cos Ujt| cos (at)
2
(41 )
and
0 0
3 K-^AC a (c) | 1 + 2 P26u2 cos ujH cos (at)
(42 )
2
Combining these with the desired signal the result is
(43)
2 2 ^ ,xo 2 m2
a (b)2PjSuj B cosujt+^— a (c) 2p^ C cos ^ *1 cosat
The spectrum of this wave form is shown in Figure 10.
Assuming these components within the IF Bandpass, the output of an AM envelope
detector will be within a multiplicative constant
3ICj 2 o 2 2
2fc~ I 2 a (b) B cos t + 2 a(c) ^2^2 ^ ^"cos Uj H ( 44 )
Equation (44) specifies the resulting output of an envelope detector due to "brute-
force" interference of two FM stations operating at frequencies b and c respectively.
For the specific example being considered in this report specific numerical
calculations of these effects can be made. For example, the peak value of the percent
AM modulation due to the interfering stations can be calculated, i.e..
e = K.A
O !
3K3 2 2 3K3 2 2 3K3
I *2|<7 8 a (b) a (c) + 2^
']
-34-
% AM- Mod =
peak
K
2 R~ ^2n (b) f}| S<-> j B2 i 2a^ (c)p2 C^6u2
3K
1 + ~J- | B2 a2 (b) + C2 a2 (c) |
x 100
2K
(45)
For the example being considered,
a(b = 102.5) = - 9 dB
a(c = 105.5) = - 4.5 dB
3K
2K,
— = 31 .7 linear
(.355 linear)
(.6 linear)
3| =32 =2.4
Ul - (2ir) (12,500)
u2 - (2ir) (10,420)
.0612
.103
as
8’ - TMHz ’ s" = Tmhz (see Fi9ure H~2)
B = -23 dBm; B = 15.8 mv (RMS)
C = -1 1 dBm; C = 56 .3 mv (RMS)
Using these (45) gives the percent AM modulation due to "brute-force" interference
% AM modulation = .04%
The above percent AM modulation due to "brute-force" interference seems minimal
when compared with that due to intermodulation as given in the previous section. This, of
course, is due to frequencies being chosen so as to produce an intermod at the frequency the
receiver is tuned to and having the modulation indices low.
D. Combined Effects of Intermod and Brute-Force Interference. Although calculations
for the example given here indicate that the "brute-force" interference is minimal when
compared with the intermod, it is desirable to indicate how these two effects can be combined.
The RF output resulting from the desired signal and an intermod is
Kj A cos at + dj (t) cos (at + <t>) + d2 (t) sin (at + O)
(46)
where it has been assumed that 2 c-b - a . If this is not the case, then the proper
frequency will have to be specified in the last two terms of (46). Using (43) and (46) the
combined effects are given by
3K3 2 2 3K3 2 2
Distortion = K.A [ 1 + — B a (b) + — C a (c) +
2K] 2K1
3K3 2 2 3K3 2 2
2 a (b) p. 5u, B cos u,t + 2 a (c) p_ 5u„ C cos u_t +
2Kj 2K1
K3 K3
d. (t) cos at + d (t) sin at
KjA K] A
(47)
Equation (47) has made some simplifying assumptions which could be considered
worst case. For example, it has been assumed that all components are in phase, which is
not true in general. This assumption will provide a worst case analysis; however, the
technique can be extended to account for different phases.
The output of an envelope detector would be (using (47) ).
KjA M + — (|B2 a2 (b) +|C2 a2 (c) + |2a2 (b) p, gU] B2
K1
cos Ujt + J 2a2 (c) P2 S"u>2 C2 cos u2 + d1 ^ )2 + d22(t) 1
2 2
K1 A
(48 )
This expression can be approximated by
3K_ _ 0 ^ 00
KiA M+ 2irB a (b)+? i^-c ° (c)
Carrier compression term due to
"brute- force"
+ | [ 2 a (b) p^ 6!j^ B2 cos Uj + 2 a (c) P2 S"u2 C2 cos
AM-modulation term due to "brute-force" interference
(cross-modu lati on)
d, (t)
(49)
In ter mod
Term
-36-
In obtaining (49) the squared terms have been neglected. It has been assumed that
K1 A
d2 (t) « 1
( -j^-)2 B2 a2 (b) + 2 B2 2 a2 (b) p2 cos ^t + | 2 02 (c)
C2 COS u„t + ^ )2 << 1
Z A
These conditions hold except in cases of extreme interference.
VII EXTENSIONS OF THE TECHNIQUES
The extensions of the techniques to handle cases where there are multiple inter-
fering sources are conceptually very simple; however, the calculations required would
be lengthy and involved. A computer program was written which would perform the
required computation for any specified number of interfering stations. As an example
we evaluate the interference potentials in the greater Birmingham, Alabama area
airport. This region was chosen due to the fact that there have been reported cases of
interference with airborne communications and navigational receivers.
Figure 11 shows the area of interest qnd Figure 12 shows an expanded view of the
area along with the various FM broadcast stations of interest.
Table 10 lists the various FM broadcast station call letters, frequencies,
coordinates and powers and Table 11 lists the localizer frequency (110.3 MHz) and its
coordinates, along with the outer marker location and the VOR frequency and location.
Using the data the approximate distances of each FM station from the localizer
aro given in Table 12.
Table 13 gives a listing of the various signal levels at the receiver assuming a
normalized distance of 1 mile from each radiating source and the receiver. In order to
apply the tabulated results they must be adjusted by a correction factor which would
account for the proper distance from the FM source to the receiver. This correction
factor is 20 log^d, where d is in miles.
Assuming a localizer power of 40 watts and a normalized distance of one mile
from the receiver the following results for the localizer are obtained:
Frequency = 110.3 MHz
Miles from localizer = 1 mile
Free space attenuation = 77.2 dB
-37-
Call
Letters
Freq. In
MHz.
Coordinates
Power
WBHM
90.3
330-29,-19"/86°-47"-58"
50 kw
WDJC
93.7
33 - 26 -36 /86 - 52 - 50
100 kw
WAPI
94.5
33 -29 -26/86 -47 -48
100 kw 1
WQCZ
96.5
33 -29 - 02 /86 - 48 - 21
50 kw
WVOK
99.5
33 -26 -28/86 - 55 -00
100 kw
WZZK
104.7
33 -29 - 02 /86 - 48 - 35
100 kw
WKXX
106.9
33 -29 -19/86 -47 -58
100 kw
WENN
107.7
33 -29 - 02 /86 - 48 - 35
100 kw
WBRC CH: 6 TV-100 kw also near l
Table 10. FM Broadcast Stations in the Birmingham Area.
BHM-VOR
114.4 MHz .
33-40-12/86-53-59
LOM
(Outer Marker)
33-30-40/86-50-44
LOC
110.3 MHz.
33-34-17/86-44-33
Table 11 . Airport Facilities.
Station
Distance
in miles
WBHM
6.1
WDJC
11.8
WAPI
5.9
WQCZ
6.4
WVOK
12.0
WZZK
6.6
WKXX
6.0
WENN
6.6
Table 12. Distance of FM Broadcast Stations from Localizer.
-40-
Power in dBm = 46 .
Antenna loss = 0
Input Fi Iter loss = 0
Resultant desired signal level at RF amplifier input = -25.1 dBm. This value
must also be corrected for the distance.
Several calculations were made to investigate the interference problems relating
to this area and are given below
(a) Receiver at location (1) in Figure 13
Referring to Figure 13 this calculation assumes the aircraft at position (1) closest
distance to the cluster of FM stations.
Table 14 gives a computer printout of the signal level computations for each
station and the various attenuation factors. Also included in Table 14 is the calculation
of the localizer signal level at position (1). The predominant type of interference
expected in this case is of the "brute-force" type as indicated by the signal levels in
Table 14. Table 15 gives the cross-modulation resulting from each interfering station
and also the resultant cross-modulation due to the combined effects of the interfering
stations. For these computations a frequency deviation of 40 KHz was used and the
slope characteristics of the receiver front-end (RF amplifier) were modeled by the
following:
L
.15 dB/100 KHz for frequencies less than 8 MHz awoy
from the receiver frequency
. ,075dB/ 100 KHz outside the range
Using this data the resultant AM modulation due to cross-modulation of the
interfering signals was computed using the techniques given, which have been expanded
to include more than two stations. The results of these calculations are given in
Table 15.
For these calculations no modulation was assumed so that the maximum inter-
ference power is at the desired localizer frequency.
The statement at the bottom of Table 15 indicates that there is significant "brute-
force" interference in this case. As a matter of fact, for this location the amount of cross-
modulation calculated which results in compression of the desired signal is in excess of
1; hence, the third-order model would not be valid. However, this is of no consequence
since there will definitely be high interference levels observed at this location.
Table 16 gives the resulting intermodulation results due to the interfering signals.
It does not consider the effects of cross-compression. In any case the significant inter-
ference at this poinf is due to "brute-force" interference; however, the resulting com-
pression of the desired signal would allow the relative weak intermod component to feed
through and cause problems.
-42-
PRINTOUT OF SIGNAL LEVEL COMPUTATIONS
STATION
MILES
STATION
FREE
NAV
RCVR INPUT
SIGNAL LEV
FREQ
FROM
POWER
SPACE
ANTENNA
FILTER
AT RFAMP IN
(MHZ)
RECEIVER
IN DBM
ATTEN-DB
LOSS-DB
ATTEN DB
DBM
90.3
2.9
77.0
84.7
18.2
19.2
-40.9
93.7
6.9
80.0
92.5
14.8
17.2
-39.8
94.5
2.9
80.0
85.1
14.0
16.7
-30.9
96.5
2.9
77.0
85.2
12.0
15.5
-30.6
99.5
6.9
80.0
93.0
9 .0
13.7
-30.1
104.7
2.9
80.0
85.9
3 .8
6.7
-12.1
106.9
2.9
80.0
86.1
1 .6
4.1
-6.8
107.7
2.9
80.0
86.2
0.8
3.1
-4.9
LOCALIZER SIGNAL LEVEL CALCUIATIONS:
110.3
6.7
46.0
93.7
0.0
0.0
-41.7
Table 14. Signal Levelsat Location (1).
L.
********* **CR0SS MODULATION CALCULATIONS **********
STATION
COMPRESSION
FREQ DEV.
% AMMOD
FREQ
OF LOC. SIGNAL
FORXMOB-
CAUSED
(MHZ)
IN DB
CALC. (KHZ)
BY STAT.
90.3
-0.0
40.
0.00
93.7
-0.0
40.
0.00
94.5
-0.0
40.
0.00
96.5
-0.0
40.
0.00
99.5
-0.0
40.
0.00
104.7
-1.6
40.
.11
106.9
-7.6
40.
1 .08
107.7
-21.3
40.
9.33
****CROSS COMPRESSION GREATER THAN 1 , THIRD ORDER MODEL OF RECEIVER NO
LONGER VALID. TOTAL PERCENT MOD., NOT CONSIDERING CROSSCOMPRESSION=
.86 COMPRESSION FACTOR 1 .679 DESIRED SIGNAL COMPRESSION IN DB*****
TOTAL PERCENT AM MODULATION = *****
Table 15. Cross- Modulation Due to Interfering Signals. Receiver at Point (1) Location.
-44-
RECEIVER FREQUENCY IS 110.30 RECEIVER BANDWIDTH IS 40.0 KHZ
FREQUENCIES WHICH PRODUCE INTERMOD INTERFERENCE ARE:
FI
F2
F3
IM TYPE
IM CENTER FREQ
93.7
106.9
90.3
FI + F2 - F3
110.30
IM LEVEL IN DBM, NO FM STAT. MODULATION
-81 .5
Table 16. Intermodulation Interference. Receiver at Point (1) location.
PRINTOUT OF SIGNAL LEVEL COMPUTATIONS
STATION
MILES
STATION
FREE
NAV
RCVR INPUT
SIGNAL
FREQ
FROM
POWER
SPACE
ANTENNA
FILTER
LEV AT
(MHZ)
RECEIVER
IN DBM
ATTEN-DB
LOSS-DB
ATTEN DB
RFAMP IN DBM
90.3
3.5
77.0
86.3
18.2
21 .0
-42.5
93.7
5.5
80.0
90.5
14.8
18.4
-37.8
94.5
3.5
80.0
86.7
14.0
17.8
-32.5
96.5
3.5
77.0
86.9
12.0
16.3
-32.2
99.5
5.5
80.0
91.1
9.0
14.1
-28.2
104.7
3.5
80.0
87.6
3.8
8.4
-13.8
106.9
3.5
80.0
87.8
1 .6
5.1
-8.5
107.7
3.5
PO.O
87.8
0.8
3.9
-6.5
LOCALIZER SIGNAL LEVEL CALCULATIONS:
110.3
8.5
46.0
95.7
0.0
0.0
-43.7
Table 17. Signal Levels at LOM Location
(b) Receiver at the LOM
Similar results are given assuming the aircraft at the Localizer Outer Marker
(LOM) as noted in Figure 13. Tables 17, 18 and 19 give these results. Again it is
observed that a significant interference due to "brute-force" is expected.
(c) Receiver at Point 2 on Figure 13
Tables 20, 21 and 22 give results when the aircraft receiver is at location 2.
****************CROSS MODULATION calculations****************
STATION
COMPRESSION
FREQ DEV.
% AMMOD
FREQ
OF LOC. SIGNAL
FOR XMOD
CAUSED
(MHZ)
IN DB
CALC. (KHZ)
BY STAT.
90.3
-0.0
40.
0.00
93.7
-0.0
40.
0.00
94.5
-0.0
40.
0.00
96.5
-0.0
40.
0.00
99.5
-0.0
40.
0.00
104.7
-1 .1
40.
0.07
106.9
-4.5
40.
0.52
107.7
-8.6
40.
1.48
******CROSS COMPRESSION GREATER THAN 1, THIRD ORDER MODEL OF RECEIVER
NO LONGER VALID. TOTAL PERCENT MOD., NOT CONSIDERING CROSSCOMPRES-
SION = .40 COMPRESSION FACTOR 1 . 1 55 DESIRED SIGNAL COMPRESSION IN
DB = ********TOTAL PERCENT AM MODULATION = *****
Table 18. Cross-Modulation Due to Interfering Signals. Receiver at LOM Location.
RECEIVER FREQUENCY IS 110.30 RECEIVER BANDWIDTH IS 40.0 KHZ
FREQUENCIES WHICH PRODUCE INTERMOD INTERFERENCE ARE:
FI F2 F3 IM TYPE IM CENTER FREQ
93.7 106.9 90.3 FI + F2 - F3 110.30
IM LEVEL IN DBM, NO FM STAT. MODULATION
-82.8
Table 19. Intermodulation Interference. Receiver at LOM Location.
-46-
PRINTOUT OF SIGNAL LEVEL COMPUTATIONS
STATION
MILES
STATION
FREE
NAV
RECVR INPUT SIGNAL
FREQ
FROM
POWER
SPACE
ANTENNA
FILTER
LEV AT
(MHZ)
RECEIVER
IN DBM
ATTEN-DB
LOSS-DB
ATTEN DB
RFAMPIN DBM
90.3
5.7
77.0
90.5
18.2
21.0
-46.7
93.7
3.2
80.0
85.8
14.8
18.4
-33.1
94.5
5.7
80.0
90.9
14.0
17.8
-36.8
96.5
5.7
77.0
91 .1
12.0
16.3
-36.5
99.5
3.2
80.0
86.4
9.0
14.1
-23.5
104.7
5.7
80.0
91 .8
3.8
8.4
-18.0
106.9
5.7
80.0
92.0
1 .6
5.1
-12.7
107.7
5.7
80.0
92.1
0.8
3.9
-10.8
LOCALIZER SIGNAL LEVEL CALCULATIONS:
110.3
11.5
46.0
98.4
0.0
0.0
-46.3
Table 20. Signal Levels at Location (2) in Figure 13.
*************** ***£^OSS MODULATION CALCULATIONS******************
STATION
COMPRESSION
FREQ DEV.
% AMMOD
FREQ
OF LOC. SIGNAL
FORXMOD
CAUSED
(MHZ)
IN DB
CALC. (KHZ)
BY STAT.
90.3
-0.0
40.
0.00
93.7
-0.0
40.
0.00
94.5
-0.0
40.
0.00
96.5
-0.0
40.
0.00
99.5
-0.1
40.
0.00
104.7
-0.4
40.
0.02
106.9
-1.4
40.
0.14
107.7
-2.3
40.
0.27
TOTAL PERCENT MOD., NOT CONSIDERING CROSSCOMPRESSION= 0.6 COM-
PRESSION FACTOR 0.488 DESIRED SIGNAL COMPRESSION IN DB= 5.2 TOTAL
PERCENT AM MODULATION = .43
Table 21 . Cross-Modulation Due to Interfering Signals. Receiver at Location (2).
RECEIVER FREQUENCY IS 110.30 RECEIVER BANDWIDTH IS 40.0 KHZ
FREQUENCIES WHICH PRODUCE INTERMOD INTERFERENCE ARE:
FI F2 F3 IM TYPE IM CENTER FREQ
93.7 106.9 90.3 FI + F2 - F3 110.30
IM LEVEL IN DBM, NO FM STAT. MODULATION
-83.5
Table 22. Intermodulation Interference. Receiver at Location (2).
From these results it is seen that the resulting cross-modulation due to "brute-
force" interference is approximately .43 percent, assuming the frequency deviation
and receiver front end characteristics given earlier. Whether or not this creates a
particular significant level of interference would be a matter of judgment and more
investigation of this important decision criterion is required.
(d) Receiver at Location (3).
The results to be expected when the receiver is at location (3) are given in
Tables 23, 24 and 25. As in the previous case whether there is an interference problem
at this position is a matter of the "definition of interference" . Since the resulting AM
modulation due to cross-modulation resulting from the interfering signals is only .16
percent and the intermod level is -89 dBm, it is expected that there would be minimal
interference at this location.
VIII CDI MODEL
A. Analytical Model. In order to predict the effects of interfering FM stations
on the navigational aids it is necessary to have an analytical model of the CDI Circuitry.
Thus far, the model has been capable of predicting responses throughout the receiver to
the AM-detector output circuitry.
Figure 14 shows a block diagram of the audio processing circuitry of the NAV 1 1
receiver, which is assumed to be typical of those to be encountered in practice. Figure 15
shows a more detailed schematic diagram of the circuitry of interest.
After rather detailed and involved investigations the CDI response was modeled
by a relative simple relationship, given in (50) below
CDI = k (VB, - 0 Vffi )
where
CDI = the measured voltage “ ^£407 as indicated in Figure 15
(measurements are made with a DC DVM).
VB1 = RMS voltage at the base of Q 409
VD_ = RMS voltage at the base of Q 410
B2
D = Ratio of the RMS voltage at the base of Q409 to the RMS voltage
at the base of Q 410 with CDI = 0 p amp
d-Vb1 I
U I 1 I r\ i a t C. 1 \
CDI =0.
(51 )
-48-
PRINTOUT OF SIGNAL LEVEL COMPUTATIONS
STATION MILES
STATION
FREE
NAV
RCVR INPUT
SIGNAL
FREQ FROM POWER
SPACE
ANTENNA
FILTER
LEV AT
(MHZ) RECEIVER IN D3M ATTEN-DB
LOSS-DB
ATTEN DB RFAMP IN (DBM>
90.3 8.C
77.0
93.5
18.2
21.0
-49.7
93.7 3.1
80.0
85.6
14.8
18.4
-32.8
94.5 8.0
80.0
93.9
14.0
17.8
-39.7
96.5 8.0
77.0
94.1
12.0
16.3
-39.4
99.5 3.1
80.0
86.1
9.0
14.1
-23.2
104.7 8.0
80.0
94.8
3.8
8.4
-21.0
106.9 8.0
80.0
94.9
1 .6
5.1
-15.6
107.7 8.0
80.0
95.0
0.8
3.9
-13.7
LOCALIZER SIGNAL LEVEL CALCULATIONS:
110.3 14.4
46.0
100.3
0.0
0.0
-48.3
Table 23. Signa
1 Levels at Location (3)
•
******************crqss MODULATION CALCULATIONS******************
STATION
COMPRESSION
FREQ DEV.
% AMMOD
1
FREQ
OF LOC. SIGNAL FOR XMOD
CAUSED
(MHZ)
IN DB
CALC. (KHZ)
BY STAT.
90.3
-0.0
40.
0.00
93.7
-0.0
40.
0.00
94.5
-0.0
40.
0.00
96.5
-0.0
40.
0.00
99.5
-0.1
40.
0.00
104.7
-0.2
40.
0.01
106.9
-0.7
40.
0.06
107.7
-1 .1
40.
0.12
TOTAL PERCENT MOD., NOT CONSIDERING CROSSCOMPRESSION= 0.01 COM-
PRESSION FACTOR 0.235 DESIRED SIGNAL COMPRESSION IN DB-2.3
PERCENT AM MODULATION 0.16
Table 24. Cross-Modulation Due to Interfering Signal. Receiver at Location (3).
Receiver frequency is 110.30 receiver bandwidth is 40.0 kh2
FREQUENCIES WHICH PRODUCE INTERMOD INTERFERENCE ARE:
FI F2 F3 IM TYPE IM CENTER FREQ
93.7 106.9 90.3 FI + F2 - F3 110.30
IM LEVEL IN DBM, NO FM STAT. MODULATION
-89.1
Table 25. Intermodulation Interference. Receiver at Location (3).
-49-
To determine the various parameters in (50), a 150 Hz and 90 Hz signal which
would result in a 0.0 microamp deflection is used as the input at point E 403 (see Figure 14)
of the receiver and adjustments are made so as to give 0.000 volts D.C. , i .e.
V - V = 0* The data obtained is given in Table 26 (see
measurements a, d and g).
Using this data the following results are obtained for the factor D in (50):
Measurement a
Measurement d
Measurement g
D = .701/. 640 = 1 .095
D = .658/. 604 = 1 .084
D = .638/. 585 = 1.090
Using the average of these as the value for D we have,
D = 1 .09
(52 )
Similarily using (50) and the data given in Table 26, k can be determined i .e. ,
(53 )
“!=VB!-DV82
k
Measurement b
CPI = .77 4 - (1 .09) (.563) = .160
nr
Using the above the measured value of k is
k measured -
CD I meas (i.e. V£404 - VE407)
VB1 -°VB2
.064
.160
(54)
= .400
Similarily using measurements c, e and f one can obtain several
independent values of k, i.e.,
Measurement c
Measurement e
Measurement f
k meas = .416
k meas = .412
k meas = .4005
The data given under measurement h was obtained by adding an assumed
interference signal with frequency of 105 Hz. Using the model above, the desired CDI
response calculated by
' CDI calculated = .4 (.744 - (1 .09) (.594) ) = .0385 volts
The measured value is .040 which gives less than 4% error between the measured
and calculated result.
For completeness several points relative to these measurements are given in Table 27.
-52-
(1) AC voltage measured with HP 3476B DVM
(2) AC voltage measured with HP 3476 DVM
(3) DC voltage measured with Digitek DVM
(4) Measured with 50 p amp deflection on ratio generator
(5) Measured with 105 Hz tone added to 90/150 Hz signal
given in measurement (g)
Table 26. Measurements of CDI Voltages.
Reference Notes
(1)
Measurement h is obtained taking the average of the
maximum and minimum voltage readings. The variation
of the voltage is due to the beat between the 105 Hz
and the 90 Hz signal.
(2)
For all measurements a 200 (jf capacitor was placed
across C 409. This makes the voltages at the emitters
of Q409 and Q410 the halfwave rectified output of
the signals appearing at their bases.
(3)
The capacitors C407 and C408 which couple the signals
from TP 402 and TP 403 into the comparator circuit have
significant impedance at 90 Hz and 150 Hz. Therefore,
to correctly calculate the CDI deflection, AC voltage
measurements must be performed at the bases of Q409
and O110.
(4)
CDI output was measured at the output of comparator
circuit to prevent errors arising due to the nonlinearity
of buffer circuit.
Table 27. Reference Notes Relative to Measurements in Table 26.
B- Modeling Receiver Filters. In order to predict the CDI response, it is
necessary to model the output of the ?0 and 150 Hz filters. Likewise to predict the
amount of audio interference caused by FM stations, the audio filter characteristics
must be known. Figure 16 shows the measured characteristics of the 90 and 150 Hz
filters. The audio characteristics are shown in Figure 17 and the detector characteristics
in Figure 18 .
Since the output of the 90 and 150 Hz filters would be highly dependent on the
properties of the modulation on the FM interfering signals*, the filters were modeled
using the following technique:
(1) Assume the input to the 90 and 150 Hz filters to be "white" noise,
i .e. , the modulation is assumed to have a constant spectral density over the passband
of the filters.
(2) Determine the noise equivalent bandwidth** of the 90 and 150 Hz
filters. For applying the model it would be necessary for the user to obtain or measure
this information .
(3) With the information contained in (1) and (2) the RMS outputs of the
90 and 150 Hz can be determined, which allows us to compute the modulation factors.
Figure 17 shows the filters with the same noise equivalent bandwidth as the
90 and 150 Hz filters used in the computer program.
Table 28 compares the results obtained from the computer program to measured
results with IM present and with desired signal noise modulated. (Details in Appendix D)
These results were compared with those obtained using a tone modulated intermod
formed from the FM signal as before.
The results show the good correspondence between the modulation caused by
IM and that caused by a noise source, justifying the analysis of IM using a noise source
model. It also shows that the computer program accurately predicts the amount of
interference .
*See Appendix D, Section 2
**See Appendix E for details in determining the noise equivalent bandwidth.
-55-
ITSSE." W81 *
I
T3
^djnQ pazjiDLUJOfsj
Figure 16. 90/150 Hz Filter Responses.
jnc^nQ pazijDuiJO^
Figure 18. Audio Filter CharacterisH
Fi Iter
Measured
Theoretical
% RMS Modulation
with desired signal
noise modulated
0)
% RMS Modulation
due to
IM Measured
(2)
% RMS Modulation
due to IM
Theoretical results
from Computer Program
Detector
12.1%
12.1%
12.1%
Audio
5.0%
4.7%
5.7%
150 Hz Filter
2 .4%
2.5%
2.4%
90 Hz Filter
2.0%
2.0%
1 .8%
(1) Desired signal present only, desired signal AM modulated by General Radio Model
1381 Random Noise Generator .
(2) Desired signal present, IM formed by 2 FM tone modulated stations.
Table 28. Summary of RMS Modulation Measurements and Calculations.
C. Effects of High Level Modulation on CPI Reading. During the experimental
verification of the model several difficulties were encountered which needed study.
One particularly important problem was that of detector overload (or clipping). The net
result of these effects is a desensitization of the receiver.
The procedure for determining these effects was to input a desired signal of
108 .5 MHz modulated with a standard 90/150 localizer signal and another signal at
lower amplitude with a frequency slightly offset from the 108.5 MHz. In this experiment,
108.501 MHz was used which results in an additional IKHz sideband in the IF stage.
This 1 KHz signal was detected along with the 90 and 150 Hz signals. This interfering
1 KHz signal caused the detector to overload and the detected signal was clipped. The
result is that the 1 KHz sideband signal simulates the effects of a high level intermod. In
theory this should have no effect on the receiver; however, due to the overloading of the
detector it does cause a significant desensitization problem.
7 fie 90 and 150 Hz filters have very narrow bandwidth, which eliminates a
considerable amount of the distortion. In order to obtain significant intermod interference,
it is necessary that the intermod level be significantly high so as to cause overload
-59-
distortion at the detector. From previous measurements (see Appendix D), it was determined
that an intermod carrier level which is 10 dB less than the desired signal (which results
in a modulation factor of .45 and a percent modulation of approximately 12% at the
detector output) causes significant interference. In this case the voltages at the outputs
of the 90 and 150Hz filters were measured to be .1 volts, which corresponds to an
equivalent modulation of about 2%. If the intermod level were increased by three
times to give an RMS modulation of 36%, the equivalent modulation at the output of the
90/150 Hz filters would be approximately 6%.
As an example of the use of the techniques consider the following:
(a) Assume the localizer signal such that it produces 60 pA CDI response,
then DDM = 60 (.155/150) = .06 or 6%
(b) In this case the receiver would see 23% modulation at the 90 Hz filter
output and 17% modulation at the 150 Hz filter output.
(c) Assuming an intermod present which results in an equivalent of 6%
modulation at the 90 Hz filter output, the modulation would be
J ( (,06)2 + (.23)2 ) x 100 = 23.8%
In a similar fashion the 150 Hz filter output would be
/( (.06)2 + ( . 1 7)2 ) x 100 = 18.1%
Using these results the CDI with the assumed interference present would be:
CDI = (23.8-18.1) (150/15.5) = 55.1 pA
This corresponds to an 8% reading change from the CDI reading with no interference
present, which would be a relatively small change in CDI reading. On the other hand
with a modulation of 40%, the CDI (assuming 60 pA without interference) changes by 20%
or gives a reading of 48 pA due to limiting or clipping of the detector output.* Therefore,
limiting due to overloading is the significant problem affecting the CDI reading.
IX COMPUTER PROGRAM
In Section VI an illustrative example of the calculations required assuming only
two interfering FM signals was given. If there exists more than two interfering signals,
the amount of calculations required becomes excessive for hand computations. A computer
program was written which is capable of making the required computations for any number
*See Appendix F for detailed data.
-60-
of interfering signals (limited only by the computer facilities available to the user).
The program performs the following tasks:
(1) Calculations of the signal levels at the RF amp input due to FM stations.
(2) Cross-modulation and cross-compression calculations.
(3) Printout of intermodulation producing stations.
(4) Calculations of % AM modulation due to IM.
(5) Computation of the effects of interference on CDI.
(6) Combined cross-modulation and intermodulation interference calculations.
Appendices G and H describe the computer program in detail and in Appendix G
is a sample printout from the program.
X CONCLUSIONS AND RECOMMENDATIONS
The research reported herein has culminated in analytical techniques capable of
predicting possible interference of airborne communication and navigation receivers due to
commercial FM broadcast stations. Approximate analytical models of the receiver were
dt .eloped which could be specified by rather simple measurements.
Both the effects of "brute-force" interference and intermodulation distortion can
be readily handled by the model. It was found, as was expected, that the majority of
the nonlinearities were due to saturation of the RF amplifier. A relative simple analytical
model using a third-order nonlinearity was found to be satisfactory for interference levels
of approximately 0 dBm and below. For higher signal levels than this, the model does not
account for limiting and other effects; however, for interfering signal levels of this strength,
it is expected that an interference problem would exist.
Measurement techniques involving only a monitoring of the AGC voltage were
developed which allows for the determination of the various parameters of the nonlinear
model. It was found that most of these parameters could be assumed relatively constant
over a wide range of input signal levels. In addition to the determination of the various
parameters of the nonlinear model, the following information must be known:
(1 ) RF frequency response
(2) IF frequency response characteristics (bandwidths and skirt attenuation
characteristics)
-61-
With this information the signals at the output of the IF-amplifier can be predicted.
In most cases it was found that the best way to handle the above characteristics was
to specify the overall frequency characteristics in terms of an input filter skirt slope attenua-
tion characteristics and an overall frequency response characteristic of the RF-amplifier
output circuitry and the IF-amplifier. For the latter both ideal bandpass and triangular
bandpass characteristics were used. Using the above analytical model, signals at the
input to the audio detector can be predicted.
Models of the audio detector circuit and the 90 Hz and 150 Hz filters in the case
of navigation receivers were developed. This requires the frequency characteristics of
the audio circuit and the 90 Hz and 150 Hz filters either be known or determined by
measurements. It is found that the interference at the output of the 90 Hz and 150 Hz
is rather small due to very narrow bandwidths of these filters. An analytical model of
CDI (course deviation indicator) was determined which could predict the effects of the
interfering signals.
Investigations were performed for determining the signal levels at the input to
the receiver given the station power and it was found that a satisfactory model to use was
the free space attenuation formula, along with an empirical correction factor to account
for the vehicle antenna loss. The empirical correction used was to assume 1 dB/l MHz
attenuation for signals below 108.5 MHz.
A computer program using the developed models and techniques was written which
can calculate and predict interference due to any number (limited only by the user compu-
ter facilities) of FM stations. The program uses the measured characteristics of the vehicle
receiver to predict the amount of interference due to high power FM stations. The program
assumes sinusoidal modulation on the FM signals and that the interference is due to 3rd
order non linearities in the RF amp of the receiver.
The user must supply the following information to analyze an interference situation:
Number of FM stations, receiver frequency, distortion parameter 3K^/2K . For each
FM station, the following information is required: Station frequency, modulation fre-
quency and modulation index, distance from the receiver and station power level. Loca-
lizer distance from the receiver and power level is also needed.
Although the program was written as general as possible, there are some specific
limitations and these are:
(1) A modulation index of 75 is a practical limit on the maximum modulation
index that the program will accept. Modulation indices higher will cause extremely long
program execution times. A modulation index of 75 corresponds to a maximum frequency
deviation of 75 KHz with a modulation frequency of 1 KHz.
(2) The program assumes that the modulation frequencies of the FM stations are
not harmonically related. For example frequencies of 1000 Hz and 400 Hz are related
whereas 1000 Hz and 398 Hz are not. The intermodulation due to stations with harmon-
ically-related modulation frequencies has components which occur only at certain frequen-
-62-
'Mgr
cies relative to the IM carrier and does not exhibit the "noise-like" (realistic) properties
which are assumed for IM calculations . Harmon! cal ly-related modulation frequencies will
be treated as though they were not related by the program. Therefore, when using harmon-
ically-related frequencies such as 1000 Hz and 400 Hz, it is advisable to check the results
to see if the same results are obtained as with frequencies of 1000 Hz and 398 Hz.
Although satisfactory analytical models and techniques have been developed in
this research, there were certain key items identified during the program which are
recommended for further research.
(1) The determination of reliable statistical criteria which would allow for
realistic decision making regarding interference potentials and which can be adequately
substantiated thus providing a strong, defendable technical basis for future judgment and
decisions concerning station allocations.
(2) Receiver modeling improvement, either by extending the current model or
the use of more sophisticated models than are currently being used.
(3) A written specification and verification of field testing procedures for
evaluating interference problems.
Although the above list is not an exhaustive list of identifiable items requiring
further investigation, those items on the list are believed to be of immediate concern and
importance for the proper enhancement of the results reported in this research. Brief
descriptions of the items recommended for further research are given below.
A. Statistical Model.
1 . Type of Modulating Signals to be Assumed. The research reported herein
has used primarily single tone modulated FM signals in the development of the model .
To a limited extent, "white" noise as a source of modulation has also been considered. Since
the CDI in a navigation receiver is preceded by rather narrow bandpass filters, the type
of modulation will have a considerable bearing on the CDI response.
Since the receivers will be operating in a real world environment, there is a
need for a statistical study to determine a model which would be truly representative of
real world modulations. Without this, one is left with only the option of talking about
probable "worst" case effect, which would be hardly a convincing argument in the real
world .
2. Statistical Basis for Interference Decision. The RMS value of the output
of an envelope detector due to the interfering signals was used as a parameter to deter-
mine a potential interference problem. It is possible that other parameters (statistics) might
be a better indicator of potential interference problems. For example, peak modulation
might be a more realistic parameter on which to base decisions regarding potential inter-
ference problems.
-63-
There is a need to investigate and determine which parameter or parameters are
useful and reliable for basing predictions of potential interference problems. It is proposed
that various parameters be investigated and evaluated and that these be related to real
world occurrences. The analytical methods and parameters would be substantiated by experi-
mental documentation.
3. Decision Criterion. For any mathematical or analytical model to be
useful, in a practical sense, one needs to know the implications of the results obtained, and
exactly how realistic they are. To i llustrate this rather involved statement, consider dis-
cussed criterion used in deciding a potential interference problem. The means of deciding
whether or not interference would occur was to simply postulate the following decision rule
using the RMS output of the envelope detector (V ) as the statistic (parameter):
Decision Rule
If V (RMS output of envelope detector due to interfering signals) > T decide
«- O. f ii • ■ • i .1 . .1 • r
in favor of an°interference problem, i.e
problem .
decide that there is a potential interference
If V < T decide that there is no significant potential interference problem. The
consequences°of the above are summarized below:
Actual
Condition
Interference
No (minimal)
Interference
V0 >T
Correct
Decision
Incorrect
Decision
Incorrect
Decision
Correct
Decision
Summary of the Results of Decision.
The peak-modulation index and the RMS output of an envelope detector were
used as the parameter (statistic) on which the decision was made. In particular, for checking
the model, T was arbitrarily set at some constant value. It was possible to provide a "profile"
of potential interference problems in terms of FM station (or FM stations) locations and
power relative to usable navigation signals. This allows for predicting the effects of adding
A
-64-
one or more FM stations in the near vicinity, or the results to be expected if signal powers
are changed .
In order to provide realistic and convincing arguments, regarding potential inter-
ference problems, two areas need further study, i.e., what decision rule and what statistic
Additional research is recommended which would result in the determination of
useful and reliable decision rules and parameter (these may be different for navigation and
communication receivers) for predicting potential interference problems. The results are
to be presented in terms of a statistical model using probability measures of the errors associ-
ated with the decision rules. This could be accomplished by specifying a "confidence"
interval describing the results of decisions regarding interference problems and/or probabilis-
tic measures of incorrect decisions.
B. Model Improvement. Although results obtained here have shown that the
analytical techniques used for modeling the propagation and the receiving of interfering
and/or desired signals, in conjunction with the all-important model of the airborne naviga-
tion and communication receivers in the presence of a multi-signal environment are useful
and applicable, there is a need for model enhancements and improvements. Enhancements
and improvements are needed in the two areas of concern, i .e., (1) propagation model and
(2) receiver model .
(1) Propagation Model. There is a need for providing an improved model
of the propagation of both the desired and interfering signals that would include more
realistically the effects of transmitting and aircraft receiving antennas. The problems
associated with modeling an aircraft antenna are of considerable difficulty and the solutions,
at most, only approximate in nature. This complication is due in large part to the presence
of the aircraft. It is suggested that investigations be undertaken which would result in a
more realistic model of the receiving antennas on board selected aircraft. For these inves-
tigations it is suggested that selected "reference" aircraft be identified and that each of these
be considered and the antennas and aircraft be modeled as a system. Such a model would
include coupling characteristics between key antennas on the aircraft. It is expected that
numerical moment method techniques performed with the aid of a digital computer will be
required to obtain these results. The end result of such investigations would be a computer
program which would be capable of modeling certain selected aircraft to a high degree of
accuracy. Theoretical results should be verified by experimental documentation.
should be used to provide realistic and convincing arguments regarding potential interfer-
ence problems .
A second phase of this investigation would involve a study which would enumerate
the resulrs and expected consequences of simplifying the propagation model. Trade-off
studies involving complexity vs. accuracy would be performed.
The results of the previously-mentioned investigations would allow for the realistic
and accurate modeling of the signal propagation from the transmitting to the receiving
antenna .
t
r
(2) Receiver Model. It has been demonstrated that the third-order receiver
model developed for predicting interference effects is useful in predicting the effects of multi-
ple interfering signals on aircraft navigation and communication receivers; however, it would
be desirable to improve the accuracy of these predictions. It is recommended that considera-
tions be given to enhancing the existing receiver model in order to improve the accuracy of
the predictions, along with investigations of other modeling schemes.
In particular, it is suggested that enhancement of the model be made so as to
be able to consider the effects of higher signal power levels either due to more interfering
signals or higher radiated power levels. It has been shown that the accuracy obtained using
the simple third-order model is limited at power levels of 0 dBm or higher.
It is recommended that research on the receiver model be continued and the best
way to enhance and extend the regions of validity of the receiver model be determined.
In particular, investigations using higher order terms in the existing model and a comparison
of these techniques in terms of complexity and accuracy with other models should be made.
In addition to the above important areas, effects of impedance mismatches, re-
flection coefficients, etc., should be considered.
Completion of these investigations along with the results obtained here would make
a complete package which would allow the user the flexibility of using a model of just
sufficient complexity to fulfill needed requirements. In some cases a very simple model
could be used to obtain results within the necessary requirements, while on the other hand
it may be necessary to use a rather complex model to obtain reliable results.
C. Standard Test Procedure. Efforts reported herein have been specifically for
the purpose of development and experimental testing of analytical models. A "Standard
Test Procedure" should be defined which would allow the engineer to set up an experimental
test using signal generators with specified modulations and antennas that would simulate
potential interference problems.
It is suggested that further research be performed which would identify such things
as signal levels, modulating levels and signals, antennas, etc. This would allow an engineer
to set up an experimental test which would realistically simulate the potential interference
problems being considered.
D. Interference Profile Mapping of Potential Airport Facilities. It is recom-
mended that further work be performed on detailed investigations of certain selected existing
and/or proposed new airport facilities as identified by FAA regarding the potential of an
interference problem existing and possibilities of such a situation developing. Typical ap-
plications would be to consider a specific airport and all possible interfering signal sources
in the near vicinity along with their respective power levels, and signal frequencies, and
using this data, calculations would be made to determine a "profile" of the interference
potentials existing. These "profiles" would be given in terms of minimum distances for the
establishment of additional FM-stations, effects of increased power levels, etc. These
"profiles" would be an indicator of how potentially close a particular facility is to having
an interference problem.
Similar techniques as described above could be applied to proposed new facilities
as identified by FAA personnel. Such results would be valuable in determining new sites
and the consequences of the selections could easily be determined.
XI. ACKNOWLEDGMENTS
The authors appreciate the encouragement and the many useful contributions
to the research reported here by the Project Director, Dr. Richard H. McFarland, and
Dr. Robert W. Lilley, Assistant Director, Avionics Engineering Center. Several other
people deserve a special word of thanks for their technical contributions. They are
Dr. Raymond Luebbers and Professor G. E. Smith. In addition thanks are given for the
valuable discussion with FAA personnel. In particular, recognition goes to Mr. Gerald
Markey and Mr. Reuben Michaeles.
A special word of thanks goes to Mrs. Shirley Wilson for her excellent typing
of the involved technical monthly reports. In addition thanks go to Ms. Hope Mills for
her coordination in the typing of the final report. Without these two peoples' contribu-
tions the research reported here would lack proper documentation and reporting.
XII. REFERENCES
ri] Chang, K.Y., "Intermodulation Noise and Products Due to Frequency Dependent
Nonlinearities in CATV Systems", IEEE Transactions on Communications, Vol.
com-23, No. I, pp. 142-155, January 1925.
T2] Bennett, W.R. , "Cross- Modulation Requirements on Multi-Channel Amplifiers
Below Overload", Bell Syst. Tech. J. , Vol. 19, pp. 587-610, October 1940.
r3] Simons, K.,"The Decibel Relationships Between Amplifier Distortion Products",
Proc. IEEE, Vol. 58, pp. 1071-1086, July 1970.
T4] Glave, F . E . , "A Statistical Approach to the study of Intermodu lation Noise" ,
Bell-Northern Research, Rep. TM 8260-1-66, July 1966.
f5] Wiener, N., "Non-linear Problems in Random Theory," Cambridge, Mass.:
Tehcnology Press; and New York: Wiley, 1958.
-67-
XIII. BIBLIOGRAPHY
Bedrosian, E., and S. O. Rice, "Distortion and Crosstalk of Linearly Filtered
Angle-Modulated Signals", Proc . IEEE, Vol. 56, pp. 2-13, January 1968.
Bedrosian, E., and S. O. Rice, "The Output Properties of Volteria Systems
(Nonlinear Systems with Memory), Driven by Harmonic and Gaussian Inputs" , Proc. of
IEEE, Vol. 59, pp. 1688-1707, No. 12,1971.
Mircea, A., E. Bedrosian, and S. O. Rice, "Further Comments on Distortion
and Crosstalk of Linearly Filtered, Angle-Modulated Signals", Proc. IEEE (letter),
Vol. 57, pp . 842-844, May 1969.
Narayanan, "Transistor Distortion Analysis Using Volterra Series Representation",
Bell Syst. Tech. M., Vol. 46, pp. 991-1023, 1967.
Narayana, "Application of Volterra Series to Intermodulation Distortion Analysis
of Transistor Feedback Amplifier", IEEE Trans. Circuit Theory, Vol. CT-17, pp. 518 —
527, November 1970.
Rice, S. O., "Second and Third Order Modulation Terms in the Distortion
Produced When Noise Modulated FM Waves Are Filtered," Bell Syst. Tech. J., Vol.
48, pp. 842-844, January, 1969.
XIV. appendices
A. Theoretical and Experimental Measurements Using Model and an FM-Interfering
Signal. Theoretical and experimental measurements were obtained using the proposed
model for the RF-amplifier . For these investigations, the desired localizer signal was
assumed to be a 108.5 MHz signal which was amplitude modulated in some cases by a
1000 Hz tone to allow for the determination of distortion at the output of the detector.
The interfering signal was assumed to bean FM modulated signal of various signal
strengths operating at 105.5 MHz. This signal was modulated by a 10 KHz sinusoid
producing a modulation index of 6, resulting in an FM bandwidth of approximately 200
KHz. The interfering signal spectrum is illustrated in Figure A-l .
Vertica I
Linear
Scale
105.5 MHz 50 K Hz/di v
Figure A- I . Interfering Signal Spectrum; Modulation
Index 6; Bandwidth 200 KHz.
Using this as the input signal and assuming no distortion due to input filtering
of the FM spectral components it can be shown that the cross -modulation terms located
near 105.5 MHz will result in only a compression term at the carrier frequency of the
desired signal (108.5 MHz). Considering the effects of the input filter (.2 dB '100 KHz
attenuation) on the FM spectral components theoretical calculations indicate the ratio
of the first sideband to the carrier term to be -44 dB compared to a measured value of
-42 dB. For the second sideband theoretical results predicted -92 dB which could not
be measured. These results are illustrated in Figure A -2.
Fic^ireA-2. Spectrum of Desired Signal (108.5 MHz) at RF-Amplifier
Output. Desired Signal Strength -17 dBm (.03 volts);
FM-Interfering S ignal (105.5 MHz, P = 6; Bandwidth =
200 KHz)0 dBm (.2 volts).
Figure A-3 shows the spectrum at the RF amplifier output with the desired signal
at -47 dBm signal level with the interfering signal level the same as given for Figure A-2 .
The sidebands are not visible because of the residual noise.
Qualitative investigations of the distortion produced at the output of the detector
were performed. Figure A— 4 shows the detector output using a 1 KHz modulation signal
with 10 percent modulation and no interfering signal present.
Figure A-5 shows the detector output when the desired signal is the same as
described in Figure A -4 and the interfering FM signal of 0 dBm, as described in Figure
A-l , is added.
Figure A-6 shows the detector output when a desired signal is reduced to -47 dBm.
Figure A- 7 indicates the results obtained using a desired signal strength of
-70 dBm (.1 mv) and no interfering signal. Figure A-8 shows the results of an interfer-
ing signal of 0 dBm (.23v) on this weak input desired signal. A significant amount of
distortion due to the FM-interfering signal is observed.
-70-
Figure A-3. Spectrum of Desired Signal (108.5 MHz) at RF-Amplifier
Output. Desired Signal Strength -47 dBm (1 mv); FM-
interfering Signal 1 105.5 MHz, P - 6, Bandwidth = 200
KHz) 0 dBm (.2 volts ^ .
5 msec/div
Figure A-4. Detector Output with No interference. Carrier
frequence - (08.5 MHz; Modulation frequency
1 KH? 10 Modulation.
71
5 rrv;ec di
Figure A-5. Del-,-. t \.'l'
(0 dBrr '• ul 10:
!csireri S
VfflJkf’Cty
7 ■ ■ 1 ■
'. 'j4> '• £>y f*viw TKtf
[tS'SsMrHrcfr '?‘wl vA'x .•&{$ i
. 5 msec div
Figure A-', Defe jrrai Level
• 0 dr.- . '\lo inferfei ng S igna I .
■ *"? v-it:
B . Filter Characteristics
1 . Measurement of RF Amplifier Input Filter Characteristics ci(u)- The test
setup to measure the RF ampl ifier fi Iter characteristics 0(0) is shown in Figure B-l.
Figure B-l. Measurement Procedure for Obtaining a (w).
The voltage at the input to the gate of dual gate MOSFET of the RF Amplifier was
measured as a function of Wavetek frequency. The voltage at the RF amplifier input was
measured using a H P 8405A vector voltmeter .
The AGC voltage of the receiver was fixed and the signal ievel from the Wavetek
3000 was held constant.
The resultant filter characteristics measured were found to be shifted in frequency
from the receiver frequency by 2 MHz. It was assumed that this was due to the
capacitive loading of the vector voltmeter X10 probe used. Therefore, the characteristic
was shifted over 2 MHz so that the resonant frequency of the filter is the desired frequency
108.5 MHz. Figure B-2 gives a simplified schematic of the Nav 11 front end.
Figure B-2. Simplified Schematic of RF Front End
of NAV 11 Receiver.
-
-74-
In order to verify that the RF Amplifier input filter characteristics were correct,
cross-compression and intermodulation measurements were made varying the frequency
of the interfering signals.
The intermod measurements given in Figure 4 of the main text shows that the
a(u)characteristics measured result in constant K^/K. (within experimental accuracy).
The test procedure illustrated in Figure B-3 was used to measure cross-compression of
the desired signal as a function of interfering signal frequency and the results give the
following for a(cj).
Figure B-3. Test Procedure for Determining a (u) Using
Cross -Compress ion Methods.
Interfering
Frequency
MHz
Equivalent a ( u )
Calculated from
Measured GC*
e(u) Found
Probing RF
Front End
107.5
- 1 dB
-1.2 dB
106.5
-3.1 dB
-2.7 dB
105.5
- 5 dB
-4.5 dB
104.5
-6.6 dB
-6.2 dB
*Gain Change
Table B-l . Comparison of Results Obtained Using Cross-
Compression and RF Measurements .
-75-
Because cross -compress ion is a function of a (u) it was not possible to obtain
enough interfering signal level with the above test procedure to measuie 1 dB of GC
for frequencies below 104.5 MHz.
2. Measurements of Variations in a (u) as a Function of Receiver Tuning.
Investigations of the variations in a(o) as a function of frequency were made by tuning
the receiver to different frequencies while keeping the interfering signal frequency at
a fixed 3 MHz below the receiver frequency and measuring the resulting gain change
(GC). The variations in a(u) with receiver tunings are given in Table B-2.
Receiver
Frequency
(MHz)
Interfering
Frequency
Calculated cr(u)
Assuming K^/K ^
Constant
108.5
105.5
-4.5 dB
110.5
107.5
-4.2 dB
112.5
109.5
-4.0 dB
114.5
111.5
-3.6 dB
116.5
113.5
-3.4 dB
117.5
114.5
-3.2 dB
Table B-2. Variations in a(u) as a Function
of Receiver Frequency.
-76-
c.
Interference Due to ELT
]. Introduction. There have been numerous reports where particular ELT's have
been shown to aggravate the interference problem by reradiating signals generated by the
nonlinear mixing in the ELT output transistor stage. It is believed that the transmitter
(inactivated) output circuit acts as a diode mixer generating interfering signals in the lo-
calizer and communication bands, particularly in the communications frequency band (118-
136 MHz).
The interference frequency is the result of a third-order nonlinearity term. For
example, an interfering signal at 122 MHz can result from the mixing of two FM stations
at 108 and 94 MHz (2 fj - ^ ) term, due to a third-order nonlinearity). It has also been
reported that it is possible to observe enchancement of the interference problem due to
the ELT as a result of the combining of an ILS , VOR and FM station. For example, an
ILS frequency of 329 MHz^TVOR of 113.8 MHz and FM station at 94 MHz could mix
producing an interferin^signal at 121.2 MHz ( lj^ - ^ “f2term)-
A third-orde/model has been investigated for modeling the effects of ELT in the
interference problerr^. It was expected such j model would be adequate for predicting
interference levels and because of its simplicity, it could be utilized effectively in prac-
tice. Figure C-l illustrates the results obtained when two interfering signals are directly
coupled into the ELT. The experimental procedure for obtaining these results is shown in
Figure C-2. Figure C-l illustrates the results obtained for various signal levels. The third-
order term (102.5 MHz) clearly shows up in the spectral plots shown in this figure. In ad-
dition, it is observed that at extremely high signal levels 4 5 dBm and above additional
intermod terms appear (see Figures C-l e,j,k and I) which would tend to indicate that a
higher order model may be required.
Since the primary interest is in the analytical modeling of the ELT's role in the
interference problem, it is necessary to be able to predict the signal levels coupled from
the EL7 antenna to the communications and/or navigational antennas. Measurements were
obtained and a worst case theoretical analysis was performed.
2. ELT Model. A proposed analytical model representing the ELT is illustrated in
Figure C-3a. Mathematical ly the model may be interpreted in two ways:
(1) The voltage e can be represented in terms of the received voltage by
. .2,3
e - k. e.+ k. e. + k„ e.
a I i z i 3 i
(C-l)
(2) A second and somewhat more satisfying way to visualize the model is illus-
trated in Figure C-3b. In this representation the incident voltage v+ is the received
-77-
Figure C-l. Spectra of the Reradiated Signals at the
Output of ELT. Vertical = 10 dB/1 .5 cm;
Horizontal scale = 2 MHz/cm.
-78-
Figure C-4. Experimental Procedures.
Wavetek Model
3000
Bi-directional
Coupler
Wavetek Model
3000
(b)
Figure C-4. Continued
-86-
I
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ANALYTICAL DETERMINATION OF THE INTERFERENCE OF COMMERCIAL FM S-ETC(U)
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FILM D
3-79
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signal and the reflected voltage is the reradiated signal , i.e.,
v = kj (v+) + \<2 (y4) + (v (C-2)
It can be shown that both of these models are essentially equivalent, the basic
difference being in the interpretation. Neither model postulated takes into account
frequency selective characteristics of the ELT output circuitry and both are limited to
third-order nonlinearities. Also, the high frequency characteristics of the p-n junction
are ignored in this preliminary investigation.
Using the models specified above the two experimental procedures illustrated in
Figure C-4 were used to determine the parameter k^ for the model. Although a consid-
erable amount of data relating to self-and cross -compress ion was obtained, the primary
important data is relative to the intermod frequency. In this section summary results are
given in graphical form. The test procedure illustrated in Figure C-4a was used to obtain
the results.
Figure 05 il lustrates the effects of two closely aligned frequencies. In particular
this curve was obtained using two signals separated by 1 MHz and extending over the FM
band. This curve tends to indicate that whenever two closely aligned frequencies interact
the coefficient k^varies approximately! 5 dB from a reference value arbitrarily chosen at
the ELT frequency of 121.5 MHz. Some of these effects can be explained by considering
the frequency characteristics of the ELT output stage which are in Figure C-6. In this the
corrected voltage measured at the ELT input with a - 10 dBm incident signal is plotted as a
function of frequency.
A rough approximation which ignores both frequency effects, (capacitance of the
junction), signal levels, etc., is to use the low frequency model of the p-n junction, i.e.,
I - I. ( e ‘>vAT-l)
where
lG = reverse current in amperes
k = Boltzmann's constant
T = temperature in °k
v = applied voltage
q = electron charge in coulombs
Using this model would imply that the intermod term would have an amplitude given
approximately by (A + 2 B + 15)
Strong Frequency 1 MHz less than intermod
Weak Frequency 2 MHz less than Intermod
FM -an Communications ran
where
A = amplitude of fhe weak signal (for the case shown in Figure C -6 = -10 dBm)
B - amplitude of the strong signal (for the case shown in Figure 06 = 0 dBm)
The 15 dBm is the result of expanding the exponential in a series. For the case
considered here this would imply that the intermod term would have an amplitude of
approximately -25 dBm. Using Figure 05 this result seems to be reasonable when the
intermod frequency is approximately 121 .5 MHz; however, it deviates somewhat from this
value for different frequencies. It must be stressed that the equation used to describe the
p-n junction is by no means accurate at these frequencies; however, bounds on the problem
can be obtained. Further investigations are required in order to arrive at a more accurate
description.
A large amount of data was obtained which tended to indicate that the coef-
ficient k^ can be assumed relatively constant over wide frequency ranges. Although the
data obtained is too numerous for inclusion in this brief report, a summary of the results is
illustrated in Figures C-7 and C-8. The data was obtained using the test procedure illus-
trated in Figure C -4a. Figure C-7 indicates the variation in k^ as a function of the inter-
mod frequency as indicated on the graphs. These curves were obtained with the two signals
held constant at -10 and 0 dBm respectively. These results indicate that the coefficient
k^ is constant within ± 5 dB of the value at 121.5 MHz (ELT frequency).
Figure C-8 shows the variation in k^ as a function of signal amplitude. For signal
levels of 0 dBm and belovjk^ can be bounded by approximately ± 5 dB. Results indicate
that k^ deviates more for signals with frequencies in the lower part of the FM band than for
frequencies in the middle of the band.
3. ELT Communications Antenna Coupling. In order to determine the effects on
communication receivers of an intermod signal reradiated by the ELT, it is necessary to have
some measure of the coupling between the ELT and communications antennas. Experimental
measurements were performed on a Cessna 150 commuter (N1600U) using the test procedure
illustrated in Figure C-9. The relative locations of the communications and the ELT antenna
are illustrated in Figure C-10. Figure C-ll shows the results obtained.
Although the mathematical calculations for aircraft antennas are very complex and
can only be approximated very crudely, it is of interest to achieve a worst case model.
The relations between a set of coupled antennas can be given by
n
v; = *j =| (2 ij)lj i = 1 to n (C-3)
-89-
Frequencies generating
Intermod term
intermod Frequency in M'’z
Figure C-7. as a function of intermod frequency
"or varying FM band generating frequencies.
Figure C-9. Antenna Coupling Measurement.
co-^
Top View
ELT Antenna
/\
Communications Antenna
Figure C-10. Antenna Locations.
-30
where
Zii = self impedance of antenna
Z ij = Z ji = mutual impedance between antenna i and antenna j .
For simplicity the following assumptions are made:
1. The ELT antenna (transmitting) has a 50 ohm self-impedance.
2 . The communications antenna (receiving) has a 50 ohm self-impedance.
3. Both antennas are matched.
4. Both antennas are \/4 monopoles separated by \/2 (actually the ELT
antenna was measured to be 16 inches and the communication antenna
was measured to be 23 inches).
5. Both antennas have infinite ground planes.
6. Antennas are parallel and on same plane.
Using the above relations and the curves of mutual impedance for two parallel
antennas as given in
"Antenna Engineering Handbook" by Henry Jasik , McGraw-Hill,
the coupling can be calculated as - 16 dB, a considerably more pessimistic value than the
measured value . Figure C — 1 1 indicates the maximum measured coupling was approximately
-28 dB. Further investigations for refining this model are required; however, the calcu-
lations could be considered a worst case analysis. For a more realistic value of the coupling,
the measured values could be used.
ELT's used on many Cessna aircraft seem to be more susceptible to third-order inter-
modulation phenomenon. Reportedly, the Cessna Company has partially solved this problem
by certain modifications. Mr. Gordon Wood of the Cessna Corporation in Wichita, Kansas,
was contacted regarding this and he said that the problems of interference are greatly re-
duced (to tolerable levels) if the ELT antenna is shortened from the original 22" to 16" and
adjustments in the output stage and cabling for matching and maximum power are made. The
effect of this would seem to be a reduction in the coupling between the ELT and communi-
cation antennas. Ohio University has available several small aircraft instrumented with the
Share 7 ELT which allowed practical measurements on both aircraft with modified and non-
modified antennas. These aircraft along with the antenna lengths are listed as follows
-96-
for reference:
Cessna 150 Commuter N1600U
Antenna Length
- 16
N 900U
M II
16
N 1200U
II II
= 22
II
II
II
In addition to the decrease in antenna length from 22" to 16", the locations of the
22" and 16" antennas on the aircraft were slightly different. Although no evidence is
present which would indicate this to be a significant factor, it is possible that the location
was moved so asto decrease the coupling between the communications antenna and the ELT
antenna. It is unlikely that the reduction in coupling obtained is totally due to decreasing
the length of the antenna.
4. Summary and Applications. In summary and as an illustration of the techniques
and models developed here a worst case analysis (very approximate) is given illustrating the
role of the ELT in the interference problem. For the example, two 100 kw FM stations are
assumed - one located 15 miles from the receiver and the other 5 miles from the receiver.
The geometry is illustrated in Figure C-12. Only the interference caused by the ELT
generated intermod is considered in this example. Using the information and data given in
this report, the following step-by-step computations can be made:
a. Aircraft with 16" ELT Modified Antenna
I. Coupling between ELT and communications antennas at 120 MHz
(intermod frequency)
From Section 3 of this report
Theory (worst case) = - 16dB
Measured = - 35dB
The large discrepancy between theory and measurement is probably due to many
factors such as:
1) The modified ELT antenna of length 16" is not a X/4 antenna as assumed in
the calcuations.
2) The possible location change of the ELT antenna.
3) Communications and ELT antennas not being parallel, as assumed.
4) ELT and communications antennas being in different planes.
II. Calculation of the incident voltage at the ELT assuming the following:
(a) Directive gain of the ELT antenna = 6 dB
(b) Attenuation equation between lossless isotropic antenna
holds, i.e. ,
a (decibels) = 36.3 + 20 log^ f + 20 log^d
where
f is the frequency in MHz
d is the distance in miles
FM station ^1 (108 MHz)
P ^ (power) = 80 dBm (50 ohm reference)
o ] = 91 dB
FM station ^ 2 (96MHz)
Pj = 80 dBm
a = 100 dB
The power at the ELT is obtained using the following equation:
P' = gain (antenna) + ERP - attenuation
llT
P' (ELT) = -5 dBm
FM *2
P'2 ELT - -14 dBm
III. Intermod Calculation:
3
Using the value of 2 k^ = - 8 dB given in this report (Figure C-8), the reradiated
signal from the ELT is given by
3
RC1 _ = A + 2B + 7 k
ELT 3
where
(A) = amplitude of station 1 (weak station) in dBm
-99-
(B) = Amplitude of station 2 (strong station) in dBm
Therefore,
(reradiated signal power) - 32 dBm
IV. Calculation of intermod input at the receiver terminals.
(1) Using the worst case coupling of - 16 dB
Intermod = - 48 dBm ( ~ 900 qv)
(2) Using the measured coupling of - 35 dB
Intermod = - 67 dBm ( ~ 100uv)
b. Aircraft with 22" ( Non-Modified) Antenna.
Investigations and inquiries as to the possible modifications of the calculation pro-
cedures to include the effect above were made. These findings indicate that numerical
procedures should be possible which would allow for a more accurate specification of the
coupling between antennas located on aircraft. Such an undertaking is beyond the work
defined under the current contract and would consist of a rather significant program in
itself. It would appear in view of the increased possibilities of interaction between
electronic devices on board aircraft (one example being the ELT and communications an-
tennas), it would be beneficial for the FAA to consider supporting investigations in these
areas either as an extension of the scope of the current study or possibly an additional project
in the future. Although neither time nor funds have been allocated on the current contract
for these investigations, the analytical techniques which have been determined are
believed to indicate worst case conditions.
Results given in Section A indicate theoretically a coupling of -16 dB between
the ELT and communications antennas, while measured values for 16" ELT antenna gives a
coupling of -35 dB. Further measurements were made on aircraft Cessna N1200U, 150
commuter equipped with a Share 7 ELT and a non-modified antenna of 22" in length and
another aircraft Cessna N900U, Commuter 150, with the modified antenna. These results
are summarized in Figures C-13, C-14, C-15, and C-16.
Figure C-13 shows the coupling between the ELT antenna (non-modified length -22")
and the communication receiver. These results were obtained by exciting the ELT antenna
and measuring the voltage at the output of the communications receiver. The results of
Figure C-13 indicate a measured coupling approximately -16.5 dB . Comparing this with the
calculated value of -16 dB given above, the agreement is very good. This is the result
gp u; 6uj|dno^)
101
Figure C-13. Coupling Between ELT Antenna and Communication Antenna as a Function ot Frequency
22" ELT Antenna Length.
C-16. Normalized (50 ohms) Self Impedance at Various
Frequencies of the Communications Antenna on
Board N1200U.
-104-
of the geometry of the ELT system on board N1200U being more representative of the worst
case system used in Section A. The calculated intermod input at the receiver was - 48 dBm
( <*> 900 |jv) using a coupling of - 16 dB. Such a level would result in an extremely severe
interference problem which would be of considerably more importance than either the
"brute-force" or the normal intermod (generated by the interaction of two or more FM
stations of appropriate frequencies) types of interference. For reference Figures C-14, C-15,
and C-16 are included which indicate the self-impedance of the 22" ELT antenna the 16"
ELT antenna and the communications antenna respectively. It is noted that impedance of
the modified 16" antenna is somewhat independent of frequency and far from the assumed
50 ohms used in the calculations.
In summary, results have indicated that the analytical model agrees with the 22" ELT
antenna measured results rather well and may be considered a worst case situation; however,
it does not agree with the measured values obtained using the modified ELT antenna. Since
this was not a specific delineated task on this contract investigations for refining the ELT
model were suspended at this point.
■
-105-
D.
Measurement of RMS Modulation Due to Intermod
1. Measurement Technique. To measure the amount of RMS modulation due to
intermod the following set up was used:
Desired Signal
The outputs of three RF generators are combined through bidirectional couplers
and inputted to the NAV 11 receiver. Two of the generators are FM modulated by audio
sine-wave generators. The other generator is the desired signal tuned to the same
frequency as the receiver. A true RMS voltmeter is used to measure the receiver filter
outputs .
Using two FM signals with characteristics given below the detector, the audio
filter output, the 90 Hz and 150 Hz filter outputs are measured, i .e..
Desired Signal: f = 108.5 MHz, Carrier only, -60 dbm signal level
FM1 : f = 102.5 MHz, fm = 400Hz, p = 30, signal level = -18 dbm
FM2 : f = 105.5 MHz, fm = 1 KHz, p = 20, signal level =-17 dbm.
Measured IM Carrier level = -70 dbm.
-106-
Detector output voltage = .155VRMS
Audio output voltage = .305 VRMS
150 Hz output voltage = .11 VRMS
90 Hz output voltage = .10 VRMS
In order to compute the necessary constants the following normalizing constants
were determined:
(1) Detector voltage with 20% AM modulation output was measured as .250 volts
volts with fm =20 Hz
(2) Audio voltage with 10% modulation at 1 KHz = .665 volts
(3) 90 Hz filter output voltage with 20% modulation at 95 Hz = .891 volts
(4) 150 Hz filter output with 20% AM modulation at 145 Hz =.999 volts
Using the normalizing constants calculations of % modulation can be made as
shown below:
Calculating Equivalent RMS Modulation of Filter Outputs
.155
Detector output = ,^q x 20% = 12.1% modulation
305
Audio output = ' ^52 x 10% ~ 4 .7%
150 Hz filter output = -gg-j x 20% = 2 .5%
90 Hz filter output = .10 x 20% = 2.0%
It is of interest to note that the theoretical results taken from output of the computer
program given in Table 28 were obtained with an IM carrier to desired signal ratio of
-7.7dB. The measured IM to signal ratio was -lOdB using AGC method and -8 .3 dB by
measuring detector voltage output with IM carrier and desired signal only and comparing
it to a detector voltage with known modulation.
2. "Flutter11 of IM Relative to Desired Signal. Several problems were observed
during the experiments due to the narrow band widths of the 90 and 150 Hz filters. One
was the "flutter" which is investigated using an intermod carrier and a desired signal
as inputs to the receiver. The detector voltage was monitored with an oscilloscope and
its frequency measured with a frequency counter. The resultant frequency was measured
-107-
to be approximately 100 Hz. The waveform observed was a sine wave with varying
frequency due to slight frequency fluctuations in the desired frequency and IM
frequency. The average frequency drift was estimated to be approximately 100 Hz.
Since the 90 and 150 Hz filter functions have very sharp bandpass characteristics on
the order of 30 Hz, the 100 Hz IM "flutter" becomes very significant.
For calculation purposes an approximation of the filter characteristics was used
in the program to compute modulations factors for the 90 and 150 Hz filter characteristics.
These factors vary as much as 25% with the modulation frequencies varying as little as
a few hertz. The theoretical modulation factorsdid not agree well with the measured <
modulation factors which were found to vary little as the modulation frequencies were
changed. In order to obtain useful theoretical modulation factors for the 90 and
150 Hz filters, ideal bandpass filters with the same noise equivalent bandwidth as the
actual filter functions were used. The ideal bandpass filters have enough bandwidth
so as to get a good sampling of the intermod generated. This is evidenced as observed
in the good agreement between theoretical results and measured results. This method
as given in Table 28 in the text seems to work. With low modulation indices and
higher modulation frequencies (when the intermod does not have enough components
which land in the receiver passband so as to make the intermod "look" noise-like)
results will not agree as well.
Although the 90 Hz filter has a half power bandwidth of approximately 35 Hz,
its noise equivalent bandwidth (found by integrating the measured filter characteristic
numerically) is 168 Hz. This is because the skirts of its characteristics do not fall off
rapidly.
Similarly the -3 dB bandwidth of the 150 Hz filter is 55 Hz and its noise
equivalent bandwidth is 195 Hz.
3. Measurement of Modulation Factors. Modulation factors due to intermod
are measured by inputting the lM carrier and desired signal into the receive jnd measuring
the filter output voltage. For the detector filter, the IM carrier frequency is set to the
desired signal frequency. For the audio filter, the IM frequency is set to 1 KHz above or
below the receiver frequency.
The interfering signals are then FM modulated (with the IM carrier frequency
equal the receiver frequency) and the RMS output of the filter is measured.
The result of measuring the IM carrier filter voltage output is to provide a
normalizing voltage. Variations in gain of various parts of the receiver are effectively
divided out by using modulation factor measurements. This is especially true for the
audio filter which has a gain determined by the setting of the volume control. (For
measurement purposes, the volume control was replaced by a 10 turn trim pot and
adjusted for 1/5 full volume.)
-108-
_ A.
i
Measured values of modulation factors were found to agree very well with
theoretical values. Measurements of the actual IM carrier level found by comparing
the filter output voltage to an equivalent filter voltage with the desired signal AM
modulated with a known percentage do not seem to agree as well. A disadvantage of
the MF method is that the 90 and 150 Hz filter modulati on factors cannot be measured
this way since the IM carrier frequency cannot be adjusted to 90 or 150 Hz away from
the desired frequency. Also it was found that the audio output overloads with more
than 20% modulation.
E- Noise Equivalent Bandwidth The noise equivalent bandwidth is defined as
the bandwidth of an ideal filter with the same RMS output voltage as the actual filter.
These concepts are illustrated in Figure E-l , where B is defined as the noise equivalent
bandwidth, n. is the input spectral density of a "wRite" noise source and S (f) is the
output spectral density. °
Figure E-l . Noise Equivalent Bandwidth of a Filter.
The RMS output voltage is given by
(N ) RMS
o
/°° I H $w) I2 df
/ -oo
The noise equivalent bandwidth is then defined by
(N°) RMS = ' "I 1 H 0 <*>) I2 df = ' H('U) max '^i
and I H (| u) I2 d f
B =
" I H (j u) I2
M max
It can be shown that the (MF) Ratio, i.e..
Modulating Factor (MF) of Audio /B Audio
(MF) Ratio =
Modulating Factor (MF) of Audio ^B Audio
= n
Modulating Factor (MF) of Detector X/B Detector
n
depends only on the filter functions or the noise equivalent bandwidths of the filters.
Several calculations were made to verify these facts and the results are given in Table E-l
Note a very high modulation index and relative low modulation frequency are used to
obtain a noise-like spectrum.
Station 1
Station 2
Carrier
Freq . i n
MHz
mm
Modulation
Index
Carrier
Freq . i n
MHz
Modulation
Freq . i n
KHz
Modulation
Index
Detector
MF
7
Audio
MF
MF
Ratio
105.5
1 .000
30.
102.5
.742
30.
.240
.113
.471
105.5
1 .250
24.
102.5
1 .042
24.
.241
.107
.444
105.5
.906
55.2
102.5
1 —
.543
55.2
.184
.085
1
.462
L
Table E-l
Comparison of Theoretical Modulation Factor Ratios
From Computer Program,
Determination of the actual noise equivalent bandwidth B of the receiver filter
(audio, detector, 90 and 150 Hz filters) requires numerical integration to find the area
under the actual filter response curves. These characteristics were obtained for the
NAV 11 receiver The results obtained are:
Audio Filter (see Figure 18 of the text for response curve):
B =1.08 KHz
n
Detector filter (see Figure 1/ of the text for response curve):
B =4.93 KHz
n
Using the above data the MF ratio is found to be
yi .08 KHz
(MF) ratio = = .468
. '4.93 KHz
(E-4)
Comparing this result with those given in Table E-l it is seen that the MF ratio
determined by filter characteristics and those from IM calculations using the computer
program agree very well. Similar techniques can be applied to the 90 and 150 Hz filter
functions. Because of the good agreement of the "noise" model of the IM, the 90 and
150 Hz filter functions were modeled in the computer program by a filter with the same
noise equivalent bandwidth. See discussion in Appendix D.
-Ill-
F. CDI Interference. Figure 18 in the text shows the test setup used to determine
the effects of high level modulation on the CDI response. These results are obtained by
injecting a 108.501 MHz signal along with a desired signal of 108.500 MHz. The
108.501MHz signal results in an injected 1 KHz sideband signal in the IF which is
detected. Tables F-l , F-2, and F-3 give the results obtained.
The results given in Table F-4 show the CDI variations as a function of sideband
frequency .
Interfering signal level
relative to desired level
Measured
CDI
Percent change in CDI
reading due to sideband
-15 dB
58 pA
3%
-12 dB
55 pA
8%
-10 dB
51 pA
15%
-8 dB
48 pA
20%
- 6 dB
42 pA
30%
- 3 dB
31 pA
48%
Table F-l . Effects of Detector Clipping on CDI (Normal Reading of CDI - 60 pA) .
Interfering signal level
relative to desired level
Measured
CDI (pA)
Percent change in CDI
reading due to sideband
-15 dB
30.7
3 .4%
-12 dB
28.9
9.1%
-10 dB
27.7
12.9%
-8 dB
25.8
18.8%
- 6 dB
21.0
34 %
- 3 dB
18.4
42 %
Table F-2. Effects of Defector Clipping on CDI (Normal Reading of CDI =30 pA).
-112-
Fixing AGC at its value with no interfering signal present and introducing 1 KHz
sideband, gives the same CDI deflections as before; therefore, the CDI interference is
not due to AGC changes of the receiver.
Table F-4 shows the CDI reading as a function of sideband frequency. Interfering
signal level is fixed at -3 dB lower than desired signal level (70% modulation).
Sideband frequency in
KHz above desired level
Measured
CDI
1 KHz
31 .2 pA
2 KHz
29.0 pA
4 KHz
34 .4 pA
6 KHz
38 pA
8 KHz
37.7 pA
10 KHz
32.5 pA
12 KHz
26.9 pA
15 KHz
49.7 pA
Table F-4. Effects of Interfering Signal Frequency on CDI (Normal Reading of CDI - 60 pA) .
Note that the CDI values as the measured IF frequency response varies (see IF/
detector characteristics, Figure 3). The CDI reading is lower at 12 KHz because of the
peak in the side of the IF response. Likewise at 15 KHz, CDI is closer to its actual
value.
•yrasagzgsrTwi '
G . User Manual
1 . FM Interference Program Users Instructions. The FM interference program
uses the measured characteristics of the Nav 11 receiver to predict the amount of
interference due to high power FM stations. The program assumes sinusoidal modulation
on the FM signals and that the interference is due to 3rd order nonlinearities in the RF
amp of the receiver.
The user must supply the following information to analyze an interference
situation: Number of FM stations, receiver frequency, distortion parameter 3/2
K3/K1 . For each FM station, the following information is required: Station frequency,
modulation frequency and modulation index, distance from the receiver and station power
level. Localizer distance from the receiver and power level is also needed.
Most parameters for the program are entered in the edit mode. In this mode the
user can enter parameters or modify them by typing commands at a remote terminal.
The user may also exit the edit mode with the ' I M' command and begin intermodulation
calculations, or begin signal level computations with the 'MXDB' command or start
cross modulation calculations with the 'XMOD' command. "STOP1 will cause the
exiting of the edit mode and normal program execution. These commands allow flex-
ibility in altering parameters and seeing their effects on the interference situation.
A summary of the program limitations are given below.
Program Limitations:
(1) A modulation index of 75 is a practical limit on the maximum modulation
index that the program will accept. Modulation indices higher will cause extremely long
program execution times. A modulation index of 75 corresponds to a maximum frequency
deviation of 75 KHz with a modulation frequency of 1 KHz.
(2) The program assumes that the modulation frequencies of the FM stations
are not harmonically related. For example frequencies of 1000 Hz and 400 Hz are related
whereas 1000 Hz and 398 Hz are not. The intermodulation due to stations with harmonically
related modulation frequencies has components which occur only at certain frequencies
relative to the IM carrier and does not exhibit the "noise-like" (realistic) properties which
are assumed for IM calculations. Harmonically related modulation frequencies will be
treated as though they were not related by the program. Therefore, when using harmon-
ically related frequencies such as 1000 Hz and 400 Hz, it is advisable to check the results
to see if the same results are obtained as with frequencies of 1000 Hz and 398 Hz .
Before using the program, it is suggested that the user read the program subroutine
descriptions given in this report. Also, the flow chart given in Figure G-l is very useful
in understanding the program. A sample terminal session is given on the following pages.
-114-
Enter Edit Mode
I.0., Coll Subroutine
Change Input
Parameter* Such As
Power Levels,
Distances, etc.
Call Subroutine
MU ED B
Calculates Signal Level
Due to FM Stat at
RF Amp Input
Cdll Subroutine XMOD
Calculates " Brute- Force"
Interference - Cross-Mod
and Cross- Compress! on
No - To*ol Restart
Calculate^
. Intermod? )
Call IMCALC
Calculate IM
Calculate % RMS AM
Modulation o» Rereiver
Filter Output*
Calculate Effects
of Both IM and
Brute Force Combined
Restcrt Mod if y Parameters
Program? *0^
Figure G-l . Flow-Chart of FM Interference Program
r
Sample Session of Interference Program
load interfer ( start nomap
EXECUTION BEGINS . . .
START OF PROGRAM
*** FM INTERFERENCE PROGRAM ***
Program is executed at a remote terminal
THIS PROGRAM CALCULATES THE INTERFERENCE DUE TO HIGH POWER FM STATIONS
AND ITS EFFECTS ON A NAV 11 RECEIVER.
READ IN NUMBER OF FM STATIONS (FORMAT NN)
User enters no. of interfering stations
.02
TYPE STATION FREQUENCIES IN MHZ, MODULATING FREQUENCY IN KHZ, MODULATION
INDEX (FORMAT XXXXXYYYYYZZZZZ)
The station frequency, modulation frequency and modulation index is inputted for each station
.105.512.50 5.0
.102.510.42 5.
TYPE RECEIVER CENTER FREQUENCY
.106.5 User enters receiver frequency which is the same as the localizer frequency
TYPE 3/2 K3/K1 IN DB
.3. The distortion parameter
*** PROGRAM PARAMETER EDIT MODE ***
FOR INSTRUCTIONS TYPE: INST
Edit mode is entered. The distance from station 1 is set at 5 miles. From station 2 is 4 miles.
.MILE 01 5.
.MILE 02 4.
Power level for both stations is 50 Kw. Localizer power is set to 40 w.
.POWER 00 50.
.POWER 20 . 040
Distance to localizer is 2 miles.
.MILE 20 2.
.TYPE 00
FM station parameters are listed
STATION STATION MODULATION MODULATION MAX FREQ LEVEL MILES
NUMBER
FREQ
FREQ
INDEX
DEVIATION AT RF AMP FROM
(MHZ)
(KHZ)
(XMOD CALC) INPUT=DBM RECEIVER
1
105.5
12.500
5.00
0.0 0.0 5.0
2
102.5
10.420
5.00
0.0 0.0 4.0
-116-
.TYPE 20
Localizer parameters are listed
STATION STATION MODULATION MODULATION MAX FREQ LEVEL MILES
NUMBER FREQ FREQ INDEX DEVIATION AT RF AMP FROM
(MHZ) (KHZ) (XMOD CALC) INPUT=DMB RECEIVER
20 108.5 0.0 0.0 0.0 0.0 2.0
.STOP
End of edit mode command
TO COMPUTE SIGNAL LEVEL AT RF AMP INPUT TYPE 1
OTHERWISE VALUES OF LEVEL ( I ) MUST BE INITIALIZED IN THE
EDIT MODE AND USED AS THE SIGNAL LEVEL AT THE RF AMP INPUT
.1
Signal levels at RF amp are calculated.
PRINTOUT OF SIGNAL LEVEL COMPUTATIONS
STATION MILES STATION FREE NAV RCVR INPUT
FREQ FROM POWER SPACE ANTENNA FILTER
(MHZ) RECEIVER IN DBM ATTEN-DB LOSS-DB ATTEN DB
SIGNAL
LEV AT
RFAMP IN (DBM)
105.5 5.0 77.0 90.7 3.0 4.5
102.5 4.0 77.0 88.6 6.0 9.0
-15.3
-20.6
LOCALIZER SIGNAL LEVEL CALCULATIONS:
108.5 2.0 46.0 83.0 0.0 0.0 -31.0
TO USE MAXIMUM FREQUENCY DEVIATION SPECIFIED BY MODULATION FREQUENCY
AND MODULATION INDEX TYPE 1 , OTHERWISE FQDEV ( I ) MUST BE SPECIFIED
.1
Cross mod and cross compression calculations made
********* CROSS MODULATION CALCULATIONS *********
STATION
FREQ (MHZ)
105.5
102.5
COMPRESSION
OF LOC. SIGNAL
IN DB
0.8
0.2
FREQ DEV.
FOR XMOD
CALC. (KHZ)
63.
52.
% AMMOD
CAUSED
BY STAT.
0.12
0.02
TOTAL PERCENT MOD., NOT CONSIDERING CROSSCOMPRESSION =0.01
COMPRESSION FACTOR =0.109
LOCALIZER SIGNAL COMPRESSION IN DB = 1 .0
TOTAL % RMS UNFILTERED AM MODULATION = 0.12
************************* ******* ****** ***** *************************************
Filtered AM modulation due to crossmod is printed.
TOTAL RMS AM MODULATION
DUE TO CROSSMOD INTERFERENCE
CROSSCOMPRESSION EFFECTS INCLUDED
DETECTOR OUTPUT AM MODUIATION: 0.1 %
AUDIO OUTPUT AM MODUIATION: 0.0 %
150 HZ FILTER OUTPUT AM MODULATION: 0.0 %
90 HZ FILTER OUTPUT AM MODUIATION: 0.0 %
Re-entry of edit mode by program
*** PROGRAM PARAMETER EDIT MODE * * *
FOR INSTRUCTIONS TYPE: INST
. / End of edit mode - no parameters altered.
Printout of intermod generating frequencies:
RECEIVER FREQUENCY IS 108.50 RECEIVER BANDWIDTH IS 40.0 KHZ
FREQUENCIES WHICH PRODUCE INTERMOD INTERFERENCE ARE:
F1 F2 F3 IMTYPE IM CENTER FREQ IM BW IN KHZ IM LEVEL
IN DBM
105.5 102.5 2F1-F2 1 08.50 425. -48.5
TO CALCULATE INTERMOD SPECTRUM TYPE 0, TYPE 1 TO STOP, TYPE 2 TO RESTART
PROGRAM, TYPE 3 TOCHANGE PARAMETERS AND RECALCULATE INTERFERENCE
.0
IM is calculated
***************** ********************************************************J
INTERMOD AM MODUIATION CALCULATIONS:
CALCULATION PARAMETERS :
INTERMOD TYPE: 2F1-F2
STATION FREQ
(MHZ)
MODUIATION
FREQ (KHZ)
MODULATION
INDEX
FI: 105.5
F2 : 102.5
12.500 5.0
10.420 5.0
INTERMOD LEVEL (NO FM STATION MODUIATION) = -48.1 DBM
DETECTOR MODULATION FACTOR = 0.156
AUDIO OUTPUT MODULATION FACTOR = 0.032
150 HZ FILTER MODULATION FACTOR = 0.0
RMS AM MODUIATION AT DETECTOR OUTPUT =2.2%
RMS AM MODUIATION AT AUDIO OUTPUT = 0.4%
RMS AM MODUIATION AT 150 HZ FILTER OUTPUT = 0.0%
RMS AM MODULATION AT 90 HZ FILTER OUTPUT = 0.0 %
-118-
FOR PRINTOUT OF TOTAL INTERFERENCE TYPE 1
.0
Typing a '1' will print out total interference due to intermod, CDI interference and
combined crossmod and intermod.
************************************** ***********************************
TO STOP TYPE 0, TO MODIFY PARAMETERS TYPE 1, FOR TOTAL RESTART TYPE 2
.0
R;
End of program execution
H . Subroutine Descriptions. In this Appendix we briefly describe each subroutine
used and its purpose. Figure H-l shows a block diagram of the various subroutines and
functions used in the interference program. Each of these will be explained in detail
in this report. Figure G-2 in Appendix G gives a flow-chart of the main program.
Table H-l gives a listing of the variable names used and each of their meanings.
1 . Subroutine CHANGE. This subroutine is entered in the parameter edit
mode. The program parameters are changed by typing the proper instruction. The instruc-
tions can also cause the program to exit edit mode and continue normal execution or jump
and perform certain tasks such as calculate IM immediately, calculate signal levels at
RF amp input, etc. A list of instructions and what action they take is given in Table H-2.
Figure H-l . Subroutine ana Functions Called by the Main Program.
-120-
VARIABLES:
NSTAT IS THE NUMBER OF FM INTERFERING STATIONS
FREQ (I) IS THE FREQUENCY IN MHZ OF THE ITH FM STATION
FMOD (I) IS THE MODULATING FREQUENCY FOR STATION I
BETA (I) IS IT'S MODULATION INDEX
LEVEL (I) IS THE SIGNAL LEVEL OF THE I TH FM SIGNAL.
IT IS THE SIGNAL LEVEL AT THE RF AMP INPUT I.E.
IT IS THE LEVEL AT THE RECEIVER INPUT TERMINAL MINUS
THE ATTENUATION OF THE INPUT FILTER
MILE (I) IS THE DISTANCE FROM THE RECEIVER TO THE ITH STATION IN MILES
POWER (I) IS POWER LEVEL OF THE ITH STATION IN KWATTS
FQRCVR IS THE CENTER FREQUENCY THAT THE RECEIVER IS TUNED TO, GIVEN IN MHZ
BW IS THE BANDWITH OF THE RECEIVER IN KHZ. I.E. THE RECEIVER BANDWIDTH.
IT IS ASSUMED TO BE IDEAL BANDPASS
IT IS GIVEN THE VALUE OF 40 KHZ
RK3K1 IS THE DISTORTION PARAMETER 3 K3/2 K1 IN DB.
Table H-l
Variable Names and Their Meaning
IN PARAMETER EDIT MODE ALL COMMANDS ARE TYPED AS:
to
<r to
! §
uj £ 2
x < O
•- £ <J
- 5 3
T LL- CO
<J X Co
§< o
> LU Cl.
Hz
o o Z
I— *“ •
Z Z H-
UO
oo < £*=
oo z
o o >
C£ _ LU
u <^> u
Z X LU
UJ UJ X
0^5
lu i
a: 7 O
n “
z2“-
3 O £
n^Q
Q- LU
1 1 1 AT
m 3 8
t!2t
0- 2
o; _
00 a. ^
• — , O
z ' z
5|u
Q- Z •
1— UJ 9:
10 Q. O
— 00
Q LU LU
Z o o
< z z
x < <
U x x
, <J U
>- ' 1
Z Z z
Qzz
0<^
2 LU ^
u. m i
3a:-
UJ O >
£°-S
~ 1 z
fz^
O O 3
00 •— o
<T LU
^a:
X I/O LL.
i/o 1/0
1/0 LU LU
Iss
x u u
(J
I I
>^Q
iOO
IM - INTERMOD INTERFERENCE IS CALCULATED
XMOD - CALCULATIONS OF CROSSMOD INTERFERENCE ARE MADE
OdB 4-
dB Attenuation
-8 MHz
Slope 1.5 dB/MHz
/ linear slope = 6 - (.1 726)
for crossmod
calculations
-.075- |f|
10
+8 MHz
Slope .75 dB/MHz
linear slope = 8 = .04326
for crossmod . iq-.0375 -|f |
u!ni lotions
.f
Frequency away from
receiver center frequency
Receiver center frequency in MHz
Figure H-2. Assumed Attenuation Characteristics .
2. Subroutine MILEDB. MILEDB calculates the signal level at the RF
amp input of the receiver using the free space attenuation formula. It takes into
account NAV antenna loss (1 dB/MHz below 1 08. 5 MHz) and the RF amp input
filter characteristics. The free space attenuation formula is
a (attenuation in dB) =36.3 + 20 log (freq. in MHz) +20 log (d in miles)
The signal level in dBm at the RF amp input due to station I:
Level (I) = Power (I) in dBm - Free Space Atten. (I) - NAV Antenna Loss
- Loss Due to RF Amp Input Filter + 6dB
(The 6dB is due to the directive gain of the NAV 11)
The loss due to the RF amp input filter characteristics is calculated by
REAL FUNCTION RF FILTER. The attenuation characteristics of the NAV 11
receiver are approximated by the characteristics given in Figure H-2.
3. Subroutine TEST. This subroutine checks to see if there is 3rd order
IM due to stations I, J, K which lands within the receiver passband. The program
uses the relation given below to calculate the bandwidth of FM signal spectra of
stations I, J, K .
-123-
Bandwidth 2 (R • 1) fm
\
where R - modulation index and fm - modulation frequency.
Any intermod component formed from a spectral component from each FM station
is given by:
IM component = FREQ of component from I + FREQ of component from J -
FREQ of component from K
To see if any of these IMs are within the receiver BW the lowest and highest
frequency IM component are calculated.
IM = FI . , t- fm. (1 t p ) + F2 . , +fm (1+P)
max carrier freq 1 1 carrier freq 2 2
- F3 + fm3 ( 1 + p3) ( H-l)
Likewise,
IM . - FI . , - fm, (1 + p.) + F2 . , -fm (1+pJ
min carrier freq 1 1 carrier freq 2 2
- F3 - fm^ ( 1 + R^)
(H-2)
The receiver frequency is denoted by FQRCVR in the program and if there is IM
interference, then
IM
freq min —
FQRCVR ±20 KHz < IM
— Freq Max
For these calculations, the bandwidth of the receiver is assumed to be 40 KHz.
4. Subroutine XMOD. XMOD calculates the amount of cross-compression
and cross-modulation due to interfering FM stations. The program uses either the maximum
frequency deviation calculated from BETA (I) and the modulation frequency FMOD (I) or
FQDEV (I) (the maximum frequency deviation is entered in edit mode). The user can
specify which to use. Entering the maximum frequency deviation for crossmod calculations
allows the user to analyze interference situations easier without specifying a BETA or
FMOD for each FM station. FQDEV =40 KHz might be a "typical" value for example.
The gain change (GC) of the desired signal due to station I is calculated.
GC =
Desired signal amplitude with interference
Desired signal amplitude without interference
= 1 - 3K./K Bj
J ( H-3 )
where B is the signal level of the Ith FM station at the RF amp input. At this point it
is assumed that the RF amp input filter attenuation has already been taken into account.
-124-
( H-4 )
The gain change in dB is:
GCdB = 20 log f 1 - ('10rr3K3//2l<l )dB + 2BdBm + 6)/2° ,
Total GC due to all stations is given by
3K„ N
GSo,al= ,r=1
Bi
.2
(H-5)
where Bi is the signal level due to the Ith station at the RF amp input.
The amount of cross-modulation due to station I is:
% Am mod - Max Freq Dev of FM Station • Slope of Input RF Amp Filter
•6K,j/Kj • B? x 100% ( H-6 )
(not considering cross-compression)
Equation (FI. 6) does not consider cross-compression of the carrier. If one wants
to consider cross-compression, the equation used is
% Ammod without
% Am Mod with _ Cross-Compressi on
compress? on 3 K~
1 -
K
B
The total RMS Am cross-modulation due to N stations is given by:
N
Total RMS % Am = [ .7 (f max. • 5-
i-l i i
6K
3 _ 2 2 1
B. ) ]
K,
I B.
( H-7)
( H-8 )
where f max; - maximum frequency deviation of station I
5. = slope of input filter characteristics at frequency of station I
Subroutine XMOD calculates % Am mod at the receiver filter outputs also. It
uses the same equation as above except that each term is weighted by y (f mod; ), where
y is the appropriate normalized filter function and f mod; is the modulation frequency
of the Ith interfering FM station. Note that if FQDEV (I) is only specified, the filtered
% cross-mod calculations will not be accurate since f mod; must be specified. The %
modulation present at the receiver filter output due to interfering signals is:
-125-
•rns". ssr
Total RMS % Am Modulation at
a Receiver Filter Output
N 6K3 2 2
f I (f max. ‘ 8. • -p— B. • y (f mod.) ) )
i=l ' ' K1 '
1 -
577
Ki
( H-9)
Table H-3 gives a listing of the variable names used in Subroutine XMOD.
.
VARIABLE NAMES:
CROSSL-LINEAR COMPRESSION FACTOR FOR ONE STATION ONLY (ITH STATION)
I.E.3 K3/K1 B**2 WHERE B IS THE SIGNAL LEVEL OF THE ITH
STATION AT THE RF AMP INPUT.
PERCNT - % CROSSMOD OF LOCALIZER SIGNAL DUE TO STATION I, CROSS
COMPRESSION NOT CONSIDERED
PERCOM - % AM MOD DUE TO STATION I CONSIDERING CROSSCOMPRESSION
SUMC - COMPRESSON FACTOR DUE TO ALL STATIONS. (RESULTANT LOC. LEVEL
IS MULTIPLIED BY (1-SUMC)
SUMCDB - COMPRESSION OF LOC. SIGNAL DUE TO ALL FM STAT. EXPRESSED IN
DB.I.E. SUMCDB=20 LOG (1-SUMC)
XMOD1 - TOTAL % RMS AM MOD AT THE DETECTOR OUTPUT DUE TO
CROSSMOD FROM ALL STAT. (IT INCLUDES EFFECTS OF
CROSSCOMPRESSION ONLY IF SUMC IS LESS THAN 1)
XMOD2 - % RMS AM MOD AT THE RECEIVER AUDIO OUTPUT
XMOD3 - % RMS AM MOD AT 150 HZ FILTER OUTPUT OF RECEIVER
XMOD4 - % RMS AM MOD AT 90 HZ FILTER OUT
Table H-3. Variable Names For Subroutine XMOD.
5. Subroutine IMCALC. This subroutine calculates the AM modulation due to
intermod interference.
IMCALC checks all combinations of 3 stations (stations I, J, K) to see if the 3rd
order intermod causes interference at the receiver frequency. This is done by calling
Subroutine TEST which checks the 3 freqs and returns with ITEST = 1 if they produce
interfering IM. Subroutine CONVOL is called which does the convolution of the
3 FM spectra and returns with the modulation factors of the receiver filter outputs (called
SUMDET , SUMAUD, SUM150, SUM90). IMCALC uses the modulation factors to calculate
the % RMs AM modulation at the filter outputs. ( called PER 1 , PER 2, PER 3, PER 4)
Total % AM modulation due to the IM from all interfering stations is summed (called
TOTAL I, TOTAL 2, etc.). The CDI with interference is calculated by calling subroutine
-126-
CDI. The above calculations do not consider effects of brute force interference. The
combined effects of cross-mod, cross compression, and intermod are added and printed
out. CDI calculations are again made.
A listing of the variable names used in the IM % AM modulation are:
TOTAL 1 is the total % RMS AM mod due to all FM stations at the output of the
detector fi Iter
TOTAL 2 is % at the audio output
TOTAL 3 is the % at the 150 Hz output
TOTAL 4 is the % at the 90 Hz filter output.
PER 1 is the % AM mod due to IM from stations I, J, K only at the detector
fi iter output.
PER 2 is the % AM mod due to stat. I, J, K at the audio output.
PER 3 is the % AM mod at the 150 Hz filter output.
PER 4 is the % AM mod at the 90 Hz output.
The IM level due to 2F1-F2 IM is given by
IM . .
carrier leve
Ko 2
3/2 -j-r- IT C
( H-10 )
where B and C are signal levels at the RF amp input of FM station 1 and FM
station 2. The IM level due to FI + F2 - F3 IM type is:
K3
IM = 3 -± BCD ( H-l 1 )
where B, C, D are signal levels of stations 1, 2, and 3 respectively.
The % Am modulation due to intermod carrier only is (no FM modulation on
the FM stations ):
% Am mod due
to IM carrier
- (Localizer
level in
1 0 dBm
IM carrier ) / 20
level in
dBM
100°i H_12 ^
The RMS AM Modulation due to the IM with modulation is
% RMS Am modulation =% Am modulation due
to carrier alone
Modulation factor
( H— 1 3 )
-127-
Total RMS % modulation due to all IM is given by
2 1 2
Total RMS % mod = ( I % Am mod due to )
all IM from 3 stations
intermods ( H-14 )
Including effects of cross-compression and cross modulation as well as IM
results in a total RMS percent modulation given by.
Total RMS % mod due
to IM and brute force
with cross compression
2 2
(total RMS % Am mod due to IM + Total Am mod
due to brute force, AM mod from cross-modulation
without cross-compression) 1/2
where GC — 1 - 3
B.2
I
GC
( H-15 )
( H-16 )
which is the gain change due to "brute force" interference due to all FM stations.
6. Subroutine CONVOL. Subroutine CONVOL calculates the 3rd order
intermod due to interfering tone modulated FM stations. There are two types of intermod
possible, 2F1 - F2 type and FI + F2 - F3 .
The 2F1 - F2 intermod is due to 2 FM stations with an IM center frequency =
2 FI - F2, where FI is the carrier frequency of the one FM station, F2 is the carrier level
of the other .
FI + F2 - F3 intermod is due to 3 FM stations and has a carrier frequency
FI + F2 - F3. The subroutine CONVOL handles each type separately.
a. 2F 1 - F2 IM Term. For2Fl - FI intermod, the IM is
Jm (2 f2)Jk °V ( H"17)
2 P2+ 1
P1 + 1
!M _ 3 .2 _ . .2 '
. rm<: - B c c<b) a (c) I I
f 2 k = -(pj+1) m=-2 P2+l
■ cos 2irt (2b - c + m -frr^ - k*fm^)
Thus the ( m, k) th intermod term is
IM
m,k
= (Pj) J (2p2) cos [ 2b - c + mfm2~ kfrr^ ] (H -18 )
Am, n
L
-128-
3
The modulation factor is calculated by
MF
( I Am, l< *| y (01 )
all terms with
frequencies wi thin
receiver passband
1/2
( H-19 )
where f =IM carrier frequency - Receiver frequency + m -fm^ - k-fm^ .
In this equati on,y(f) is the normalized filter function of one of the receiver filter
outputs and f is the frequency of the IM term relative to the receiver center frequency,
y (f) is assumed symmetrical with respect to frequency. The maximum value of the
modulation factor is 1 and this occurs only if all IM terms are received in the receiver
passband and y(f) = 1 .
b. Fl + F2 - F3 IM Term . The FI + F2 - F3 intermod term is given by:
IM = 3 B C D a(b) a(c) a (d) I I l J. (B,) J. (P2) Jk (P3) cos 2nt
terms ' i k
( H-20 )
( FI + F2 - F3 + ifm1 + jfm2 - kfm3 )
For convenience let
A i j k = J. (P,) J. (P2) Jk %)
Using (H-21) the modulation factor (MF) is given by
( H-21 )
where
Modulation = ( I
factor all IM terms
that pass through
receiver bandwidth
f = FI + F2 - F3 + ifrr^ + jfm2 - kfm3
- Receiver center frequency
A i i kf y (f)l )
1/2
( H-22 )
( H-23 )
The program stores in Array A X B and array A X BFQ the intermediate result
of convolving two stations together. In addition, A X B holds the amplitude and A X BFQ
contains the relative frequency of the intermediate result.
For a two-station case the intermod is
A X B (I) = JUM (2 P})
( H-24 )
-129-
and
AX BFQ (I) ( L - I - 1 ) ‘ fm1
where I ranges from 1 fo 2L - 1
and L = integer value of I (2 1
Si mi lari ly for a three-station case the IM is
A X B (I) = JL ( B1 ) Jn ( P2)
A X BFQ (I) = L • fm + m • fm2
H-23
( H-26 )
( H-27 )
where A X B and A X BFQ have been sorted in order of ascending frequency and
. and M are indices which range from
INT [ - (P1 + 1 ) ] L ' INT C P, f 1]
INT [ - (p2 H ) ] < M < INT rp2+ 1]
( Note - INT stands for take integer value)
( H-28 )
( H-29 )
c Convolution of AXB with the Spectrum of Station K. A flow chart of
the program part of subroutine tU convolves the intermediate resuTTAXB w.th spectrum
of F3 (or F2 Fn the case of 2F2 - F2 IM), is given in Figure H-3. To save computation
Hme in calculating which intermodulation components fall into the rece.ver passband
the program uses the fact that AXB is ordered as to increasing frequency. The mtermod-
ulation frequency is given by:
IM component - IM carrier t-
frequency frequency
A X BFQ (I) - K* fm3
( H-30 )
The program starts with K = 1 and begins to search through the array AX BFQ for
on intermodulation component that lands just inside the low end of the rece.ver possband.
, , ” , , the Val„e | is stored so that when K is incremented after going through
re\"nM,e X « BFQ a sl^ch starts at that value of I. colled UST in the pr^ram,
ft the next va)ue of IM which just falls within the receiver possband . Note that w en
the IM components begin to fall outside of the high end of the rece.ver possbund, £« °
need, no longer to be seorched since oil other components will pcocktM IM I arms h g
in frequency. So, K is then incremented and search begins through AX BFQ again.
This program calls subroutine SORT which is o bubble sort program to , >ut the
elements of AX B and AX BFQ in order. It is colled only for FI + F2 - IM-
-130-
Real Functions: FILDET, FILAUD, FIL90, FI LI 50 are straight line approximations
of the measured filter outputs of the receiver. They are normalized and are symmetrical
with respect to frequency above and below the receiver frequency. For IM calculations
real functions EQ90 and EQ150 are used which are bandpass filters with the same noise
equivalent bandwidth as the 90 and 150 Hz filter functions.
Subroutine CONVOL uses Real Function BESSEL to calculate the bessel function
of a given argument and integer order. Real Function BESSEL allows negative orders
to be used and calls the IBM Scientific Subroutine Package (SSP). Subroutine BESJ is
used to calculate the actual bessel function.
7. Subroutine CDI . This subroutine calculates the CDI with interference
present. The % modulation at the 90 and 150 Hz filter outputs are inputs to the program.
The subroutine first calculates DDM (difference in the depth of modulation) for
a CDI reading without interference.
DDM = CDI • 15.5/150% ( H-31 )
Let % modulation 90 denote the % modulation at the 90 Hz filter due to localizer
signal with no interference present, i.e.,
% mod 90 = 20% + DDM/2 ( H-32 )
Likewise, for the 150 Hz filter output,
% mod 150 = 20% - DDM/2 ( H-33 )
If interference is added with a certain percentage modulation the resultant
modulation is given by:
% mod 90 new = (% mod 90^ + % mod interference 90^ ( H-34 )
Si mi lari ly,
% mod 150 = (% mod 150^ + % modjnterference^
new at 150 Hz out) ' ( H-35 )
The resulting CDI response is given by:
CDI. = (% mod 90 - % mod 150 ) • 150/15.5 ( H-36 )
NEW new new
In this section the basic operation of the computer program written for considering
cases of multiple interfering signals was described. Complete listing of these programs
is given in Appendix I.
-132-
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■ 134-
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■A I THIN HZ 3tCSI Vr F AW
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call tt <jt( r j~.3( I ) . F - “Of J) , = r,- )( y ) , f • «.JD < 2 ) . F^ V-, ( J > , <1 ,
C TFT A < I t ,f<-.TA( J ) , T A I < ) ,L r V _ ( I > iL’V’Ll J) , L _ V * L ( < ) 3 ACV - . n* .
C I T* ST , 1 , PK3K 1 )
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C ®EC AL CU L At £ I NT EPFrPfNCF ' )
’EAD 17, ICALO
FORMAT (111
IF( I CALC.^Q. T ) GO TO TQoq
IF ( I CALC-1 ) 1 OP. 1 1 0, 1
CALCULATION OF INTCRMPO ....
CALL IMCALC
PPINT 1000
FOPVAT(//,ix,-’-’( ),//)
OPIN’" 1 t 00
FQCVIAT(« to STOP TYnF 0. T n ‘‘flOIPy CABiv'T'
C ‘TOTAL RESTART TYP- ? •)
READ 17, ICALC
I F ( ICALC-1 )1 10.3P9O, 1
STOP
END
. TYPE.
BinA'C
T - 5 - -j
">e AND
T Y3;. l.FpP
C = =
SUB5 C UT I NS T5ST( -P“D‘ .^DE>2 .“O-IQ'.F MODI .fyqo2, 3ETA1 . 3FTA2.
C npT4 7.R.EV1 , CL - VS » "L’ V 7, r JRCVP .R I TF jt . IPr- I JT,r<3Ki)
C
THIS SUOOPUTIfir T £ c T E' FM fts/jc : F~ r Jl ,FPFO? , Fo: U> ” o 3?-
Ic TOT F1+F2-F? I A* IS v I T MI • i the 3ECFIVFS PW wJTh PECEIV'T’
FPrOlFQPCVP. IF T H r- •»' ” IS , I T.S T S- T to 1 , r THr o 'M I S c S ,‘T tj j
I PO I NT = 2 .POINTS 7|jt M^ADINGS
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60 1
I T ES t = j
? U *-*L K V IS THE NO MC •VILA” I CM ! N T T •- v 00 LlV "L iE D"
FPfQl IS NOT T Hz. SAwr A “3 Ft-JS
SU‘-1Lr- V-»Lr VI ♦ «L f V2 ♦ -’L r- V 3+ 5 K ‘ K 1
I f < rc -- 01 • N" , F£ “Q * ) S 1 IML " V=SU ML~ V .
I f ( I AD I N T — 1 ) ? ,2 , 1
A..'):.D ir
OP ! NT I No
HEATING’ *iF*| I P": I NT =2
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f-ipvit (////,« .‘.Fti-IV-.fi F ‘ l.lfM’Y I*- '.o .-1
C IE. * , F 6 . 1 , ‘ K -H 7 • >
P« I NT e ) 1
n^'tf (• - : _ 0 J~NC I rr yHI’H ujTDt'O; i * j T E S m * p IYT
V :W‘- » Da 1 r>T i
A
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THIS PAGE IS BEST QUALITY PRACTICABLE
PROM COPY EURN.ISHED TO ULC ,
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23
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52 0?
P^INT n32
F^OMAT ( 3x • 1 "1 • if X , • c ? • , 5X . • F~ • , RX < • I M T Y HE • . 2 X , • I M F ■< < O',
C JXiM" DW 1*0 KHZ Iw Lf V~L IN r« r~AT. M'~ OUL ATI CN • , / >
FH TUPN
T-ST IS P<~ BF TtfM=D TP e-r-f j- [‘jTr.jyn., cp-p-fA-Jv =>i r"»UC" O
ny Thp:S ccc jijlnci -5 will r, i v" a C r nt i hut I r_ n a t th..
-HEC5IV-? FFUOUHNCY
FMIN IS THr MIN FCF) _-r jmtfpw 'O
FJAX IS MAXIMUM
FUL5 0- THUMB Fir TH~ =)AN0wIDTH jF A F M SIGNAL!" TZ
CALCULATE WHLTHES I NTrH'M'T) Tc # I TH I N F«,:C ~ I VC 3 PA'S’UTJ
F.TT ! 8 W=2*Fh 5 QMOOIJL A t I NGC 1 +MUDUL A -I UN I ND-rx )
T” ST T*i S=f Ic I NT HP vr r, j c n;,at-j within r<SC;iV '
0r LT A = = MODI * ( I . +BE T A1 ) ( 1 . + BET A£ I+I- M-)0 3$ ( 1 . + -v:t A T )
FFMiN-p^rai hfi- eo ■'-f~ op cv-
FF'M X = F F M I N
/
FN*IN AND FV AX a r- - C "IN V~ ° T ) Tp
FMtN=cFvlN*l 0 0 J • -DELTA
F‘< A X = rrM A X* 1 0 0 0. +1r L TA
CHECK T ■) gc 1 tF FMI‘I ‘ * A x F A L L c « I THIN —_Cr I V „
IF ( ABS( - MAX) . LT. ( ° W/Z - A . AN-, ( F»I -:) T . (PW/2 .)) c,r, TJ - 2 J j
CHUCK TO S'- T- TNT 3 un; t.TJ ~ -CV»
IF ( F v In.L ~ . ( -'l#/ - . ) . AN-. - ma x .C. . ( 3 a/ ’ . ) ) GO TO - ’00
GT TC 520?
F ;UMzF':-.il +F --o-'-h- - ; i
f ? a = D“LTA*2.
I F ( h - 5 0 1 . NT . = ?•- or . AND. I ~ I* I T . J . \ ) P- I r • T ' 3 , F •; 5 0 ' “ 0 - . - S J
C M , FF-w , =" JML f V
nr'MtT(-)FH,l ,=X, 1 KHF’-M ,,;X,FV,JX,Fr,J>!:X,”,')
Ic(cr JJl.iG.FP-0 :,X'n.IAt.!-:’,-l|.1)o ! N” r J 0 1 . F - II ,r. ; J • , F; j c j„
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F IBM at ( 2F s. I ,1 OX , • ?f;_t 1 , 5X.c-h' , H, -c , j, ! cX.F‘.l I
u^Tljr »j
'* IS Nr T IN Th c~r. T v"F < *
I TES T= )
‘NO
C
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C* ****************************************************** **************
-137-
l
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C THIS SU-IB^UTI NS CALC'JUT‘iS THF AMT ,1F CFJSS MOOJLA’I^N DJ~
C TO INTERFERING "m S t AT ! >' S. AL S 0 COMPUTES THE Avr 'if CPJSE
C COMPASSION.
c
DI M'NS I ON FREQ ( 20 > ,FMOD( ? 0 > . SETA < 2 0)
C
PEAL MXLFI 20 ) , PJW^Pt >0),FQ">cV( ">0 )
PEAL L-VF.H20)
C
COMMON FQ?fi/<,X‘-IJPi . XMOOr . X M-10 ’ . XMOlOA . SUMC i JW »F< 2K 1
COMMON CP"() , LS VE L . FMOO , 2F T A
COMMON MIL^.POvxEP.FaOEV.NFTAT
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C 1= THB am MODULATION IS TO COMPUT'D USING the F p C OJt NCI'S OF *'ODU.
C MODULATION S PFC I F I FO F CALCULATIONS A ° E MADE
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of INtt
l FOPMAM* t0 USE maxIM.jm FP E iU~NCY DEVI ATI r' \j C^cCtcIED OY M TOUL A •
C » * T I ON F Pc OUT NC Y •,/,« and mdu J L ATI ON INDEX TYO 1, 0 ’ HE P W I S ,£
C FODEV(I) moot Sd:CIFI~D»)
p E AO El . I Fl AG
51 FOPMtT(M)
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C
C » ; I NT ! NO ■" f M-«HMGr
C
C
Prj I N T ' J
20 FDEMATI* a AA *A A * A* '•r.n ? r VCPULA’IDN CALCULAT! NS < a A A * A A A A A A A • )
DP I NT 21
21 c-iVM ATI • STATION r '.MPPr SS I 'N FFFQ O'- V . \ \ vv "I • , / ,
C* F — CO T LHC .SIGNAL ftp XV CD CAUSED'./.
C • ( MH l i I N DP FAUC.IKH/) Hy STAY.',/)
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-138-
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THIS PAGE IS BEST QUALITY PRACTICABLE
FROM COFY FURNISHED TO DOC
I 3 K3/KI *1**2 «HF.op n IS TH~ SIGNAL L'lV L OF tHE ITh
ST AT ION at t hf »‘<p IN^UT.
Pr PC NT- Si CPOSSMOD '1 - LOCAL I2"p SIGNAL DUS TP ',TlT In‘J [ ,C '1SS
COMDR'SSI JN NOT CuNSIPFPUD
PER COM- X AM MT!> DU* T) STATION I c OUS I Dr C I NG IN j'6 T<3» Z c S I rN
SL)MC-CONPPcSSON FACT^p FHJf 1) ALL S T AT t Ot''S . ( : If JL T ANT LDC. L'-v/f.
IS MULTIPLIED MY (1-StjMP)
SUMCDU-COMWRiSSI ON f'c LOG. SIGNAL DUr- Tf All. rv ST A T , " xp: . S ' - ' IN
03. I. E. SU MCU 3=2 0 LOG C-SUMC)
XMODt-TOTAL X WM$ AM V(V) AT -i-|r OrT^^Ty. r'UTr>')~ nj. tp
CPCSSAOD FCDM ALL STAT.( jt IMCLUOF.S EFFECT r- 1. f
GPOSSCOMP vHSS ION ~NLY I F SU«C IS LSS3 Than \
XMPP?-% C NS AM MOO at THC JECc IVF‘< AUDIO 1UTOUT
XMODt-tj 9>'S Am MOO AT ISO N 7 FILTpF OUTPUT OF •‘-C IVT-
XMODA- x 'MS AM MOD AT A) 02 Fi^-pp. r,UT
TO TAL =0.
X M 0 D l = o .
X M " 0 2 = 0 ,
xm;d j- j,
X MTI d a - ,
SUMC = 0 •
DO 50 I=1,NSTAT
f 3MPJT AT I ON OF TU- Cp >* ,M*,0 "S: I "■! DU= T.t T 3 * J -- STATION, IN 03
C
C
C
C^niSiROKH'.Al.’V L ( I ) 4-P .
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C GONV- ' -I NG -•■'MM r;p TP Ll’j*'. ■
c!’:?ri.= io.*i‘('' Nc-/n. >
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C CALCULATION of r n-o: <r; - \ t C'L1’‘-
C '•TATI- I
C SITING C H M P 7 S T } A LAf'GF VALUe Ti 'JIN' > -
C 1MD“S=1 000 .
T p ( ( 1 . -C- '•SSL ) .GT . J . )CDVP- ? =■-' 0 . A A l 0010(1.
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C '••JV'i OS C ~ C S r CN-rL-LMM 'U T. . A j l TA'l N
-• JMP-r Si 1 *c t-C J •" 3
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C CALCULATING max pr ) P YT ", t t \ 1- . .1 i( c[ j] * j -4 - V , ' - N T I. •' 40
C IN FS 0*1 AMOVE
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-139-
IHIS PAGE IS BEST QUALITY PRACTICABLE
FROM COPY FURiilSHED TO DDC «•-
IF< I^LAG.tO. 1 ) FQD~V( I ) =<3F TA( J) *c«aD( I )
r
C THE R F AMP INPUT FILTER SLOPE IS APPROXIMATED TC BE .15DB /100KHZ
C FOR FREOS LESS THAN 8 MHZ FFCM RECFIVFF FREQ. ,.07SD8 / 1 COK HZ
C OTHERWISE * REVISED JUNE 78
C
C COMPUTATION OF SLOPE
SLOPE3 ( ( 2. 302) / 20.) *(. 15/10 0.) *10** (- { (FQRCVR-FREQ <T))*1. 5/20. ) )
IF ( (FORCVP-FREO (I) ) .GT. 8.) SICPE=.2511*(.C7 5/ 100. >*(2.303/20.)*
C 10** (-( (-8. ♦FQRCVR-FREQ (I)) * .7 5/2 C.) )
C CALCULATION! OF PERCENT CROSS v JP OUT TP STATION I
C
C
FHOCNT = 3LOP>E*FQDtV( I )*?.*rn«TL* 11).
C
c
C SUMMING PMS am mod DUE TO ALL STATIONS
C
C
C TOTAL IS THE. UNFILTEPFD TOTAL % am mtp
T1T4L = A£CCNTt* ?tTTry_
c
C
C
C CALCULATING THE 5v; \ am MiO AT T-T- >JTPUT 1" TF :.'IVC)
C f ! LTES;
C
c
XMOO I =XM0D1 F ( PFPCNT*ri LO= -T( p*.,r oil)))**?
XM3D2 = XMOO?F ( PER CNT*3IL 4JT( I ) ) ) ** ?
X»»CjO 3=XMOD3 + ( PF“CN‘T* F I L 1 s O ( =V->D( 1 > > ) ***
XVO J A = XMCDAF ( P£A COT* 3 I LOO ( F M ',0 ( I ) ) ) * *2.
C CALCULATION of 3ftCf’lT M-OJLAT ICM C INS ID*"- I N » C ~ 'SE :i <p?-a;,I 1\
c pu? n: stati jn i
f £&cr v=pf«cmt/( i . -cpos - l )
c
SO PPINT lJO.r?r1(! I.CI^n-5,1- J^ryj n,P---C:iW
130 t-noyAT(Tx,F5.1.pX.FF.i,t-!X.rA. ) , tx , f S. 2)
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C I F T jTAL c pMp.v-r " r V -F L'jr • SIGNAL ^ J ~ ALL S T A T I P N S I
C IS GREATER than 1 THJFD OLNL- 4-jr>e L OF Pr C.~ IV‘» D*'r E NOT APPLY
C
IF((1.-AUMC).LT.0.)C, ) t-< >-)0
S' )Mpp --?o. *alogi o ( 1 ,-Tjr )
N'T TO ->10
30 0 PL I NT ’01
301 *M*T4 jP S G. c S c 1 r ’< ,L Aft1 THAN ’ , THU’S '.P'T> i,
r .y - r, *.p 3«rrj vr- •(' LfN ■ - V»L I .» *♦♦*♦** • >
140.
SHIS PAGE IS best QUALITY practicable
from cof* furnished to ddc
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C Setting DUMMY VALUF eod total rCMBpf $?i on. I . c. 1 UMCDt1
C TO PRINT ASTERISKS WHEN S'JMCDH I? P^tNTcD
c
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SUMCD^-IOOOO.
c
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C CALCULATING nT4L MODULATION in ff " >Nf , CCN? IDE.R !f"C. "OM3 ;r =■ 3 I UN
C C>e tup DFSIRFD SIGNAL
c
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313 SUMM=sqqT( TOTAL) /( 1 . -5'JMC )
PS I NT 4 00 • TOT AL , SUMC . SUM CD 3 , SUM m
400 FO smaT ( # TOTAL sfrcpnT MOD. ,NCT C ON A I DLL I N G CR "S f C LVOi S 1 1 ON = • .
C -S.n./.* CJMOprSSI0N) FACT-P- I, F3. ->,/,• L C'C AL I 7ra F I5N AL C'USPE
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C TOTA_ X ptlt-c-o a v MOD 'A LCUL ATI
C
C
C !c THE T0TtL C»0SSC0MPPH<5SI fN DU? T ’ ALL F T AT I r N “ I? '.R*- a- ; -
C THAR 1 ,TH-DI THE PFF'FTS np CL'S? C CMPPESS I C-N AS; N T INCLUDED
C IN THE X A M M.DO C-*- 1 E'JLAT I ON S , t Tin; W I ■>£ IT I? CCN5I0*- -:.;0.
C
c
r = 1 .
I P7 ( S U • L T .1 . )C=1 .-?'|MC
C
c
X*"*01 -?OFT ( X m: !D! )/‘~
fed ’ = : )st( xmom- > /c
XMCD ! = - OCT ( X '"9; )/C
XND94 -30°T( X'LjOI I /C
c PRINTOUT OF TH- " ra|_ AMOUNT r AM < SOUL ~ I ON
C
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3000 F 1PM A T (//, 1 X .■''»(•*•)./. ’x .* Tr T AL -M- AM M-'D JLA-l ON* .
C /, ax, 'JUe T / CR" 3SMTD L- • )
IE ( FUMF.l I . ) PS INTO JJ-
30 0*3 FDPM AT < ix » • D -0?SC0mp.t: c AI >»• j "F'-CT? INCLUD'D' ,/)
I r ( *u .;c . Gr: . i . ) ps i nt to ) -
30 0 3 (X.'D.d^ccvP'J-'F'oi TE •>. Tt Nr>- I »:C| ,/>
M., I KjT
•» 0 01 . XMUD1
PRINT
•’302, XMOO’
I ■ | T
■"103. X NOD 3
p- I NT
'OJA , X M JDA
30o: f'jivuri ix,'j:Tr:cL dut->ut a ■ i m if'ui. a* i on : • «r a . : , • .„•,/)
300.0 F V- ma- ( 3X. • ;jr y 11 IT a ■ j r V MODULATIONS '04,1,' ■.',/)
3003 F'»M.1T{3X,'1-J H / f IL'-s DiTnijT am 'O OiJL A T I >j S S',/)
30 0 A H4M4T|1X, • MO MX E n T -r -|jr-''UT am MODULATIONS ' ,-*.1 ,'
F-FTU- N
141
BBS PAGE IS BEST
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SUBROUTINE MIL ED n
THIS SUBROUTINE CONVERTS THE DISTANCE FROM THE -M STATION
TQ SIGNAL LEVEL IN DOM t T THE R'FAMR INPUT.
THE PROGRAM TAKES INTO ACCOUNT THF OF AMP FILTF® CHJ 3»CTt- ICHCS
AND THF ATTENUATION dF THE NAV A NT CNN A .
US'S FREE SPACE ATTENUATION FORMULA
DIMENSION FR'Q(’J) , PMODI? 0 ) . HFT A ( «- J )
REAL LEV EL (20)
rF AL mIlEIEJI.POWERI’OI.^OOEVI ^D )
COMMON FQ»C VR . XMJDI , XM->d.-> ,x MOD 7,XMC->A.SUMC.Bl*,R<3Kl
c DM MON FREU , Lf.VF. L . RM.OD , ^T A
COMMON MIL"* PGWE R ,FODr V ,NST » "
PR I NT S
FDPMJTC T o COMPUTE SIGNAL LEVEL AT CF AMD ]'PJT TYPJ 1*
C,/,* GTHFR WISE VALUES DF LrV'L(I I MUST FF INITIALIZED IN Tur •
C ./. • EDIT NODE and HScD as T|f SIGNAL LEVS L AT THE - F AM’.» IN »JT • )
c-ac e. I flag
F D " M A T ( I 1 >
I r ( I FLAG .NT.1I RETURN
PRINT 40
FORMAT! • PRINTOUT fF SIGNAL L'V'L C DM PUT A T I ON S • • / )
POINT 41
FORMAT! • STATION MIL'S STATION FREE NAV ACV = IN*.
C ‘PUT SIGNAL'./. • FPrO PRIM PPACc AN',
C 'TF IMA FILTER LrV -A T ')
PRINT 42
FJRMAT(« (MH7) R "OF IV IN Dl<m a T T N -R J bT5>iV, A T T " N DR',
c • RP AMP in ( d <M » • , / )
DO S3 1 = 1 .DO
IF { I . GT.NSTAT. and. I , N- . -> ) )G 3 T i GJ
R:: SPAC= ATTENUATION C ' VP U" A T I C’l
At"pn=36 . ’t’O . * AL DC, I D( pR" J< I)) + ’J.*ALQG1J( * I L’ ( I ) >
R«rv*P R = 6 0. 4- l D. *A LCC.l 3 ( P OW -’(I) )
COMO JT AT J ON OF LOSS DU" TC t NT * NN A CHA ' AC TE '• I ST I •“ 5 I OR PER MHZ
nrL’1H I3a.:'!H?
A L D S S = J .
! F ( P - -()( I ) ._ T . ID R.S ) f.L J = S= 1 3 i. -5-FR F 0 ( I )
OF l c S S = «FP Ilt { FQC CVO ,F---D ( r ) )
* nFi GAIN IS ADDED FTP r,| d=ctI VE GAIN PR NAV AM‘'\‘;S
L" v/FL ( I | = r. n I*p - ATT ON- AL ">S S LO SS ♦- .
I p ( I . :'3.?J)RR INT t 0 )
PRINT I 00 . F'RP 1( I ) . M I L- ( I ) ,'P-wFR , A TTEN, AlDSS . RF . "S - . LrV-_ ( * )
F 3 = MAT(Tx,FS,1 ,'tX.FA.I ,'X,' . 1 . S X . F S . I , ■> ( 4 X . F E . 1 ) . X , p " . 1 )
CONTI NUE
PDPMATI/,' LDCAlIZ" SIGNAL L E V f L CALCULATIONS:*./)
Rr TURN
PNO
REAL FUNCTION ^MLMS - rrv.P^N'u)
-142-
IMt.ttUUUC
non n nn nnnnnr -> -» on
THIS PAGE IS BEST QUALITY PRACTICABLE
7ROU COPY FURNISHED TO DDC
THIS FUNCTION COMPUTES THE A HEN U A TIC N OF THE RF AMP INPUT FILTER
FOR THE NAV 11 RECEIVER * RFVTSED JUNE 78
RFFIL?=0. 0
DELTA=PRORCV-FMFFFO
IF (DELTA. LT. 0 . ) RETURN
IF (DELTA. GT. 8. )00 TO 10
RFFILT= 1.5*DELTA
RETURN
0 RFFILT=12. ♦ (DELTA-8. )*. 75
RETURN
END
*« •* A****************************** *************************** **< * * * *
SUBROUT INF CHANGE! JUMP)
»<.«*********************************•**«************•***********
THIS fCOG^A-4 MA< :.S CHANG* « 1\ PC (X,c AM
PE 4L NAME ( 1 5 ) / »K-iFO • ( ' - ML D* , • 7 r.T A • , • LSTV* • , ■ *■*! L • . • P'n; • ,
C • , • I NST* . • T YPC • . • Srn= • , • MX03 • , 'XW I M
01 MENS ! ON F«* ()(."> ’j ) ,F'nn( ? 1 ) ,“-ta { ->3)
■';l ‘i i Lf ( 30) , piwcf < 7 0) so )
fpal l::vfl<20)
C!"M?N FQOCV^ . XV joi , X‘"~r'> , <*»( U4 . SIJMC. • )W . 7K l
r o M ON F p nU . L = V z L < f v DC* » U : T A
CO'* VC N MIL”, PJ W: f i r O r> F V . \ <iT A T
04c avc-t = F JJ I" T 9 C = TU - NF O «I7f A VALU1- V-ltCH T"L!_E XH?C
CONTF “L is 71 >)“ TCAN'F^C J«-n . JJ '>P: ) !c N1CMA.
JUVD=;
D? j NT
• ( • *** PFPGPA 11
FTC INST '-JCT I r NG
* A* • . / ,
TYP'-: I Nc T
c ~ t > i n sr c )>• v a mp
c - AS1 1 , o A-1 A , M, X
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FLAG I
1 W
I &G -0
I F ( N . - 1.0) I F 1_ AG- I
I r ( N . 1 . 0 ) N = 1
143
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rcTcpMI'JING WHICH C 0 MW A NO T ^ li^AO I N QY COMPARING PARA T r
NA'»F( I )
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DO £0 1=1,15
IC(PAR'A.EQ.NAWE( I ) ) G O TO «3
20
CONTINUE
POINT ?1
21
FORMA T( • ERROR IN INSTRUCTION .RETYPE •)
GO TO 1
C
c
c
CONTROL IS TRANSFERRED TO THE PROPER STATEMENT ACCORDING
T C
c
THE INPUTTED COMMAND
c
c
c
30
GO TP (41, 42,43,44,45,45,4"’', 40,40,50, 51. 52. 53. 5 4, 5 5). I
♦ 1
FREU( N )=X
GO TO ?
42
FMTD ( N >=X
co n ’
43
Q=TA( N)=x
GO TO 2
44
LE VEL ( N) =X
GO TO ?
45
NILE( N)=X
GO TO 2
*
45
POWER ( N ) =x
GD T1 ?
[
47
FODEV ( N) = x
CO TO 2
45
PRINT 4=1
PR I NT 432
GC TO 1
49
I F ( I FL AG.c3. 1 . ANP.N t -5 . I P AO . “Q. 3) SD TJ 44«-
50 TO 405
49^
PR INT 491
49 !
roPVAT(t FTATIj-4 ST4~I )N ■< O'JL'T I IN ‘4 ISOLATION PAX F-
C L NILES STATION')
- 0
L - Vr
PR I NT 49 2
49 1
CIU>4T(I BJJNOOP FO^q =t-E ) (K!J( ) IN^tx V I A -
I 1 N
AT 3
CP AMD .“COM POw'C- t<P*l
4
P? int ,q3
49 ’
r jONA-( 1 ox , 1 ( «H2 ) • . 2 -X . • ( X wop CALC) INPUT =*>3T ~ if C f I V • J *
•
r • ( Km ) • )
4='
PRINT I 30 . N, RREUl N ) , FW TD( N) ,l ‘ T A ( N ) , FO 35VI N) ,Lr V _(N),
r «-n. _ ( n) ,pow"p< n)
10 0
rORM4^(3x.I7.5X,4 4 , 1 , 5X . r - , ',H,FP.’,7X,t‘i,| , A X , c ^ . 1 , 4 X ,
,7X ,-
C7.p|
ro TP 2
50
5 J TO 39
5 1
JU^Dp1
c,r T o so
-144-
- 1
UHIS PAGE IS BEST QUALITY PRACTICABLE
FROM COPY FURNISHED TO DDC
52
JUMP: T
GO TO 1
51
JJMP - 1
GO TO 05
54
JU*AP = 4
C.O TO 0 4
55
JUMP: 1
GO TO 49
C
c
C I F IFLAG =1 THFN TH~ C’MMAm ) IS >■ T D FT C AT*- ?TAT 1 p.N
C (EXCtPT FTP "T
…[truncated]