Document text
NASA TECHNICAL
MEMORANDUM
NASA TM X- 64647
END-TO-END RMS ERROR TESTING ON A
CONSTANT BANDWIDTH FM/FM SYSTEM
By G. R. Wallace
Astrionics Laboratory
W. E. Salter
Sperry Rand Corporation
March 10, 1972
NASA
George C. Marshall Space Flight Center
Marshall Space Flight Center, Alabama
MSFC - F orm 3190 (Rev June 1 971 )
TECHNICAL REPORT STANDARD TITLE PAGE
1, REPORT NO. 2. GOVERNMENT ACCESSION NO.
NASA TM X- 64647
3. RECIPIENT'S catalog NO.
4. TITLE AND SUBTITLE
End-to-End Rms Error Testing on a Constant Bandwidth
FM/FM System
5. report date
March 10, 1972
6. PERFORMING ORGANIZATION CODE
7. AUTHOR (S)
G. R. Wallace (MSFC) and W. E. Salter (Sperry Rand Corp.)
a. PERFORMING ORGANIZATION REPORT ^
9. PERFORMING ORGANIZATION NAME AND ADDRESS
George C. Marshall Space Flight Center
Marshall Space Flight Center, Alabama 35812
10. WORK UNIT NO.
11. CONTRACT OR GRANT NO.
13. TYPE OF REPORT a PERIOD COVERED
Technical Memorandum
12. SPONSORING AGENCY NAME AND ADDRESS
National Aeronautics and Space Administration
Washington, D. C. 20546
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
Prepared by Astrionics Laboratory, Science and Engineering
16 . abstract
This paper describes end-to-end root- mean-square ( rms) tests performed on a con-
stant bandwidth ( GBW) FM/FM system with various settings of system parameters ( trans-
mission noise, system data loading, data shapes, etc.) . The testing technique employed is
that of sampling, digitizing, delaying, and comparing the analog input against the sampled
and digitized corresponding output. Total system error was determined by fully loading all
channels with band-limited noise and conducting end-to-end rms error tests on one channel.
Tests were also conducted with and without a transmission link and plots of rms errors
versus receiver signal- to- noise (S/N) values were obtained. The combined effects of inter-
modulation, adjacent channel crosstalk, and residual system noise were determined as well
as the single channel distortion of the system.
Note: The activity reported here is a portion of the effort under RTOP 150-22-03, Mission
Spacecraft Compatibility with Telemetry Data Relay Satellite System, and was accom-
plished at the Astrionics Laboratory.
1 7. KEY WORDS
Telemetry
Constant Bandwidth
FM/FM
Rms Error
Sampling Measuring Techniques
19. SECURITY CLASSIF. (of thU report)
1
20. SECURITY CLASSIF. (of this page)
21. NO. OF PAGES
22. PRICE
Unclassified
Unclassified
22
$ 3.00
MSEC - Form 1291 (May 1969>
TABLE OF CONTENTS
Page
INTRODUCTION 1
TEST PHILOSOPHY, TECHNIQUES, AND PROCEDURES 1
CAUSES OF SIGNAL DISTORTION 4
TEST RESULTS. 5
CONCLUSION . . . . 17
iii
LIST OF ILLUSTRATIONS
Figure Title Page
1. CBW FM/FM system 2
2. Filtered white noise data spectra 3
3^. Constant bandwidth system using 4-kHz lowpass output
filters — rms error versus data bandwidth 6
4. Constant bandwidth system using 2-kHz lowpass output
filters — rms error versus data bandwidth 7
5. Performance of a CBW FM/FM system as a function of
receiver IF S/N ratio 8
6. Single channel distortion test 9
7. Distortion present in unmodulated channel 11
8. Total waveform distortion with system fully loaded 13
9. Tests to determine effects of transmission noise — one channel
loaded 13
LI ST OF TABLES
Table Title Page
1. Preemphasis Settings for the Tested Constant Bandwidth
System 4
2. Data From Setup of Figure 6 10
3. Data From Setup of Figure 7 12
4. Data From Setup of Figure 8 14
5. S/N Levels Versus Rms Error
15
TE'CHNICAL memorandum X- 64647
END-TO-END RMS ERROR TESTING ON A CONSTANT
BANDWIDTH FM/FM SYSTEM
INTRODUCTION
End-to-end root- mean-square (rms) tests were performed on a constant
bandwidth ( CBW) FM/FM system. The test philosophy, techniques, and
actual test procedures are outlined. The different ways distortion may be
introduced on a signal are described as well as the various tests performed and
the data taken. Total system error was determined by fully loading all chan-
nels with band-limited noise and conducting end-to-end rms error tests on one
channel. The combined effects of inter modulation, adjacent channel crosstalk,
and residual system noise were determined as well as the single channel dis-
tortion of the system. Tests were also conducted with and without, a trans-
mission link and a plot of rms error versus receiver signal-to-noise ( S/N)
values was obtained.
The CBW FM/FM system under test is relatively simple in concept;
consequently little space is devoted to its explanation. Eleven channels are
employed as shown in Figure 1 (note that no translation devices are used) .
These eleven channels are fed into a mixer amplifier and the output of the
mixer amplifier is then fed into a radio frequency (RF) assembly. After the
signal has passed through the transmitter and power amplifier, the channels
are demultiplexed and the individual data signals are regained by using band-
pass filters and frequency discriminators. The tested CBW FM/FM system
is shown in Figure 1.
TEST PHILOSOPHY, TECHNIQUES, AND PROCEDURES
The end-to-end rms testing of the CBW FM/FM system is simple in
concept. The input is sampled at time tj and digitized, the output is sampled
at ti + T (t being the system delay) and digitized, and the two samples are
compared. The differences are squared and divided by the discrete sample
length ( 1024 in the experiment) thus yielding dVn or the mean squared error.
Figure 1 outlines this setup. As would be expected, the e3q)eriment is con-
ceptually simple, but many operations are required. The Systems Engineer-
ir^ Laboratory (SEL) telemetry data analysis system (TDAS) is an ideal
AIRBORNE GROUND
2
Figure 1. CBW FM/FM system.
instrument to do these operations as its speed of operation, input and output
devices, and ease in programing are all designed to perform these types of test
calculations .
The data used for the tests were band-limited white noise. The spec-
tral shapes are outlined in Figure 2. The amplitude probability density was
approximately Gaussian, but with a 46 limit. The rolloff was obtained by feed-
ing the effectively flat spectrum of white noise into a 3-pole lowpass Butter-
worth filter ( 18 dB per octave) . The ’’corner" or 3 dB points for the filters
were variable.
Figure 2. Filtered white noise data spectra.
The sampling rate necessary to perform the testing is a function of the
system delay. The actual repetition time of samples was selected to be ten
times the system delay (t) to assure that independent samples were taken.
3
/
The discussion of the CBW system has been fairly well covered. The
one item not discussed in the airborne system involves the preemphasis curve
used on the eleven subcarrier oscillators (SCOs) . The basic criterion used
in establishing the preemphasis curve was that the SCO levels were adjusted such
that a constant S/N ratio (in the receiver) for all SCO bands would be obtained.
This criterion was established with a given signal level into the receiver.
Table 1 outlines the exact values used.
TABLE 1. PREEMPHASIS SETTINGS FOR THE TESTED
CONSTANT BANDWIDTH SYSTEM
CHANNEL
FREQUENCY (kHz)
DEVIATION (kHz)
- .
16.00
14
—
24.00
16
—
32.00
17
—
40.00
18
—
48.00
19
—
56.00
20
64.00
21
—
72.00
22
—
80.00
23
88.00
24
96.00
25
A critical elenaent of the overall system was the groimd station which
was composed of a receiver and discriminator ( Fig. l) . The receiver, a late
version produced by Defense Electronic, Inc. (model 711), has a pluggable inter-
mediate frequency (IF) filter (3.3 MHz, 1.0 MHz, 300 kHz, or 100 kHz). The
discriminator, a late version phase-lock type produced by Data Controls
Systems, Inc. (model GFD-13), has pluggable bandpass filters and data filters.
The bandpass filter used was 40 kHz ±2 kHz in all tests, while the lowpass
output filter was either a 2-kHz or a 4-kHz constant amplitude filter ( the exact
filter is specified with the experiment data tabulation).
CAUSES OF SIGNAL DISTORTION
A signal transmitted through a telemetry channel undergoes distortion
caused by effects within the chaimel as well as interchannel effects, Tests
were performed to determine the contribution of each of these effects to the
total distortion. All potential sources of distortion were considered in this
4
study except for' the error produced by the propagation medium which was
removed by hard-wiring the transmitter to the receiver through suitable
attenuators. . .
Sources of Distortion
Airborne System. Distortion of the data signal is caused by nonlinear-
ities in the amplitude and phase response of the SCO lowpass filter. Additional
distortion occurs because subcarrier harmonics and their associated side-
bands are not infinitely attenuated. The result is an overlapping of subcarrier
spectra when the SCO outputs from the various channels are combined in the
linear mixer. The mixer- amplifier and FM transmitter provide still other
sources of error called inter modulation distortion.
Ground System. Any noise created within the airborne system, trans-
mission medium, or "front end" of the ground receiver is combined with the
RF signal prior to demodulation. The receiver limiter eliminates the ampli-
tude variation caused by the noise,, but the phase variation results in an error in
frequency. In FM, this phase variation appears as amplitude distortion on the
demodulated signal output. i
Additional errors are introduced by the channel- selecting bandpass
filter. Since attenuation is not infinite outside the passband, some of the fre-
quency components of the adjacent channels are transmitted along with those
of the desired signal. The bandpass filter also clips some of the higher-order
sidebands of the desired signal. Further distortion results from the nonlinear
amplitude and phase response of this filter .
• .
Distortion is also introduced by the subcarrier discriminator. Any
nonlinearity in the frequency/amplitude transfer function will cause errors -
as well as any nonlinearity in the amplitude and phase characteristics of the
lowpass output filter.
TEST RESULTS
Results are shown in Figures 3, 4, and 5 for the channel centered at
40 kHz. In Figures 3 and 4, the errors resulting from RF noise are eliminated
by connecting the output of the mixer-amplifier directly to the ground dis-
criminator. Test data were taken for both the 2-kHz and 4- kHz lowpass out-
put filters while the channel-selecting bandpass filter was set at 40 kHz ±2 kHz
5
RMS ERROR (PERCENT)
Figure 4. Constant bandwidth system using 2-kHz lowpass output
filters — rms error versus data bandwidth.
7
for all measurements. In all cases, the random data were amplitude adjusted
to 0.625 volts rms ( 5 volts peak-to-peak) . The error readings are given in
percent normalized to the rms full scale of 0, 625 volts. With the 46 data used
in this experiment, this is a factor of eight more than comparable peak-to-peak
error plots.
The first tests performed eliminated the effects caused by interference
from other channels by disconnecting the SCOs froni the remaining channels
in the system (Fig. 6 and Table 2),. The increase in waveform distortion with
data bandwidth ( Curve A in Figs. 3 and 4) can be attributed primarily to non-
linearities in the transfer characteristics of the various filters in the system.
Also, as the input signal bandwidth approached that of the channel, the higher
frequency components were severely attenuated, resulting in a further increase
in distortion. Curve B represents the error when all the other channel SCOs
are present and are modulated with thirdr-order random data band-limifed to
2 kHz, while 2. 5 volts dc are applied to the test channel (Fig. 7 and Table 3) .
The distortion caused by effects from the other channels was found to have an
rms value of 1. 96 percent for the 4-kHz output filter nnd 0.33 percent for the
2-kHz output filter. Curve C of Figures 3 and 4 represents the total waveform
distortion in the 40-kHz test channel when all channels in the system contain
third-order random data ( Fig. 8 and Table 4) . The data bandwidth for the test
channel is varied from dc to 2 kHz while bandwidth for the other channels are
fixed at 2 kHz. Mathematically, points on curve G may be found by rms sum-
ming of corresponding points on curves A and B. :
OUTPUT
SAMPLE — *
POINT
FOR SEL TDAS
NOTE! THE DATA SOURCE WAS A WHITE NOISE GENERATOR WHICH WAS
FED INTO A VARIABLE CUTOFF FREQUENCY 3-POLE (18-dB) LOWPASS
BUTTERWORTH FILTER
INPUT
SAMPLE
POINT
FOR SEL TDAS
Figure 6. Single channel distortion test.
9
TABLE 2. DATA FROM SETUP OF FIGURE 6
A; 4-kHz THmD ORDER LOWPASS OUTPUT FILTER
^data
System
Delay
(ps)
dVn
mm
( Counts)
Normalized Error (%)
500 Hz
456
7.93
8.40
8.74
8.23
8.80
2.90
14.50
1
1
2.32
1000 Hz
461
1
79.5
72. 1
86. 5
78.5
79.6
8.90
1
44. 50 '
7.12
1500 Hz
462 ^
■|
288. 1
288. 1
295.4
289.0
294. 5
17.0
85. 00
13.6
2000 Hz
462
750.4
739. 8
713.9
682.9
729/2
26.8
134.0
21.5
1
B: 2-kHz THIRD ORDER LOWPASS OUTPUT FILTER
500 Hz
644
18.31
17.33
16.94
17.56
16.93
4. 17
20. 85
3.34
1000 Hz
649
221. 8
205.7
198.7
214.4
209.2
14.48
72.40
11.77
1500 Hz
667
23.92
NOTES 1. 40-kHz ±2-kHz and 4-kHz lowpass constant amplitude filters on the discriminator.
2. N = 1024 samples.
3. The data shown result in curve A of Figure 6. j,
4. The counts figure is the results of multiplying the (dVn)'^ by the 5 mV bit
transfer function of the sampling system.
5. The normalized error (%) is the result of dividing the counts by 625.
10
POINT POINT
FOR SEL TDAS FOR SEL TDAS
NOTES: 1. THE DATA SOURCE WAS A WHITE NOISE GENERATOR WHICH WAS
FED INTO A VARIABLE CUTOFF FREQUENCY 3-POLE(18-dB)
LOWPASS BUTTERWORTH FILTER
2, 2-kHz AND 4-kHx 3-POLE LOWPASS OUT BUTTERWORTH FICTERS
WERE USED.
Figure 7. Distortion present in unmodulated channel.
In Figure 5, the effects of noise in the RF transmitter and receiver are
depicted. The test channel (40 kHz) contained third-order random data band-
limited to 500 Hz, while the other channels remained in the static condition
( 2. 5 volts dc) . The transmitter output was hard-wired through a series of
variable attenuators to the receiver input. S/N ratio, read at the 10-MHz
linear output of the receiver, was varied by inserting different attenuators
between the transmitter and the receiver, while the rms error was measured
(see Figure 9 for test setup) . As shown, results were obtained for three
different IF filters. For the 3.3-MHz filter and the 1.0-MHz filter, as the
S/N ratio was made larger, the error asymptotically approached 2. 32 percent,
the value measured when the transmitter and receiver were omitted from the
circuit. In the case of the 0.3-MHz filter, as the S/N I’atio was made larger,
the error leveled off at 2. 8 percent, revealing that more of the outermost side-
bands of the transmitted spectrum were lost in the filtering process. The
data taken for the various S/N and IF bandwidth conditions are outlined in ,
Table 5.
11
12
ir (%) is the result of dividing the counts by 625 .
KOTESi 1. DATA SOURCE OF THE 40-kHi SCO.
2. OATA SOURCES 2 AND 3 WERE ALSO WHITE
NOISE GENERATORS FED INTO 3-FOLE
LOWPASS BUTTERWORTH FILTERS.
Figure 8. Total waveform distortion with system fully loaded.
(^= SAMPLE POINTS FOR SEL TDAS
Figure 9. Tests to determine effects of transmission noise —
one channel loaded.
TABLE 4. DATA FROM SETUP OF FIGURE 8
A: 4-kHz THIRD ORDER LOWPASS OUTPUT FILTER
^data
System Delay (ps)
dVn
( dVn)
( Counts)
Normalized Error (%)
500 Hz
456
14.94
13.52
14.89
12.86
14.60
3.75
18.75
3.01
1000 Hz
461
87.9
87.8
88.6
87. 1
89.9
9.39
46.95
7. 52
1500 Hz
462
274.9
303.4
292.6
286. 8
291. 5
17.0
85.0
13.62
2000 Hz
462
746.9
768.8
719.7
739.6
739.3
27.4
137.0
21.80
NOTES 1. N = 1024 samples.
2. The data taken result in curve C of Figure 8. y
3. The counts figure is the result of multiplying the ( dVN)'^ by the 5 mV/bit transfer
function of the sampling system.
4. The normalized error (%) is the result of dividing the counts by 625.
14
TABLE 5. S/N LEVELS VERSUS RMS ERROR
Receiver Meter Signal
S + N
IF Bandwidth
System Delay
Percent
Adjusted
Above Noise (dB)
(dB)
^(dB)
(MHz)
(ns)
dVn
Error
S/N (dB)
Without RF link, the delay is 456 HB and the error is 2.44% .
46
-10.3
-81
3.3
456
8. 96
10.06
9.74
9.87
9. 12
2.47
40.3
51
-10.0
-78
1.0
460
9.62
9. 67
9.53
. 9.46
9.85
2.48
42.8 .
54
-9.5
-77
0.3
467
13. 82
12. 66
12.33
14.46 ■
13.51
2.92
47.5
59
-9.9
-86
3.3
459
9.00 j
8.78
9.63
9.98
9.11
2.44
45.7
63
-9.8
-84
1.0
460
9.23
9.79
9.28
9.43
8.70
2.44
49.0
65
-9,7
-83 ,
0.3
467
13,35
14.07
12.61
14. 16
14.54
2,96
53.3
35
-10.7
-7.5
3.3
459
10.22
9.61
10.17
10.46
9.78
2.54
33.9
40
-10.5
-72
1.0
460
10.88
10. 89
10.81
11.61
10.44
2.64
36.3
43
-10.4
-71
0.3
'467
14.78
15.73
16. 18
15.45
15. 35
3. 15
40.6
Without the RF link,
the delay is 456 ns and the error is 2. 31% .
29
-11
-70.7
I
3.3
459
10. 98
11.48
11.34
10. 99
10.13
2. 90
29.3
34
-10.8
-67.5
1.0
460
12. 21
13. 73
13. 87
12. 55
13.45
2. 90
31.5
36
-10.7
-66
0.3
467
18. 59
19.04
19.05
19.61
19.54
3.50
35.3
15
TABLE 5. ( Concluded)
Without the RF link, the delay Is 456 na and the error is 2. 30% .
24
-11.2
-67.6
3.3
459
13.33
14.23
14.20
13.19
13. 15
2.95
26.0
30
-11.0
-65.0
1.0
460
- 16. 88
17.86
■ ' ■-
17.43
17.28
16.70
3.32
29.8
32
-10.8
-64
0.3
467
3.99
33.2
Without the RF link.
the delay is 456 ps and the error is 2. 32% .
20
1
-11.4
-65
■
459
19.03
18.09
19.43
19.21
18.85
3.48
23.2
26
-11.0
-62.5
460
24.77
24.67
24.16
23.17
23.00
3.92
26.2
30
-10.9
-61.5
■
467
33.45
35. 55
32.26
33.46
33.93
4.65
30.6
Without the RF link,
the delay is 456 ps and the error is 2. 34% .
10
-11.7
-58,5
3.3
459
53.67
56.72
59.78
59.05
58. 10
6.06
15.0
18
-11.4
-57.0
1.0
460
72.92
65.44
66.59
68.54
62. 80
6. 56
19.75
21
-11.1
-56.5
0.3
467
80.78
91.44
85. 17
86.83
75.32
7.33
24.65
6
-12.3
-55.0
3.3
459
133.84
126.30
128. 66
134.63
136.22
9. 18
9.75
13
-11.6
-54.0
1.0
460
131.50
143.84
134.03
133.74
137.58
9.33
16.00
17
-11.3
-54.0
0.3
467
174.88
158.94
168.03
164.91
170. 14
10.35
22.00
NOTES 1. The setup of Figure 9 was used to take these data.
2, The dVN column is particularly interesting as it shows the dispersion of samples. Each entry is in itself 1024 samples.
3, The percent error Is tabulated from the dVn entries which arc averaged and the square root taken. Then this value Is
mult4>Ued by 5 mV/count conversion factor and the result multiplied by 100 and divided by 625 mV to get percent error.
4, The data of this table are plotted in Figure 5.
16
CONCLUSION
The curves of Figures 3, 4, and 5 should allow one to make some basic
parameter estimations on new (or existing) systems. The overall accuracy
on which these figures are based is better than 99. 7,5. per cent with the bulk of
the inaccuracy. being lost in two analog- to-digita;i conversions (after the .analog
data. are sampled, they are digitized for SEL telemetry data analysis system
manipulations) .
17
APPROVAL
END-TO-END RMS ERROR TESTING ON A CONSTANT
BANDWIDTH FM/FM SYSTEM
By G. R. Wallace and W. E. Salter
The information in this report has been reviewed for security classifi-
cation. Review of any information concerning Department of Defense or Atomic
Energy Commission programs has been made by the MSEC Security Classifica-
tion Officer. This report, in its entirety, has been determined to be unclassi-
fied.
Chief, Telemetry and Data Technology Branch
O. T. DUGGAIO d
Chief, Instrumentation and Communication Division
F. B. MOORE
Director, Astrionics Laboratory
18
MSFC— RSA, Ala
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