Analysis of ranging system for lunar surface electrical properties experimen

Osborn, J. D.

English

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ANTENNA AND PROPAGATION STUDIES FOR SPACECRAFT
TASK E-53F
TECHNICAL REPORT
AN ANALYSIS OF THE RANGING SYSTEM FOR THE
LUNAR SURFACE ELECTRICAL PROPERTIES EXPERIMENT
NAS 9-8166
	
October 13, 1970
Prepared for
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
MANNED SPACECRAFT CENTER
HOUSTON, TEXAS
',	 IPrepared by
J. D. Osborn
(Approved by di-Ilu ^
J < W. Pool, Manager
T s E-53F
Approved by	 11^,-^
J. DeVillier, Manager
/Communication and Sensor
Systems Department
'N 71 ' 1 12 4
°o	 (ACCESSIOt{NU	 R)	 /THr
f	 (/oc0	 WAGEw^
)-3
	
(CODE)
a (NASA CR OR TMX OR AD NUMBER)
	 (CATEG0 Y)
•F
C^ TABLE OF CONTENTS
•
Page
1.0	 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . .
	 1-1
2.0 RANGING SYSTEM ANALYSIS 	 . . . . . . . . . . . . . . . . . . . .
	 2-1
2.1 RANGING SYSTEM ACCURACY IN FREE SPACE . . . . . . . . . . . 2-1
2.2 RANGING SYSTEM ACCURACY ON THE LUNAR SURFACE . . . . . . . 2-6
2.3 AZIMUTH ACCURACY	 . . . . ... . .
	 . . . . . . . . . . . .
	
2-6
3.0
	 CONCLUSIONS	 . . . . . . . . . . . . . . . . . ... .
	
. .	 . .
	 3-1
REFERENCES	 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	 R-1
ii
1
6
ILLUSTRAl10NS
Page
	
1-1	 Overall View of the Experiment . . . . . . . . . . . . . . . .
	 1-2
	
1-2
	 Transmitter Deployed	 . . . . . . . . . . . . . . . . . . . .
	 1-3
	
2-1	 Free Space Path Loss	 . . . . . . . . . . . . . . . . . . . .
	 2-3
	2-2	 Measured Field Data From Reference 3. . . . . . .
	 . . . .	 2-7
^J
1
iii
I•
1.0 INTRODUCTION
This report covers an analysis of a ranging system which has been pro-
posed by the Massachusetts Institute of Technology for use on the Surface
Electrical Properties (SEP) Experiment. The proposed ranging system measures
range by measuring the power level of the received signal, and it measures
azimuth angle by comparing the phase of a signal received from a rotating
antenna beam to that of a marker pulse received from a non-rotating beam.
The phase difference between these two signals is a measure of azimuth angle.
The method for generating the rotating beam is discussed in detail in Refer-
ence 1. The experiment in the deployed configuration using the above ranging
system is illustrated in Figure 1.0 where the receiver is shown mounted on the
Lunar- Rover Vehicle (LRV). If the LRV is used in the experiment, the range
will be extended out to a maximum of 10 km.
Power measurements for determing range and phase measurements for deter-
mining azimuth angle are made at the frequencies used for electromagnetic
detection, so no separate antenna is required for either function. This does,0
	
however, require that crossed dipoles be used at the transmitter to generate
the rotating antenna beam used in the phase measurement. The antenna is
shown in Figure 2.0 in the deployed configuration.
It is concluded in this report that the-method-of determining range by
received power measurement will .ut provide the required range accuracy of
1% which is specified in Reference 2. This conclusion is based upon an anal-
ysis of propagation in a free-space environment which is extended to include
the approximate effects of deploying the transmitter and receiver on the
lunar surface. For the azimuth angle measurement, it is concluded that it
1	 is feasible to obtain the required accuracy of ± 5 degrees which is also
specified in Reference 2.
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TRANSMITTER
SIDE DEPLOYED
Figure 2.0 Transmitter Antenna
1-3
s2.0 RANGING SYSTEM ANALYSIS
Since a model for the SEP experiment on the lunar surface has not been
completed to date, the ranging system accuracy is determined for a free space
environment, and measured data taken from Reference 3 are used to estimate
the effects of deployment on the lunar surface. In Reference 3, experimental
data was obtained by the Massachusetts Institute of Technology by recording
electromagnetic interference patterns from the water table under the Gorner
Glacier. These data are informative because the dielectric properties of the
glacier and the lunar surface are similar.
2.1 RANGING SYSTEM ACCURACY IN FREE SPACE
This analysis is confined to free space in order to obtain first approx-
imations to the range accuracy which can be obtained with this system. The
effect of locating the transmitter and receiver on the lunar surface will be
examined in later paragraphs.
In free space, the power at the receiver is given by the Friis trans-
mission equation
2
P r	 P tGtGr 4
	 (2-1)
where
Gt
 = the gain of the transmitter antenna
G  = the gain of the receiver antenna
Pt = the transmitter power
P r = the receiver power
X = wavelength
r _ range
The parameters P t . Gt , and G  are constants, so the received power will vary
in direct proportion to the path loss, 1 p , which is
2
_	 a
1p
'17T 
r	 (2-2)
0
1 1
2-1
2
_	 a
Pr	
k 4nr
(2-4)
In dB this becomes
L p = 20 log
4nr
(2-3)
The path loss for the eight operating frequencies is shown plotted in
Figure 3 which illustrates the relative insenitivity of the power level to
incrimental charges in range. If the range is to be measured using power
level, then a high degree of precision will be required in the measurements.
To illustrate, the power level changes by only 6 dB for every octave change
in range, and the SEP specifications call for a range accuracy of W of the
actual range. The power level accuracy required is determined from the,
following:
Using Eq 1, the received pow?r is
where k = P tGtGr , a constant. The power level change for a change in range
can be determined by expressing the derivative
? _3dPr = _2kr
	
(2-5)
dr	 (_4 rr
in the differential form
2 _3
AP  = -2k 
4n 
r or	 (2-6)
Since the range accuracy is expressed in percent of the actual, the para-
meter
a=r
	
(2-7)
0
s
2-2
40
80
1
30
O
-70
0.5 MHz
1 .0 MHz
2.0 MHz
4.0 MHz
8.0 MHz
16.0 MHz
24.0 MHz
32.0 MHz
50
-a
NN
D
	 1 60
Qa
0	 1	 2	 3	 4	 5	 6	 7	 8	 9	 10
RANGE (km)
40	 Figure 3.0 Free Space Path Loss
n 1
2-3
6C?
PLA = 10 log (1 + 0.02) = 0.09 dB (2-12)
may be substitued in Equation (5). This gives
2
0= -2ka
(X
r	 4nr
The power level accuracy, PLA, in dB is
P + AP	 I
PLA = 10 leg	 r	 rP
r
4
(2-8)
(2-9)
or
2	 2a	 a
k Orr	
+ 2ka
 
(TTTrPLA = 10 log
2
k (4F r
which reduces to simply
PLA = 10 log (1 + 2a)
(2-10)
(2-11)
For the specified accuracy of 1% (a = 0.01), the required power level
accuracy is
That is, the receiver power will have to be determined to an accuracy of
± 0.09 dB to meet the requirement for a l% range accuracy. This is an ex-
treme requirement for power measurement accuracy which will probably be
unattainable in a practical system.
O
N
2-4
6Further insight into the relationship 'Oetween range accuracy arid
power measurement accuracy can be obtained from the ratio of the inc-imental
power, AP r , and received power, P r . This ratio is
2
GP	 2ka	 —
_F_	 k ' ^,	 2
^4 77 r
or
AP
Pr = ^a	 (2-14)
r
Using the substitution a = r this becomes
AP 	 =	
or
2
	 (2-15)
P r	
This leads to the following conclusions:
1. The percent tolerance on the power measurement is twice the per-
cent tolerance on the range. The specified 1% range accuracy gives
arequired power accuracy of 2%.
2. The % range error is equal to half the power measurement accuracy
in percent.
3. In dB, the required power level accuracy is PLA = 10 log
(1 + 2a) where a is the range accuracy r .
2-5	 ' e
%M
2.2 RANGING SYSTEM ACCURACY ON THE LUNAR SURFACE
When the SEP equipment is deployed on the lunar surface, the mode of
propagation will not be the same as that of free space as sug g ested by the
analysis in Reference 4. Data taken from field measurements on the water
level below the Gorner Glacier also suggest that the mode of propagation is
not that of free space. In addition, the data suggest that the mode is
dependent upon frequency. Data from the glacier measurements were obtained
from Reference 2 and reproduced in Figure 4. It is assumed that the ordinate
{	 represents field strength in dB, and the abscissa represents distance from
the transmitter to receiver in wavelength. It should be observed from Figure A
that the average slope of each pattern decreases with frequency. If the mode
of propagation were that of free space,.the slopes would be equal and the
curves simply displaced as in Figure 3. This change in slope .with frequency
suggests that power is being transmitted in both the space and surface wave
propagation modes. The proportion of total transmitter power contained in
each mode is dependent upon frequency as indicated in Reference 4.
If received power level is to be used to determine range, the functional
relationship between power and range must be known to within an accuracy
on the order of li. This requirement for exact knowledge of the functional
relationship between power and rt-ne for propagation on the lunar surface
places further limitations on the ranging method. In addition, surface
roughness will add uncertainty into the accuracy of the power measurements.
2.3 AZIMUTH ACCURACY
The proposed method for determining azimuth angle involves comparing the
phase of a signal received from a rotating antenna beam to the phase of a
marker pulse from beam that does not rotate. An analysis of this technique
is contained in Reference 1 where it is shown that the phase angle is equal
to the azimuth angle. The specified azimuth accuracy is 5 degrees which
implies that the phase between the two signals must be measured to within a
5 degree tolerance. This would appear to be feasible with a moderately
sophisticated method of phase measurement.
S
2-6
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.0
r
•r
0 2 4 6 8
Range in Wavelengths
0 2 4 6 8
Range in Wavelengths
0 2 4 6 8
Range in Wavelengths
c^
0 2 4 6 8 10
Range in Wavelengths
0. 2 4 6 8 10
Range in Wavelength!
Figure 4.0 Measured Field Data From Reference 3
0
2-7
6r
3.0 CONCLUSIONS
It is concluded that measuring range from received power will require
i
precision in the power measurement and exact knowledge of the functional 	 I
relationship between range and power, both of which will be difficult or
Y
impossible to obtain in a practical situation. 	 It will be particularly
difficult to obtain an exact functional relationship between power and range
because there is both theoretical and empirical data which suggest that two
propagation modes exist when the equipment is deployed on the lunar surface.
That is, power is transmitted in both the surface and space wave modes, and
the relative power contained in each mode is dependent upon frequency.
For idealizes free space propagation, the power measurement accuracy
is + 0.09 dB for the specified range accuracy of + 1%. Even in the ideal
situation of free space propagation, this is an extreme requirement for
power accuracy.
The required azimuth accuracy is specified as ± 5 degrees in Refer-
ence 2. There is a direct relationship i,etween the phase angle and geo-
metrical angle which implies that the required accuracy of the phase mea-
surement is also + 5 degrees. This is not an extreme requirement for the
phase measurement accuracy.
L
3-1


Antenna and propagation studies for spacecraft task E-53F - An analysis of the ranging system for the lunar surface electral properties experiment

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