Page 257 - Radar Technology Encyclopedia

247 loss, antenna pattern factor loss, atmospheric (attenuation)

range calculation is normally carried out for the angle of the beacon or jamming equations, one-way loss is applicable.
beam axis, and scaled directly by F for other angles. If a sin- (See also ATTENUATION.)
gle detection range number is to be derived, applicable to all The one-way loss L is a function of range R and eleva-
a1
targets within a given sector, the statistical beamshape loss tion angle q for the path and can be found from
should be used in both coordinates, modified if necessary for where h is the height determined by R and q, n(h) is the
the effects of reflection lobing (e.g., and average value of F
()
hR
+
h
can be used in the radar equation). [ V h () V ()]
0
w
d
L ( R q, ) = ò ----------------------------------------------------------- h dB (1)
As with other antenna gain and loss factors, radars hav- a1 n cos q 2
0
ing different transmit and receive patterns will use subscripts 0 1 – -------------------------------------
(
nh () 1 + hr ¤ )
0
(f and f ) to represent the two patterns. DKB
t
r
Barton (1988), pp. 290–296. refractive index at height h, n is the surface refractive index,
0
6
r is the earth’s radius (6.5 ´ 10m), and V (h) and V (h) are
o
w
0
Array bandwidth loss occurs when the bandwidth B of an
a
array antenna is insufficient to pass all signal components in frequency-dependent models of the absorption coefficients, in
decibels per unit length, for oxygen and water vapor. Based
their proper phase relationship. For a signal of half-power
on this equation, the total attenuation for earth-based radar, on
bandwidth B, the loss in decibels is
a path extending through the entire atmosphere (beyond 30
æ 2B 2 ö km in altitude) are as shown in Fig. L17. Plots for attenuation
L = 10log ç 1 + --------- ÷
z 2 indifferent frequency bands, as functions of range and eleva-
è B ø
a tion are available in Blake (1980).
DKB
Barton (1988), pp. 185–187.
Array phase error loss is the reduction in antenna gain
caused by errors in phase shifters, feed networks, or amplifier
modules in a phased-array antenna. The loss as a power ratio
is given by
2 2
»
L = exp ( s ) 1 + s
f f f
2
and in decibels is L f dB » 4.3s , where s is the rms phase
f
f
error in radians, assumed << 1. For the case of phase error
caused by quantization, see the next entry. If there are ampli-
2
tude errors as well as phase errors, a second variance s rep-
a
2
resenting the amplitude error should be added to s in
f
calculating loss caused by the feed network, phase shifters,
and amplifier modules. DKB
Ref.: Mailloux (1994), p. 399.
Array phase quantization loss is the reduction in antenna
gain caused by phase quantization error in phase shifters of a
phased-array antenna. The loss as a power ratio is given by
2
2 2 p
»
L = exp ( s ) 1 + s = 1 + ---------------
q q q 2p
32 × Figure L17 Total earth-based radar attenuation (two-way) vs.
2
2p
and in decibels is L qdB » 4.3s .= 14.15/2 , where s is the frequency for target outside the troposphere for different eleva-
q
q
rms phase quantization error and p is the number of bits in the tion angles in standard atmosphere (from Blake, 1980),
Fig. 5.25, p. 219).
quantized command. For the common case p = 4, the loss is
0.05 dB. Since quantization error is uncorrelated with other The use of (1) requires complicated computations of
phase errors (the phase variances add directly), this loss may absorption coefficients, V (h) and V (h), which are functions
w
o
be calculated separately from other components of phase of atmospheric pressure and temperature, height, and radar
error loss, and the two loss values multiplied (added in deci- frequency. Simplified approximations to calculate two-way
bels) to arrive at the total phase error loss. DKB atmospheric loss are
Ref.: Barton (1969), p. 193.
¤
L ( R q, ) k R 1 –= [ exp – ( RR )] (dB)
Atmospheric (attenuation) loss is experienced by the radar a a a a
signal in passing from the transmit antenna to the target and
where k is the sea-level attenuation coefficient and
a
back to the receive antenna, as a result of interaction with
atmospheric molecules and precipitation particles. In the
radar equation, the two-way attenuation is applicable; in the