Chapter 9 
TARGETS 
SCATTERING PARAMETERS 
Radar Cross Section 
N DETERMINING the coverage to be expected of 
I radar systems, it is important to know what 
fraction of the power incident upon a target will be 
returned to the receiver. A parameter involving the 
dimensions and orientation of the target, and usually 
also the wavelength, and which measures the propor- 
tion of power returned, is called a scattering para- 
meter. 
The most generally used of these parameters is the 
radar cross section introduced in Chapter 2. It 
is denoted by c and is defined by 
W. 
= 4rd? — 1 
o 7 W. , ( ) 
2 
where W, is the scattered power per unit area at the 
receiver and W,, is the incident power per unit area at 
the target. In terms of c, the radar gain is 
2 
Ea gigi’ = Ay? 
4rd? \8rd 
This equation may also be written in the form 
(2) 
where 
is the gain factor introduced earlier (see Chapter 5 ), 
Ap is the free-space gain factor and A, is the path- 
gain factor. 
Target Gain 
Another scattering parameter is Gp, the target 
gain, discussed in Chapter 2. It is the gain of the 
target in the direction of the receiver relative to a 
shorted (dummy) doublet antenna. The target gain 
is connected with o by the relation 
_ Vane 
G 3 3 
R 5 (3) 
The corresponding radar gain is 
Pa _ sGQGpA'. (4) 
1 
The factor 4 is due to the calculation of Gp relative to 
a shorted doublet rather than to a matched load 
doublet. If the calculation of Gz were made relative 
471 
to the matched load doublet, the factor 4 would be 
replaced by 1. 
Echo Constant 
The echo constant, denoted by K, is defined by 
W, (2)' 
=—{- 5 
WAx (5) 
and is related to « by 
o 
=——., 6 
And? (6) 
The corresponding power ratio is 
I? 2 (=) 
— = KG,G,{ — ) A’. 7 
P, nod Wes (7) 
Except for the factor 147, K is just ¢ measured 
in square wavelengths. 
Equivalent Plate Area 
A plate of area S placed normal to the direction of 
propagation has a radar cross section given by 
2. 
c= 40 ; (8) 
provided the linear dimensions of the plate are large 
compared with X. Any target may be supposed to 
scatter (in the direction of the radar) an amount of 
energy equal to the amount that a plate of area S 
would scatter in this direction. This area S is called 
the equivalent plate area of the target. The corre- 
sponding radar gain is 
Le Ge: ye 
a (9) 
Scattering Coefficient 
or Characteristic Length 
This parameter has also been called the radar 
length of the target. The definition is 
Ee az (10) 
where L, = field strength at the receiver, 
E, = field strength incident on target. 
It is evident that 
b= (11) 
4a 
connects L with radar cross section. The radar gain 
