Radar Cross Section (RCS) - MATLAB Simulations for Radar Systems Design - page 535

Thus, the H ρ expressions for the three regions defined in Fig. 11.30 become

1

∞

∑

I

H =− a vJ ( k ρ ) s( v ϕ α − ) in( v ϕ α − )

ρ nv 1 0

j ωµρ

n = 0

∞

1

(11.93)

( )

∑

II

H =−

(2)

ρ ϕα ϕα cos ( v − )sin ( v − )

vbJ k () ρ + cH () k

ρ 0

nv n v

j ωµρ

n = 0

1

∞

∑

III

H =−

d

vH

(2)

( s( k ρ v ϕ α − in( v ϕ α − )

ρ n 0

j ωµρ

v

n = 0

11.6.1. Far Scattered Field

In region III, the scattered field may be found as the difference between the
total and incident fields. Thus, using Eqs. (11.68) and (11.69) and considering
the far field condition (

ρ∞ → ) we get

2 j

∞

∑

III i s − jkρ v

EEE =+= e dj sin v φα v φα ( − − ) sin ( )

z z z n 0

πkρ

n = 0

(11.94)

11 ∂ E

ωȺ 2 j

H =−

z

( ) i − jkρ + jkρ cos φ φ −

EI =−

0

e e

0 0

ρ

j ωµρ φ ∂

z e

4 πkρ

Note that d n can be written as

ωȺI

%

(11.95)

d =−

0
4

e

d

n n

where

( ) ( ) ( ) ( ) ( )

 ′ ′ 

kJ k a  J ka Y kρ − YkaJ kρ  + K

 

v 1 v ν 0 ν v 0

 

( ) ( ) ( ) ( ) ( )

 kJ ′ ka  Y ka J kρ − JkaY ρ  

π
dj παβ

4  

 

%

1 v 1 ν v 0 v ν 0

(11.96)

=

  n

2 −−

() ()() () ()()

′

2 2

kH ka J k a − k H ka J ′ k a

 

ν v 1 1 ν v 1

 

 

 

Substituting Eq. (11.95) into Eq. (11.94), the scattered field f () is