Radar Cross Section (RCS) - MATLAB Simulations for Radar Systems Design - page 532

Thus, the magnetic field component H ϕ in the various regions may be written

as

k

∞

∑

( ) ( ) ( )

I

′

H =

1

a J k ρ sin v φα v φα − sin −

φ nv 1 0

jωȺ
k

n =

∞

0

0

(11.72)

( )

∑

() () ()

′

( ) ( )

II

′

2

H = b J kρ + cH kρ sin v φα v φα − sin −

φ nv n ν 0

jωȺ
k

n =

∞

0

0

∑

() () ( ) ( )

′

2

H

III

= d H kρ sin v φα v φα − sin −

φ n ν 0

jωȺ

n = 0

0

Where the prime indicated derivatives with respect to the full argument of the
function. The boundary conditions require that the tangential electric field
components vanish at the PEC surface. Also, the tangential field components
should be continuous across the air-dielectric interface and the virtual bound-
ary between region II and III, except for the discontinuity of the magnetic field
at the source point. Thus,

(11.73)

E = 0at φαπβ = ,2 −

z

I II



EE =



(11.74)

z z

at ρ = a



I II

HH =



φ φ

II III



EE =



z z

at ρ = ρ


− − 
J e

(11.75)

0

II III

HH J

φ φ e

The current density may be given in Fourier series expansion as

I 2 I

∞

( )

−− ∑

( ) ( )

J =

e

δφ φ − =

e

sin νφ α νφ α − sin − (11.76)

e 0 0

ρ 2 π α β ρ

n = 0

0 0

The boundary condition on the PEC surface is automatically satisfied by the
dependence of the electric field Eq. (11.72). From the boundary conditions in
Eq. (11.73)

ϕ

∞

∑

( ) ( ) ( ) aJ ka sin vφα v φα − sin − =

nv 1 0

n = 0

(11.77)

∞

( ) ∑

() () () ( ) ( )

2

bJ ka + cH ka sin vφα v φα − sin −

nv n ν 0

n = 0