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h Y π

1 =

Where ,

b = c =

[ ] a =

n m =

1 2k1 nm nm

E E

c a

1 2 (a, g a) +

n

E E

c b

g b 2 E E) E

2 (b, J k b Y k1a Y k b J k1ae ' 1 e n e − n ' 1 e n − a b

2 c

y(a b),

2 (k be −1){ ( ) ( ) ( ) ( )} − 2 2

2

E E aφ( , )….(5) E E bφ( , )…..(6) E E cφ( , )…..(7)

nm

In which (c, 0) is the feed location and denotes the electric field distribution for ARMSA for TMmn mode and given by

E nm ρ,φ) = z J k b Y k a Y k b J k ae )}cos nφ ( ˆ{ n ( 1

e n) ( 1 '

e )− n ( 1 e n ( 1 '

)

And y(a,b) = mutual apertures between the apertures g(a,a) = edge conductance at inner radius g(b,b) = edge conductance at outer radius Where a = inner radius of ARMSA ae = effective inner radius of ARMSA

b = outer radius of ARMSA be = effective inner radius of ARMSA

µ = permeability of the substrate h = thickness of the dielectric substrate k1 = resonant wavenumber εe = effective relative permittivity εr = relative permittivity of the substrate

3.0 Input Impedance of gap coupled ARMSA

Input impedance for gap coupled ARMSA is given as ( )

Z Z Zin o( ) in e in = + ….(9)

Where, Zin(e) = input impedance for even mode Zin(o) = input impedance for odd mode From above fig:

Z Z in e( ) in o( ) i 1n

= + + = + +

Z Z j f Ce 1 1

Z Z j f C π

1 1 in1

in1 in2 2 in2 12 1 2π 12 i 2n o

Z is the input impedance of the inner ring and is expressed as the parallel combination of R, L and C. Z

in

Z is the input impedance of the outer ring and is given as: 1

= 1

R j C j Lω ω1 + +

1 1 1 1 (12) 1

(10) (11)

…………..(8)

ISSN: 2231-1963

----------(3)

πk a (k ae −1) 2 2

4

2 2 1

1 e .(4)

154

Vol. 1,Issue 2,pp.151-158

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