International Journal of Advances in Engineering & Technology, May 2011. ©IJAET


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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