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By Jackson M.A

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5 . 14) Substituting Eqs. 15) where the terms q and q are called the partial filling factors, and they are   equal to K(k )  q :  K(k  )  K(k )  q :  K(k  )  Further v  K(k ) K(k ) \   ; , K(k  ) K(k  )   K(k ) K(k ) \   ; . 19) where c is the velocity of light in free space. 19) give 1 , Z :  cC (  60 K(k ) K(k ) \  ;  : . 3(a) to (c). Since these structures resemble those in the previous example, Eqs. 10) are still valid. However, the only change is in the equation for the partial capacitance C , which is as follows [3]:  K(k )  .

24) K(k )  . 25) Hence Eq. 2) for C becomes  When  is set equal to 1 in Eq. 5), C becomes zero, that is,  C : 0.  Lastly, when h : h : -, Eqs. 3 Configuration for partial capacitances for a CPW on a double layer dielectric substrate: (a) C , (b) C , (c) C . 4 Schematic of a CPW on an infinitely thick dielectric substrate. and hence Eq. 8) for C  simplifies to K(k )  . 28) Substituting Eqs. 28) into Eq. 1) gives C K(k )  . 29) Substituting Eqs. 14) gives : 1;  . 30) Substituting Eq. 31) and Eqs.

34) From Eqs. 35)(a) K(k )  . 35)(b) and Substituting Eqs. 35) into Eq. 5 Schematic of a CPW on a dielectric substrate of finite thickness. CONVENTIONAL COPLANAR WAVEGUIDE ON A MULTILAYER DIELECTRIC SUBSTRATE 21 which yields from Eq. 14), C ( 9 1) K(k ) K(k  )  . 37) Lastly, from Eq. 38) The expression above of and Z is identical to those given by [4], [5]. 6(a) and (b), respectively, for  a CPW on an alumina substrate. 2) is about 10 to 15 percent. Hence the propagation characteristics of lines with high Z , and therefore large  slot widths on thin substrates, should be determined using Eqs.

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