Coplanar Waveguide (CPW)

2010/10/30 Takuichi Hirano (Tokyo Institute of Technology)

(Subscript[ϵ, eff])

G. Ghione, C.U. Naldi, "Coplanar Waveguides for MMIC Applications: Effect of Upper Shielding, Conductor Backing, Finite-Extent Ground Planes, and Line-to-Line Coupling," IEEE Transactions on Microwave Theory and Techniques, Vol.35, No.3, pp.260-267, March 1987.

c=2.99792458*(10^8);
ϵ0=((10^7)/(4*π*(c^2)));
μ0=4*π*(10^(-7));
ϵeff[ϵr_,a_,b_,h_]:=Module[{k3,k4,k3b,k4b},
k3=Tanh[((π*a)/(2*h))]/Tanh[((π*b)/(2*h))];
k4=a/b;
k3b=(Sqrt[1-(k3^2)]);
k4b=(Sqrt[1-(k4^2)]);
q2=(((EllipticK[k3])/(EllipticK[k3b]))/(((EllipticK[k3])/(EllipticK[k3b]))+((EllipticK[k4])/(EllipticK[k4b]))));
1+q2*(ϵr-1)
];

ϵr=4.0;
h=5.0*(10^(-6));
a=9.6*(10^(-6))/2;
b=a+4.0*(10^(-6));
ϵeff[ϵr,a,b,h]

f=60.0*(10^9);
c=2.99792458*(10^8);
λ0=(c/f);
λg=λ0/(Sqrt[ϵeff[ϵr,a,b,h]])

Z0

z0[ϵr_,a_,b_,h_]:=Module[{k3,k4,k3b,k4b},
k3=Tanh[((π*a)/(2*h))]/Tanh[((π*b)/(2*h))];
k4=a/b;
k3b=(Sqrt[1-(k3^2)]);
k4b=(Sqrt[1-(k4^2)]);
((60*π)/(Sqrt[ϵeff[ϵr,a,b,h]]))(1/(((EllipticK[k3])/(EllipticK[k3b]))+((EllipticK[k4])/(EllipticK[k4b]))))
];

z0[ϵr,a,b,h]