Microstrip Line (MSL)

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

h: 基板誘電体高さ
w: マイクロストリップ線路幅
t: マイクロストリップ線路厚さ

Z0

H.A. Wheeler, "Transmission-Line Properties of a Strip on a Dielectric Sheet on a Plane," IEEE Transactions on Microwave Theory and Techniques, Vol.25, No.8, pp.631-647, August 1977.

z0[ϵr_,w_,h_,t_]:=Module[{dw,we},
dw=t*(((1+1/ϵr)/(2*π)))*Log[(10.82/(Sqrt[((((t/h)))^2)+(((((1/π)/(w/t+1.1))))^2)]))];
we=w+dw;
(42.4/(Sqrt[ϵr+1]))*Log[1+(((4*h)/we))*((((14+8/ϵr)/11))*(((4*h)/we))+(Sqrt[(((((14+8/ϵr)/11)))^2)*(((((4*h)/we)))^2)+((1+1/ϵr)/2)*(π^2)]))]
];

ϵr=4.0;
h=5.0*(10^(-6));
w=10.0*(10^(-6));
t=1.0*(10^(-6));
z0[ϵr, w, h, t]

(Subscript[ϵ, eff])

E.O. Hammerstad, "Equations for Microstrip Circuit Design," 5th European Microwave Conference, pp.268-272 , Hamburg, Germany, September 1-4, 1975.

ϵeff[ϵr_,w_,h_]:=((ϵr+1)/2)+((ϵr-1)/2)*(1/(Sqrt[1+((12*h)/w)])) /; 1.0≤w/h≤20.;
ϵeff[ϵr_,w_,h_]:=((ϵr+1)/2)+((ϵr-1)/2)*((1/(Sqrt[1+((12*h)/w)]))+0.04*(1-(w/h))) /; w/h<1.;

ϵr=4.0;
h=5.0*(10^(-6));
w=10.0*(10^(-6));
ϵeff[ϵr,w,h]

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