S-Y-Z parameter conversion

S-Y-Z parameter conversion

射频微波领域，N 端口的 S-Y-Z 参数矩阵的转换

公式说明

S：S参数矩阵
Y：Y参数矩阵
Z：Z参数矩阵
Z0： Z0n为端口的特征阻抗
G：

MATLAB实现

S 参数转 Y , Z

function [Y,Z] = f_s(Z0,S)
E = eye(length(S));
for index=1:length(S)
    G(index,index)=1/(abs(real(Z0(index,index))))^0.5;
end
Y = inv(G)*inv(S*Z0+conj(Z0))*(E-S)*G;
Z = inv(G)*inv(E-S)*(S*Z0+conj(Z0))*G;
%Z = inv(Y);
end

Z 参数转 S, Y

function [S,Y] = f_z(Z0,Z)
E = eye(length(Z));
for index=1:length(Z)
    G(index,index)=1/(abs(real(Z0(index,index))))^0.5;
end
S = G*(Z-conj(Z0))*inv(Z+Z0)*inv(G);
Y = inv(Z);
end

Y 参数转 Z , Y

function [S,Z] = f_y(Z0,Y)
E = eye(length(Y));
for index=1:length(Y)
    G(index,index)=1/(abs(real(Z0(index,index))))^0.5;
end
S = G*(E-conj(Z0)*Y)*inv(E+Z0*Y)*inv(G);
Z = inv(Y);
end

例子：

clear
Z0=[50 0;0 50];
Z =[3.5300075762455 + 88.8803135004042i  3.0440285374530 + 53.4186689038448i
  3.0440285374530 + 53.4186689038448i  5.1050513192128 + 111.3927579984047i];
[S,Y] = f_z(Z0,Z)