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function z = s2z(s,ref)
% z = s2z(s [,ref])
%
% Scattering to Z transformation
%
% input:
% s: S-matrix matrix nxnxf (f: number of frequencies)
% ref: (optional) reference impedance (default 50 Ohm)
%
% output:
% z: Z-matrix nxnxf
%
% Reference: http://qucs.sourceforge.net/tech/node98.html
%
% Thorsten Liebig <thorsten.liebig@gmx.de>
% Feb. 2013
if nargin < 2
Z0 = 50;
else
Z0 = ref;
end
N = size(s,1);
Nf = size(s,3);
if (numel(Z0)==1)
Z0 = Z0*ones(N,1);
end
E = eye(N);
Zref = zeros(N,N);
G = Zref;
for n=1:N
Zref(n,n) = Z0(n);
G(n,n) = 1/sqrt(real(Z0(n)));
end
z=zeros(N,N,Nf); %preallocate
for f=1:Nf
z(:,:,f) = G\ ((E-s(:,:,f))\(s(:,:,f)+E))*Zref*G;
end
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