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Topic: Q: Efficient multi-dimensional matrix handling
Replies: 0

 Jens Benecke Posts: 10 Registered: 12/7/04
Q: Efficient multi-dimensional matrix handling
Posted: May 16, 2005 6:33 AM

Hello everybody,

I have implemented the algorithm displayed at
http://qucs.sourceforge.net/tech/node5.html to convert a S matrix (as
generated by an Agilent network analyer, in Touchstone format) into a Z
impedance matrix (see below).
However, I *suspect* that this would be much more efficient using a
three-dimensional matrix instead of the "for" loop, a single command to do
the actual calculation, and return a 2x2xf matrix, where "f" is the number
of samples.

But I'm not sure how to do that - and how to work with a matrix like this
(like matrix multiplication etc). Can anybody help out? I'm using Matlab
14.1 (SP2) under Linux (SuSE 9.1 / 9.3). I looked at various Matlab FAQs on
the Web but couldn't find anything related to working with
(N>2)-dimensional matrices.

Thank you!

My code:

%
% [f, Z11,Z12,Z21,Z22] = S2P2Z(f, S11,S12,S21,S22, Z0);
%
% formula: Z = Gref * (E-S)^-1 * (S * Zref + Zref*) * Gref
%
% Z = result matrix
% S = input matrix
% E = identity matrix
% Gref = E * 1/(2*sqrt(|Re(Z_0)|))
% Zref = E * Z_0
%

function [f, Z11,Z12,Z21,Z22] = S2P2Z(Z0, fS11,fS12,fS21,fS22)

S_11 = dlmread(fS11, '', 6, 0);
S_12 = dlmread(fS12, '', 6, 0);
S_21 = dlmread(fS21, '', 6, 0);
S_22 = dlmread(fS22, '', 6, 0);

f = S_11(:,1); f = f';

S11 = S_11(:,2)+i.*S_11(:,3);
S12 = S_12(:,2)+i.*S_12(:,3);
S21 = S_21(:,2)+i.*S_21(:,3);
S22 = S_22(:,2)+i.*S_22(:,3);

E = eye(2,2);
Gref = E .* 1/(2.* sqrt(abs(real(Z0))));
Zref = E .* Z0;

for t = 1:size(S11,1),
S = [S11(t) S12(t); S21(t) S22(t)];
Z = inv(Gref) * inv(E-S) * (S * Zref + conj(Zref)) * Gref;
Z11(t) = Z(1,1);
Z12(t) = Z(1,2);
Z21(t) = Z(2,1);
Z22(t) = Z(2,2);
end

end

--
Jens Benecke
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