[SI-LIST] Re: Multi-line S-parameters to RLGC matrices
- From: elie issa <eliaissa1@xxxxxxxxx>
- To: elie issa <eliaissa1@xxxxxxxxx>, John <johndp@xxxxxxxx>, "si-list@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
- Date: Wed, 9 Nov 2011 22:23:33 -0800 (PST)
Also, it is +jwL and you are having it as -jwL in your matrice
From: elie issa <eliaissa1@xxxxxxxxx>
To: John <johndp@xxxxxxxx>; "si-list@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
Sent: Thursday, November 10, 2011 1:06:49 AM
Subject: [SI-LIST] Re: Multi-line S-parameters to RLGC matrices
Your R11 is negative, you are having passivity issues in your sims of the S
parameters
From: John <johndp@xxxxxxxx>
To: "si-list@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
Sent: Wednesday, November 9, 2011 5:19:04 PM
Subject: [SI-LIST] Multi-line S-parameters to RLGC matrices
I am trying to convert multi-line S-parameters to RLGC matrices. I have
found a IEEE paper
"On Addressing the Practical Issues in the Extraction ofRLGC Parameters
for Lossy Multiconductor Transmission Lines using S-parameter Models"
Which I implemented in Matlab scripts to implement the algorithm, the
first stage is to convert the S-parameters to T-parameters
*******************************************************************************************
function [ T_params ] = S_2_T( sparams, Zref )
% If you have the rf toolkit you can use the function s2z to create the
% Z-Parameters
%----------------------------------------------------------------------
% Create the reference impedance matrix for all ports.
Z0=Zref*eye(size(sparams,1));
% Create an Identity matrix
ident=eye(size(sparams,1));
% Create Z-parameters
Z_params=Z0*(ident + sparams)/(ident-sparams);
%----------------------------------------------------------------------
% Divide up the n by n Z-parameter matrix into m by m sub-matrices
z_11=Z_params(1:size(Z_params)/2,1:size(Z_params)/2);
z_12=Z_params(1:size(Z_params)/2,(size(Z_params)/2+1):size(Z_params));
z_21=Z_params((size(Z_params)/2+1):size(Z_params),1:size(Z_params)/2);
z_22=Z_params((size(Z_params)/2+1):size(Z_params),(size(Z_params)/2+1):size(Z_params));
% Build up the T-parameters from the Z-parameters
T_params=[z_11/z_21 (z_11/z_21)*z_22-z_12;z_21\eye(size(z_21)) z_21\z_22];
end
****************************************************************************************
The second is to create modified T-parameters.
****************************************************************************************
function [gamma, Zo, Rm, Lm, Gm, Cm] = T_2_RLGC( T1, T2, deltax, freq )
% Calculate the modified ABCD matrices using the T parameters of two
% different length lines.
X=T1+T2;
Y=T1-T2;
M1 =(Y/X + X/Y)/(X/Y - Y/X);
M2 = inv(X/Y-Y/X);
% now extract the sub-matrices DM1 and CM2
DM1=M1((size(M1)/2+1):size(M1),(size(M1)/2+1):size(M1));
CM2=M2((size(M2)/2+1):size(M2),1:(size(M2)/2));
% now compute the complex propagation constant and characteristic
% impedance
gamma=(1/deltax)* acosh(DM1);
Zo=(CM2\sinh((gamma * deltax)))/2;
% Now calculate the RLGC matrices
ohmega=2*pi()*freq;
Rm=real(Zo*gamma);
Lm=(1/ohmega)*imag(Zo*gamma);
Gm=real(gamma/Zo);
Cm=(1/ohmega)*imag(gamma/Zo);
end
****************************************************************************************
I created some S-parameters extracted at 1 GHz using a field solver for
100 Ohm differential lines with lengths of 400 and 500 mils.
s_param_400mil
0.0202 + 0.0349i 0.0182 + 0.0383i 0.8965 - 0.4114i -0.0032 -
0.0036i
0.0182 - 0.0383i 0.0203 + 0.0349i -0.0032 - 0.0036i 0.8965 -
0.4114i
0.8965 - 0.4114i -0.0032 - 0.0036i 0.0203 + 0.0349i 0.0182 +
0.0382i
-0.0032 - 0.0036i 0.8965 - 0.4114i 0.0182 + 0.0382i 0.0203 +
0.0349i
s_param_500mil
0.0258 + 0.0341i 0.0275 + 0.0452i 0.8468 - 0.4985i -0.0047 -
0.0044i
0.0275 + 0.0452i 0.0258 + 0.0341i -0.0047 - 0.0044i 0.8468 -
0.4985i
0.8468 - 0.4985i -0.0047 - 0.0044i 0.0258 + 0.0341i 0.0275 +
0.0452i
-0.0047 - 0.0044i 0.8468 - 0.4985i 0.0275 + 0.0452i 0.0258 +
0.0341i
However when I use these with my functions I do not get the results I
expect for Gamma and Impedance matrices (and hence the resulting RLGC
matrices). I was expecting the Z matrix to be symmetrical and around 50
Ohms for Z11 and Z22 but this is not the case.
gamma
0.0337 + 0.9961i 0.0002 -15.7096i
0.0016 -15.7080i 0.0336 + 0.9879i
Zo
1.0e+002 *
-0.0087 - 0.0194i -5.3170 - 0.1077i
-5.1093 - 0.1262i -2.1089 + 0.0956i
Can anybody comment as to what I might be doing wrong ?
Regards
John
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