# Transmission Line 2-Port Parameters

I am checking some Spice models of transmission lines.

I have a Belden 1583A Ethernet Cable, with the following parameters $$\R=93.8 \ \Omega\text{/km}\$$ and $$\Z_0=100 \Omega\$$, hence $$\C=47.652 \ \text{pF/km}\$$ and $$\L=0.47652 \ \text{uH/km}\$$, for $$\D=1 \ \text{km}\$$ (check).

I took an approximation with $$\n=8\$$ discrete modules of RLC circuits each with one series R + one series L + one parallel C with the above given parameters, divided by $$\n\$$, as depicted.

I considered a sinusoidal source with $$\v=1\ \text{Vp}\$$, (peak to zero amplitude) $$\f=100\ \text{MHz}\$$.

I took an Inverse Hybrid G Parameters 2-port Matrix, with the following code in Matlab.

%% Belden 1583A Cat5e
% V: 1V,100MHz
clear all; clc;

c=299792458;
VF=0.7; Z0=100;
C=1/c/VF/Z0; L=Z0/c/VF; R=93.8;

% Distributed Impedances
v1=1; f=1e8; k=8;
j=sqrt(-1);
ZC=1/(j*2*pi*f*C/k); ZL=j*2*pi*f*L/k; ZR=R/k;
% B: ABCD' Form / Two Port Network Matrix
% V1I1 -> V2I2
B=([1 -ZL-ZR;0 1]*[1 0;-1/ZC 1])^k;
% G=inv(H): Inverse Hybrid Form
% G: V1I2 -> I1V2
G=1/B(2,2)*[-B(2,1) -1; det(B) -B(1,2)];
% Open Loop
i2=0;
x1=[v1;i2];
x2=G*x1;
i1=abs(x2(1)); v2=abs(x2(2))


This brings an output of $$\v_2=0.924\ \text{Vp}\$$, phasor magnitude.

However the same circuit simulated in two different programs, with zero initial conditions, and for any convergence settings, brings $$\v_2=0.873\ \text{Vp}\$$, sinusoidal steady state. Too much difference for an accuracy setting.

Why could I be having this difference?

• Are you modeling just a meter of the cable? or an entire kilometer? – analogsystemsrf Feb 9 at 8:47
• The purpose is to have a handy model for the kilometer range, now for digital, later for analog. I am comparing some built in models and I wished to refresh an old 2-port parametrization, but I was unable to equal them... – Brethlosze Feb 9 at 8:49
• Is there a reason you are modeling driving this with an unmatched (0-impedance) source, and with an open-circuit termination? What other simulators did you try, and did you use the same terminations for those simulations? – The Photon Feb 9 at 15:56
• Also, is there a reason for making a unbalanced model of a balanced transmission line? The Belden spec of 94 ohms/km appears to be per conductor, but in a differential configuration you need to account for both signal and return currents passing through this resistance. – The Photon Feb 9 at 16:00