Today most electronic equipment consists of signal generators and processing units. These units are connected with transmission lines. These lines have a big influence on signal distortions. On these lines depends transmission lines stability. Let’s see how transmission lines affect transmitted signals.

(G- signal generator; Z_{a}– output impedance; I- signal receiver Z_{b}– input impedance; L- transmission line length; Z_{0}– Line impedance.

When line is tuned and without losses then input voltage:

U_{b}(t) = Z_{b}E(t-t)/(Z_{a} + Z_{b})

E(t)- generators signal amplitude; t- signal delay in line.

t =l/v ;

l- line lenght; v- signal speed.

If the line is not tuned up, then there are distortions in line because of reflections inline:

If signal E(t) is step function:

Then signal in line exit in discrete time moments will be:

U(0) = p;

U(t) = p*(1+p_{b})

U(2t) = p*(1+p_{b}+p_{a}*p_{b})

U(3t) = p*(1+p_{b}+p_{a}*p_{b}+p_{a}*p_{b}^2);

U(4t) = p*(1+p_{b}+p_{a}*p_{b}+p_{a}*p_{b}^2+p_{a}^2*p_{b}^2);

U(5t) = p*(1+p_{b}+p_{a}*p_{b}+p_{a}*p_{b}^2+p_{a}^2*p_{b}^2+p_{a}^2*p_{b}^3) â€¦

where

Depending on reflectance coefficients and their signs distortions can differentiate or integrate:

A real model using MathCAD was implemented to see how the signal looks on exit depending on parameters. Below you see used algorithm structure used in modeling:

Part 2:

One of results using trapezoid signal:

In exit we get distorted signal.

Download your MathCAD Transmission Line (13, 12, and 2001i versions ) file to test various parameters and different signal shapes.