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# Impulse signal distortion in transmission line

2017-12-23 19:54
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Today most electronic equipment consists of signal generators and processing units. These units are connected with transmission lines. These lines have big influence in signal distortions. On these lines depends transmition lines stability. Leta€?s see how transmition lines affect transmitted signals.

(G- signal generator; Za- output impedance; I- signal receiver Zb- input impedance; L- transmission line length; Z0- Line impedance.

When line is tuned and without losses then input voltage:

Ub(t) = ZbE(t-t)/(ZaZb)

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

t=l/v ;

l- line lenght; v- signal speed.

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

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 pb)

U(2t) = p*(1 pbpa*pb)

U(3t) = p*(1 pbpa*pbpa*pb^2);

U(4t) = p*(1 pbpa*pbpa*pb^2 pa^2*pb^2);

U(5t) = p*(1 pbpa*pbpa*pb^2 pa^2*pb^2 pa^2*pb^3) a€|

where

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

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

Algorithm Part 1
Algorithm Part 2

One of results using trapezoid signal:

In exit we get distorted signal.

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