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.
![first.JPG](https://scienceprog.com/wp-content/uploads/2021/01/image-135.jpeg)
(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)/(Za + Zb)
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:
![image017.gif](https://scienceprog.com/wp-content/uploads/2021/01/image-63.gif)
![image019.gif](https://scienceprog.com/wp-content/uploads/2021/01/image-64.gif)
If signal E(t) is step function:
![image034.gif](https://scienceprog.com/wp-content/uploads/2021/01/image-65.gif)
Then signal in line exit in discrete time moments will be:
U(0) = p;
U(t) = p*(1+pb)
U(2t) = p*(1+pb+pa*pb)
U(3t) = p*(1+pb+pa*pb+pa*pb^2);
U(4t) = p*(1+pb+pa*pb+pa*pb^2+pa^2*pb^2);
U(5t) = p*(1+pb+pa*pb+pa*pb^2+pa^2*pb^2+pa^2*pb^3) …
where
![image023.gif](https://scienceprog.com/wp-content/uploads/2021/01/image-66.gif)
Depending on reflectance coefficients and their signs distortions can differentiate or integrate:
![image025.jpg](https://scienceprog.com/wp-content/uploads/2021/01/image-136.jpeg)
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:
![](https://scienceprog.com/wp-content/uploads/2021/01/image-67.gif)
Part 2:
![](https://scienceprog.com/wp-content/uploads/2021/01/image-68.gif)
One of results using trapezoid signal:
![image030.gif](https://scienceprog.com/wp-content/uploads/2021/01/image-69.gif)
In exit we get distorted signal.
![image032.gif](https://scienceprog.com/wp-content/uploads/2021/01/image-70.gif)
Download your MathCAD Transmission Line (13, 12, and 2001i versions ) file to test various parameters and different signal shapes.