Different types of reflection/TDR casic

Question

I am trying to understand the theory of operation of a time domain reflectometer (TDR).

TDR is a time domain instrument with measurement the impedance versus the distance. If with a VNA one can measure s-parameters, then with TDR one measures impedance.

Why would TDR be called S-parameters measurement method?

Ok, if I know the impedances, then I can create matrix U= Z I, where Z and I are matrices. But How I can use TDR for S-parameter measurement?

I have found the some slides (enter link description here)

pictures from this pdf:

Answer 1

Q: What do they mean?

Those graphs are voltages at source terminal vs time.

The x-axis has two inflections, t=0 and t when wave reach the source again. The input is always Ei and the second value you see is the voltage at input terminal after reflecting.

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Q: How to get these?

Deriving Zl=f(Eo,Ei)*Zo using reflection coefficient formula,

$$Γ=\frac{\ Z_L-Z_o}{\ Z_L+Z_o}$$

rearranging

$$Z_L=\frac{-(Γ+1)Z_o}{(Γ-1)}$$

and using

$$Γ=\frac{E_o}{E_i}$$

we have

$$Z_L=\frac{E_o+E_i}{E_i-E_o}Z_o$$

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You can use this formula by substituting Ei=1 and Eo=-1/3 , 1/3, 0, 1. For example Eo=-1/3, $$Z_L=\frac{1}{2}Z_o$$