[SOLVED] Reflection Coefficient of Cascaded Transmission Line

[fobos3]

I have a series of 5 transmission lines connected in series. I was wondering how best to analyse the circuit. I am not entirely sure how to calculate the reflection coefficient of the TL. Consider the following:
o-----o-----o-----o
\[Z1\,\,\,\,\,\,\,\,\,\,Z1\,\,\,\,\,\,\,\,\,\,Z2\,\,\,\,\,\,\,\,\,\,\] | 50 Ohms
o-----o-----o-----o

If I start working from the load, is the reflection coefficient just:
\[\frac{Z_m - Z_{m-1}}{Z_m + Z_{m-1}}\]
where $Z_m$ is the characteristic impedance of the TL on the right and $Z_{m-1}$ is the characteristic impedance of the TL on the left, without considering multiple reflections for now.

Regards

 

[biff44]

the easiest way is to use a modern microwave linear analysis program. There is a free one called Qucs that I have seen people use.

If you want to calculate out the solution youself, I would form "T" matrices for each element, cascade the T matrixes together by multiplying on some matrix math computer program, and you will get your answer. You, of course, realize that there will be a different answer at each frequency analyzed.



where:

a1 is the incident wave at the first port.


b1 is the reflected wave at the first port.


a2 is the incident wave at the second port.


b2 is the reflected wave at the second port.