A Question About Transmission Line Impedances

RF Cafe visitor L. Joseph wrote to request that the following question be posted in hope that someone will provide an answer. If you care to reply, please either e-mail your answer to me so I can post it, or maybe reply on LinkedIn.

"This is the question I am trying to get an answer for:

Let us take a 100 ohm termination in a 50 ohm system and add a 50 ohm transmission line of 0.2 lambda (0.2λ) length.

At the end of this 0.2 lambda line I will get an impedance corresponding to some VSWR1.

Then, I change the termination from 100 ohms to 75 ohms and at the end of the 0.2 lambda line VSWR2 will be

VSWR2 = VSWR1 / (100 / 75) = VSWR1 / 1.33

Will the same rule apply if the 0.2 lambda line impedance is not 50 ohms... say 25 ohms?

Is there an easy way to make calculations in situations like this?"

Thanks to the folks who took the time to provide an answer

Greg F.

September 4, 2013

Dear L. Joseph and RF Café readers,

In regards to your Transmission Line Impedance question. The length of the transmission line can be largely ignored here. A theoretical lossless transmission line will only rotate the terminating impedance around on the same VSWR circle. You would only need to take the transmission line length into account if it were long enough for its attenuation characteristics to become significant.

The direct answer to your question is yes, for (your) two termination impedances the VSWR ratio will always be 1.33 regardless of the transmission line impedance. As long as the transmission line impedance stays lower than your lowest termination impedance.

I used Mathcad for the equations, but you should be able to make spread sheet calculation to do the job. You'll find it interesting to play with the line impedance. It will cause the VSWR ratio to change when it is between the two termination impedances.

I hope my solution helped, it was a fun distractions from work. I continued to play with it after I sent my email. I found it very interesting that the VSWR ratio became dynamic when the Line Impedance was between the two Termination Impedance. As you know, for all practical purposes, transmission line impedance is fixed so I've never spent any time exploring the effect of varying that parameter. I decided to plot the VSWR Ration as a function of Line Impedance. You can post this as well if you think it will be of interest.

L. Joseph responds:

September 5, 2013