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
email your answer to me so I can post it, or maybe reply on LinkedIn.
See answers below:
"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 VSWR_{1}.
Then, I change the termination
from 100 ohms to 75 ohms and at the end of the 0.2 lambda
line VSWR_{2} will be VSWR_{2} = VSWR_{1}
/ (100 / 75) = VSWR_{1} / 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.
Added
on September 5, 2013
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
"Thanks for the detailed answer!"
Posted September 3, 2013
