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Transmission line impedance matching and frequency changes
If we have a certain transmission line at f0 , it has a load at its end ZL=R+jX then we insert a quarter wave transformer at the first position of voltage maximum dmax or minimum dminwhere the input impedance is purely real (resistance only ( RL) ), such that the characteristic impedance of the transformer Zc=Z0RL−−−−−√.
When we change the frequency from f0
to another value, the line becomes no longer matched. So if I want to find the input reflection coefficient (after changing the frequency), I need to find the distance dmax or dmin in terms of the new wavelength and move that distance on Smith chart then find zin at that point and re-normalize Zin with respect to ZC. Then we find the length of the transformer in terms of the new wavelength and move that distance on Smith Chart (starting from the position of the new zin which is normalized with Zc, at this new point we can find the input reflection coefficient after frequency change.
Are there any other parameters that change other than the wavelength?

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