# What's the difference between mismatch and return loss when talking about filters?

I have been learning about filters recently, but am confused about what the difference between mismatch and return loss is. Could anyone explain the difference to me in an easy to understand way, or point to to a resource that does?

Thank you!

-

I am most familiar with three parameters that measure the reflection properties of a filter, and all give more or less the same information:

• The input reflection coefficient, $\Gamma$, is the complex ratio of the returned travelling wave to the input travelling wave when the output port of the filter is perfectly terminated. This is the same as the s-parameter $S_{11}$.

• The voltage standing wave ratio, or VSWR, is the ratio between the maximum and minimum voltage signal measured at different distances along the transmission line feeding into the filter, where the voltage variation is caused by interaction of the incoming travelling wave and the reflected wave. VSWR is calculated as

VSWR = $\frac{1+|\Gamma|}{1-|\Gamma|}$.

• Return loss, R, is the ratio of the power in the reflected travelling wave to the power in the input travelling wave. It's normally expressed in dB, and sometimes it's expressed as a positive number in dB even though the ratio is normally less than 1. Return loss is calculated as

R[dB] = $-20 \log |\Gamma|$.

All of these parameters are non-zero due to the effects of mismatch; that is, the reflected wave is generated because the input impedance of the filter is not perfectly equal to the characteristic impedance of the feed line. Beyond that general characterization, I have not seen the term mismatch used to denote a specific numerical parameter.

Doing some investigation, I do see that Wikipedia and some other sites do define a mismatch loss, which is the ratio of the output wave from the filter to the input wave, as affected by the loss due to input reflections. As such, the mismatch loss is given by

$-10 \log (1-|\Gamma|^2)$.

So, to get back to your specific question, return loss measures the signal reflected back from the input of the filter. Mismatch is the cause of this loss. But mismatch loss measures the amount of power transmitted through the filter.

-