# Finding total return loss between transceivers

I was wondering how one finds the total return loss between transceivers. In particular, how return losses of connectors are added. Say if I have two connectors with a return loss of -10dB. How do I calculate the total return loss of these two connectors? Is it simply -7dB, or is there a more complicated way to sum the losses?

Edit: cascading the s parameters of each connector appears to be the best way to so this.

Return loss is the magnitude of the signal being reflected back from the connector, its phase is undefined.

You might expect two identical connectors to have the same phase of return loss, and so two -10dBs would add up to -4dB (*)(reflections are linear, not power, so add as an extra 6 dB, not 3) if the connectors were 'close' to each other. That may be true if the connectors have a poor return loss because of a consistent fault, like a design error, or being used in the wrong impedance system. If a good connector is nominally correct, then random manufacturing defects may cause it to have any phase of error.

Two identically bad connectors separated by a significant length of transmission line may, depending on the frequency (which controls the electrical length of the line) add in any phase, to get total return losses from -4dB to -infinity (*), or perfectly matched.

(*) I've neglected that the first connector, because of its return loss, transmits a little less signal to the second connector, so the two return losses will not add up to exactly -4 or exactly cancel, only approximately. As the return losses get better, the error in this approximation will drop dramatically.

• Also, if the transmission line between the two connectors is lossy, the effect of the second connector's return loss will be mitigated (attenuated).
– Hyp
Aug 15, 2022 at 8:25
• That's very helpful thanks. If I had even more connectors, would I find the total worst case return loss by adding all of the individual reflection coefficients together? Aug 16, 2022 at 8:10
• @AdamMakin yes, allowing for the fact that each connector transmits less than full signal to the next, and see Hyp's comment about line between the connectors as well. Several connectors separated by the same length of line gives some unexpected results at frequencies where the line lengths are lambda/4, put it into a simulator and have a play. Aug 16, 2022 at 9:13

Return loss can be equated to reflection coefficient like this: -

$$RL =-20\cdot \log_{10}(\Gamma)$$

And $$\\Gamma\$$ (the reflection coefficient) equals: $$\\hspace{1cm}\dfrac{Z_{LOAD} - Z_0}{Z_{LOAD} + Z_0}\$$.

But, as you can see, to take the log of a negative number results in an error so, the magnitude return loss formula is used: -

$$RL =-20\cdot \log_{10}(|\Gamma|)$$

And that no-longer recognizes whether $$\Z_{LOAD}\$$ is greater or less than $$\Z_0\$$ hence, you can't reliable assume that two return loss numbers can be joined together numerically.