# S11 to Return Loss Calculator

Use this tool to calculate the Return Loss (RL) from S11.

Return Loss is a measure of mismatch at a transition in an RF circuit.

Enter

• S11 – either linear or dB value can be used

## Background

S11 is the input reflection coefficient [1] with a value between 0 and 1. (Entering values outside this range will result in meaningless output). Referring to the picture of a two port network shown below, S11 = b1/a1 (when a2=0)

## Formula

If a1, b1 and S11 are all linear numbers,

Return Loss = 10*Log10(a1/b1)

or

RL = -10*Log10(S11)

On the other hand, if S11 is expressed in dB

RL = -S11dB

Return Loss is always a positive number as a1 > b1

## Example Calculations

If the reflected signal b1 = 0, then all of the input signal a1 is transmitted forward and the return loss RL = âˆž.

If all of the input signal is reflected back, then b1=a1 and none of it is transmitted forward. This is the poorest match possible and RL = 0.

If S11 = 0.1, the Return Loss is calculated to be 20 dB.

## References

[1] Scattering Parameters on Wikipedia