By inserting a matched (nominal system impedance) attenuator in front of a mismatched load impedance, the
mismatch "seen" at the input of the attenuator is improved by an amount equal to twice the value of attenuator.
The explanation is simple.
Here is a JavaScript calculator for
VSWR / Return Loss / Reflection
Coefficient / Mismatch Error / Improvement
Return loss is determined by the portion of the input
signal that is reflected at the load (due to impedance mismatch) and returned to the source. A perfect load
impedance (complex conjugate of the source impedance) would absorb 100% of the incident signal and therefore
reflect 0% of it back to the source (return loss of ∞ dB).
For the sake of illustration, assume that the
load is an open (or short) circuit, where 0% of the incident signal is absorbed by the load and 100% is reflected
back to the source. The reflected signal would therefore have a return loss of 0 dB. Insert a 3 dB attenuator in
front of the load. Now the incident signal is referenced to the input of the attenuator.
As signal at the input of the attenuator will experience a 3 dB reduction in power by the time it reaches the
load. That 3 dB less power will be 100% reflected by the load and experience another 3 dB reduction in power by
the time is returns back to the input, for a total loss of 6 dB. The same principle applies for a load anywhere(
§)
between zero and infinite load impedance (short and open circuits, respectively).
Calculate the improved
VSWR as follows. Note that by my convention the loss value is returned as a positive number, since the word "loss"
implies the negative. If it were to be termed "return gain," then the result would be reported as a negative
number. Equally qualified experts will disagree on whether return loss should take on a negative value or a
positive value; the important thing is to keep the sign correct in your calculations; i.e., if you use a positive
value, then subtract it, and vice versa.

Convert the load VSWR to load return loss per the following equation:
RL_{LOAD}=20*log
dB
 Add twice the attenuation value to RL_{LOAD}: RL_{NEW}=R_{LOAD} + 2*ATTEN dB
(where RL=Return Loss)
 Convert back to VSWR per the following equation: VSWR=
Of course, the method can be reversed to predict the attenuator required to improve a load VSWR by a
predetermined amount. To do so, calculate the desired return loss and subtract the known load return loss. Divide
the answer by two to get the attenuator value needed.
See the
VSWR
Calculator page.
§
Actually, the attenuator is only rated for its specified attenuation level when it is connected between two
nominal impedances. Therefore, the attenuator will either have to be designed to closely match the two impedances
at its input and output (source and load, respectively), or an adjustment will need to be made in the specified
attenuation value to compensate for the mismatched load impedance.