# Return Loss Bridge – some woolly thinking

Some discussion on groups.io nanovna-users attempts to explain the behavior of the RF Return Loss Bridge used in some VNAs and other instruments, proof if you will that the instruments are not capable of measuring more than a few hundred ohms. Above is his diagram. He gives an expression that he states applies when R1=R3=R4=Rm: im = sqrt(Vf*(Rm – R2)/(12*Rm + 4*R2)).

This is deeply flawed, if R2>Rm the expression results in the square root of a -ve number… which might be acceptable in a complex number scenario, but this is a DC circuit.

Nevertheless, let us calculate the current with R2=0 and R2=5 while R1=R3=R4=Rm=50.

• R2=0: Im=0.28867513459481287;
• R2=5: Im=0.26940795304016235.

We can calculate $$ReturnLoss=20 log10 \frac{0.28867513459481287}{0.26940795304016235}=0.6 \;dB$$.

Wrong, the ReturnLoss of a 5Ω load on a 50Ω Return Loss Bridge should be 1.7dB.

So, the circuit / expression does not have the response of a Return Loss Bridge.

That is understandable, the schematic is not that of a Return Loss Bridge. If a Return Loss bridge uses R1=R3=R4=Rm, then its source MUST also have a source impedance Rs where Rs=R1=R3=R4=Rm for an accurate Return Loss response.

Analysis based on the schematic above with Zs=0 is not representative of the Return Loss Bridge used in accurate instruments, and conclusions are not soundly based.

The Return Loss Bridge is a deceptively simple thing… it does take careful attention to all details to obtain accurate results.

In the more general sense of a VNA, the reflection bridge must respond proportionally to the complex reflection coefficient.

Oristopo's graph would imply that the nanoVNA can measure down to zero ohms but not above a few hundred ohms. The simple fact is that a reflection bridge calibrated for 50Ω returns the same magnitude voltage for 2.5+j0Ω load as for 1000+j0Ω, just the phase is opposite… so if measurement noise is a problem for one, it is likely to be much the same for the other.

Generalised assertions by online experts that VNAs cannot accurately measure impedance above a few hundred ohms are not borne out by careful measurement experience of known DUTs in appropriate fixtures… or they have unreal expectations about the accuracy required for common analyses.