Matching Is Not Just About S11 — What Return Loss Hides

When evaluating a matching network, most people look at return loss first. Specs such as "−15 dB or better passes" are common. But return loss alone does not tell you how much power the circuit actually passes.

If it is lossless, whatever is not reflected gets through

Start with the simple case. If the circuit has no loss, power that goes in is either reflected or transmitted:

|S21|² = 1 − |S11|²

Whatever is not reflected gets through — an obvious relationship. In this case, and only in this case, return loss also tells you the transmission. At −15 dB, |Γ| = 0.178, so the transmitted share is 1 − 0.0316 = 96.8 %. Watching return loss alone does no harm.

Checking the L-section designed earlier (200 Ω → 50 Ω, shunt C 1.3783 pF, series L 13.783 nH):

|Γ|   ≈ 0
|S21| = 0.000 dB

A perfect match, and all the power gets through. This relationship holds only when the circuit is lossless.

Add one resistor

Add a single 8 Ω series resistor to the same circuit. Think of it as trace resistance or an inductor's equivalent series resistance (ESR).

Zin  = 58.00 − j0.00 Ω
|Γ|  = 0.0741   →  22.6 dB return loss
|S21| = −0.669 dB

22.6 dB of return loss. Against a "−15 dB or better" spec, that is a comfortable pass. On this number alone, the circuit looks well matched.

Yet |S21| is −0.669 dB. 14 % of the power is gone. Laying out the budget shows the gap:

Not reflected, yet not transmitted either. The 13.7 % difference is turned into heat in the resistor. Return loss reports none of this loss.

The reason is simple: a resistor both reflects and absorbs. With loss in a matching network, the input impedance can even appear to improve toward the target. An extreme case makes this clear.

An extreme case — a "matching network" made of a resistor

Put a single 50 Ω series resistor between a 50 Ω source and a 50 Ω load.

Zin  = 100 Ω
|Γ|  = 1/3     →  9.54 dB return loss
|S21| = 2/3    →  −3.52 dB

A return loss of 9.54 dB is not good, but not catastrophic either. Yet transmission is −3.52 dB — more than half the power is thrown away.

Taking it further: put a large enough resistor in series on the source side and you can improve return loss as much as you like. Reflection drops because the returning wave is absorbed by the resistor, not because the match got better.

That is the danger of chasing return loss alone. S11 is a measure of reflection, not of efficiency.

Which one to watch

What to watch depends on the application:

• Transmitter output stage — efficiency is directly at stake, so |S21| or the loss itself. Reflection matters separately, as stress on device voltage ratings or on an isolator
• Receiver input stage — loss adds straight onto the noise figure, so again loss takes the lead
• Measurement systems and cables — reflections create standing waves that disturb the measurement, so |S11| takes the lead
• Filters — |S21| in the passband, attenuation in the stopband. |S11| is a guide to ripple

In many cases the objective function of the design lies on the S21 side. S11 is more often a constraint that just has to be "good enough".

Telling them apart in practice

Whether there is loss can be judged by whether this relationship breaks:

|S21|² < 1 − |S11|²   →  something is turning into heat

In simulation and in measurement alike, the reliable approach is to check the two side by side. If the gap is bigger than expected, the causes are few:

• The inductor's Q is too low (ESR is at work)
• The board material's loss tangent is high
• Resistance in vias or connections
• Conductor loss (skin effect, which grows with the square root of frequency)

The shape of the frequency dependence points to the cause. Roughly flat with frequency suggests a DC-like resistance; growing with the square root suggests conductor loss; growing in proportion to frequency suggests dielectric loss.

Try it

When you can see S11 and S21 side by side, this relationship is easy to check.

Smith Match — Matching Network Designer

This is exactly why the response view plots |S11| and |S21| together. Add a series R to a matching network and you can watch the point on the chart move toward the center while |S21| drops. It is the kind of failure you cannot notice while watching only one of them.