S-Parameters Explained: S11, S21, S12, S22
Scattering parameters — S-parameters — describe how a device behaves at its ports when driven by RF signals. They are the standard language for characterizing RF components because they work at frequencies where voltage and current are hard to measure directly.
Each parameter is a complex ratio written Sxy = b_x / a_y, where a_y is the wave incident on port y and b_x is the wave leaving port x. The first index x is the responding port, the second index y is the driven port; all other ports are terminated in the system impedance (usually 50 Ω).
Magnitude is reported in dB: Sxy(dB) = 20·log10|Sxy|. Return loss at port 1 is RL = -20·log10|S11| = -S11(dB); the more negative S11(dB) is, the better the match. For example, S11 = -10 dB means |S11| ≈ 0.316 and RL ≈ 10 dB.
Apply this reference
For port-count, calibration and measurement-reporting considerations when applying these definitions, read VNA & S-Parameter Basics: Reading S11, S21.
At a glance
- ▹Sxy = b_x / a_y. Driven port is the second index (y), responding port is the first (x).
- ▹S11 and S22 are reflection terms; S21 and S12 are transmission terms. Read all four against a 50 Ω reference unless told otherwise.
- ▹Return loss is the matching figure buyers usually quote: RL = -20·log10|S11| = -S11(dB).
- ▹S21 is a complex transmission coefficient. Under matched conditions, insertion loss is -20·log10|S21| and small-signal gain is 20·log10|S21|; S12 describes reverse transmission.
- ▹S-parameters are frequency-dependent and must be read across the band of interest, not at one spot frequency.
Reference table
| Parameter | What it represents | Notes |
|---|---|---|
| S11 | Reflection at port 1 (input match). S11 = b1/a1 with the other ports terminated in the system impedance (usually 50 Ω). | Reported as magnitude |S11| in dB: S11(dB) = 20·log10|S11|. The matching figure quoted by buyers is usually return loss RL = -20·log10|S11| = -S11(dB). Example: S11 = -10 dB means |S11| ≈ 0.316 and RL ≈ 10 dB. |
| S21 | Forward transmission from port 1 to port 2. S21 = b2/a1 with the other ports terminated. | S21(dB) = 20·log10|S21|. Under matched reference conditions, passive insertion loss is -S21(dB); amplifier small-signal gain is S21(dB). Read across frequency and specify the reference impedance. |
| S12 | Reverse transmission from port 2 to port 1. | A low S12 means little signal leaks backwards; high isolation between ports. S12 and S21 are equal for a reciprocal two-port. |
| S22 | Reflection at port 2 (output match). S22 = b2/a2 with the other ports terminated. | Same convention as S11: read |S22| in dB; return loss at the output port is -S22(dB). |
The four S-parameters of a two-port device and what each one means. Values are typical engineering reference points.
Frequently asked
What is a good S11 value?
There is no universal threshold, but input return loss better than 10 dB (S11 below -10 dB, RL ≈ 10 dB) is a common starting acceptance point for general RF hardware. Matching-critical front ends often specify 15 dB or better. Always check the value across the whole operating band.
What is the difference between S21 and S12?
S21 is forward transmission from port 1 to port 2; S12 is reverse transmission from port 2 to port 1. For a passive reciprocal part the two are usually similar in magnitude. For an amplifier, S21 is the gain and S12 indicates how much signal leaks backwards, which relates to isolation and stability.
Are S-parameters measured at a single frequency?
No. An S-parameter is a function of frequency, so a vector network analyzer sweeps the band and reports a trace. A single-number quote is only meaningful if the frequency and the reference impedance are stated with it.
Related reference
Reference sources
Sources support the cited engineering concepts, not product availability or supplied-component ratings. Confirm the selected model's datasheet.
First published 2026-09-26; last updated 2026-10-19. Editorial update, not an engineering sign-off. Reference content only — no models or pricing, and not a statement of supplied-component specifications.