What are S-parameters?

From RF Design Wiki · By the RF Design Wiki editorial team · Published October 21, 2026 · Last reviewed October 21, 2026 · How we research

Scattering parameters (S-parameters) describe a linear N-port by the ratios of outgoing to incoming power waves, measured with all other ports terminated in the reference impedance. For a two-port, b₁ = S₁₁a₁ + S₁₂a₂ and b₂ = S₂₁a₁ + S₂₂a₂. S₁₁ is input reflection, S₂₁ forward transmission (gain or insertion loss), S₁₂ reverse transmission and S₂₂ output reflection.^[1]^[2]

Why use S-parameters instead of Z or Y?

Z and Y parameters require open or short terminations, which are hard to realize at microwave frequencies and can make active devices oscillate. S-parameters use matched (50 Ω) terminations and relate directly to measurable quantities: |S₂₁|² is transducer power gain with matched source and load, and |S₁₁| is the reflection magnitude.^[3]

What are the wave variables?

With reference impedance Z₀: a = (V + Z₀I)/(2√Z₀), b = (V − Z₀I)/(2√Z₀), so |a|² and |b|² are incident and reflected power. Kurokawa generalized these as power waves for complex reference impedances.^[2]

What properties do S-matrices have?

Reciprocal networks (passive, no ferrites or active parts): S = S^T, so S₂₁ = S₁₂.
Lossless networks: S is unitary, S^HS = I, so |S₁₁|² + |S₂₁|² = 1.
Shifting a reference plane by electrical length θ multiplies S_ii by e^−j2θ.

^[1]

How are S-parameters expressed in dB?

|S_ij|(dB) = 20·log10|S_ij|, because S-parameters are voltage-wave ratios. S₂₁ = −0.5 dB means 0.5 dB insertion loss; S₁₁ = −20 dB means 20 dB return loss. Files store them as magnitude/angle, dB/angle or real/imaginary in Touchstone format.

Frequently asked questions

Are S-parameters only for linear networks?

Yes; they are small-signal. Large-signal behavior requires load-pull or behavioral models.

What reference impedance is used?

Usually 50 Ω, but any real value can be specified.

Is S21 gain?

|S21|² is the transducer gain when source and load are both the reference impedance.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

“Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.
“Power Waves and the Scattering Matrix”. K. Kurokawa, IEEE Transactions on Microwave Theory and Techniques, vol. 13, no. 2, pp. 194-202. March 1965.
“S-Parameter Design (Application Note 154)”. Keysight Technologies. application note.

Categories: Matching and S-parameters

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