S-parameter viewer

How it works

Scattering parameters describe how a one-port or two-port network reflects and transmits a signal at each frequency. This viewer reads a Touchstone file (.s1p or .s2p), turns the numbers into the quantities engineers read off a plot, and writes the data back out in another format.

1. Read the file. The option line gives the frequency unit (Hz, kHz, MHz or GHz), the parameter type, the number format and the reference resistance. Each data line is a frequency followed by complex values as magnitude and angle in degrees (MA), dB and angle (DB), or real and imaginary parts (RI). A two-port line holds S11, S21, S12 and S22 in that order. Comments start with an exclamation mark. Missing option fields take the defaults GHz, S, MA and 50 ohm.S = mag x (cos angle + j sin angle) for MA; mag = 10^(dB / 20) for DB; S = real + j imaginary for RI
2. Return loss, insertion loss and VSWR. Return loss is how far below the incident wave the reflection sits, so a higher figure is a better match. Insertion loss is the loss from port 1 to port 2; a negative insertion loss is gain. VSWR follows from the size of the reflection coefficient and is not defined when the reflection exceeds 1.return loss = −20 log10 |S11|; insertion loss = −20 log10 |S21|; VSWR = (1 + |S11|) / (1 − |S11|)
3. Input impedance. The reflection coefficient of port 1 gives the impedance looking into it when port 2 is terminated in the reference resistance Z0.Zin = Z0 x (1 + S11) / (1 − S11)
4. Group delay. The phase of S21 (S11 for a one-port) is unwrapped so it has no jumps of 360 degrees, and the delay is minus its slope against angular frequency, taken by central differences between neighbouring points. The frequency step must be fine enough that the phase moves by less than 180 degrees from one point to the next.group delay = −d(phase) / d(omega) = −(phase[i+1] − phase[i−1]) / (2 pi x (f[i+1] − f[i−1]))
5. Stability of a two-port. The Rollett factor K and the determinant Delta give the classical test. The Edwards and Sinsky factors mu and mu' give the same answer with one number each: a two-port is unconditionally stable when both exceed 1. Below that, the maximum stable gain is the most gain you can have without a stabilising network; above it, the maximum available gain applies.Delta = S11 S22 − S12 S21; K = (1 − |S11|^2 − |S22|^2 + |Delta|^2) / (2 |S12 S21|); mu = (1 − |S11|^2) / (|S22 − Delta S11*| + |S12 S21|); MSG = |S21 / S12|; MAG = |S21 / S12| x (K − sqrt(K^2 − 1))
6. Markers and bandwidth. The worst return loss is the highest S11 in the data; the best match is the lowest. The bandwidth is found around the peak of S21 where it stays within the chosen drop (3 dB by default), and around the best match where return loss stays above a limit (10 dB by default). Crossings are found by straight-line interpolation between points.band = frequencies around the peak where |S21| (dB) ≥ peak − drop; match band = frequencies where return loss ≥ limit
7. Convert the format. The same data can be written as MA, DB or RI, in Hz, kHz, MHz or GHz, with the reference resistance kept. The conversion is exact apart from rounding to eight significant figures.dB = 20 log10 |S|; angle = atan2(imaginary, real); real = mag cos angle; imaginary = mag sin angle

Sources

The methods and default figures rest on these public sources. The wording here is our own; read the source for its full text.

• Touchstone File Format Specification, Version 2.0 (opens in a new tab), IBIS Open Forum (EIA/IBIS), ratified 24 April 2009. Option line, data layout, MA, DB and RI formats, the two-port data order and comment rules; version 1 files stay valid.
• Microwave Engineering, 4th edition (S-parameters, ABCD conversion, stability and gain), David M. Pozar, John Wiley and Sons, 2012. Definitions of S-parameters, return loss, the conversion between ABCD and S, and the K and Delta stability test.
• A new criterion for linear 2-port stability using a single geometrically derived parameter (opens in a new tab), M. L. Edwards and J. H. Sinsky, IEEE Transactions on Microwave Theory and Techniques, vol. 40, no. 12, pp. 2303 to 2311, December 1992. The mu and mu-prime stability factors.
• S-Parameter Design, Application Note 154 (opens in a new tab), Keysight Technologies (originally Hewlett-Packard Application Note 154), undated Keysight reprint, document 5952-1087. S-parameter basics, gain, VSWR and stability for amplifier design.