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S11 and S21 Explained: Reading Touchstone S-Parameter Files

S11 tells you what comes back at port 1; S21 tells you what reaches port 2. Both are complex ratios measured or simulated over frequency. A Touchstone file stores the frequency points, format and reference impedances needed to interpret them. Read those before comparing the plot with a board or interface requirement. ^{[1, 2]}

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Four numbers for a two-port network

Term	Question it answers
S11	How much of a wave entering port 1 is reflected there?
S21	How much of that wave reaches port 2?
S12	How much passes from port 2 back to port 1?
S22	How much of a wave entering port 2 is reflected there?

For a passive, reciprocal connector S21 and S12 should agree apart from measurement or model error. S11 and S22 can differ when the launch geometry differs at the two ends. The file's port reference, often 50 Ω for single-ended ports, defines what a match means. ^{[1, 2]}

Reading decibels without swapping the sign

A network analyser often plots 20 log₁₀|S11| and 20 log₁₀|S21|, so a passive network appears at negative dB. Positive return loss and insertion loss are the negatives of those readings: RL = −20 log₁₀|S11| and IL = −20 log₁₀|S21|. If S11 is −20 dB, the reflected power is |S11|² = 1%; if S21 is −1 dB, the forward power ratio under the file's matched-port conditions is 10^−1/10 ≈ 79.4%. The other 19.6% is not automatically cable loss; reflection and other paths must be considered too. ^{[2, 3]}

Open an .s2p or .s4p file and inspect the markers →

The common .s2p trap: order and reference

For the conventional two-port Touchstone layout, the four data pairs are ordered S11, S21, S12, S22, not row-major S11, S12, S21, S22. Touchstone 2.x can explicitly declare either order. The option line also says whether each complex value is real/imaginary (RI), magnitude/angle (MA) or dB/angle (DB), and gives the frequency unit and reference resistance. Ignoring either line can put a perfectly good connector model on the wrong plot. ^[1]

For a differential pair, use the differential response

A four-port model has single-ended S-parameters for two conductors at each end. Its differential through term SDD21 is formed from a combination of those terms with the correct port pairing; it is not just one single-ended S21. Check the pin-to-port mapping supplied with the model. The viewer can show SDD21 and differential-to-common-mode conversion for a 4-port file, but a wrong pairing makes even a sound channel look broken. ^[1]

What the file includes

An S-parameter file describes the network between its calibration or simulation reference planes. A connector model may include its launch; a measured board file may include test fixtures until they are de-embedded. The plot cannot tell you which structures were included. Read the model documentation before adding its insertion loss to a separately estimated PCB trace loss or claiming that a whole channel passes an interface budget. ^{[3, 4]}

Tools used in this guide

S-Parameter Viewer (.s2p, .s4p) – Open .s1p to .s16p Touchstone files in the browser: insertion and return loss, phase, group delay, mixed-mode SDD21/SCD21 for 4-ports, TDR impedance and interface loss budgets.
Interface Design Rules – Impedance, skew, loss budget and length limits of PCIe, USB, Ethernet, HDMI, DDR and other interfaces, applied to a layer of your own stackup with the field solver.
Trace Loss (Insertion Loss) Calculator – Insertion loss in dB/in and over the full length: conductor loss with copper roughness and dielectric loss from the field solver, with laminate Dk/Df across frequency.

Sources

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