S-Parameter Reference

Free reference guide: S-Parameter Reference

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About S-Parameter Reference

The S-Parameter Reference is a comprehensive, searchable guide to RF and microwave scattering parameters. It covers the 2-port S-parameter matrix (S11, S21, S12, S22), dB conversions, return loss, VSWR, insertion loss, and mismatch loss calculations. Each parameter is defined with its measurement condition (e.g., a2=0 for S11) and practical quality thresholds such as S11 < -10 dB for good matching (VSWR < 2.0).

Organized into six categories -- Fundamentals, Conversions, Smith Chart, Impedance Matching, Touchstone, and Practical Reference -- this tool provides the formulas and visual concepts needed for RF circuit design. The Smith chart section explains normalized impedance and admittance reading, constant-VSWR circles, and series/parallel element movements, while the matching section covers L-network, Pi/T-network, and quarter-wave transformer design with step-by-step formulas.

Beyond theory, the reference includes practical engineering data: RF connector types with frequency ranges (SMA to 18 GHz, 2.4mm to 50 GHz, 1.0mm to 110 GHz), Rollett stability factor (K > 1) and mu-factor criteria, Friis cascade noise figure formula, mixed-mode S-parameters for differential signaling (USB, HDMI, PCIe), Touchstone v1/v2 file formats with MA/dB/RI options, and de-embedding techniques for removing fixture effects from measurements.

Key Features

Complete S-parameter definitions: S11 (input reflection), S21 (forward transmission/gain), S12 (reverse isolation), S22 (output reflection) with measurement conditions
Conversion formulas and tables for dB, return loss, VSWR, insertion loss, and mismatch loss with practical threshold values
Smith chart guide covering normalized impedance/admittance reading, chart positions (center=match, left=short, right=open), and constant-VSWR circles
Three impedance matching topologies: L-network (series+shunt) with Q-based formulas, Pi/T-networks for bandwidth control, and quarter-wave transformer (Z_T = sqrt(Z_in x Z_L))
Touchstone file format reference for v1 (.s2p) and v2 (.ts) including option line syntax, MA/dB/RI data formats, and multi-port support
RF connector specifications: BNC, SMA, 3.5mm, 2.92mm(K), 2.4mm, 1.85mm(V), 1.0mm(W), N-Type with impedance and frequency limits
Stability analysis with Rollett K-factor, mu-factor (single-parameter criterion), and cascade noise figure calculation using the Friis formula
Mixed-mode S-parameters (Sdd/Scc/Sdc/Scd) for differential signal analysis and de-embedding techniques for fixture removal

Frequently Asked Questions

What do S11 and S21 represent?

S11 is the input reflection coefficient (measured with port 2 matched), indicating impedance matching quality. S21 is the forward transmission coefficient, representing gain for amplifiers (e.g., S21 = 15 dB) or insertion loss for passive devices (e.g., S21 = -0.5 dB). Both are typically expressed in dB.

How do I convert between S11 and VSWR?

VSWR = (1 + |S11|) / (1 - |S11|). For example, S11 = -10 dB gives |S11| = 0.316, so VSWR = 1.316/0.684 = 1.92. The reference includes a complete conversion table from VSWR 1.0 (perfect match) to infinity (total reflection).

How do I read impedance on a Smith chart?

The center point (0,0) represents z=1+j0, which is a perfect 50-ohm match. The left end is a short circuit (z=0), the right end is an open circuit (z=infinity). The upper half represents inductive reactance (+jX) and the lower half capacitive reactance (-jX). Normalize any impedance by dividing by Z0 (typically 50 ohm).

When should I use an L-match vs Pi/T-match?

L-matching (series+shunt element) is simplest but has a fixed Q determined by the impedance ratio. Pi-network (shunt-series-shunt) and T-network (series-shunt-series) allow independent Q selection, enabling bandwidth control. Use Pi/T when you need a wider or narrower bandwidth than the L-match provides.

What is the Touchstone file format?

Touchstone (.s1p, .s2p, .snp) is the standard file format for S-parameter data. The option line specifies frequency units (Hz/kHz/MHz/GHz), parameter type (S/Y/Z), data format (MA=magnitude-angle, dB=dB-angle, RI=real-imaginary), and reference impedance (typically 50 ohm). Version 2.0 adds multi-port and mixed-mode support.

How do I determine if an RF amplifier is unconditionally stable?

Calculate the Rollett stability factor K and determinant Delta. If K > 1 AND |Delta| < 1, the amplifier is unconditionally stable. Alternatively, use the single mu-factor: mu > 1 means unconditionally stable. The reference includes both formulas and their relationship to S-parameters.

What is the Friis cascade noise figure formula?

F_total = F1 + (F2-1)/G1 + (F3-1)/(G1*G2) + ... This shows that the first stage (usually an LNA) dominates the total noise figure. For example, an LNA with NF=1dB and G=20dB followed by a mixer with NF=8dB gives a total NF of only 1.18 dB.

What are mixed-mode S-parameters used for?

Mixed-mode S-parameters decompose 4-port measurements into differential (Sdd), common-mode (Scc), and mode-conversion (Sdc/Scd) components. They are essential for characterizing differential signal interfaces like USB, HDMI, and PCIe, where Sdd21 represents the desired differential transmission and Sdc/Scd indicate unwanted mode conversion.