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S-Parameters have been with us a long time but few of us really have a good feel for them. A modern RF engineer would be "up the creek" if he or she could not manipulate / use / and understand s-parameters.

This page provides links to s-parameter tutorials, application examples, s-parameter tools / demos and manufacturer's s-parameter data files. We hope you will find enough material here to help you get over any "fear" of this important subject!


Contents of This Page

S-Parameters Explained
S-Parameter Tutorials
S-Parameter Application Examples
S-Parameter Tools & Demos
S-Parameter Files
Reference Books on S-Parameters
Explore SSS Online

See Also: Smith Chart Stuff

See Also:
RF Globalnet
RF Globalnet's Demo Software Files
Page with Lots of FREE Design, Analysis and
Modeling "Goodies" inclucing APLAC and RFCAD!

S-Parameters Explained

Tutorial on S-Parameters
Scattering Parameters, or s-parameters, are the reflection and transmission coefficients between the incident and reflection waves. They describe completely the behavior of a device under linear conditions at microwave frequency range. Each parameter is typically characterized by magnitude, decibel and phase. The expression in decibel is 20log(Sij) because s-parameters are voltage ratios of the waves.

S11: input reflection coefficient of 50W terminated output.
S21: forward transmission coefficient of 50W terminated output.
S12: reverse transmission coefficient of 50W terminated input.
S22: output reflection coefficient of 50W terminated input.

The advantage of s-parameters does not only lie in the complete description of the device performance at microwave frequencies but also the ability to convert to other parameters such as hybrid (H) or admittance (Y) parameters. Additionally, stability factor (K) and many gain parameters can be computed using the following equations:

   Stability Factor, K:
     1 + |S11 * S22 - S12 * S21|2 - |S11|2 - |S22|2
K = ---------------------------------------------- 2|S12| * |S21|
   Maximum Stable Gain, MSG
MSG = -----    (if K < 1)

   Maximum Available Gain, MAG
MAG = ----- * (K - SQR(K2 - 1))  (if K > 1)
   MAXIMUM Unilateral Transducer Power Gain, Gu
Gu = ---------------------------
     (1 - |S11|2) * (1 - |S22|2)
   Forward Current Gain, h21
                  - S21
h21 = ---------------------------------
      (1 - S11) * (1 + S22) + S12 * S21

Thanks to OKI for this note!

For another good definition of S-parameters, see National Instruments definition.

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S-Parameter Tutorials

Download Agilent's Classic S-Parameter Interactive Tutorial (1400K -- pdf + QT Movie)

Download Agilent's Classic S-Parameter Interactive Tutorial (1300K -- pdf file only)

Download another Agilent Application Note on S-Parameters (843K)

A short tutorial/definition of S-Parameters from National Instruments

"Converting S-Parameters to Y-Parameters," — winter 2001 article from

"Measuring S-Parameters," — winter 2001 article from

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S-Parameter Application Examples:

Agilent's Wireless Design Tips, including application notes and other literature to help the designer. To get here from the link, press "Library" in the small blue box, then "Wireless Library" and scroll down to the bottom

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S-Parameter Tools & Demos:

SSS Online's Software Downloads Index

Mathworks section on how to Model a nonlinear amplifier using its S-parameters


Agilent's Interactive JAVA-based "Impedance Matching Game"

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S-Parameter Files:

Agilent logo

Download Agilent's RF & Microwave S-Parameter Data Files. From this link, press "Library" in the small navy box, the "Wireless Library"; then scroll down the page to "Models" and follow the link to S-Parameter files.


Download RF Micro Devices' RF & Microwave S-Parameter Data Files

Murata S-Parameter Download Service

Coilcraft S-Parameter and PSPICE Model Files

Minicircuits S-Parameters

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Reference Books on S-Parameters:

Click on a Title Below for a Direct Link to Purchase


Microwave Differential Circuit Design Using Mixed Mode S-Parameters , by William R. Eisenstadt, Bob Stengel, & Bruce M. Thompson. Hardcover - 244 pages (May 1, 2006).


Network Scattering Parameters (Advanced Series in Circuits and Systems, Vol 2) , by R. Mavaddat. Hardcover (June 1996).


Electromagnetic Waves in Stratified Media (Ieee/Oup Series on Electromagnetic Wave Theory), by James R. Wait. Hardcover - 372 pages Reprint edition (July 1995).


Microwave Circuit Design Using Linear and Nonlinear Techniques , by George Vendelin, Anthony M. Pavio, & Ulrich L. Rohde. Paperback - 784 pages Reprint edition (May 1992).

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Design of Amplifiers and Oscillators by the S-Parameter Method , by George D. Vendelin. Hardcover, 190 pages (January, 1982).


Microwave Field-Effect Transistors : Theory, Design, and Applications , by Raymond S. Pengelly. Hardcover 3rd edition (December 1995).

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