Scattering parameters

Scattering parameters or S-parameters (the elements of a scattering matrix or S-matrix) describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals.

The parameters are useful for several branches of electrical engineering, including electronics, communication systems design, and especially for microwave engineering.

The S-parameters are members of a family of similar parameters, other examples being: Y-parameters,^[1] Z-parameters,^[2] H-parameters, T-parameters or ABCD-parameters.^[3]^[4] They differ from these, in the sense that S-parameters do not use open or short circuit conditions to characterize a linear electrical network; instead, matched loads are used. These terminations are much easier to use at high signal frequencies than open-circuit and short-circuit terminations. Contrary to popular belief, the quantities are not measured in terms of power (except in now-obsolete six-port network analyzers). Modern vector network analyzers measure amplitude and phase of voltage traveling wave phasors using essentially the same circuit as that used for the demodulation of digitally modulated wireless signals.

Many electrical properties of networks of components (inductors, capacitors, resistors) may be expressed using S-parameters, such as gain, return loss, voltage standing wave ratio (VSWR), reflection coefficient and amplifier stability. The term 'scattering' is more common to optical engineering than RF engineering, referring to the effect observed when a plane electromagnetic wave is incident on an obstruction or passes across dissimilar dielectric media. In the context of S-parameters, scattering refers to the way in which the traveling currents and voltages in a transmission line are affected when they meet a discontinuity caused by the insertion of a network into the transmission line. This is equivalent to the wave meeting an impedance differing from the line's characteristic impedance.

Although applicable at any frequency, S-parameters are mostly used for networks operating at radio frequency (RF) and microwave frequencies. S-parameters in common use - the conventional S-parameters - are linear quantities (not power quantities, as in the below mentioned 'power waves' approach by Kaneyuki Kurokawa [ja] (黒川兼行)). S-parameters change with the measurement frequency, so frequency must be specified for any S-parameter measurements stated, in addition to the characteristic impedance or system impedance.

S-parameters are readily represented in matrix form and obey the rules of matrix algebra.

^ Pozar, David M. (2005); Microwave Engineering, Third Edition (Intl. Ed.); John Wiley & Sons, Inc.; pp. 170–174. ISBN 0-471-44878-8.
^ Pozar, David M. (2005) (op. cit.); pp. 170–174.
^ Pozar, David M. (2005) (op. cit.); pp. 183–186.
^ Morton, A. H. (1985); Advanced Electrical Engineering; Pitman Publishing Ltd.; pp. 33–72. ISBN 0-273-40172-6.

[1] Pozar, David M. (2005); Microwave Engineering, Third Edition (Intl. Ed.); John Wiley & Sons, Inc.; pp. 170–174. ISBN 0-471-44878-8.

[2] Pozar, David M. (2005) (op. cit.); pp. 170–174.

[3] Pozar, David M. (2005) (op. cit.); pp. 183–186.

[4] Morton, A. H. (1985); Advanced Electrical Engineering; Pitman Publishing Ltd.; pp. 33–72. ISBN 0-273-40172-6.

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