SParameter

S-parameters, or scattering parameters, are a set of measures used to describe how radio frequency and microwave networks respond to incident signals at their ports. They express how much of an incoming wave at one port is reflected back or transmitted to other ports, under a defined reference impedance Z0. S-parameters are defined for linear, time-invariant networks and are typically evaluated in the frequency domain.

In a multi-port network, the incident waves at each port are denoted a_k and the reflected waves b_k. The relationship between the vectors b and a is b = S a, where S is the S-parameter matrix. For a two-port network, the elements S11, S21, S12, and S22 quantify input reflection, forward transmission, reverse transmission, and output reflection, respectively. S-parameters are generally complex-valued, containing both magnitude and phase, and are frequency dependent.

Measurement and use of S-parameters rely on vector network analyzers (VNAs) and careful calibration to reference the response to a chosen impedance Z0, commonly 50 ohms. Results are reported as magnitudes and angles, or in decibels and degrees. S-parameters are especially convenient for high-frequency design because they preserve linear superposition and are directly related to power exchange when ports are matched.

Key properties include reciprocity (S12 = S21 for reciprocal networks) and the ability to convert between parameter sets, such as Z, Y, and ABCD parameters, via Z0-dependent transformations. S-parameters are widely used to characterize antennas, filters, amplifiers, transmission lines, and other RF components, providing a compact, frequency-specific description of their behavior under matched conditions.