SParametern

SParametern is a term used in electrical engineering to denote the set of scattering parameters that describe how an electrical network interacts with incident signals at its ports. It is most commonly applied to linear, time-invariant networks in the RF and microwave domain, though the concept has been extended in modern practice to address nonlinear or time-varying systems.

For an N-port network, the incident waves a_q and the reflected waves b_p are defined at frequency f. The relationship b_p(f) = sum_q S_pq(f) a_q(f) holds in the linear, single-frequency case, where S(f) is the scattering matrix. The element S_pq is the complex ratio of the reflected wave at port p due to an excitation at port q, with diagonal elements S_pp representing reflections and off-diagonal elements S_pq representing transmissions.

Extensions: In nonlinear or time-varying networks, linear S-parameters are generalized to multi-tone or harmonic S-parameters, requiring higher-order descriptions or Volterra kernels. These parameters capture how power at one frequency can generate responses at other frequencies.

Measurement: SParametern are measured with vector network analyzers (VNAs) using calibration methods such as SOLT or TRL to de-embed reference planes. They are reported as magnitude and phase across frequency and are used to derive metrics like return loss, insertion loss, and isolation.

Applications and limitations: They underpin the design and analysis of RF components such as filters, couplers, amplifiers, and antennas. The main limitations are the linear, time-invariant assumption and sensitivity to calibration, connection quality, and temperature. See also S-parameters, vector network analyzer, SOLT, TRL calibration.