Sparametre

Sparametre, commonly known as S-parameters, are a set of parameters used to characterize the electrical behavior of linear networks at radio and microwave frequencies. They describe how incident signals at the ports of a network are reflected or transmitted, using complex amplitudes of propagating waves. For a two-port network, the S-parameter matrix consists of four complex numbers: S11, S21, S12, and S22. S11 is the reflection coefficient at port 1 with port 2 matched; S21 is the forward transmission from port 1 to port 2; S12 is the reverse transmission from port 2 to port 1; and S22 is the reflection coefficient at port 2 with port 1 matched. The quantities are frequency dependent and defined relative to a reference impedance Z0, typically 50 ohms in RF practice. In wave notation, the incident and reflected waves are labeled a1, a2 and b1, b2, with the relation b = S a.

S-parameters are particularly suited to linear, time-invariant networks and are widely used in RF and microwave engineering for components such as filters, amplifiers, antennas, and microwave interconnects. They are measured with a vector network analyzer (VNA) and require calibration to reference the measurements to the desired impedance, commonly using methods such as SOLT (short-open-load-through) or TRL.

Key properties include reciprocity and non-reciprocity. For passive reciprocal networks, S12 equals S21. For lossless networks, the S-matrix is unitary. In general, S-parameters can be transformed to other parameter sets, such as Z-parameters, Y-parameters, or ABCD-parameters, and are central to RF design and analysis.

Limitations include the assumptions of linearity, time invariance, and matched terminations; S-parameters provide an accurate description only within these conditions.