# scattering parameter

Scattering parameters, S-parameters, are frequency-dependent parameters of high-frequency circuits, components, devices and systems and represent the transmission values and reflection values from the inputs and the outputs. S-parameters are expressed as complex numbers in magnitude and phase, magnitude in decibels( dB), phase in angular degrees. They are dimensionless and are subject to a given nomenclature. This nomenclature depends on the number of ports, respectively the number of ports.

A single port is a device with two connections, a two-pole, and is described by a single scattering parameter (S11). A two-port corresponds to a four-port and is described by four S-parameters, S11, S21, S12, and S22. This can be used to describe most circuits and RF modules. A three-port is described by the nine S-parameters S11, S12, S13, S21, S22, S23, S31, S32 and S33 and a four-port by sixteen S-parameters.

The S-parameter S11 represents the input reflection coefficient at matched output. It represents the characteristic impedancematching of the input to the impedance of the test lead, which is 50 ohms or 75 ohms.

A low S11 value tells that the return loss is low. S21 corresponds to the forward transmission factor with matched output. This is the transmission and therefore the insertion loss or gain that a multipole causes. If an amplifier is present in the circuit, then S21 may indicate gain (i.e., S21 > 0 dB). This means that, for example, if there is 1 W of power at input port port 1, there will be more than 1 W of power at output port 2. S12 is the reverse transmission factor with matched input. It corresponds to S-parameter S21 for passive components with bidirectional characteristics. And S22 is the output reflection coefficient at matched input and thus the matching of the output to the impedance of the measurement system.

Scattering parameters are measured with network analyzers( NWA), they are displayed in Smith charts.