Scattering parameters describes the input-output relationships between ports in an electrical system. Specifically at high frequency it becomes essential to describe a given network in terms of waves rather than voltage or current. Thus in S-parameters we use power waves.

In RF design, we cant use other parameters for analysis such as Z,Y,H parameters as we can't do short circuit and open circuit analysis as it is not feasible.

For a two port network, s-parameters can be defined as

S11 is the input port voltage reflection coefficient

S12 is the reverse voltage gain

S21 is the forward voltage gain

S22 is the output port voltage reflection coefficient

The S-parameter matrix can be used to determine reflection coefficients and transmission gains from both sides of a two port network. This concept can further be used to determine s-parameters of a multi port network. 

These concepts can further be used in determining Gain, Return loss, VSWR and Insertion Loss.

Return Loss can be thought of as a measure of how close the actual input/output impedance of the network is to the nominal system impedance value.

VSWR is defined as,                                 VSWR

S-parameters (or scattering parameters) are used to describe how energy can propagate through an electric network. S-Parameters are used to describe the relationship between different ports, when it becomes especially important to describe a network in terms of amplitude and phase versus frequencies, rather than voltages and currents. S-Parameters are used to show a complicated network as a simple black box, and to easily present what happens to the signal in that network.

The S-parameters can be saved e.g. as a S4P-file that contains all the combinations of the reflection and transmissions in a network, and this shows how the device under test behaves with a signal in both forward and reverse directions.