Scattering Parameters - Two-Port S-Parameters

Two-Port S-Parameters

The S-parameter matrix for the 2-port network is probably the most commonly used and serves as the basic building block for generating the higher order matrices for larger networks. In this case the relationship between the reflected, incident power waves and the S-parameter matrix is given by:

Expanding the matrices into equations gives:

and

Each equation gives the relationship between the reflected and incident power waves at each of the network ports, 1 and 2, in terms of the network's individual S-parameters, and . If one considers an incident power wave at port 1 there may result from it waves exiting from either port 1 itself or port 2 . However if, according to the definition of S-parameters, port 2 is terminated in a load identical to the system impedance then, by the maximum power transfer theorem, will be totally absorbed making equal to zero. Therefore

and

Similarly, if port 1 is terminated in the system impedance then becomes zero, giving

and

Each 2-port S-parameter has the following generic descriptions:

is the input port voltage reflection coefficient

is the reverse voltage gain

is the forward voltage gain

is the output port voltage reflection coefficient