In the context of electrical engineering and microwave systems, a four-port network can be represented using S-parameters (scattering parameters). S-parameters describe the relationship between the incident and reflected electromagnetic waves at the ports of a network. For a four-port network, the S-parameters are arranged in a matrix form known as the S-matrix.
The S-matrix for a four-port network has the following form:
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[ b1 ] = [ S11 S12 ] [ a1 ]
[ b2 ] [ S21 S22 ] [ a2 ]
Where:
a1 and b1 represent the incident and reflected waves at Port 1.
a2 and b2 represent the incident and reflected waves at Port 2.
S11, S12, S21, and S22 are the S-parameters of the network.
Here's what each S-parameter represents:
S11: Also known as the "input reflection coefficient" or "reverse transmission coefficient," this parameter represents the portion of the incident wave at Port 1 that is reflected back towards Port 1 when Port 2 is terminated with a matched load (matched impedance).
S12: Also known as the "reverse transmission coefficient," this parameter represents the portion of the incident wave at Port 1 that is transmitted to Port 2 when Port 2 is terminated with a matched load.
S21: Also known as the "forward transmission coefficient," this parameter represents the portion of the incident wave at Port 2 that is transmitted to Port 1 when Port 1 is terminated with a matched load.
S22: Also known as the "output reflection coefficient" or "forward reflection coefficient," this parameter represents the portion of the incident wave at Port 2 that is reflected back towards Port 2 when Port 1 is terminated with a matched load.
These S-parameters are frequency-dependent, meaning their values may change with the frequency of the input signals. In practice, these parameters are often obtained through measurements or simulations using specialized equipment or electromagnetic simulation tools.
S-parameters are widely used in the design and analysis of microwave circuits, antennas, and communication systems, as they provide a convenient way to understand and characterize the behavior of multi-port networks.