In the context of electrical engineering and RF/microwave systems, a three-port network can be represented using S-parameters (Scattering Parameters). S-parameters are a set of parameters used to describe the behavior of linear electrical networks in the frequency domain.
A three-port network has three ports, and it can be represented by a 3x3 S-parameter matrix, known as the S-matrix. The S-matrix relates the incident and reflected waves at each port, and it can be defined as follows:
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[ V1 ] [ S11 S12 S13 ] [ V1 ]
[ V2 ] = [ S21 S22 S23 ] * [ V2 ]
[ V3 ] [ S31 S32 S33 ] [ V3 ]
Where:
V1, V2, and V3 are the voltage waves incident at ports 1, 2, and 3, respectively.
S11, S12, S13, S21, S22, S23, S31, S32, and S33 are the S-parameters of the network.
The S-parameters are defined as follows:
S11: The reflection coefficient at port 1 when only a wave is incident at port 1.
S12: The transmission coefficient from port 1 to port 2 when a wave is incident at port 1.
S13: The transmission coefficient from port 1 to port 3 when a wave is incident at port 1.
S21: The transmission coefficient from port 2 to port 1 when a wave is incident at port 2.
S22: The reflection coefficient at port 2 when only a wave is incident at port 2.
S23: The transmission coefficient from port 2 to port 3 when a wave is incident at port 2.
S31: The transmission coefficient from port 3 to port 1 when a wave is incident at port 3.
S32: The transmission coefficient from port 3 to port 2 when a wave is incident at port 3.
S33: The reflection coefficient at port 3 when only a wave is incident at port 3.
It's important to note that the S-parameters are typically measured or simulated at a specific frequency, and the network's behavior may vary with frequency.
With the S-matrix, you can analyze and predict the behavior of the three-port network, including the power transfer, reflection, and isolation between ports at the specific frequency of interest. S-parameters are widely used in RF/microwave engineering for designing and characterizing components like amplifiers, filters, mixers, and other networks.