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Scattering Matrix (Other features (Change of reference impedances (One…
Scattering Matrix
Definition
A matrix used to describe the electrical state of a two-port device, made up by distributed parameters
Distributed elements
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N-port devices
b parameters depends on the a parameters through the scattering values; the "z" axis is always oriented toward the device
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Lumped elements
Two different matrices:
- Open circuit impedance matrix
- Short circuit admittance matrix
Different properties:
- In case of lossless devices, the matrix values are pure imaginary
- In case of reciprocal devices, the matrices are symmetrical
- The power absorbed by the device is the sum of the power flowing toward the port
Scattering values
Terms on the main diagonal are reflection coefficients at port "i" when the other ports are closed on reference impedances
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Properties
- Reciprocal devices → symmetrical scattering matrices
- Lossless devices → unitary scattering matrices
- Passive devices → all the eigenvalues of
have a magnitude less than "1"
- Active devices → at least one eigenvalue of
has magnitude greater than "1"
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Transmission matrix
Describes the electrical state on the edges of a device, using one "z" axis for the two sides
(the device is characterized by the same number "N" of input/output ports)
If two devices are connected, the whole device transmission matrix is defined as the matrix product between transmission matrices of the single devices
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