An isolator is a one-way two-port, transporting incoming waves lossless from the input (port 1) to the output (port 2), but dissipating all waves flowing into the output. The ideal isolator with reference impedances (input) and (output) is determined by the following Z parameters (for DC and AC simulation).
A more useful MNA representation is with Y parameters.
Isolator with reference impedance (input) and (output) and temperature :
With the reference impedance of the input and the one of the output , the scattering parameters of an ideal isolator writes as follows.
Being on temperature , the noise wave correlation matrix of an ideal isolator with reference impedance and (input and output) writes as follows.