Nyquist's and Thevenin's Theorems Generalized for Nonreciprocal Linear Networks

It is shown that an N-node nonreciprocal linear network, with a system of internal thermal noise generators at temperature T, is equivalent to the source-free network together with a set of correlated nodal current generators, with infinite internal impedance, such that 〈iris*〉Avdν=2kT(yrs+ysr*)dν where yrs is an element of the network admittance matrix and ir is the rth nodal noise current with frequency v. The noise sources can also be represented by a system of nodal voltage generators, with infinite internal admittance, such that 〈vrvs*〉Avdν=2kT(zrs+zsr*)dν. The application of these results to a system of coupled antennas in an equi-thermal enclosure is noted and necessary conditions for the realizability of passive nonreciprocal networks are derived.