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 ${\mathrm{〈i}}_r{i}_s^{*}{〉}_{\mathrm{Av}}{\text{dν=2kT(y}}_{\mathrm{rs}}{\mathrm{+y}}_{\mathrm{sr}}^{*}\mathrm{)d\nu }$ where y_rs is an element of the network admittance matrix and i_r 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 ${\mathrm{〈v}}_r{v}_s^{*}{〉}_{\mathrm{Av}}{\text{dν=2kT(z}}_{\mathrm{rs}}{\mathrm{+z}}_{\mathrm{sr}}^{*}\mathrm{)d\nu }$ . 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.