Theory of weakly non-linear noisy systems

This paper gives a treatment of the theory of noise in general non-linear multiport systems by use of the Volterra series representation. Expressions for the response of a non-linear noisy (N + l)-port system with N signal input ports and one output port under excitation of noise and a deterministic signal at each input port are determined. Noise generated in the system itself is accounted for by equivalent random variable noise voltage or current generators. These internal noise generators are extracted from the system and applied at separate external ports. A noise-free equivalent of the noisy system is obtained with N signal input ports and Q – I input ports accounting for the systemgenerated noise. the Volterra series representation is used to describe the input-output response relation of the system. Once the Volterra transfer functions of the system are determined and cross-and autocorrelations of the noise generators are specified, it is possible to determine the noise performance of the system under arbitrary noise and deterministic signal excitation. the investigation leads to the determination of expressions for the equivalent average exchangeable output noise power density and the average output noise power flow from the system. Expressions for the noise power densitypand the noise power flow at the load of the non-linear system are determined. As an example of the theory an expression is derived for the effective input noise temperature of a non-linear system.