Nonlinear Interference Effects in EMC

Receiver systems are normally described in terms of operating frequencies, bandwidth, type of modulation, sensitivity, and dynamic range. Such considerations are based upon intended receiver operation. However, they do not take into account the unintentional nonlinearities that exist in actual receivers. This tutorial is devoted to a discussion and analysis of unintended nonlinear interference effects which can result in susceptibility of a receiver to undesired signals. The tutorial begins with a discussion of nonlinearities that arise in passive and active components. Equivalence between nonlinear component characteristics and time-variant parameters such as resistance, capacitance, and inductance are pointed out. Nonlinear phenomena of importance to EMC engineers are then described. In particular, consideration is given to harmonic generation, gain compression/expansion, intermodulation, spurious responses, cross modulation, and desensitization. Cochannel, adjacent channel, and out of band signals are defined in the context of the super heterodyne receiver. Equations for average power in the sinusoidal steady-state are developed and the linear power gain of an amplifier is derived. The classical power series approach for analysis of weakly nonlinear receivers is then introduced where the model consists of a zero-memory nonlinearity preceded and followed by a linear filter. Expressions are obtained for the linear power gain of the classical model and the third-order intermodulation power as a function of the third-order intermodulation coefficient. The third-order intercept point is defined and the relationship between the third-order intermodulation coefficient and third-order intercept point is obtained. After deriving an expression for gain compression/expansion, the relationship between the 1-dB gain compression point and third-order intercept point is developed. Expressions for the two-signal spurious-free dynamic range are also derived. Shortcomings of the classical power series approach are then discussed. To provide background for the more general Volterra series approach, a derivation of the convolution integral for linear circuits is provided. This is then extended to weakly nonlinear circuits resulting in their Volterra series representation. It is shown that weakly nonlinear circuits can be modeled in the time domain by their nonlinear impulse responses and in the frequency domain by their nonlinear transfer functions.