Analytic investigations on the susceptibility of nonlinear
analog circuits to substrate noise

Abstract. This work deals with the conducted susceptibility of nonlinear analog circuits with respect to substrate noise. The substrate coupling mechanism is modeled by a passive three-terminal network that is obtained by means of the finite element method with a subsequently performed model order reduction. Applying this substrate model to the bulk terminal of MOS transistors in integrated analog circuits, it is possible to examine the influence of substrate noise on the circuit's functionality. By means of a block-oriented approach, analytic expressions for the output behavior of the circuits are found. The utilized multi-input Wiener model separates the linear dynamic from the nonlinear static circuit properties. Due to this separation the frequency response of both signals, i.e.,input signal and substrate noise, respectively, can be identified, and hence, the frequency range in which the circuit is most susceptible to substrate noise. Since the nonlinear static behavior of each MOS transistor depends on two signals, truncated multivariate Taylor series expansions of the nonlinear elements are performed on the basis of the EKV model description (Enz et al., 1995). The proposed modeling is illustrated by a simple example.