The Composition Rule for Multivariate Volterra Operators and its Application to Circuit Analysis

The work generalizes the composition rule for single-input-single-output Volterra operators to the multivariate case applying the Kronecker product formalism. The formalism allows a compact description of the composition of such operators. The composition of multivariate functions is briefly discussed and represents the starting point of the analysis. Based on the derived composition rule, a novel nonlinear generalization of the classical modified nodal analysis (MNA) is introduced, namely the multilinear MNA. It allows to automatically extract the higher order frequency domain Volterra kernels of a weakly nonlinear analog circuit and just involves sparse matrix multiplications and Kronecker products