A generalized method for the derivation of non-linear state-space models from circuit schematics

Digital emulation of analog circuits for musical audio processing, like synthesizers, guitar effect pedals, or vintage amplifiers, is an ongoing research topic. David Yeh proposed to use the nodal DK method to derive a non-linear state-space system from a circuit schematic in a very systematic way. However, this approach has some drawbacks and limitations, especially with respect to the modeling of individual circuit elements. Therefore, in this paper, we present an alternative that is more flexible than the nodal DK method and hopefully allows for easier integration of almost arbitrary element models. This flexibility and generality in our opinion outweighs the relatively small cost associated with it in terms of increased matrix sizes. We therefore believe the proposed method to be a useful tool for circuit simulation.