Stable structures for nonlinear biquad filters

Biquad filters are a common tool for filter design. In this writing, we develop two structures for creating biquad filters with nonlinear elements. We provide conditions for the guaranteed stability of the nonlinear filters, and derive expressions for instantaneous pole analysis. Finally, we examine example filters built with these nonlinear structures, and show how the first nonlinear structure can be used in the context of analog modelling.