Generalized Moog Ladder Filter: Part II–Explicit Nonlinear Model through a Novel Delay-Free Loop Implementation Method

Abstract

One of the most critical aspects of virtual analog simulation of circuits for music production consists in accurate reproduction of their nonlinear behavior, yet this goal is in many cases difficult to achieve due to the presence of implicit differential equations in circuit models, since they naturally map to delay-free loops in the digital domain. This paper presents a novel and general method for non-iteratively implementing these loops in such a way that the linear response around a chosen operating point is preserved, the topology is minimally affected, and transformation of nonlinearities is not required. This technique is then applied to a generalized model of the Moog ladder filter, resulting in an implementation that outperforms its predecessors with only a modest computational load penalty. This digital version of the filter is shown to offer strong stability guarantees w.r.t. parameter variation, allows the extraction of different frequency response modes by simple mixing of individual ladder stage outputs, and is suitable for real-time sound synthesis and audio effects processing.