Virtual Analog Modeling of Nonlinear Musical Circuits

Recent advances in semiconductor technology eventually allowed for affordable and pragmatic implementations of sound processing algorithms based on physical laws, leading to considerable interest towards research in this area and vast amounts of literature being published in the last two decades. As of today, despite the efforts invested by the academic community and the music technology industry, new or better mathematical and computational tools are called for to efficiently cope with a relatively large subset of the investigated problem domain. This is especially true of those analog devices that inherently need to be studied by lumped nonlinear models. This research is, in this sense, directed towards both general techniques and specific problems. The first part of this thesis presents a generalization of the wave digital filter (WDF) theory to enable interconnections among subnetworks using different polarity and sign conventions. It proposes two new non-energic two-port WDF adaptors, as well as an extension to the definitions of absorbed instantaneous and steady-state pseudopower. This technique eventually removes the need to remodel subcircuits exhibiting asymmetrical behavior. Its correctness is also verified in a case study. Furthermore, a novel, general, and non-iterative delay-free loop implementation method for nonlinear filters is presented that preserves their linear response around a chosen operating point and that requires minimal topology modifications and no transformation of nonlinearities. In the second part of this work, five nonlinear analog devices are analyzed in depth, namely the common-cathode triode stage, two guitar distortion circuits, the Buchla lowpass gate, and a generalized version of the Moog ladder filter. For each of them, new real-time simulators are defined that accurately reproduce their behavior in the digital domain. The first three devices are modeled by means of WDFs with a special emphasis on faithful emulation of their distortion characteristics, while the last two are described by novelly-derived systems in Kirchhoff variables with focus on retaining the linear response of the circuits. The entirety of the proposed algorithms is suitable for real-time execution on computers, mobile electronic devices, and embedded DSP systems.