Wave digital filter modeling of circuits with operational amplifiers

IEEE/ACM Trans. Audio Speech Lang. Process.

Maffezzoni

Sarti

2019

There is a growing interest in Virtual Analog modeling algorithms for musical audio processing designed in the Wave Digital (WD) domain. Such algorithms typically employ a discretization strategy based on the trapezoidal rule with fixed sampling step, though this is not the only option. In fact, alternative discretization strategies (possibly with an adaptive sampling step) can be quite advantageous, particularly when dealing with nonlinear systems characterized by stiff equations. In this article, we propose a unified approach for modeling capacitors and inductors in the WD domain using generic linear multi-step discretization methods with variable time-step size, and provide generalized adaptation conditions. We also show that the proposed approach for implementing dynamic (energystoring) elements in the WD domain is particularly suitable to be combined with a recently developed technique for efficiently solving a class of circuits with multiple one-port nonlinearities, called Scattering Iterative Method. Finally, as examples of application, we develop WD models for a Van Der Pol oscillator and a dynamic diode-based ring modulator, which use different discretization methods.

“…1; i.e., applying the scattering relations (17) or (19), respectively. In case of adaptation, the simplified scattering relations (18) or (20) can be directly used.…”

Section: General Wd Models Of Dynamic Elements Based On Lmsdmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linear Multistep Discretization Methods With Variable Step-Size in Nonlinear Wave Digital Structures for Virtual Analog Modeling

IEEE/ACM Trans. Audio Speech Lang. Process.

Maffezzoni

Sarti

2019

“…As an example, the stamps corresponding to port A are highlighted in light gray and the stamps corresponding to the nullor are highlighted in dark gray. Although we have chosen to model the op-amp with a nullor, consider modeling it with a VCVS as a thought experiment [33]. The procedure would be identical although the VCVS stamp from Tab.…”

Section: B Frequency Booster Pedalmentioning

confidence: 99%

“…The circuit comprises 5 capacitors (C z and C a · · · C e ), 7 resistors (R 0 , R a , and R c · · · R h ), a potentiometer (R b ) controlling the boost amount, an op-amp, and a battery (dc ideal voltage source V b ). The op-amp is configured in negative feedback and modeled as ideal using a nullor [33]. 1) WDF Model: A graph representing the circuit is shown in Fig.…”

Section: B Frequency Booster Pedalmentioning

confidence: 99%

“…This greatly expanded the class of circuits that could be modeled with WDFs. Audio circuits that were previously intractable using WDFs, including the op-amp-based tone stage from the Ibanez Tube Screamer [25], simplified analog drum machine voices [33], the Hammond Organ vibrato/chorus [34], [35], op-amp-based Sallen-Key filters [36], [37], operationaltransconductance-amplifier-based state variable filters [38], and filters based around linearized emitter followers [39] have been modeled using this approach.…”

Section: Scattering Of Non-reciprocal Junctionsmentioning

confidence: 99%

See 1 more Smart Citation

Modeling Circuits With Arbitrary Topologies and Active Linear Multiports Using Wave Digital Filters

Werner

IEEE Trans. Circuits Syst. I

Smith

et al. 2018

Self Cite

Abstract-The Wave Digital Filter (WDF) technique derives digital filters from analog prototypes which classically have been restricted to passive circuits with series/parallel topologies. Since most audio circuits contain active elements (e.g., opamps) and complex topologies, WDFs have only had limited use in Virtual Analog modeling. In this article we extend the WDF approach to accommodate the unbounded class of nonseries/parallel junctions which may absorb linear multiports. We present four Modified-Nodal-Analysis-based scattering matrix derivations for these junctions, using parametric waves with voltage, power, and current waves as particular cases. Three derivations afford implementations whose cost in multiplies are lower than multiplying by the scattering matrix. Negative port resistances may be needed in WDF modeling of active circuits, restricting the WDF to voltage or current waves. We propose two techniques for localizing this restriction. Case studies on the Baxandall tone circuit and a "Frequency Booster" guitar pedal demonstrate the proposed techniques in action.

Advances in Wave Digital Modeling of Linear and Nonlinear Systems: A Summary

Special Topics in Information Technology

2019

This brief summarizes some of the main research results that I obtained during the three years, ranging from November 2015 to October 2018, as a Ph.D. student at Politecnico di Milano under the supervision of Professor Augusto Sarti, and that are contained in my doctoral dissertation, entitled "Advances in Wave Digital Modeling of Linear and Nonlinear Systems". The thesis provides contributions to all the main aspects of Wave Digital (WD) modeling of lumped systems: it introduces generalized definitions of wave variables; it presents novel WD models of one-and multi-port linear and nonlinear circuit elements; it discusses systematic techniques for the WD implementation of arbitrary connection networks and it describes a novel iterative method for the implementation of circuits with multiple nonlinear elements. Though WD methods usually focus on the discrete-time implementation of analog audio circuits; the methodologies addressed in the thesis are general enough as to be applicable to whatever system that can be described by an equivalent electric circuit.