Modeling nonlinear wave digital elements using the Lambert function

Bernardini, Alberto; Werner, Kurt James; Sarti, Augusto; Smith, Julius O.

doi:10.1109/tcsi.2016.2573119

Cited by 34 publications

(29 citation statements)

References 28 publications

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“…As (10) is a transcendental equation, the derivation of a wave mapping is not straightforward. A closed-form scattering relation involving the Lambert function can be found using the approach described in [28]. Another possible efficient approach, which uses a one-dimensional Newton-Raphson (NR) solver, is explained in [8] and reported hereafter.…”

Section: B Modeling One-port Memoryless Circuit Elementsmentioning

confidence: 99%

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

Bernardini

Maffezzoni

Sarti

2019

IEEE/ACM Trans. Audio Speech Lang. Process.

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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.

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Section: B Modeling One-port Memoryless Circuit Elementsmentioning

confidence: 99%

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

Bernardini

Maffezzoni

Sarti

2019

IEEE/ACM Trans. Audio Speech Lang. Process.

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“…Certain transcendental equations involving exponentials can be expressed in explicit form using the Lambert W function. Chapter 5 presents the content of the published journal article [15], which explores how the W function can be used to derive explicit WD models of some one-ports [32] and multi-ports characterized by exponential nonlinearities, such as banks of diodes in parallel and/or anti-parallel or BJTs in certain amplifier configurations.…”

Section: Wave Digital Modeling Of Nonlinear Elements Using the Lambermentioning

confidence: 99%

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

Bernardini

2019

Special Topics in Information Technology

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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.

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“…. We used Ebers-Moll model [25] to obtain the state space equations. Ebers-Moll equations are: 25) and (26) can be expanded using Taylor's series expansion as: ) 9 10 11 12 13 14 15 16…”

Section: Fig 1 Circuit Diagram Of Common Emitter Amplifiermentioning

confidence: 99%

State Estimation of Common Emitter Amplifier using Iterated Extended Kalman Filters

Gautam¹,

Majumdar²

2019

IJITEE

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This paper presents the output voltage estimation of bipolar junction transistor (BJT) common emitter (CE) using iterated extended Kalman filter (IEKF). For this, state space model has been derived using Kirchhoff's current law (KCL) and Ebers-Moll model of the transistor. The performance of IEKF has been compared with extended Kalman filter (EKF). The simulation results show large signal to noise ratio (SNR) and small root mean square error (RMSE) using IEKF as compared to EKF, as IEKF considers the error due to linearization. The advantage of the proposed method is that the derived extended state space equation can be used for parameter estimation of both, the transistor state and transistor parameters as the derivation includes transistor model

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Modeling nonlinear wave digital elements using the Lambert function

Cited by 34 publications

References 28 publications

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

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

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

State Estimation of Common Emitter Amplifier using Iterated Extended Kalman Filters

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