Nonlinear circuit analysis using the method of harmonic balance—A review of the art. Part I. Introductory concepts

Gilmore, Rowan; Steer, M.B.

doi:10.1002/mmce.4570010104

Cited by 182 publications

(75 citation statements)

References 48 publications

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“…Based on the above, we define a general MPDE form for (12) to be (34) Next, we prove a key theorem: that if and together constitute a solution of (34) …”

Section: Appendix Generalized Wampde Formsmentioning

confidence: 99%

Analyzing oscillators using multitime PDEs

Narayan

Roychowdhury

2003

IEEE Trans. Circuits Syst. I

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Abstract-Oscillators are often difficult to analyze or simulate, because they generate waveforms that can span a range of widely separated time scales. We present a general oscillator formulation that separates slow and fast dynamics without approximations, and captures amplitude and frequency modulation in a natural and compact manner. To handle frequency-modulation effectively, we make use of a novel concept, warped time, within a multitime partial differential equation framework. The equations incorporate an explicit time-varying frequency variable that matches intuitive notions of changing frequency in a frequency-modulated signal. The formulation is useful for both hand analysis and numerical simulation. Index Terms-Frequency modulation (FM), multitime partial differential equation (MPDE).

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“…Based on the above, we define a general MPDE form for (12) to be (34) Next, we prove a key theorem: that if and together constitute a solution of (34) …”

Section: Appendix Generalized Wampde Formsmentioning

confidence: 99%

Analyzing oscillators using multitime PDEs

Narayan

Roychowdhury

2003

IEEE Trans. Circuits Syst. I

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“…It offers an alternative to time-domain methods for the analysis of equations where a periodic steady-state is sought and has been used for years in electrical engineering for studying nonlinear circuits [1]. The usual onedimensional HBM is limited to predicting periodic vibrations only whereas aperiodic (quasiperiodic) solutions made up with incommensurate tones are frequent.…”

Section: Introductionmentioning

confidence: 99%

n-dimensional Harmonic Balance Method extended to non-explicit nonlinearities

Legrand

Roques

Pierre

et al. 2006

European Journal of Computational Mechanics

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The harmonic balance method is widely used for the analysis of strongly nonlinear problems under periodic excitation. The concept of hypertime allows for the generalization of the usual formulation to multi-tone excitations. In this article, the method is applied to a system involving a nonlinearity which cannot be explicitly expressed in the multifrequency domain in terms of harmonic coefficients. The direct and inverse Discrete Fast Fourier Transforms are then necessary to alternate between time and frequency domains in order to take into account this nonlinearity. The results show the efficiency and the precision of the method. Keywords: harmonic balance method, hypertime domain, unilateral contact RésuméLa méthode de l'équilibrage harmonique permet l'analyse de problèmes fortement non linéaires sous excitation périodique. En utilisant le concept d'hyper-temps, il est possible de généraliser la formulation usuelle à des excitations apériodiques. Dans cet article, cette méthode est appliquée à un système impliquant une non-linéarité qui ne s'exprime pas de façon explicite dans l'espace multi-fréquentiel des coefficients harmoniques. Les transformées de Fourier rapides directe et inverse sont alors nécessaires pour alterner domaines temporel et fréquentiel afin de prendre en compte cette non-linéarité. Les résultats montrent l'efficacité et la précision de la méthode.

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“…This fact is exploited for their simulation -for example, harmonic balance (e.g., [RN88, KWSV90,GS91,dCP97]) relies on the absence of strongly nonlinear behaviour to be effective. In recent years, however, IC techniques have been applied to microwave design, resulting in an increase in the nonlinearity encountered.…”

Section: Introductionmentioning

confidence: 99%

Analyzing Strongly Nonlinear Multitone Circuits by Multi-Time Methods

Roychowdhury¹

1998

28th European Microwave Conference, 1998

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Harmonic balance and traditional time-domain simulation techniques are limited in their applicability when strong nonlinearities and multi-tone signals are both present. In this paper, new simulation algorithms are described and used to analyse strongly nonlinear microwave circuits with multi-tone excitations.The techniques are based on representing multi-tone waveforms as functions of several "tim"' variables, and solving a partial differential form of the circuit equations using tim-domain methods. The methods scale linearly with increasing circuit size, regardless of the number of nonlinearities. A switching mixer is analyzed using the new methods. Speedups of over two orders of magntude over tadional techniques are obtaed. Moreover, the multi-time representations obtained from the new methods provide intuitive and powerful visualisations of the operation of the circuit.

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Nonlinear circuit analysis using the method of harmonic balance—A review of the art. Part I. Introductory concepts

Cited by 182 publications

References 48 publications

Analyzing oscillators using multitime PDEs

Analyzing oscillators using multitime PDEs

n-dimensional Harmonic Balance Method extended to non-explicit nonlinearities

Analyzing Strongly Nonlinear Multitone Circuits by Multi-Time Methods

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