Fast simulation of the steady-state of circuits by the harmonic balance technique

Brachtendorf, Hans Georg; Welsch, G.; Laur, R.

doi:10.1109/iscas.1995.520406

Cited by 21 publications

(5 citation statements)

References 5 publications

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“…Let us remark that, depending on the problem, other high frequency numerical methods may also be adapted like for example fast integral equations solvers [19] or even asymptotic adpproximation techniques [5]. Finally, let us notice that the finite Fourier expansion method which leads to the coupled system of PDEs has also been used in the past under the name of the harmonic-balance method or the multi-harmonic approach [6,11,32,33,35,41,46]. It has been proved to be particularly efficient for engineering problems, including situations related to wave-like equations [22,26,47].…”

Section: Introductionmentioning

confidence: 99%

A frequency domain method for scattering problems with moving boundaries

Gasperini

Beise²,

Schroeder³

et al. 2021

Wave Motion

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We propose a multi-harmonic numerical method for solving wave scattering problems with moving boundaries, where the scatterer is assumed to move smoothly around an equilibrium position. We first develop an analysis to justify the method and its validity in the one-dimensional case with small-amplitude sinusoidal motions of the scatterer, before extending it to large-amplitude, arbitrary motions in oneand two-dimensional settings. We compare the numerical results of the proposed approach to standard space-time resolution schemes, which illustrates the efficiency of the new method.

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Section: Introductionmentioning

confidence: 99%

A frequency domain method for scattering problems with moving boundaries

Gasperini

Beise²,

Schroeder³

et al. 2021

Wave Motion

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“…The perturbations caused by nonlinear products including intermodulation distortions and harmonics responses can be estimated by substituting Equations ( 13) and ( 14) into Equations ( 9) and (10). The nonlinear stress T N and nonlinear electric displacement D N for third-order harmonics (H3) are derived as:…”

Section: Derivation Of Third-order Nonlinear Responsesmentioning

confidence: 99%

“…For BAW devices, the one-dimensional (1D) Mason equivalent circuit model and modified Butterworth Van Dyke (MBVD) model are commonly employed [ 3 , 7 , 8 ]. Shim and Feld [ 9 ] proposed a 1D nonlinear Mason model using the harmonic balance (HB) technique [ 10 , 11 ]. The proposed Mason model is applicable to arbitrary piezoelectric nonlinear sources, and it simulates well for nonlinear signals generated in RF BAW.…”

Section: Introductionmentioning

confidence: 99%

A General FEM Model for Analysis of Third-Order Nonlinearity in RF Surface Acoustic Wave Devices Based on Perturbation Theory

Zhang

Zhao

et al. 2022

Micromachines

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This article presents a general-purpose model that enables efficient and accurate calculation of third-order nonlinear signals in surface acoustic wave (SAW) devices. This model is based on piezoelectric constitutive equations combined with perturbation theory, which can be analyzed by full finite element method (FEM). For validation, third-order harmonic (H3) responses and intermodulation distortions (IMD3) in SAW resonators are simulated, and their calculation results fit well to experimental data in the literature. Then, the generation mechanisms of the third-order nonlinearity in SAW resonators are discussed. The dominant generation mechanisms for different nonlinear signals and the relation between electrode materials and H3 peak magnitude are revealed, which provides an important guideline for further nonlinear suppression.

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“…These methods solve Ax = b by repeatedly performing matrix-vector multiplications involving A. (10) in matrix-vector products, the cost of simulation grows almost linearly with number of frequencies. We compare both the QMR and GMRES methods…”

Section: State Of the Art Of Harmonic Balancementioning

confidence: 99%

“…Two Krylov methods exploited for harmonic balance are the quasi-minimrd residual (QMR) [10], [11] and generalized minimal residual (GMRES) methods [12], [13].…”

Section: Iterative Unear Solversmentioning

confidence: 99%

Simulation of high-Q oscillators

Gourary¹,

Ulyanov

Жаров

et al. 1998

Proceedings of the 1998 IEEE/ACM International Conference on Computer-Aided Design - ICCAD '98

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We present a new technique, based on a continuation method, for oscillator analysis using harmonic balance. Whh the use of Krylov subspace iterative linear solvers, harmonic balance has become a very powerful method for the analysis of general nonlinear circuits in the frequency domain. However, application of the harmonic balance method to the oscillator problem has been difficult due to the very small region of convergence. The main contribution of this paper is a robust and efficient continuation method that overcomes this problem.

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Fast simulation of the steady-state of circuits by the harmonic balance technique

Cited by 21 publications

References 5 publications

A frequency domain method for scattering problems with moving boundaries

A frequency domain method for scattering problems with moving boundaries

A General FEM Model for Analysis of Third-Order Nonlinearity in RF Surface Acoustic Wave Devices Based on Perturbation Theory

Simulation of high-Q oscillators

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