Determining the steady-state output of nonlinear oscillatory circuits using multiple shooting

Parkhurst, Jeffrey Richard; Ogborn, L. L.

doi:10.1109/43.391735

Cited by 33 publications

(16 citation statements)

References 15 publications

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“…In the literature various mathematical methods, basically classified as time-domain or frequencydomain have been proposed to compute the steady-state periodic solution and its period. Time-domain approaches are based mainly on the so-called shooting method which determines the initial condition and the period for the periodic solution by solving a sequence of nonlinear initial value problems with the Newton-Raphson method, [1], [2], [3]. The main drawback of this method is the evaluation of the sensitivity matrix, which is often computationally expensive and becomes even more complicated for nonsmooth systems, [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Computing period and shape of oscillations in piecewise linear Lur'e systems: A complementarity approach

Sessa

Iannelli

Acary

et al. 2013

52nd IEEE Conference on Decision and Control

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e n tA c a r y ♭ ,B e r n a r dB r o g l i a t o ♭ and Francesco Vasca Abstract-Autonomous piecewise linear systems in the Lur'e form may exhibit periodic steady-state oscillations. For many practical systems belonging to this class the period and the shape of the oscillation is difficult to be predicted a priori. In this paper the complementarity approach is used to tackle the issue. The complementarity formalism is used to represent the closed-loop system and a phase condition acting as an anchor equation for the periodic solution. By discretizing the dynamics a mixed complementarity problem is formulated. The corresponding solution provides an accurate prediction of the steady-state oscillation and its period. Numerical results show the effectiveness of the proposed technique for the computation of stable and sliding periodic solutions. The analysis of the steady-state solution of a Colpitts oscillator is considered as an illustration.

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Section: Introductionmentioning

confidence: 99%

Computing period and shape of oscillations in piecewise linear Lur'e systems: A complementarity approach

Sessa

Iannelli

Acary

et al. 2013

52nd IEEE Conference on Decision and Control

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“…Moreover, in RF circuit design, it is more useful to examine the periodic steady state response than the transient response. Current computation methods exist to find the periodic steady state response of circuits usually described by ordinary differential equations (ODE) [6][7][8][9][10]. Although there are few methods used to simulate the circuits founded on the device simulator in which the devices are described by PDE, they are very inefficient and not practicality for circuit simulation [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…Shooting method is applied to the circuit ODE only, with the transistor currents computed from the lumped model at each iteration. The pseudo-inverse method [7] is used to update the initial value of the state variables and the period, which gives an efficient way to find the unknown period in oscillator and enhances the stability of shooting iteration either. Performing the transient analysis for a few cycles at the beginning make it easy to select good initial guesses.…”

Section: Introductionmentioning

confidence: 99%

Periodic steady-state analysis of coupled ODE-AE-CGE systems for MOS RF autonomous circuit simulation

Chen

Lai

et al. 2003

Proceedings of the 2003 Conference on Asia South Pacific Design Automation - ASPDAC

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-This paper studies the steady-state analysis of a system of ODE-AE-CGE arising from simulation of MOS RF autonomous circuits in which the transistor plays as current generator and its current equations could adequately represent the transistor large-signal dynamic behavior. Gauss-Seidel relaxation is applied to decouple the system so that shooting method, which is used to find the periodic steady-state response, can be performed with low-order sensitivity matrix. This simplifies the solution process and results in a fast algorithm. We illustrate the new algorithm with the simulation of a typically voltage-controlled oscillator (VCO), the simulation results show good agreement with those obtained by MEDICI, a device simulator.

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“…Because of the high nonlinearity, the Van der Pol oscillator is served as a benchmark circuit for various steady-state algorithms for autonomous circuits, such as those in [4], [8], [9]. The circuit schematic is quite simple as illustrated in Fig.…”

Section: Van Der Pol Oscillatormentioning

confidence: 99%

“…3 is one of the several examples that has been used in the past to test various steady-state analysis algorithms for nonautonomous circuits [1], [2], [4], [7]. The input excitation in Fig.…”

Section: B Power Supplymentioning

confidence: 99%

A wavelet balance approach for steady-state analysis of nonlinear circuits

Ling

et al.

ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196)

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Abstract-In this paper, a novel wavelet-balance method is proposed for steady-state analysis of nonlinear circuits. Taking advantage of the superior computational properties of wavelets, the proposed method presents several merits compared with those conventional frequency-domain techniques. First, it has a high convergence rate ( ), where is the step length. Second, it works in time domain so that many critical problems in frequency domain, such as nonlinearity and high order harmonics, can be handled efficiently. Third, an adaptive scheme exists to automatically select proper wavelet basis functions needed at a given accuracy. Numerical experiments further prove the promising features of the proposed method in solving steady-state problems.

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Determining the steady-state output of nonlinear oscillatory circuits using multiple shooting

Cited by 33 publications

References 15 publications

Computing period and shape of oscillations in piecewise linear Lur'e systems: A complementarity approach

Computing period and shape of oscillations in piecewise linear Lur'e systems: A complementarity approach

Periodic steady-state analysis of coupled ODE-AE-CGE systems for MOS RF autonomous circuit simulation

A wavelet balance approach for steady-state analysis of nonlinear circuits

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