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2021
The harmonic balance method is a version of Galerkin’s weighted residual method. The harmonic balance is to seek an approximate periodic solution of a differential-algebraic equation by a truncated Fourier series. Substituting a guessed periodic solution into the differential equation leads to a residual term.
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The harmonic balance method is a version of Galerkin’s weighted residual method. The harmonic balance is to seek an approximate periodic solution of a differential-algebraic equation by a truncated Fourier series. Substituting a guessed periodic solution into the differential equation leads to a residual term.
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IEEE Microwave and Wireless Components Letters, 2003
This letter introduces a new approach to steady state analysis of nonlinear microwave circuits under periodic excitation. The new method is similar to the well known technique of Harmonic Balance, but uses wavelets as basis functions instead of Fourier series.
N. Soveiko, M. Nakhla
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This letter introduces a new approach to steady state analysis of nonlinear microwave circuits under periodic excitation. The new method is similar to the well known technique of Harmonic Balance, but uses wavelets as basis functions instead of Fourier series.
N. Soveiko, M. Nakhla
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1996 IEEE MTT-S International Microwave Symposium Digest, 2002
Harmonic balance has established itself as an important technique for simulating high frequency circuits. However, this simulator struggles on strongly nonlinear circuits, particularly if there are several input signals at different frequencies. An important observation is that multi-tone nonlinear circuits usually react in a strongly nonlinear fashion
Y. Thodesen, K. Kundert
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Harmonic balance has established itself as an important technique for simulating high frequency circuits. However, this simulator struggles on strongly nonlinear circuits, particularly if there are several input signals at different frequencies. An important observation is that multi-tone nonlinear circuits usually react in a strongly nonlinear fashion
Y. Thodesen, K. Kundert
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A new development of the harmonic balance method: The hybrid harmonic balance method
Analysis and ApplicationsThe harmonic balance (HB) method is efficient in predicting the limit cycle oscillations for many dynamic systems including very high dimensional systems in fluid dynamics. Recently, some variations and extensions of the HB method have been developed and employed in the computation of large systems.
Liping Liu +2 more
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Harmonic balance and almost periodic inputs
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2002We consider the equations of a large class of nonlinear circuits driven by asymptotically almost periodic inputs, and give an analytical basis for the use of harmonic balance to find steady-state solutions. More specifically, we show that in a certain setting of general interest there is a unique solution to the problem of obtaining a harmonic balance ...
Irwin W. Sandberg, Gideon J. J. Van Zyl
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2019
Harmonic Balance relies on the representation of time-periodic variables as Fourier series. Hence, we first compile useful definitions, notation, and theory of Fourier analysis. Next, we mathematically formulate the problem of finding periodic solutions of differential equation systems.
Malte Krack, Johann Gross
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Harmonic Balance relies on the representation of time-periodic variables as Fourier series. Hence, we first compile useful definitions, notation, and theory of Fourier analysis. Next, we mathematically formulate the problem of finding periodic solutions of differential equation systems.
Malte Krack, Johann Gross
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SOME ADVANCES OF THE HARMONIC BALANCE METHOD
Journal of Sound and Vibration, 1996-
Senjanović, Ivo, Fan, Ying
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1990
This chapter describes practical algorithms for implementing harmonic balance. Most of these algorithms have been implemented and tested in Spectre, a simulation program suitable for analog and microwave circuits. There are two fundamental ideas presented in this chapter.
Kenneth S. Kundert +2 more
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This chapter describes practical algorithms for implementing harmonic balance. Most of these algorithms have been implemented and tested in Spectre, a simulation program suitable for analog and microwave circuits. There are two fundamental ideas presented in this chapter.
Kenneth S. Kundert +2 more
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Continuation method in multitone harmonic balance
2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), 2004Design of communication circuits often requires computing quasi-periodic steady state response to multiple inputs of different frequencies that may not always be harmonically related. Multitone harmonic balance method can be used to provide an accurate solution if the circuit is mildly nonlinear.
Suihua Lu, Amit Narayan, Amit Mehrotra
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The Method of Harmonic Balance
2011This method may be used to determine the approximate periodic solutions of nonlinear differential equations. If a periodic solution does exist, it may be sought in the form of a Fourier series, whose coefficients are determined by requiring the series to satisfy the equation of motion.
Vasile Marinca, Nicolae Herisanu
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