Harmonic Analysis Method Based on Power Balance

Huang, Biqin; Yang, Guang; Wei, Ya Fen; Huang, Ying

doi:10.4028/www.scientific.net/amm.325-326.1508

Cited by 4 publications

(6 citation statements)

References 5 publications

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“…The bounded oscillation solutions include chaotic and periodic state, they can all be sought by using the harmonic analysis and the power balance theorem. The Table 1 and Table 2 are main harmonic component of oscillation solution, it approximate the simulate solution displayed in phase portraits Figure 7 and Figure 8 [14]- [17].…”

Section: Chaotic Boundedness Is Different From Its Attractivenessmentioning

confidence: 87%

“…Then (13) can be derived according to conservative circuit without excited source ( F u short circuit), and (14) can be derived according to zero-loss circuit with excited source. The circuit parameters in Figure 6 are shown in (15), and scalar equation is shown in (16). There are two situations when change rules of oscillation characters are analyzed.…”

Section: Chaos Oscillation Generated In Lossless Circuitmentioning

confidence: 99%

“…The main harmonic solutions of the (16) can be found by Program Tab1.nb and listed in Table 1. The phase portraits in Figure 7 are drawn from the (16). The change rule of oscillation character can be displayed.…”

Section: The Excited Source F U Keep Constant When a 3 Changementioning

confidence: 99%

“…The chaotic function of the three variable has not concretely explicit math expression, but it is bounded. It can only be expressed by using general parametric forms (17) or phase portraits, The change rules of the (17) are constrained by the differential Equations (16).…”

Section: The Solution Of the Equations (16) Is Described By Bounded Smentioning

confidence: 99%

See 3 more Smart Citations

Describing Chaos of Continuous Time System Using Bounded Space Curve

Binghua¹,

Wei²,

Huang³

et al. 2014

JMP

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The qualitative solutions of dynamical system expressed with nonlinear differential equation can be divided into two categories. One is that the motion of phase point may approach infinite or stable equilibrium point eventually. Neither periodic excited source nor self-excited oscillation exists in such nonlinear dynamic circuits, so its solution cannot be treated as the synthesis of multiharmonic. And the other is that the endless vibration of phase point is limited within certain range, moreover possesses character of sustained oscillation, namely the bounded nonlinear oscillation. It can persistently and repeatedly vibration after dynamic variable entering into steady state; moreover the motion of phase point will not approach infinite at last; system has not stable equilibrium point. The motional trajectory can be described by a bounded space curve. So far, the curve cannot be represented by concretely explicit parametric form in math. It cannot be expressed analytically by human. The chaos is a most universally common form of bounded nonlinear oscillation. A number of chaotic systems, such as Lorenz equation, Chua's circuit and lossless system in modern times are some examples among thousands of chaotic equations. In this work, basic properties related to the bounded space curve will be comprehensively summarized by analyzing these examples.

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Section: Chaotic Boundedness Is Different From Its Attractivenessmentioning

confidence: 87%

Section: Chaos Oscillation Generated In Lossless Circuitmentioning

confidence: 99%

Section: The Excited Source F U Keep Constant When a 3 Changementioning

confidence: 99%

Section: The Solution Of the Equations (16) Is Described By Bounded Smentioning

confidence: 99%

See 2 more Smart Citations

Describing Chaos of Continuous Time System Using Bounded Space Curve

Binghua¹,

Wei²,

Huang³

et al. 2014

JMP

Self Cite

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“…Each element parameter are shown in (10), they is different from Example 1. The state equation is shown in (11), scalar equation is shown in (12). The comparison between state (11) and (1) shows that the two equations are identical in form, the comparison between scalar (12a) and (2a) shows that the two equations are also identical in form, and only their parameters and nonlinearities in the formulae are different, where The initial phase angle θ is arbitrary, it means the harmonic solution has no determined θ .…”

Section: Frequency Conversion and Power Conservationmentioning

confidence: 99%

Power Balance of Multi-Harmonic Components in Nonlinear Network

Binghua¹,

He²

2014

JMP

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The main harmonic components in nonlinear differential equations can be solved by using the harmonic balance principle. The nonlinear coupling relation among various harmonics can be found by balance theorem of frequency domain. The superhet receiver circuits which are described by nonlinear differential equation of comprising even degree terms include three main harmonic components: the difference frequency and two signal frequencies. Based on the nonlinear coupling relation, taking superhet circuit as an example, this paper demonstrates that the every one of three main harmonics in networks must individually observe conservation of complex power. The power of difference frequency is from variable-frequency device. And total dissipative power of each harmonic is equal to zero. These conclusions can also be verified by the traditional harmonic analysis. The oscillation solutions which consist of the mixture of three main harmonics possess very long oscillation period, the spectral distribution are very tight, similar to evolution from doubling period leading to chaos. It can be illustrated that the chaos is sufficient or infinite extension of the oscillation period. In fact, the oscillation solutions plotted by numerical simulation all are certainly a periodic function of discrete spectrum. When phase portrait plotted hasn't finished one cycle, it is shown as aperiodic chaos.

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Chaos Structured by First Order Differential Circuit

黄¹

2014

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Chaos is the most universally common form of bounded nonlinear function. It commonly exists in the various subject areas of nature. Chaos is the universal term of variously bounded nonlinear aperiodic oscillation. This paper proves that the first order differential circuit which is constituted by mixing of three harmonic sources with different frequency also can produce chaos. It sufficiently explains that the extensiveness of chaotic functions exists in nature. The main harmonic components in the differential equations can be solved by using the harmonic balance principle and power balance theorem. Their correctness of solving results can be verified by phase portrait plotted by simulation. In last century, the era when chaos theory was first published, chaos was considered as a singular attractor in a lot of literatures. The recognition is obviously unilateral and wrong. In fact, people can also make a completely opposite conclusion, the motional trajectory of phase point will neither diverge to be infinite nor converge to stable limit cycle. The phase point freely and arbitrarily wandering in phase space is ordinary and universal motional form, but it is non-random. Chaotic phase portraits on which trajectories are not repeated are pervasive phenomenon. The constant periodic oscillation which continuously repeats original orbit is an individual and special motion form.

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Harmonic Analysis Method Based on Power Balance

Cited by 4 publications

References 5 publications

Describing Chaos of Continuous Time System Using Bounded Space Curve

Describing Chaos of Continuous Time System Using Bounded Space Curve

Power Balance of Multi-Harmonic Components in Nonlinear Network

Chaos Structured by First Order Differential Circuit

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