Aperiodic Oscillation Structured by Lossless Circuit

黄, 炳华

doi:10.12677/mp.2013.31001

Cited by 3 publications

(6 citation statements)

References 5 publications

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“…The cube nonlinear term ( ) (19) by harmonic analysis method. We can verify that the data of results from Program harmo.nb accords with the data found by Program Power.nb.…”

Section: Above Results Verified By Harmonic Analysis Methodsmentioning

confidence: 99%

“…The ha p cannot be replenished by the power produced from the pa u . When the nonlinear factor 3 0 α = , the ( ) ha i t is only determined by the harmonic voltage ha u , and [19]. For example, for an autonomous circuit without external excitation source, the active power cannot be balanced to maintain sustained self-excited oscillation owing to positive damping.…”

Section: Coupling Relation Among Various Harmonic Must Be Commonly Obmentioning

confidence: 99%

See 1 more Smart Citation

Power Balance Theorem of Frequency Domain and Its Application

Binghua¹,

Li²,

Liu³

2014

JMP

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This paper proves a power balance theorem of frequency domain. It becomes another circuit law concerning power conservation after Tellegen's theorem. Moreover the universality and importance worth of application of the theorem are introduced in this paper. Various calculation of frequency domain in nonlinear circuit possess fixed intrinsic rule. There exists the mutual influence of nonlinear coupling among various harmonics. But every harmonic component must observe individually KCL, KVL and conservation of complex power in nonlinear circuit. It is a lossless network that the nonlinear conservative system with excited source has not dissipative element. The theorem proved by this paper can directly be used to find the main harmonic solutions of the lossless circuit. The results of solution are consistent with the balancing condition of reactive power, and accord with the traditional harmonic analysis method. This paper demonstrates that the lossless network can universally produce chaos. The phase portrait is related closely to the initial conditions, thus it is not an attractor. Furthermore it also reveals the difference between the attractiveness and boundedness for chaos.

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“…The cube nonlinear term ( ) (19) by harmonic analysis method. We can verify that the data of results from Program harmo.nb accords with the data found by Program Power.nb.…”

Section: Above Results Verified By Harmonic Analysis Methodsmentioning

confidence: 99%

Section: Coupling Relation Among Various Harmonic Must Be Commonly Obmentioning

confidence: 99%

Power Balance Theorem of Frequency Domain and Its Application

Binghua¹,

Li²,

Liu³

2014

JMP

View full text Add to dashboard Cite

show abstract

“…If no period is formed during observation, then the chaos will be defined as aperiodic. All of these phenomena show that chaos is sufficient (or infinite) extension of oscillation period [12] [13]. There is no transient process in the linear zero-loss circuit.…”

Section: Chaotic Boundedness Is Different From Its Attractivenessmentioning

confidence: 99%

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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“…The variable u contains a large number of frequency-doubling and combined-frequency components besides the two signal frequencies. In order to strengthen this available difference frequency component, the resonant frequency of LC circuit is designed to be equal to the difference frequency 12 w as shown in (2b). The excited source F u is shown in (2c).…”

Section: ( )mentioning

confidence: 99%

“…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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Aperiodic Oscillation Structured by Lossless Circuit

Cited by 3 publications

References 5 publications

Power Balance Theorem of Frequency Domain and Its Application

Power Balance Theorem of Frequency Domain and Its Application

Describing Chaos of Continuous Time System Using Bounded Space Curve

Power Balance of Multi-Harmonic Components in Nonlinear Network

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