Power Balance Theorem of Frequency Domain and Its Application

Binghua  Huang; Guangming  Li; Huijie  Liu

doi:10.4236/jmp.2014.512112

Binghua Huang^*, Guangming Li, Huijie Liu

Abstract: 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.

Keywords: Tellegen’s Theorem, Harmonic, Conservative System, Chaos, Lossless Circuit

Cite this paper: Huang, B. , Li, G. and Liu, H. (2014) Power Balance Theorem of Frequency Domain and Its Application. Journal of Modern Physics, 5, 1097-1108. doi: 10.4236/jmp.2014.512112.

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