Power Balance of Multi-Harmonic Components in Nonlinear Network

ABSTRACT

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.

KEYWORDS

Frequency Domain, Complex Power, Difference Frequency, Nonlinear Coupling, Chaos, Harmonic, Oscillation

Frequency Domain, Complex Power, Difference Frequency, Nonlinear Coupling, Chaos, Harmonic, Oscillation

Cite this paper

Huang, B. and He, X. (2014) Power Balance of Multi-Harmonic Components in Nonlinear Network.*Journal of Modern Physics*, **5**, 1321-1331. doi: 10.4236/jmp.2014.514132.

Huang, B. and He, X. (2014) Power Balance of Multi-Harmonic Components in Nonlinear Network.

References

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[2] Huang, B.H., Huang, X.M. and Li, C.B. (2011) Mathematics in Practice and Theory, 41, 172-179.

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[7] Huang, B.H. and Kuang, Y.M. (2007) Journal of Guangxi University (Natural Science Edition), 32.

[8] Huang, B.H., Li, G.M. and Wei, Y.F. (2012) Modern Physics, 2, 60-69.

[9] Huang, B.H., Huang, X.M. and Li, H. (2011) Main Components of Harmonic Solutions. International Conference on Electric Information and Control Engineering, New York, 15-17 April 2001, 2307-2310.

[10] Huang, B.H., Huang, X.M. and Li, H. (2011) Procedia Engineering, 16, 325-332.

http://dx.doi.org/10.1016/j.proeng.2011.08.1091

[11] Huang, B.H., Yang, G.S., Wei, Y.F. and Huang, Y. (2013) Applied Mechanics and Materials, 325-326, 1508-1514.

[12] Huang, B.H., Li, G.M. and Liu, H.J. (2013) Modern Physics, 3, 1-8.

http://dx.doi.org/10.12677/MP.2013.31001

[1] Feng, J.C. and Li, G.M. (2012) Journal of South China University of Technology (Natural Science Edition), 40, 13-18.

[2] Huang, B.H., Huang, X.M. and Li, C.B. (2011) Mathematics in Practice and Theory, 41, 172-179.

[3] Huang, B.H., Niu, L.R., Lin, L.F. and Sun, C.M. (2007) Acta Electronica Sinica, 35, 1994-1998.

[4] Huang, B.H., Huang, X.M. and Wei, S.G. (2008) Journal on Communications, 29, 65-70.

[5] Huang, B.H., Chen, C., Wei, S.E. and Li, B. (2008) Research & Progress of Solid State Electronics, 28, 57-62.

[6] Huang, B.H., Huang, X.M. and Wang, Q.H. (2006) Research & Progress of Solid State Electronics, 26, 43-48.

[7] Huang, B.H. and Kuang, Y.M. (2007) Journal of Guangxi University (Natural Science Edition), 32.

[8] Huang, B.H., Li, G.M. and Wei, Y.F. (2012) Modern Physics, 2, 60-69.

[9] Huang, B.H., Huang, X.M. and Li, H. (2011) Main Components of Harmonic Solutions. International Conference on Electric Information and Control Engineering, New York, 15-17 April 2001, 2307-2310.

[10] Huang, B.H., Huang, X.M. and Li, H. (2011) Procedia Engineering, 16, 325-332.

http://dx.doi.org/10.1016/j.proeng.2011.08.1091

[11] Huang, B.H., Yang, G.S., Wei, Y.F. and Huang, Y. (2013) Applied Mechanics and Materials, 325-326, 1508-1514.

[12] Huang, B.H., Li, G.M. and Liu, H.J. (2013) Modern Physics, 3, 1-8.

http://dx.doi.org/10.12677/MP.2013.31001