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