Analytical determination of the waveforms of nonlinear oscillators

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Analytical determination of the waveforms of nonlinear oscillators

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© The Institution of Electrical Engineers
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A set of equations has been derived which describes the steady-state oscillations of any nonlinear device with a loopless current/voltage characteristic in any frequency-dependent circuit. The equations are expressed in terms of the amplitudes of the waveform harmonic components, the admittances or impedances at the harmonic frequencies, and the time-averaged integrals of the derivatives of the oscillation voltage and current.

Inspec keywords: oscillators; nonlinear network analysis; waveform analysis; harmonic analysis

Other keywords: loopless voltage; nonlinear oscillators; amplitudes; impedances; waveform analysis; admittances; loopless current; steady state oscillation; harmonic frequencies

Subjects: Nonlinear network analysis and design; Oscillators

References

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      • B. van der pol . The nonlinear theory of electric oscillations. Proc. IRE , 1051 - 1086
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      • J.P. Quine . A generalised locking equation for oscillators. IEEE Trans. , 418 - 420
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      • K.W.H. Foulds . LSA circuit admittance at fundamental and second harmonic frequencies. IEEE Trans.
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      • J. Groszkowski . The interdependence of frequency variation and harmonic content and the problem of constant frequency oscillators. Proc. IRE , 958 - 981
    5. 5)
      • W.J. Cunningham . (1958) , Introduction to nonlinear analysis.
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      • C.W. Clenshaw , D. Greenspan . (1966) The solution of van der Pol's equation in Chebỹshev series, Numerical solutions of nonlinear differential equations.
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