Computing all the Floquet eigenfunctions of oscillators using harmonic balance Jacobian matrices

Nonlinear systems and circuits, while required for many applications, presently require a design procedure that is often complex. In many cases, the design process is either based upon measurements or complex nonlinear models. This paper presents periodicity preservation (PP) and time invariant PP (TIPP) system theory as a simple way to characterize behavior for a significant class of nonlinear systems. PP systems preserve signal periodicity and are conducive to modeling harmonic coupling. When linearized to small perturbations, the harmonic coupling is described by the Jacobian about the operating point. The harmonic coupling weights, which are elements of the Jacobian, can be measured experimentally. For some TIPP systems such as LTI systems and memoryless nonlinearities, a single experiment suffices to determine the harmonic coupling weights. Other PP systems, including mixing and linear time variant systems, require more experimental queries. TIPP system theory is foundational to the theory of X-parameters®, S-functions and polyharmonic distortion.

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“…Circuit Jacobians are commonly used to perform harmonic load balance [43], [48], [49]. Define (4) where denores Fourier transformation.…”

Section: Foundationsmentioning

confidence: 99%

Small Perturbation Harmonic Coupling in Nonlinear Periodicity Preservation Circuits

Baylis

Marks

2012

IEEE Trans. Circuits Syst. I

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“…Extracting the PPV is only possible for oscillators whose responses are characterised by a set of ordinary differential equations or differential‐algebraic equations [21]. It should be computed from the Floquet analysis which has its own analysis complexities [22, 23]. Furthermore, AN–PN conversions are not considered in their analysis.…”

Section: Introductionmentioning

confidence: 99%

Frequency‐domain behavioural noise analysis of analogue phase‐locked loops

Abtahi

Jahanbakht

2020

IET Microwaves, Antennas & Propagation

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Noise spectrum characterization of optoelectronic oscillators in the presence of laser frequency noise

Jahanbakht

2016

Appl. Opt.

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Frequency domain formulation for computing the noise spectrum of a single loop optoelectronic oscillator (OEO) under the effect of laser frequency noise (LFN) based on the conversion matrix approach is presented. The validity of this approach is verified by comparing its results regarding the phase noise of the OEO with the measurements and simulations of two references in the literature. By performing various simulations, it is observed that the LFN-induced phase noise is approximately independent of the length of the fiber delay line at offset frequencies less than the free spectral range, i.e., the inverse of the time delay of the fiber, and, at larger offset frequencies, the phase noise grows even with increasing the fiber length. Furthermore, it is observed that this phase noise is approximately independent of the distance between the oscillation frequency and the center frequency of the RF filter as well as the value of the small signal loop gain of the OEO. However, the LFN-induced amplitude noise is affected by the distance between the oscillation frequency and the center frequency of the RF filter.

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Computing all the Floquet eigenfunctions of oscillators using harmonic balance Jacobian matrices

Cited by 4 publications

References 10 publications

Small Perturbation Harmonic Coupling in Nonlinear Periodicity Preservation Circuits

Small Perturbation Harmonic Coupling in Nonlinear Periodicity Preservation Circuits

Frequency‐domain behavioural noise analysis of analogue phase‐locked loops

Noise spectrum characterization of optoelectronic oscillators in the presence of laser frequency noise

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