Characterizing Components Under Large Signal Excitation: Defining Sensible "Large Signal S-Parameters"?!

Verspecht, Jan; Bossche, Marc Vanden; Verbeyst, Frans

doi:10.1109/arftg.1997.327217

Cited by 27 publications

(16 citation statements)

References 3 publications

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“…Theorem 3: Linear Systems: For linear PP systems, the characterization in (19) through (22) are exact. The HCWs are given by the impulse response of the (possibly time variant) linear system.…”

Section: Periodicity Preservation Systemsmentioning

confidence: 96%

“…A PP system is linear if Thus and the response to a perturbed operating point is where is given by (19). Equations (20)- (22) are alternate descriptions of the same identity.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Indeed, any linear system with impulse response can be made a PP system using (24) where for and is zero otherwise. The proof is in Appendix D. Theorem 4: Memoryless Nonlinearities: A special class of PP systems is characterized by a memoryless nonlinearity (see (19)) (25) Then the harmonic coupling weights are (26) where is the Fourier series coefficient of the periodic signal .…”

Section: Periodicity Preservation Systemsmentioning

confidence: 99%

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Small Perturbation Harmonic Coupling in Nonlinear Periodicity Preservation Circuits

Baylis

Marks

2012

IEEE Trans. Circuits Syst. I

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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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Section: Periodicity Preservation Systemsmentioning

confidence: 96%

“…A PP system is linear if Thus and the response to a perturbed operating point is where is given by (19). Equations (20)- (22) are alternate descriptions of the same identity.…”

Section: Proof Of Theoremmentioning

confidence: 99%

Section: Periodicity Preservation Systemsmentioning

confidence: 99%

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Small Perturbation Harmonic Coupling in Nonlinear Periodicity Preservation Circuits

Baylis

Marks

2012

IEEE Trans. Circuits Syst. I

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“…The analysis in the previous section requires stimulus of the PP system with complex sinusoids in (14). Using real signals, the HCWs and can be found from two experiments using two real tickle tone perturbations.…”

Section: A Experiments Using Real Signalsmentioning

confidence: 99%

“…The tickle tone in (14) has a single Fourier series coefficient, i.e., (15) where the Kronecker delta, , is one for and is otherwise zero. Substituting into (12), the response perturbation is (16) The output's affine approximation follows as .…”

Section: Measuring the Harmonic Coupling Weights The On-frequencmentioning

confidence: 99%

Evaluation of Harmonic Coupling Weights in Nonlinear Periodicity Preservation Systems

Baylis

Marks

2012

IEEE Trans. Circuits Syst. I

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When stimulated by a periodic stimulus, every component of a possibly nonlinear periodicity preservation system oscillates periodically with the same period as the stimulus. Changes in the harmonic structure of the the stimulus couples each input harmonic to, in general, every response harmonic. Knowledge of harmonic coupling weights (HCWs) allows model free characterization of effects of all small stimulus perturbation. This paper develops foundational methodology for experimentally measuring the HCWs. The on-frequency method uses small tickle tones at harmonic frequencies to do this. The off-frequency method places tickle tones adjacent to harmonic frequencies and is applicable to PP systems that are locally frequency invariant. Memoryless nonlinear PP systems are an example where the approach works exactly. The off-frequency method also requires fewer experiments. In some cases, the off-frequency method can be extended to measure numerous HCWs in a single experiment. Some system types such as the memoryless nonlinearity, require fewer experiments than general PP systems. Methods to experimentally measure the Hessian are also presented.

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Measuring Amplifiers

2012

Handbook of Microwave Component Measurements

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Characterizing Components Under Large Signal Excitation: Defining Sensible "Large Signal S-Parameters"?!

Cited by 27 publications

References 3 publications

Small Perturbation Harmonic Coupling in Nonlinear Periodicity Preservation Circuits

Small Perturbation Harmonic Coupling in Nonlinear Periodicity Preservation Circuits

Evaluation of Harmonic Coupling Weights in Nonlinear Periodicity Preservation Systems

Measuring Amplifiers

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