Multi-tone, Multi-port, and Dynamic Memory Enhancements to PHD Nonlinear Behavioral Models from Large-signal Measurements and Simulations

Verspecht, Jan; Gunyan, D.; Horn, Jason; Xu, Jianjun; Cognata, A.; Root, David E.

doi:10.1109/mwsym.2007.380180

Cited by 51 publications

(15 citation statements)

References 5 publications

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“…Given (25), the response Fourier series coefficient is Therefore from the chain rule of differentiation where is defined in (27).…”

Section: E Proof Of Theoremmentioning

confidence: 99%

“…Groundbreaking nonlinear system harmonic coupling characterizations [11]- [15] such as VIOMAP [15], S-functions [16]- [20], polyharmonic distortion (PHD) models [22]- [27] and X-parameters® [28]- [39] have been offered as approaches to the "black-box" modeling of nonlinear devices. They differ from more traditional nonlinear models such as those of Volterra & Norbert Wiener [40]- [45] and Hermite [46].…”

Section: Introductionmentioning

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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“…Given (25), the response Fourier series coefficient is Therefore from the chain rule of differentiation where is defined in (27).…”

Section: E Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Small Perturbation Harmonic Coupling in Nonlinear Periodicity Preservation Circuits

Baylis

Marks

2012

IEEE Trans. Circuits Syst. I

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“…From the two measurements, we evaluate the HCWs (21) and (22) Measurements are repeated for all desired input harmonics corresponding to any values of and positive .…”

Section: A Experiments Using Real Signalsmentioning

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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“…(1), außerhalb des Arguments der X-Parameter liegt, indem man das Prinzip der Zeitinvarianz anwendet [2; 3]. (Zu beachten ist, dass [2; 3] und [6] eine andere Konvention der X-Parameter-Indizes verwenden und, verglichen mit Gl. (2), die X (F) -Terme in die X (S) -Terme subsumieren.…”

Section: Beiträgeunclassified

X-Parameter: Das neue Paradigma zur Beschreibung nichtlinearer HF- und Mikrowellenbauelemente

Root¹,

Horn

Betts

et al. 2010

Tm - Technisches Messen

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Zusammenfassung Zur Beschreibung nichtlinearer hochfrequenter Bauelemente wie Mischer oder Verstärker reichen herkömmliche Größen wie S-Parameter nicht aus. Wir zeigen, wie sich das Großsignalverhalten solcher Bauelemente, die Arbeitspunktabhängigkeit ihrer Eigenschaften und ihre Erzeugung neuer Frequenzanteile mit Hilfe so-genannter X-Parameter wiedergeben lassen. Das Verfahren wird an mehreren Beispielen demonstriert.Summary Non-linear RF devices such as mixers or amplifiers cannot be described in sufficient detail by common quantities such as S-parameters. We show how the largesignal characteristics of such devices, the influence of the operating point on their characteristics, and the generation of new frequency components can be modeled by the so-called X-parameters. The approach is demonstrated by way of several examples.

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Multi-tone, Multi-port, and Dynamic Memory Enhancements to PHD Nonlinear Behavioral Models from Large-signal Measurements and Simulations

Cited by 51 publications

References 5 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

X-Parameter: Das neue Paradigma zur Beschreibung nichtlinearer HF- und Mikrowellenbauelemente

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