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On Correct Understanding and Classification of Saleh’s and Related Models of AM/AM and AM/PM Conversions

Borys A.

International Journal of Electronics and Telecommunications

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2018

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Vol. 64, No. 1

39--44

EN

In this paper, some of the existing classifications of the Saleh’s and related models of the AM/AM and AM/PM conversions occurring in communication power amplifiers (PA) are reviewed. It is shown that these classifications are inconsistent and must be refined. Obviously, carrying out such a refinement properly needs a good knowledge and correct understanding of the mechanisms leading to the AM/AM and AM/PM conversions. This was achieved in this paper by performing a thorough analysis of the PA behavior using an analytical tool, the Volterra series. The main points of this analysis are presented here in great detail. Among others, it is shown that the influence of the PA memory on the AM/PM conversion is two-fold: direct and indirect. The former can be however fully neglected. On the other hand, the indirect influence caused by “the interaction of the carrier with the PA memory” cannot be neglected when the PA has not enough wideband frequency characteristics. The latter effect mentioned causes changes in the carrier phase that are received as the phase changes of the baseband modulating signal.

2

Saleh's Model of AM/AM and AM/PM Conversions is not a Model without Memory : Another Proof

Borys A.

International Journal of Electronics and Telecommunications

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2017

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Vol. 63, No. 1

73--77

EN

The so-called Saleh's representation for description of the AM/AM and AM/PM conversions, occurring in communication power amplifiers, consists of two expressions that describe them as functions of a real-valued baseband signal modulating the carrier amplitude. It is a common view that this description forms a model without memory. We show here that the above belief is not correct; just the opposite is true. To prove this, we take into account an equivalent description of the Saleh's model called the quadrature model of bandpass nonlinearities and express it in a form of a nonlinear operator. Afterwards, we check whether this operator possesses a zero memory. To this end, we use an appropriate theorem of the nonlinear systems theory. Finally, as a result of this investigation, we observe that the memory of the above operator is nonzero.

3

Fractional Diffusion Equation with Spherical Symmetry and Reactive Boundary Conditions

Lenzi M. K., Lenzi E. K., Novatski A., Menechini N. R., da Silva L. R.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

341--354

EN

We analyze the behavior of a system governed by a fractional diffusion equation with spherical symmetry and subjected to integro–differential boundary conditions which can simulate sorption, desorption and reaction processes. We consider the processes defined in terms of kinetic equations that couple the surface processes with the bulk dynamic enable us to describe scenarios where the surface modifies the bulk dynamics and this may change the behavior on surface. This problem is presented in terms of a general formulation satisfying the mass balance and a particular application characterized by a reversible process on the surface is analyzed. For this application, we obtain exact solutions in terms of the Green function approach and evaluate the concentrations on the spherical surface and in the bulk for different processes. These results lead to a rich class of scenarios which can be related to an anomalous diffusion.

4

Quadrature Mapping, Saleh’s Representation, and Memory Models

Borys A.

International Journal of Electronics and Telecommunications

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2016

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Vol. 62, No. 4

389--394

EN

In the literature, Saleh’s description of the AM/AM and AM/PM conversions occurring in communication power amplifiers (PAs) is classified as a representation without memory. We show here that this view must be revised. The need for such revision follows from the fact that the Saleh’s representation is based on the quadrature mapping which, as we show here, can be expanded in a Volterra series different from an usual Taylor series. That is the resulting Volterra series possesses the nonlinear impulse responses in form of sums of ordinary functions and multidimensional Dirac impulses multiplied by coefficients being real numbers. This property can be also expressed, equivalently, by saying that the nonlinear transfer functions associated with the aforementioned Volterra series are complex-valued functions. In conclusion, the above means that the Saleh’s representation incorporates memory effects.

5

Fractional-order derivative and time-dependent viscoelastic behaviour of rocks and minerals

Kawada Y., Yajima T., Nagahama H.

Acta Geophysica

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2013

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Vol. 61, no. 6

1690-1702

EN

A general constitutive equation for viscoelastic behaviour of rocks and minerals with fractional-order derivative is investigated. This constitutive law is derived based on differential geometry and thermodynamics of rheology, and the fractional order of derivative represents the degree of time delay. Analyzing some laboratory experimental data of high temperature deformation of rocks and minerals such as halite, marble and orthopyroxene, we propose how to determine the orders of fractional derivative for viscoelastic behaviours of rocks and minerals. The order is related to the exponents for the temporal scaling in the relaxation modulus and the stress power-law of strain rate, i.e., the non-Newtonian flow law, and considered as an indicator representing the macroscopic behaviour and microscopic dynamics of rocks.