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

Abstract

Abstract-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.Kyeywords-Saleh's model of AM/AM and AM/PM conversions, power amplifiers, memory effects, in-phase and quadrature representation of nonlinear devices

International Journal of Electronics and Telecommunications

“…Finally, the third formulation states that all the three models mentioned: of Rapp, of Saleh, and of Ghorbani are memoryless ones. We show here, confirming by the way also the results [8] achieved by the author of this paper in with the use of another approach, that only the Rapp's model is memoryless. But, the models of Saleh and of Ghorbani are representations incorporating memory effect.…”

“…With regard to the second formulation quoted, we show here, once again, confirming thereby the results obtained by the author of this paper elsewhere [5][6][7] with the use of other approaches, that the property of having no memory by a PA excludes demonstrating by it nonzero values of the AM/PM conversion.…”

“…So, let us now start with a wideband PA whose nonlinear impulse responses [5], [6], [10], similarly as in [8], are given by    …”

“…In what follows, we proceed similarly as in [8]. However, since the details of the calculations are a little bit tedious, they are moved into the appendix.…”

International Journal of Electronics and Telecommunications

“…The prominent example are the authors of the publication [3]. Because of this reason the above points were discussed recently in a series of papers [4][5][6].…”