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Non-analytic at the origin, behavioral models for active or passive non-linearity

Published online by Cambridge University Press:  05 March 2013

Jacques Sombrin
Jacques Sombrin*
Affiliation:
TéSA, 14-16 Port Saint-Étienne, 31000 Toulouse, France. Phone: +33 5 61 24 73 79
*
Corresponding author: Jacques Sombrin Email: jacques.sombrin@tesa.prd.fr
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Abstract

Most non-linear behavioral models of amplifiers are based on functions that are analytic at the origin and thus can be replaced by their Taylor series development around this point, e.g. polynomials of the input signal. Chebyshev Transforms can be used to compute the harmonic response of the model to a sine input signal. These responses are polynomials of the input signal amplitude. A second application of the Chebyshev transform to the first harmonic response or radio frequency (RF) characteristic will lend the carriers and intermodulation (IM) products for a two-carrier input signal, again polynomials. An important class of non-analytic non-linear behavior encountered in practice, such as hard limiters and detectors are either empirically treated or only approximated by an analytic function such as the hyperbolic tangent. This work proposes to generalize the polynomial non-linearity theory by adding non-analytic at the origin functions that, like polynomials, are invariant elements of the Chebyshev Transform. Devices modeled with these non-analytic at the origin functions exhibit intermodulation behavior significantly different from that of classical polynomial models, giving theoretical foundation to a number of important unexplained practical measurement observations.

Keywords

Power Amplifiers and LinearizersModelingSimulation and characterizations of devices and circuits
Type
Research Papers
Information
International Journal of Microwave and Wireless Technologies , Volume 5 , Special Issue 2: Special Issue on Power Amplifier Linearization , April 2013 , pp. 133 - 140
Copyright
Copyright © Cambridge University Press and the European Microwave Association 2013

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