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

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.