Most nonlinear behavioural 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 RF characteristic will lend the carriers and intermodulation (IM) products for a 2-carrier input signal, again polynomials. An important class of non-analytic nonlinear behaviour 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 nonlinearity theory by adding non-analytic at the origin functions that, like polynomials, are invariant elements of the Chebyshev Transform. Devices modelled with these non-analytic at the origin functions exhibit intermodulation behaviour significantly different from that of classical polynomial models, giving theoretical foundation to a number of important unexplained practical measurement observations.

This paper describes existing and new criteria for comparison and optimization of non-linear power amplifiers such as RF or microwave transmitters. In addition to intermodulation, receiver noise, and losses in the transmission system, the proposed new criteria take into account efficiency or consumed power. This results in the global optimization of a combined signal-to-noise-plus-intermodulation ratio as a function of saturated or nominal power but also consumed or dissipated power. Saturated power is limited by available technology. Consumed power and dissipated power are some of the main constraints in telecommunication satellite payloads, mobile phone handsets, and RFID (Radio Frequency IDentification). Another constraint comes from the limited size of antennas, which limits the system equivalent isotropic radiated power and gain-to-temperature ratio. With the proposed criteria the designer will be able to compare different amplifier technologies and to optimize the design and operating point of each stage of a multistage amplifier or a linearizer for a given amplifier. Interference from same or other systems is also introduced in the optimization through the use of signal-to-noise-plus-IM-plus-interference ratio criteria.

EVM is defined in many communication standards. These definitions are generally procedures to result in a percentage always slightly different in different standards cookbook recipes and not mathematical definitions. Uncertainty on this measurement difficult to assess : problem for evaluation of measurement equipment by users, problem for calibration of measurement equipment.

Passive intermodulation products may occur when two or more carriers are transmitted through a passive device such as a filter, a transmission line or an antenna or if they are reflected from one object. These products are generally due to distributed non-linearity along the transmission path or the reflector of the antenna. We show that ray optics can be used to determine easily the directions in which these products are in phase and reinforced. This is particularly significant for multihorn fed reflector antennas, for multiple antennas systems and for higher dynamic in measurement of passive intermodulation.

Passive intermodulation products may occur when two or more carriers are transmitted through a passive device such as a filter, a transmission line or an antenna or if they are reflected from one object. These products are generally due to distributed non-linearity along the transmission path or the reflector of the antenna. We show that ray optics can be used to determine easily the directions in which these products are in phase and reinforced. This is particularly significant for multihorn fed reflector antennas, for multiple antennas systems and for higher dynamic in measurement of passive intermodulation.

This paper proposes a multi-tone signal pattern designed for accurate and easy measurements of nonlinear devices linearity factors of merit. The stimulus signal we propose ensures that DUT’s third order intermodulation products won’t overlap. Thus, the relative phases of source tones do not affect the amplitudes of intermodulation products. The usual metrics for linearity factors, ACPR (Adjacent Channel Power Ratio) or NPR (Noise Power Ratio), can be acquired with a greater accuracy only with amplitude measurements. This work has been carried out with a sampler-based receiver, using FFT (Fast Fourier Transform) filtering for tone separation.

Les produits d’intermodulation passifs ne suivent pas la loi classique d’augmentation de puissance de 3 dB par dB de puissance d’entrée. Un modèle basé sur des fonctions non-analytique permet de simuler correctement ce comportement pour deux ou plusieurs porteuses. Le modèle explique l’amélioration du rapport C/I lorsque le nombre de porteuses augmente et permet de calculer cette amélioration à partir des mesures à deux porteuses et de la pente. Ceci permet de relâcher les spécifications à deux porteuses de 4 dB si la pente est de 2,5 dB/dB et de 8 dB si la pente est de 2 dB/dB pour une même performance en multi-porteuse. Cette relaxation peut permettre d’utiliser une technologie d’antenne de masse ou de coût plus faible alors qu’elle n’aurait pas été acceptée en l’absence de modèle.

We propose to use memristors as memory nonlinear circuits to build behavioral models useful in the simulation of passive inter-modulation in RF and microwave devices such as filters, antennas and in general connections

Leon Chua introduced memristors in 1971 [1] as an ideal two-terminal circuit element in complement to the already known three basic circuit elements: resistor, inductor and capacitor (RLC). Memristors are defined by a non-linear memristance that relates the flux (or integral of voltage across the device) to the charge (or integral of current in the device). Because of this definition the memristor will generate passive intermodulation products and their power will depend on the memory of the past current that is contained in the device.