Identification of Nonlinear Interference Sources with the Use of the Discrete Technique

This paper deals with a dichotomous method for the computer-aided search of nonlinear interference sources in complex electromagnetic environment. Compared to the onesignal method, the dichotomous method allows one to carry out a much more faster search (by factor of tens or more). An example of the search process and an estimation of the number of the required analysis cycles as well as description of the algorithm are given. The relation between identification and optimization problems is outlined. INTRODUCTION Computer-aided modeling of a radio electronic system is a very useful tool for electromagnetic compatibility/interference (EMC/EMI) analysis, in that it allows for the simulation of system behavior for a wide variety of initial conditions, excitations and system configurations in a rapid and inexpensive way [1]. A system can often reveal nonlinear behavior and nonlinear phenomena (intermodulation, crossmodulation, gain compression/expansion etc.) has profound effect on EMC/EMI in some cases [2]. Taking into account nonlinear interference at the system/subsystem design phase makes it possible to reduce the cost of its removal considerably. An identification of nonlinear interference sources is a very important task from the viewpoint of their removal. A computer-aided simulation tool can be used for such an identification in a very efficient way [3]. This article deals with a method of automatic identification of nonlinear interference sources, which is used in order to solve EMC/EMI problems in complex electromagnetic environment (for instance, in mobile communications environment, where there is a lot of emitters and receptors of EMI) . The specific character of this task is that a very accurate simulation of signals and interference levels is not required. However, in this case the analysis of complex systems must be carried out. Because of this, the simulation should be carried out at the system level. A nonlinear modeling technique (so called ‘discrete technique’) for numerical EMC/EMI simulation at the system level has been proposed in [4,5]. This technique allows one to carry out rapid numerical EMC/EMI analysis of a complex system or subsystem (i.e. receiver, transmitter etc.) or a set of systems/subsystems in a wide frequency range taking into account nonlinear effects (including spurious responses of a receiver) and maintaining accurate spectra representation. Such an analysis is, for instance, a very important part of EMC/EMI modeling of a mobile communication system [6-8]. THE DISCRETE TECHNIQUE The basis of the discrete technique [4,5] is a representation of the equivalent block diagram of a system as linear filters (LF) and memoryless nonlinear elements (MNE) connected in series (or in parallel). Thus a stage which employs a nonlinear element, for example, an amplifier, can be represented as a typical radio stage (see Figure 1), which employs the linear filter at the input, the memoryless nonlinear element and the linear filter at the output [2]. Linear Filter Linear Filter Memoryless Nonlinear Element Input Output Figure 1. Representation of a typical radio frequency stage This representation reflects characteristic peculiarities inherent to the construction of typical amplifying and converting stages. The utilization of the model with memoryless nonlinearity is not a significant limitation on the method for two reasons. First, non-zero memory effects can partially be factorized at the level of input or output filters, that is, this representation is equivalent with respect to the simulation of the "input-tooutput" link. Second, the prediction of a signal spectrum at the system input taking into consideration EMC problems is, as a rule, not very accurate the error can be as large as several dB or even tens of dB. It is an essential limitation on the simulation accuracy (the accuracy a signal at the system output can be predicted with). Thus great accuracy of system simulation is not necessarily required when the input signal is known with small accuracy. Therefore our viewpoint is that the utilization of the Volterra series for the analysis of nonlinear effects with respect to EMC problems [2] causes an essential increase of complexity without any essential increase in the analysis accuracy taken as a whole. IEEE International Symposium on Electromagnetic Compatibility, Denver, Colorado, Aug. 24-28, 1998, pp. 882-887 