Neuromodeling and Natural Optimization of Nonlinear Devices and Circuits

Introduction

Versatility, efficient computation, reduced memory occupation, stability of learning algorithms and generalization from representative data are some characteristics that have motivated the use of neural networks in many areas of microwave engineering (Patnaik & Mishra, 2000; Zhang & Gupta, 2000). In circuit simulation, neuromodeling applications reported in literature to improve the harmonic balance method have been used as nonlinear device models for microwave circuit steady-state analysis (Santos, Romariz, & Carvalho, 1997). On the order hand, neuromodeling technique is evaluated in time-domain, in order to improve nonlinear GaAs MESFET logic gate circuit transient and sensitivity analysis (Silva, Melo, & Neto, 2001; Silva, Melo, & Neto, 2002).

Circuit simulators like SPICE (with integrated circuit emphasis) are formed around semiconductor devices like diodes, BJTs, MOSFETs, MESFETs etc. (Raghuram, 1989). In general, the quality of simulation is decided by the accuracy of device models. On the other hand, a very detailed model would naturally slow down the program. A compromise between accuracy and speed of computation has to be struck. Using neural networks enables to overcome this problem.

Generally, the use of circuit simulation packages presents difficulties to the designer in implementing their own nonlinear model applied to a new device (Raghuram, 1989). Numerical simplifications are required. Then, the use of empirical models increases the computational efficiency of numerical simulations. In this context, artificial neural networks trained by accurate electromagnetic (EM) data, are very suitable for developing computer aided design (CAD) tools. Neural models combine the accuracy of EM-simulators with the computational efficiency of empirical models (Silva, 2002). For this reason, ANN models for nonlinear RF/microwave devices and circuits have been widely used (Zhang & Gupta, 2000). Various hybrid neuromodeling techniques incorporate previously EM knowledge to ANN in order to obtain more consistent training, reliability and accuracy for the resulting ANN models. Versatility, stability of learning algorithms and generalization abilities permit us to employ neural models for complex ill-defined input-output mappings in new (not well-known) devices (Santos et al., 1997).

Neuromodeling methodology can be described by two steps: i) neural network model development - that includes selection of representative training data, network configuration and training algorithms; ii) neural model validation - the neural network model is tested and validated according to its interpolation and generalization capacities in a given region of interest.

Natural optimization algorithms, which are stochastic population-based global search methods inspired by nature, such as simulated annealing (SA), genetic algorithm (GA) and particle swarm optimization (PSO) are effective for optimization problems with a large number of design variables and inexpensive cost function evaluation (Haupt & Werner, 2007; Kennedy & Eberhart, 1995). However, the main computational drawback for optimization of nonlinear devices and circuits relies on the repetitive evaluation of numerically expensive cost (or fitness) functions. Finding a way to shorten the optimization cycle is highly desirable. In the case of GA, for example, several schemes are available in order to improve its performance, such as: the use of fast full-wave methods, micro-genetic algorithm, which aims to reduce the population size, and parallel GA associated with parallel computation (R. Haupt & S. Haupt, 2004).