Automatic Synthesis of Active Electronic Networks using Genetic Algorithms

Analogue electronic networks can be synthesised by genetic optimisation. Active linear networks containing a single operational amplifier have been generated to meet both frequency-domain and time-domain specifications. In spite of the fact that no expert rules are built into the synthesis program, the networks generated are practical and effective. Introduction Numerical optimisation is rightly considered to be a valuable tool for synthesising electronic networks. By minimising a suitable objective function it is possible to determine component values which provide the best performance measured against some target specification. Unfortunately numerical optimisation suffers from the serious limitation that it only operates on networks of fixed topology. Selecting a suitable network configuration is usually the most difficult part of electronic network design, and this must be completed manually before numerical optimisation can take place. Genetic algorithms (GAs) are a class of optimisation methods which have been successfully applied to a wide range of numerical and non-numerical optimisation problems [1,2]. Based on the principle of "survival of the fittest", GAs have proved to be both robust and efficient. Providing that a method exists for analysing design solutions, and for measuring their performance against predetermined criteria, GAs can be used to close the design feedback loop. Methods for analysing electronic networks in both the frequency domain and time domain are well established. It is to be expected, therefore, that GAs should be suitable for optimising the topology of electronic networks, and this has been found to be the case. The synthesis of passive electronic networks using GAs was described in a previous paper [3]. Passive networks containing resistors and capacitors can only generate voltage transfer functions with real poles, and this seriously restricts the frequency-domain and time-domain behaviour. Including inductors in the network removes this restriction, but inductors suffer from a number of drawbacks (including cost, size and non-linearity), particularly at low frequencies. Fortunately RC-active networks do not suffer from this limitation and can be used to realise any stable voltage transfer function. Below about 100 kHz RC-active networks are preferable to LCR networks. This paper describes the use of GAs to synthesise active electronic networks containing a single operational amplifier. Active Network Synthesis using GAs Operational amplifiers have long been established as the preferred active element in low-power linear networks at frequencies below about 100 kHz. There are many reasons for this, including their near-ideal performance and low cost. It was therefore decided to use operational amplifiers as the active elements in automatic network synthesis. The network synthesis in fact uses infinite-gain four-terminal operational amplifiers, or nullors (nullator/norator combinations) which have two input terminals and two output terminals. The reason for using nullors is that they