**Automatic Circuit Synthesis using GAs**

Analog and digital circuit synthesis has been a challenge for desginers for decades.
While there exists algorithms to synthesize and optimize digital networks, analog circuit
syynthesis has been considered an 'art' (*courtesy* Gilbert). Its been a handiwork
of the long standing experience, insight and intuition of the designer.

For the last some years, analog circuit synthesis using GAs has been attempted and surprisingly produced successful results. Design of filters, cmos opamp internals, optimization of element values are some of the studies undertaken by different researchers. What is more surprising is that some of the designs synthesized by GAs were found to be better than existing designs. Work done by John Koza, Adrian Thompson, Paul Layzell and Grimbley are significant in this regard.

I planned to personally test these ideas. Two applications were conceived and the implementaion is going on. It is a thrilling feeling to know that the first application i.e. evolution of sinosuidal oscillators using genetic algorithms has given positive results. Infact, the genetic algorithm could evolve some OTRA based canonic SFOs, which are unpublished to my best knowledge.

A brief description of the two projects is given underneath and you can also have a look at the preprint copy of the paper which discusses the concept and implementation of the first application.

**Evolving Sinosuidal Oscillators using GAs**

*August - December, 2002*

The present work focuses on synthesizing Sinusoidal Oscillators using Genetic Algorithms. Traditionally, design of sinusoidal oscillators has been carried out based on intuition, inference or analysis. There is no deterministic way to synthesize sinusoidal oscillators (except for exhaustive search!) as in case of other analog synthesis problems. It was only in 1984, when an exhaustive study of such oscillators was conducted by Bhattacharya and Darkani [1]. But, this study was constrained to synthesis of single-opamp oscillators with minimum elements and two capacitors, where also it proved to be very tedious. An exhaustive search for oscillators with larger number of components or more than 2 capacitors would become almost impossible manually or highly expensive algorithmically. At the same time, authors argue that other oscillators (apart from the ones studied [1]) may show better properties than the existing oscillators with regard to frequency distortion, frequency stability, amplitude of oscillation, frequency range, total harmonic distortion, power consumption, ease of fabrication, etc. Novelity of an oscillator topology can be due to the aforesaid factors than just the number of components.

Fitness evaluation is done using a software called topcap [2], which has the capability to find the transfer function of any given ideal opamp circuit. Topcap is used together with the code written in MATLAB for running the GA. For each circuit, its transfer function is analysed and thus is assigned a fitness value on basis of the order of the system, constraints on condition of oscillation, frequency of oscillation, etc. We modified the fitness function by also taking in consideration the capability of the circuit to learn, based on 'Fitness evaluation based on learning for automatic analogue circuit synthesis using Genetic Algorithms' [3]. The results showed improvement.

The GA could synthesize all 12 canonic SFOs [1], generated two topologies of 3 capacitor minimum element oscillators and interesting topologies of OTRA, DDCC based oscillators.

*All coding is being done in MATLAB. We have completed the study. In future,
we plan to evolve oscillators using new building blocks (active elements) using the same
strategy.*

*Acknowledgement*

I thank Prof. Raj
Senani, AIC Lab, NSIT, Delhi for stating the present problem to be solved by Genetic
Algorithms. I also acknowledge his constant support, encouragement and guidance, which
were very much needed to do this work. Apart from this, I thank him for making available
previous technical papers for this work.

A very special thanks to Dr. Paul Layzell for reviewing my paper and sending me very
useful comments.

I thank Dr. James Grimbleby for making available the software to symbolically analyze
circuits. I am also grateful to him for answering my queries through email.

I thank C. Goh, Navid Azizi for answering my emails.

**Anonymous acknowledgement**: Finally I acknowledge the support of a
person (whose name I dont know), who told me to make an implementation of my hypothesis
four days before I had to present my paper 'Solving Transcendental Equations using GAs' at
DITECH. Though I hated him at the moment, it took me 4 days straight to make an
implementation for multimodal GAs. Thereafter, I had the confident of coding any
application using GAs. Thanks dude!!!

*Click to download preprint copy of paper *

**‘Evolving Active Circuits: Thinking the human way’**

The second project is in implementation stage. In this project, we aim towards tuning the genetic algorithm to synthesize human-thinkable circuits. Basically, we want to show that genetic algorithms can rediscover conventional designs previously conceived by intuition or some analysis. Initial results have been encouraging.

**References**

1. A unified Approach to the Realization of Canonic RC-active, Single as well as Variable frequency Osicillators Using Operational Amplifiers, Bhattacharya and Darkani, 1984

2. Topcap, developed by Dr. James Grimbleby link:

3. Fitness evaluation based on learning for automatic analogue
circuit synthesis using Genetic Algorithms. (Ideas page, Varun's *Griha*)

4. Automatic Analogue Circuit Synthesis using Genetic Algorithms, Grimbleby, 2000

5. Automated Analog circuit Synthesis using Linear Representation, Lohn and Colombano, 1998