Proceedings of the World Congress on Engineering and Computer Science 2013 Vol II WCECS 2013, 23-25 October, 2013, San Francisco, USA

CMOS Differential Amplifier Area Optimization

with Evolutionary Algorithms

Revna Acar Vural, Member, IEEE, Burcu Erkmen, Member, IEEE, Ufuk Bozkurt,

Tulay Yildirim, Member, IEEE

Besides, gain maximization [10] objective of a two stage operational amplifier are accomplished with GA. Seven real world cases such as buffer, amplifiers, delay, NAND of IC design were evaluated by DE algorithm considering circuit Abstract—This work presents efficient constrained

optimization methods for sizing of a differential amplifier with current mirror load. The aim is to minimize MOS transistor area using three evolutionary algorithms, differential evolution, artificial bee colony algorithm and harmony search. Simulation results demonstrate that proposed methods not only meets design specifications and accommodates required functionalities but also accomplishes the design objective and improves some design specifications in a shorter computational time with respect to previous method.

Keywords—; analog integrated circuit sizing; differential evolution; harmony search; artificial bee colony; constrained optimization

I. INTRODUCTION Analog circuit synthesis is the process of designing and constructing a network to meet the multiple and complex performance specifications by the large number of design variables. Robust analog circuit design which fulfill the design constraints in several different operating environments and under the influence of manufacturing process variations is a very important, complex and time consuming task [1,2]. Optimal CMOS transistor sizing for minimum area oriented optimization, which is only a part of a complete analog circuit CAD tool remains between topology selection and actual circuit layout [3]. Those two tasks are beyond the scope of this work.

An evolutionary algorithm (EA) based transistor sizing

approach of a differential amplifier with current mirror load

for minimum occupied MOS transistor area is presented. Here, population based nature–inspired three EA methods are used to synthesize a CMOS differential amplifier where bias current and MOS transistor sizes are optimized for minimum area requirement while fulfilling particular design specifications such as gain, power dissipation, slew rate, phase margin, common-mode rejection ratio (CMRR), power supply rejection ratio (PSRR), input common-mode range

(ICMR) considering design objective. EA methods have

been successfully utilized for various analog integrated

circuit design schemes [4]. In literature, particle swarm optimization (PSO) [3,5], genetic algorithm (GA)[6], differential evolution (DE) [7,8], non-dominated sorting genetic algorithm NSGA [8,9] techniques have been used for optimizing analog circuits such as a operational transconductance amplifier, differential amplifiers, analog active filter and operational amplifier, low noise amplifiers.

In [6], GA method is used for active filter transfer function providing desired feature implemented with

adjusted component instead of standard resistance.

Revna Acar Vural1, Burcu Erkmen2, Ufuk Bozkurt3, Tulay Yildirim4 {racar1,bkapan2,tulay4}@yildiz.edu.tr, ubozkurt@gmail.com3,

Yildiz Technical University Department of Electronics and

Communication Engineering, , Istanbul, Turkey

ISBN: 978-988-19253-1-2

ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

area as design goal in [7]. DE method is utilized for sizing of operational transconductance amplifier considering power minimization and gain maximization and results are compared with NSGA in [8]. In [3,5] PSO is applied for transistor area minimization of two stage operational amplifier and differential amplifier while fulfilling particular design specifications. Optimum device sizes are obtained by NSGA for low noise amplifiers using in RF receivers.

In this work, DE, HS and ABC algorithms are applied for automated sizing of CMOS differential amplifier. Among

them, ABC algorithm has not been used for analog sizing

beforehand. The comparative performances of the optimizing circuit using these algorithms have been evaluated in terms of design criteria and computational efforts.

Rest of the paper is organized as follows. Brief information about differential evolution, harmony search and artificial bee colony methods is given in section II. Section III describes design procedure for differential amplifier. Simulation results of EA based sizing methodology are presented in section IV. Finally, concluding remarks and comments are given in section V.

II. EVOLUTIONARY ALGORITHMS Evolutionary algorithms (EA) are iterative in nature and may move to not-necessarily improving solutions which avoids being stuck at local minima [11]. DE, HS and ABC algorithms are three evolutionary methods used for CMOS differential amplifier sizing. All of them utilize constrained procedures where new solutions are not generated unless constraints are satisfied. Details of those are provided in the following.

A. Differential Evolution DE is a real coded population-based optimization technique based on parallel direct search method and diverges from GA by adding the weighted difference between two chromosomes to the third in order to generate new ones [12].

DE uses a population P having NP individuals that evolves over G generations to reach the optimal solution.

Each individual Xi is a vector that features a dimension size of D. Each vector in population matrix is assigned as follows.

Xj=Xjmin+ηj(Xjmax-Xjmin), j= 1,…,D (1) where Xjmax, Xjmin are the upper, lower bounds, respectively and ηj is a uniformly distributed random number within [0,1] of the jth feature. The optimization process in DE WCECS 2013

Proceedings of the World Congress on Engineering and Computer Science 2013 Vol II WCECS 2013, 23-25 October, 2013, San Francisco, USA

is carried out using three operations; mutation, crossover and

’

vij?xij??ij(xij?xkj)selection. Mutation operator generates mutant vectors (Xi) (4)

according to (2) where φij is a uniformly distributed real random number

Xi’(G) = Xa(G)+F(Xb(G) – Xc(G)), a≠b≠c≠i (2) within the range [-1,1], k is the index of the solution chosen randomly from the colony and j is the index of the dimension where Xa, Xb and Xc are randomly selected vectors among of the problem. After producing v, this new solution is

ij

population matrix including NP different vectors. F is the compared to x solution and the employed bee exploits a

scaling constant used to improve algorithm convergence. The crossover operation is employed to create trial vectors (Xi’’) by mixing the individuals of the mutant vectors (Xi’) with the target vector (Xi) according to (3) X??Xi'(,Gj),if(?'j?CR)or(j?q)i'',(Gj)

?? (3) ??Xi(,Gj),otherwise where q is a randomly chosen index within [1,NP], guaranteeing that trail vector employs at least one individual from the mutant vector. CR is the crossover constant within [0,1] that controls the population diversity. Finally selection operator compares the fitness values of trial vectors and target vectors. If trial vectors yield better fitness values then they replace the target vectors with which they were compared, otherwise predetermined population member is retained. The above procedure restarts until the chromosomes have been successfully updated to improve their fitness values to a specified value [12].

B. Harmony Search

HS is based on the improvisation process of jazz

musicians [13]. HS searches an optimal combination of inputs by usage of harmony memory, pitch adjusting and randomization just as musicians seek a fantastic harmony by playing any known tune from their memory, playing a similar tune or composing new and random notes.