Audio Circuits Evolution through Genetic Algorithms

P. H. G. Coelho, J. F. M. do Amaral, E. N. Da Rocha and M. C. Bentes

State Univ. of Rio de Janeiro, FEN/DETEL, R. S. Francisco Xavier, 524/Sala 5001E, Maracanã, RJ, 20550-900, Brazil

Keywords: Genetic Algorithms, Artificial Intelligence Applications, Evolutionary Electronics.

Abstract: This paper focuses on the implementation of an extrinsic platform in order to develop audio electronic

circuits with known topologies. This platform uses genetic algorithms to choose the best components to

achieve a specific goal. All the proposed topologies have been consolidated in the audio market and due to

this aspect, the technique has not proposed new possibilities for them. However, the generation mechanism

of these alternatives is studied in depth, approaching their theoretical potential. User specifications of the

proposed interface define the evolution of the circuit. The developed platform compares the graphic of a

simulation with a graphic which is generated by a function in MATLAB. The similarity between these

curves is used as the fitness function to evolve the circuit components values. All the work was done in

MATLAB and Simulink. As MATLAB is used to run the codes and create desired curves with its function,

its tool Simulink is used to simulate circuits and to carry out transfer functions analysis. Case studies are

presented to illustrate the method which are analogic filters used in audio applications. These circuits were

evolved by using the free package GAOT for MATLAB.

1 INTRODUCTION

Evolutionary projects are proposals for global

optimization and can be understood as search

procedures for optimal solutions, in order to design a

project. Artificial intelligence is usually inspired by

nature for modeling algorithms. Examples are neural

networks based on brain behavior, genetic

algorithms inspired on biological evolution and

other approaches found in works of researchers in

the field of artificial intelligence. For instance, the

Gray Wolf Optimizer (GWO) proposed by (Mirjalili

et al., 2020) is a stochastic algorithm based on the

hunting behavior of a pack of gray wolves. This

paper will address applications through the use of

genetic algorithms, whose properties will be used in

the field of evolutionary electronics. Its operations

have little complexity, and its structure has very

well-defined, easy-to-understand steps. The act of

programming, in general, has been inspired by

nature even for naming its terms. Artificial

intelligence is no exception for this aspect. For

example: Object-oriented languages work with the

concept of inheritance, that is, a child class can

inherit certain attributes from the parent class, as

desired by the coder. It is also common for these

terms to appear in articles e.g., the Heapsort sorting

algorithm, (

Sedgewick, 1998) which uses parent and

child elements. Evolutionary electronics purpose is a

new paradigm for problem solving inspired by

Natural Selection as proposed by Darwin, conceived

after his observations carried out in the Galapagos

Islands. From the observation of birds with different

beaks on these islands, the scientist concluded that

the birds should have a common ancestor, but would

have evolved in different environments: those that

underwent beneficial mutations for their

environment survived and managed to pass their

traits on to their descendants (Coello Coello, 1999)

(Coello Coello, 2013). It was proposed that species

could always change over time, and that new species

would emerge from pre-existing species, all of

which would share a common ancestor. In this

model, each species has a unique set of heritable

genetic differences compared to the common

ancestor, which gradually accumulated over time.

Repeated events of differentiation, in which new

species diverge from their common ancestor,

produce a multilevel "tree" that connects all living

things, known as Darwin's tree for life. When

developing an evolutionary platform, the practitioner

must choose one of three implementation methods:

intrinsic, extrinsic, or hybrid (Greenwood and

Tyrrel, 2007), (Reorda et. al., 2017). In the intrinsic

514

Coelho, P., M. do Amaral, J., N. Da Rocha, E. and Bentes, M.

Audio Circuits Evolution through Genetic Algorithms.

DOI: 10.5220/0011062500003179

In Proceedings of the 24th International Conference on Enterprise Information Systems (ICEIS 2022) - Volume 1, pages 514-520

ISBN: 978-989-758-569-2; ISSN: 2184-4992

evolutionary platform, the circuit is designed in

hardware by the genetic algorithm. The

implementation also takes place in hardware. In the

extrinsic evolutionary platform this entire process

takes place in software. The hybrid platform mixes

the concept of both. The first method is better in

terms of the possibility of also being able to verify

the circuit's operation physically, while the second

only addresses the operation through a simulator.

This work will follow the second option and

presents the implementation of an extrinsic platform,

in order to enable the evolution of usual audio

electronic circuits. The modeling presented is based

on a genetic algorithm for evaluating the choices of

components that approximate the circuit's operation

to the desired specification. This paper is organized

in four sections. The second section describes the

basics of evolutionary environment and the proposed

platform. Section three discusses case studies in

connection with the evolutionary circuits’ platform.

Finally, section four ends the paper with the

conclusions.

2 EVOLUTIONARY PLATFORM

2.1 Extrinsic Platform

The extrinsic platform (Coelho et. al., 2021) is

carried out through the use of circuit simulators,

with implementation only in software. It gives the

designer more freedom to find more varied solutions

regarding topology. There is no limitation on the

types and components that can be used in the

population. However, extrinsic evolution will

require a much longer time compared to its intrinsic

equivalent, requiring high processing capacity of the

machine on which the genetic algorithm and

simulator will be executed. Figure 1 shows the

working diagram of this type of platform.

The simulator brings to the process the ability to

establish a specific configuration for calculations of

some regime parameters such as noise, temperature

and others, and thus generate candidates even closer

to the desired ones.

The developed platform focuses

on analyzing the numerical values generated by the

genetic algorithm directly within MATLAB, which

was used to trigger Simulink within the development

environment itself, to simulate the circuit with the

solutions proposed by the genetic algorithm and also

to obtain functions circuit transfer. MATLAB has

several toolboxes, some important for the area of

artificial intelligence, such as neural networks,

genetic algorithms and fuzzy logic. There is a

toolbox named GAOT (Genetic Algorithm

Optimization Toolbox) whose algorithm was

developed by researchers at North Caroline State

University, so that it could be used directly within

the MATLAB development environment.

Figure 1: Extrinsic platform.

This toolbox was used in this work for several

reasons, the main one is that it has open code,

without any restrictions for changes. It should be

noted that MATLAB has an optimization function

based on genetic algorithms, the GA function, which

comes with the software. Figure 2 shows a flowchart

of the developed evolution platform, based on a

genetic algorithm, allowing the transfer function of a

circuit to be obtained, and also the analysis of any

system through this function. Simulink has two

functions within the platform. It is used to obtain

circuit transfer functions, at the time of modeling, in

which the platform user does not know the

mathematical description of the relationship between

the output and input of the circuit. In addition, it can

be used as a simulator after obtaining the optimal

values. In order to make the platform's operation

clearer, figure 3 presents a brief description of the

evolution process. First, the circuit topology is

chosen for the evolution of the component values.

Next, their ranges of values are related to the genes

of the individuals in the genetic algorithm, thus

determining the size of the chromosomes. After

these steps, the parameters for executing the genetic

algorithm must be defined. This configuration will

depend on the designer's objective as well as the

design specifications. Finally, the solution is

analyzed using the best chromosome, i.e. the transfer

function obtained for the optimal solution is

compared with the one considered ideal, that is, the

one conceived by a MATLAB function. The

Audio Circuits Evolution through Genetic Algorithms

515

comparison match is a guarantee that the evolved

circuit meets all circuit specifications.

Figure 2: Flowchart of the evolutionary platform using

GAOT.

Figure 3: Evolution process through the extrinsic platform.

2.2 Platform Facts

The extrinsic platform development steps are then:

1. Choose the topology for which an optimal

solution is sought.

2. Describe the behavior of the circuit that

comprises the modeling of its frequency

response.

3. Calculate the error.

4. Obtain the desired evolved circuit.

The choice of the fitness function in order to assess

the evolutionary adequacy of the platform is given

by equations 1 and 2.

Fitness

error

(1)

() ()

Goal Observed

Output i Output i

error

−



(2)

3 CASE STUDIES

The developed extrinsic platform is capable of

synthesizing a circuit and presenting an optimal

solution, given the specification and topology of a

circuit. In order to analyze its efficiency, several

case studies were developed for the analysis of the

electronic evolutionary process, of which two were

selected. The first case addresses a notch filter for

which an optimal solution was sought that would

meet an attenuation at a specific frequency. The

second case study is a low pass filter, aiming to meet

a first order active filter.

3.1 Case Study 1: Notch Filter

Notch filters, also known as band-rejectors, are

conceived in their idealization through the

superposition of a high-pass filter and a low-pass

filter. The notch filter used is based on the topology

shown in Figure 4.

Figure 4: Notch filter basic circuit.

The evolution parameters are:

• Number of generations: 100

• Number of individuals per generation: 100

• Crossover Probability: 0.85

• Probability of mutation: 0.001

Circuit specifications are given in table 1.

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Table 1: Range of resistor and capacitor values for

simplified notch filter topology.

Parameters Range of Values

Resistor 10 kΩ - 100 kΩ

Capacitor 100 nF - 700 nF

Attenuated Bandwidth 2 Hz

Attenuation frequency 60 Hz

Figure 5 shows the evolution of fitness for individuals in

the population from the genetic algorithm to the notch

filter.

Figure 5: Notch filter evolution.

The fitness curve starts from a relatively high value

(approximately 0.85) and quickly converges to 0.95.

The average fitness converges to a value close to

0.95 as well. It is possible to simulate the circuit in

Simulink or any external simulator. The evolved

notch filter including the values proposed by the

genetic algorithm is shown in Figure 6. The

proposed platform does not work with components

commercial values. Therefore, it is necessary to

adapt the values obtained, either considering the loss

of efficiency, exchanging for the equivalent of a

close value, or associating resistors and capacitors to

be as close as possible to the solution proposed by

the genetic algorithm. After obtaining the optimal

values, it is possible to simulate the circuit in

Simulink or any other external simulator. Therefore,

the response curve of the circuit evolved by the

genetic algorithm on the platform and the target

response curve can be compared.

Figure 6: Notch filter evolved circuit.

Figures 7 and 8 show the graphs of the Bode

frequency response in magnitude and phase of the

evolved curve and that of the target, confirming the

high degree of similarity between them.

Figure 7: Notch filter frequency response for target and

evolved circuit.

Figure 8: Notch filter in the region after the rejection band.

3.2 Case Study 2: Low Pass Filter

The low pass filter chosen for the evolution was an

active filter, composed of op-amp, resistors and

capacitor whose basic circuit is shown in figure 9.

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517

Figure 9: Low pass filter basic circuit.

The filter specifications are shown in Table 2.

Table 2: Low pass filter specifications.

Parameters Range of Values

Resistor 10 kΩ - 100 kΩ

Capacitor 0.01 nF - 10 nF

Gain 2

Quality Factor (Q) 4

Cut-off Frequency 200 Hz

The evolution parameters considered for the present

case are:

• Number of generations: 100

• Number of individuals per generation: 30

• Crossover Probability: 0.95

• Probability of mutation: 0.001

Figure 10 shows the evolution of fitness for the low

pass filter case study for the best chromosome. It is

noted that, unlike the graph generated for the notch

filter case, the first generations would not provide

good solutions for the circuit. The evolution of each

generation in relation to the previous one was more

significant. Note also that, again, the maximum

fitness stabilized at a value close to 0.95. However,

this value was reached with fewer generations than

in the previous case, and, again, the convergence of

the algorithm was fast. Table 3 summarize

satisfactory results obtained for the evolution of the

low pass filter.

Table 3: Summary results for the low pass filter.

Parameter Value Error

Gain 2.09 0.09

Cut-off Frequency 196 Hz 4 Hz

Figure 10: Low pass filter evolution best result.

The evolved low pass filter including the values

generated by the extrinsic platform is shown in

Figure 11.

Figure 11: Low pass filter evolved circuit.

Figure 12 compares the frequency responses of the

target and the evolved low pass filter indicating the

good performance of the extrinsic platform.

Figure 12: Low pass filter frequency response for target

and evolved circuit.

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Finally, figure 13 show the Bode diagram of the

evolved low pass filter as conceived by the platform.

Figure 13: Low pass filter frequency response solution

given by the platform.

4 CONCLUSIONS

The evolutionary process described in this study also

has applications in the digital area, such as adaptive

filters. The same process for the synthesis of the

filters described is a viable tool for the design of

other filters, such as Butterworth and Chebyshev

filters. The same evolution procedure could be

adopted with continuous genetic algorithms. This is

not the case with the application of the GAOT

package, which uses a binary genetic algorithm. It is

important to point out that these algorithms can be

modeled by a programmer in other programming

languages, or a package from another language, such

as R and Python. The most relevant fact of the

procedure is the fit in the complete process, in which

functions are used to generate considered curves and

ideas and simulators for the observed curve, later

establishing the comparison between the curves and

assigning a representative value to the degree of

similarity. In relation to continuous genetic

algorithms, the concepts of elitism, mutation,

selection and crossover have the same meaning in

relation to those existing for binary algorithms.

However, for a continuous algorithm, the parents are

generated within a limit set by the code. The

crossover generates heirs within the region by the

parents and it is the mutation, in a manner analogous

to its behavior described for binary genetic

algorithms, that will produce solutions outside the

limits established by the parents. The development

steps follow the same method. In the case of

adaptive filters, this technique has the potential to be

applied to purely digital filters, without component

synthesis. An adaptive filter is built on the basis of

an FIR or IIR filter. MATLAB has work tools for

both. There is, in the audio field, a growing market

for the use of artificial intelligence applied to digital

processing. MATLAB has many filter functions that

can be used on this extrinsic platform. Finally, it is

noted that this platform can be used for other

applications in subsequent studies, and that

MATLAB has all the necessary basis for each step

of the described evolutionary process.

The developed project had as main objective the

application in synthesis of electronic circuits used in

the audio area. Through the design of an extrinsic

platform, it was possible to obtain optimal solutions

for known topologies, without considering the

evolution of the topology. As a future work it is

being considered by the authors to include the

evolution of the topology as well. That will need a

reformulation the optimization process due to the

expansion of the search space. All this study was

carried out using the MATLAB software and its

SIMULINK extension, evolving only component

values and comparing the behavior of the transfer

functions obtained for the solution with a target

behavior, generated by mathematical functions of

MATLAB filters. For some circuits, prior

knowledge of the transfer function was necessary for

their design. However, it is emphasized here that this

fact does not create difficulties for the user of the

platform, since it is possible to obtain the transfer

function of any circuit through the joint work tools

of SIMULINK and SIMSCAPE.

Curves close to those idealized were obtained,

with satisfactory efficiency, which demonstrates the

ability of the developed platform for situations of

reasonable engineering complexity. The

combination of MATLAB tools with the

evolutionary concepts of the genetic algorithm

allowed to obtain good solutions for previously

known circuits in relation to their topology. In fact,

the only limitation of this process is that it starts

from a known topology, without evolving it, which

would increase the possibilities of solutions, but

justified by the established configurations in the

market. Finally, it was possible to verify the ability

to search for optimal solutions through evolutionary

electronics for the synthesis of analog circuits, and

also that the proposed evolution technique has other

fields of application.

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519

ACKNOWLEDGEMENTS

This study was supported in part by the

Coordenação de Aperfeiçoamento de Pessoal de

Nível Superior – Brazil (CAPES) – Finance Code

001.

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