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A hybrid genetic algorithm for analog active filter component selection
Int. J. Electron. Commun. (AEÜ) 86 (2018) 1–7
Contents lists available at ScienceDirect
Int. J. Electron. Commun. (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Regular paper
A hybrid genetic algorithm for analog active filter component selection Turgay Kaya, Hasan Guler
⁎
T
Firat University Engineering Faculty Electrical-Electronics Engineering Department, 23119 Elazig, Turkey
A R T I C L E I N F O
A B S T R A C T
Keywords: Analog active filters HGA TS ABC DE
Analog filters are circuits that process electrical signals on a frequency-dependent basis. Analog filter circuits can be implemented using resistors, capacitors and inductors and they can also be implemented with only resistors and capacitors with the use of active circuit equipments. The selection of optimum component values is difficult because of the number of possible filter combinations. This paper presents an effective algorithm that hybridizes the Genetic Algorithm (GA) to form a Hybrid Genetic Algorithm (HGA) and proposes the use of Tabu Search (TS) for the analog active filter component selection. The GA has a powerful global searching ability and so is used to perform exploitation and because TS also has good local searching ability, it too is applied to perform exploitation. Thus, the proposed HGA will have very good searching ability. In this study, a band-pass Sallen-Key filter circuit was used, and the filter component values were found using HGA with LabVIEW. The results are compared to other reported state-of-the-art algorithms, such as the artificial bee colony (ABC) and differential evaluation (DE) to demonstrate the effectiveness and efficiency of the developed method. It can be said that the developed LabVIEW based HGA gives satisfactory results with regard to amplitude response, the minimum fitness values and the computational time.
1. Introduction Active analog filters consist of different circuit components such as resistors, capacitors and op-amps. The main advantages of this kind of filters are that they are small and lightweight. In addition, they feature high reliability and produce low noise signals. However, pole frequencies are limited due to the finite bandwidth of the active element and also, the quality factor and pole frequencies are inversely proportional. However, an optimum solution can be found. Passive circuit components such as resistors and capacitors are used in active filters. The choice of passive circuit components in active filter design is important to obtain the desired amplitude response. Thus, literature shows that many researchers have studied how to determine optimal analog filter component values. Zebelum et al. compared DE methodologies for analog passive filter design [1]. Das and Vemuri developed an automated passive analog circuit framework that uses GA [2]. Koza et al. improved an automated synthesis of analog electrical circuit by means of genetic programming (GP) [3]. In [4], a novel GP based tree representation method was studied for passive filter synthesis. Hu et al. developed GP to determine robust low-pass and high-pass analog passive filter components [5]. Goh and Li attempted to obtain optimal component values by using GA [6]. They used a GA-based growing technique in their algorithms. In [7], the
⁎
Corresponding author. E-mail addresses: tkaya@firat.edu.tr (T. Kaya), hasanguler@firat.edu.tr (H. Guler).
https://doi.org/10.1016/j.aeue.2018.01.015 Received 21 June 2017; Accepted 16 January 2018 1434-8411/ © 2018 Elsevier GmbH. All rights reserved.
advantages of DE over numerical optimization for the selection of best values for passive circuit components were presented. Vural et al. developed two nature-inspired metaheuristics, which are the DE and harmony search (HS) algorithms, for analog active filter component selection [8]. Ning et al. improved a simulated annealing method (SA) to optimize analog circuit dimensions [9]. Kalinli developed ant colony algorithm (ACA) for component value selection in active filters [10]. Horrocks et al. investigated GA algorithms for component value selection in active filter design [11,12]. Vural and Yildirim improved a particle swarm optimization algorithm for component value selection in analog filter circuits [13]. Kaya and Ince investigated analog active filters with different component values using GA [14]. LabVIEW software has been widely used to control systems and develop algorithms [15,16]. To sum up, Table 1 shows the methodology used and distinguishing features of different heuristic algorithms. In this study, a LabVIEW-based HGA algorithm was developed to optimize analog active filter component selection. Component values of a 6th order band-pass Sallen-Key active filter were calculated by using the LabVIEW-based HGA, and the results obtained from the developed algorithm are presented in Tables and Figures in next sections. It can be seen that the developed algorithm gives satisfactory results with regard to amplitude response.
Int. J. Electron. Commun. (AEÜ) 86 (2018) 1–7
T. Kaya, H. Guler
Table 1 The properties of different algorithms. References
Algorithm
Usage of method
Novelty/Features
[1,7] [2,3,5,6,11,12,14] [4] [8] [9] [10] [13] [18]
DE GA GP DE and HS SA ACA PSO GA and ABC
Finding an optimum parameter for numerical optimization problem Inspired by natural and seek solution for optimization problem Inspired by natural and seek solution for optimization problem Finding an optimum parameter and working principles of the harmony improvisation Finding local search ability Mimics real ant colony’s behavior Mimics bird’s behavior Inspired by natural and seek solution and Mimics real bee colony’s behavior
Good global search ability Good global search ability Determining robust parameter Minimizing total design error and time elapsed time – Good global search ability Good global search ability Good global search ability
2. Materials and methods
RB / RA = 3− 2.1. Band-pass filter A band-pass filter is a circuit that passes frequencies within a certain range and rejects frequencies outside that range, and its response can be characterized by a frequency band ωL < ω < ωH. In Fig. 1, a 2nd order band-pass Sallen-Key active filter can be seen. The transfer function for this circuit is given in (1) [17].
1
s2 + ⎡ R C + ⎣ 1 1
1 R3 C1
+
1 R3 C2
+
(1 − K ) ⎤·s R1 C1 ⎦
+
R1 + R2 R1 R2 R3 C1 C2
RA RB
(1)
(2)
Step 1: Set the parameters (initial population size, mutation and crossover) of the developed HGA, Step 2: Generate random chromosome and set Gen = 1, Step 3: Evaluation: Upgrade the chromosome in the population by the objective; Step 4: Does this result in convergence? If yes, go to Step 7: Else, go to Step 5: Step 5: Produce the new population for the new generation: Step 5.a: Use genetic operators (selection, crossover and mutation) to produce the new population Step 5.b: Apply the TS to improve the quality of every individual; Step 6: Gen = Gen +1 and go to Step 3; Step 7: Select the best chromosome.
If R1 = R2 = R3 = R and C1 = C2 = C are chosen in (1), the new transfer function is shown in (3).
Hc,P (s ) =
s2 +
K ·s RC (4 − K ) ·s ⎡ ⎣ RC ⎤ ⎦
+
2 R2C2
(3)
If (3) is used for a simple circuit solution, it can be simplified to (4).
Ha,H (s ) =
x·s s 2 + y1 ·s + y2
(4)
where x is equal to K/RC, y1 is equal to (4-K)/RC and y2 is equal to 2/R2C2. If these equations are solved, Eqs. (5)–(7) can be found:
R=
2 y2 C 2
K = 4−
The parameters of HGA are given in Table 2. To obtain the best results the parameters in Table 2 were varied. The parameter values in Table 2 were preferred since the performance of algorithm gave satisfactory results at these values.
(5)
2y12 y2
(7)
Many studies have been implemented recently using a hybrid algorihm. This new method seen in published literature provides more successful results than conventional methods [18,19]. In this study, the developed HGA hybridizes GA [20] and TS to select component values for an active filter. In published literature, there are various methods to implement the HGAs, and in this case, TS is inserted into GA to provide local searching. The flowchart of the developed HGA is illustrated in Fig. 2. The procedure for the developed approach is described as follows:
K in (1) is constant and can be defined as
K=1+
y2
2.2. Hybrid genetic algorithms (HGA)
K ·s R1 C1
Hc,P (s ) =
2y12
(6)
2.3. Local search using Tabu search
R2
One of the meta-heuristic methods successfully applied in a number of optimization problems is Tabu Search. TS explores the best solutions
R1
C2 Table 2 The HGA parameters.
+ Op-amp
Parameters
-
C1 Vin
R3 RA
RB
The size of the population, SizPop The total number of generations, TotGen The permitted maximum step size with no improving Reproduction probability, Rp Crossover probability, Cp Mutation probability, mp The maximum iteration size of TS, MaxTS Length of tabu list, LTL
Vout
Fig. 1. 2nd order Sallen-Key band-pass filter.
2
250 400 18 0.004 0.6 0.2 600 × (Gen/TotGen) 9
Int. J. Electron. Commun. (AEÜ) 86 (2018) 1–7
T. Kaya, H. Guler
Fig. 2. The flowchart for the developed HGA.
2.4. The developed LabVIEW-based HGA
without decreasing the objective function value during the searching process [21,22]. TS consists of several parts such as the neighborhood structure, the move attributes, the Tabu list, the aspiration criteria and the termination criteria [21]. The fundamental flowchart for TS is demonstrated in Fig. 3.
In this study, LabVIEW is used to develop the HGA structure. There are many steps and sub-VIs (Virtual Instruments subroutines) in the process. The sub-VIs created for the initial population and selection, and the crossover and mutation stages, are shown in Figs. 4 and 5, respectively. Fig. 3. The flowchart for the TS algorithm.
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Int. J. Electron. Commun. (AEÜ) 86 (2018) 1–7
T. Kaya, H. Guler
Fig. 4. The developed sub-VI for initial population.
Fig. 5. The developed sub-VI for selection, crossover and mutation.
R2-1
R2-2 R2-3
R1-1
0.01 R1-2
+
0.01 0.01
Opamp
-
0.01
0.01
RB
Opamp -
R3-2
RA
218
+
-
R3-1
Vin
R1-3
+
Opamp
0.01 RA
R3-3 10.5
RB RA
RB
Vout
Fig. 6. The 6th degree Sallen-Key bandpass active filter circuit.
3. Results In this study, an HGA-based active filter value extraction process was designed. The Intelligent Control Toolkit was used to achieve this. The 6th degree Sallen-Key bandpass active filter circuit design is given in Fig. 6. In Fig. 6, there are three stages in the circuit, and the aim is to find
Table 3 The average fitness function of the initial population for performances with different values. Parameters
HGA1
HGA2
HGA3
Average fitness Iteration numbers CPU time (sec)
0.23 207 116.45
0.2 218 120.83
0.17 230 140.41
Fig. 7. The performance of each HGAs for average fitness, iteration numbers, and CPU time.
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Int. J. Electron. Commun. (AEÜ) 86 (2018) 1–7
T. Kaya, H. Guler
implemented to obtain the resistance values. These algorithms were HGA1 that consists of GA-TS, HGA2 that combines GA-ABC, and HGA3 that contains GA-DE. The performance of each HGA was compared with regard to average fitness, iteration numbers, and CPU time in Table 3 and Fig. 7. Fig. 8 represents logarithmic error versus iteration number for each of the algorithms for the 6th degree Sallen-Key band-pass active filter (see Table 4). In this paper, the developed block diagram for active filter component selection was illustrated in Fig. 9. The filter amplitude responses for different algorithms are given in Fig. 10 and the obtained resistance values are given in Table 5. When the amplitude responses in Fig. 10 are examined-plotted using the values in Table 5, HGA 1 showed the nearest performance to the amplitude responses meeting the desired characteristics. The worst amplitude response performance belongs to HGA 3. At the lower and upper cut-off frequency, the performance of HGA1 will be best and will give the best response in filtering the signals. The other two algorithms
Table 4 Performance parameter of the resulting active filter.
HGA1 HGA2 HGA3
Error value for average deviation
Error value for maximum deviation
CPU time
Iteration
0.00105 0.00206 0.00301
0.0092 0.01 0.075
0.17 230 140.41
198 205 213
the optimum resistances values at each stages. The resistances to be found by HGA are R1-1, R2-1 and R3-1 in the first stage, R1-2, R2-2 and R3-2 in the second stage and R1-3, R2-3 and R3-3 in the last stage. In addition, in this circuit, all capacitor values are 0.01µf, and the RA and RB values for gain in the first and second stages are 10 kΩ and 24.5 kΩ, respectively, while those for the last stage are 10 kΩ and 18.4 kΩ, respectively. In this study, three different local search algorithms were
Fig. 8. Logarithmic error versus iteration number for each of the algorithm for the 6th degree Sallen-Key band-pass active filter.
Fig. 9. The developed block diagram for active filter value extraction.
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Int. J. Electron. Commun. (AEÜ) 86 (2018) 1–7
T. Kaya, H. Guler
Fig. 10. The filter response for different algorithms.
allow such optimization to be calculated in a uniform manner and will help to ease the determination of passive component values in analog active filters.
Table 5 Performances for different values of the average fitness function of the initial population. Resistance (kΩ)
HGA1
HGA2
HGA3
R1-1 R2-1 R3-1 R1-2 R2-2 R3-2 R1-3 R2-3 R3-3
1.4111 6.6466 4.4445 5.1511 5.5888 7.0241 2.2212 2.1202 2.2222
19.9929 11.1112 11.1111 9.1196 26.4221 23.1411 19.8889 22.7222 33.8123
19.1969 11.6142 11.2131 9.5196 25.2221 23.7411 9.8881 23.6292 32.1121
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.aeue.2018.01.015. References [1] Zebulum RS, Pacheco MA, Vellasco M. Comparison of different evolutionary methodologies applied to electronic filter design. IEEE Conf Evol Comput 1998:434–9. [2] Das A, Vemuri R. An automated passive analog circuit synthesis framework using genetic algorithms. In: IEEE Computer Society annual symposium on VLSI; 2007. p. 145–52. [3] Koza JR, Bennett FH, Andre D, Keane MA, Dunlap F. Automated synthesis of analog electrical circuit by means of genetic programming. IEEE Trans Evol Comput 1997;1(2):109–28. [4] Chang S-J, Hou H-S, Su Y-K. Automated passive filter synthesis using a novel tree representation and genetic programming. IEEE Trans Evol Comput 2006;10(1):93–100. [5] Hu J, Zhong X, Goodman E. Open-ended robust design of analog filters using genetic programming. Genet Evolut Comput Conf 2005:1619–26. [6] Goh C, Li Y. GA automated design and synthesis of analog circuits with practical constraints. IEEE Congr Evol Comput 2001:170–7. [7] Sheta AF. Analogue filter design using differential evolution. Int J Bio-Inspired Comput 2010;2(3/4):233–41. [8] Vural RA, Bozkurt U, Yildirim T. Analog active filter component selection with nature inspired metaheuristics. Int J Electron Commun (AEÜ) 2013;67:197–205. [9] Ning Z, Kole M, Mouthaan T, Willings H. Analog circuits design automation for performance. In: Proceedings of the 14th CICC, New York, I1 Press, 8.2.1.–8.2.4; 1992. [10] Kalinli A. Component value selection for active filters using parallel tabu search algorithm. Int J Electron Commun (AEU) 2006;60(1):85–92. [11] Horrocks DH, Khalifa YMA. Genetically evolved FDNR and leap-frog active filters using preferred component values. In: Proc European conference on circuits theory and design, Turkey; 1995. p. 359–62. [12] D.H. Horrocks, Y.M.A. Khalifa, “Genetic algorithm design of electronic analogue circuits including parasitic effects”. Proc. First On-Line Workshop on Soft Computing (WSC1), Nagoya University, Japan, 1996, 71–78. [13] Vural RA, Yildirim T. Component value selection for analog active filter using particle swarm optimization. Computer and Automation Engineering (ICCAE), 2010 The 2nd International Conference on, vol. 1; 2010. p. 25–8. [14] Kaya T, Ince MC. The design of analog active filter with different component value using genetic algorithm. Int J Comp Appl 2012;45(8):45–7. [15] Guler H, Turkoglu I, Ata F. Designing intelligent mechanical ventilator and user interface using LabVIEW (R). Arab J Sci Eng 2014;39(6):4805–13. [16] Guler H, Ata F. Design of a Fuzzy-Labview-based mechanical ventilator. Comput Syst Sci Eng 2014;29(3):219–29.
(HGA2 and HGA3) perform poorly, especially at the upper cut-off frequency. 4. Conclusion Resistors, capacitors and op-amps are generally used in active filters. These kinds of filters are small, lightweight, have high reliability and produce low noise signals. The choice of passive circuit components such as resistors and capacitors in active filter design is important to obtain the desired amplitude response. In a circuit design implemented by using equal component values, the design does not provide for different component values that the user may have. This problem has been removed with the help of the improved method. This study tried to choose the values of passive circuit components by using LabVIEW-based GA-TS. The extraction of filter values with HGA in LabVIEW is an easy calculation and offers easier circuit design possibilities for users. The component values of the 6th order band-pass Sallen Key active filter were estimated by the developed algorithm. The obtained values for resistors used in the active filter are presented in Tables. The amplitude response for GA-TS, GA-ABC and GA-DE algorithms were plotted. According to the amplitude response, GA-TS gave better results than the other algorithms. It can be seen from these figures that even the worst amplitude response obtained from the developed algorithm gave close to the desired amplitude response. Although a 6th order band-pass filter was used, the developed algorithm can be easily generalized for low-pass, high-pass and band-stop filters with different circuit models. This will
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Int. J. Electron. Commun. (AEÜ) 86 (2018) 1–7
T. Kaya, H. Guler
[20] Kaya T, Ince MC. The FIR filter design by using window parameters calculated with GA. ICSCCW- Fifth international conference on soft computing, computing with words and perceptions in system analysis, decision and control; 2009. [21] Li X, Gao L. An effective hybrid genetic algorithm and tabu search for flexible job shop cheduling problem. Int J Prod Econ 1, vol. 74; 2016. No. 93–110. [22] Glover F, Laguna M. Tabu search. Norwell, MA, USA: Kluwer Academic Publishers; 1997.
[17] Thede L. Analog and digital filter design. New Jersey: Prentice Hall; 1996. [18] Kumar A, Kumar V. Hybridized ABC-GA optimized fractional order fuzzy precompensated FOPID control design for 2-DOF robot manipulator. Int J Electron Commun (AEU) 2017;79:219–33. [19] Kumar Mahto S, Choubey A. A novel hybrid IWO-WDO algorithm for nulling pattern synthesis of uniformly spaced linear and non-uniform circular array antenna. Int J Electron Commun (AEU) 2016;70:750–6.
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Contents lists available at ScienceDirect
Int. J. Electron. Commun. (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Regular paper
A hybrid genetic algorithm for analog active filter component selection Turgay Kaya, Hasan Guler
⁎
T
Firat University Engineering Faculty Electrical-Electronics Engineering Department, 23119 Elazig, Turkey
A R T I C L E I N F O
A B S T R A C T
Keywords: Analog active filters HGA TS ABC DE
Analog filters are circuits that process electrical signals on a frequency-dependent basis. Analog filter circuits can be implemented using resistors, capacitors and inductors and they can also be implemented with only resistors and capacitors with the use of active circuit equipments. The selection of optimum component values is difficult because of the number of possible filter combinations. This paper presents an effective algorithm that hybridizes the Genetic Algorithm (GA) to form a Hybrid Genetic Algorithm (HGA) and proposes the use of Tabu Search (TS) for the analog active filter component selection. The GA has a powerful global searching ability and so is used to perform exploitation and because TS also has good local searching ability, it too is applied to perform exploitation. Thus, the proposed HGA will have very good searching ability. In this study, a band-pass Sallen-Key filter circuit was used, and the filter component values were found using HGA with LabVIEW. The results are compared to other reported state-of-the-art algorithms, such as the artificial bee colony (ABC) and differential evaluation (DE) to demonstrate the effectiveness and efficiency of the developed method. It can be said that the developed LabVIEW based HGA gives satisfactory results with regard to amplitude response, the minimum fitness values and the computational time.
1. Introduction Active analog filters consist of different circuit components such as resistors, capacitors and op-amps. The main advantages of this kind of filters are that they are small and lightweight. In addition, they feature high reliability and produce low noise signals. However, pole frequencies are limited due to the finite bandwidth of the active element and also, the quality factor and pole frequencies are inversely proportional. However, an optimum solution can be found. Passive circuit components such as resistors and capacitors are used in active filters. The choice of passive circuit components in active filter design is important to obtain the desired amplitude response. Thus, literature shows that many researchers have studied how to determine optimal analog filter component values. Zebelum et al. compared DE methodologies for analog passive filter design [1]. Das and Vemuri developed an automated passive analog circuit framework that uses GA [2]. Koza et al. improved an automated synthesis of analog electrical circuit by means of genetic programming (GP) [3]. In [4], a novel GP based tree representation method was studied for passive filter synthesis. Hu et al. developed GP to determine robust low-pass and high-pass analog passive filter components [5]. Goh and Li attempted to obtain optimal component values by using GA [6]. They used a GA-based growing technique in their algorithms. In [7], the
⁎
Corresponding author. E-mail addresses: tkaya@firat.edu.tr (T. Kaya), hasanguler@firat.edu.tr (H. Guler).
https://doi.org/10.1016/j.aeue.2018.01.015 Received 21 June 2017; Accepted 16 January 2018 1434-8411/ © 2018 Elsevier GmbH. All rights reserved.
advantages of DE over numerical optimization for the selection of best values for passive circuit components were presented. Vural et al. developed two nature-inspired metaheuristics, which are the DE and harmony search (HS) algorithms, for analog active filter component selection [8]. Ning et al. improved a simulated annealing method (SA) to optimize analog circuit dimensions [9]. Kalinli developed ant colony algorithm (ACA) for component value selection in active filters [10]. Horrocks et al. investigated GA algorithms for component value selection in active filter design [11,12]. Vural and Yildirim improved a particle swarm optimization algorithm for component value selection in analog filter circuits [13]. Kaya and Ince investigated analog active filters with different component values using GA [14]. LabVIEW software has been widely used to control systems and develop algorithms [15,16]. To sum up, Table 1 shows the methodology used and distinguishing features of different heuristic algorithms. In this study, a LabVIEW-based HGA algorithm was developed to optimize analog active filter component selection. Component values of a 6th order band-pass Sallen-Key active filter were calculated by using the LabVIEW-based HGA, and the results obtained from the developed algorithm are presented in Tables and Figures in next sections. It can be seen that the developed algorithm gives satisfactory results with regard to amplitude response.
Int. J. Electron. Commun. (AEÜ) 86 (2018) 1–7
T. Kaya, H. Guler
Table 1 The properties of different algorithms. References
Algorithm
Usage of method
Novelty/Features
[1,7] [2,3,5,6,11,12,14] [4] [8] [9] [10] [13] [18]
DE GA GP DE and HS SA ACA PSO GA and ABC
Finding an optimum parameter for numerical optimization problem Inspired by natural and seek solution for optimization problem Inspired by natural and seek solution for optimization problem Finding an optimum parameter and working principles of the harmony improvisation Finding local search ability Mimics real ant colony’s behavior Mimics bird’s behavior Inspired by natural and seek solution and Mimics real bee colony’s behavior
Good global search ability Good global search ability Determining robust parameter Minimizing total design error and time elapsed time – Good global search ability Good global search ability Good global search ability
2. Materials and methods
RB / RA = 3− 2.1. Band-pass filter A band-pass filter is a circuit that passes frequencies within a certain range and rejects frequencies outside that range, and its response can be characterized by a frequency band ωL < ω < ωH. In Fig. 1, a 2nd order band-pass Sallen-Key active filter can be seen. The transfer function for this circuit is given in (1) [17].
1
s2 + ⎡ R C + ⎣ 1 1
1 R3 C1
+
1 R3 C2
+
(1 − K ) ⎤·s R1 C1 ⎦
+
R1 + R2 R1 R2 R3 C1 C2
RA RB
(1)
(2)
Step 1: Set the parameters (initial population size, mutation and crossover) of the developed HGA, Step 2: Generate random chromosome and set Gen = 1, Step 3: Evaluation: Upgrade the chromosome in the population by the objective; Step 4: Does this result in convergence? If yes, go to Step 7: Else, go to Step 5: Step 5: Produce the new population for the new generation: Step 5.a: Use genetic operators (selection, crossover and mutation) to produce the new population Step 5.b: Apply the TS to improve the quality of every individual; Step 6: Gen = Gen +1 and go to Step 3; Step 7: Select the best chromosome.
If R1 = R2 = R3 = R and C1 = C2 = C are chosen in (1), the new transfer function is shown in (3).
Hc,P (s ) =
s2 +
K ·s RC (4 − K ) ·s ⎡ ⎣ RC ⎤ ⎦
+
2 R2C2
(3)
If (3) is used for a simple circuit solution, it can be simplified to (4).
Ha,H (s ) =
x·s s 2 + y1 ·s + y2
(4)
where x is equal to K/RC, y1 is equal to (4-K)/RC and y2 is equal to 2/R2C2. If these equations are solved, Eqs. (5)–(7) can be found:
R=
2 y2 C 2
K = 4−
The parameters of HGA are given in Table 2. To obtain the best results the parameters in Table 2 were varied. The parameter values in Table 2 were preferred since the performance of algorithm gave satisfactory results at these values.
(5)
2y12 y2
(7)
Many studies have been implemented recently using a hybrid algorihm. This new method seen in published literature provides more successful results than conventional methods [18,19]. In this study, the developed HGA hybridizes GA [20] and TS to select component values for an active filter. In published literature, there are various methods to implement the HGAs, and in this case, TS is inserted into GA to provide local searching. The flowchart of the developed HGA is illustrated in Fig. 2. The procedure for the developed approach is described as follows:
K in (1) is constant and can be defined as
K=1+
y2
2.2. Hybrid genetic algorithms (HGA)
K ·s R1 C1
Hc,P (s ) =
2y12
(6)
2.3. Local search using Tabu search
R2
One of the meta-heuristic methods successfully applied in a number of optimization problems is Tabu Search. TS explores the best solutions
R1
C2 Table 2 The HGA parameters.
+ Op-amp
Parameters
-
C1 Vin
R3 RA
RB
The size of the population, SizPop The total number of generations, TotGen The permitted maximum step size with no improving Reproduction probability, Rp Crossover probability, Cp Mutation probability, mp The maximum iteration size of TS, MaxTS Length of tabu list, LTL
Vout
Fig. 1. 2nd order Sallen-Key band-pass filter.
2
250 400 18 0.004 0.6 0.2 600 × (Gen/TotGen) 9
Int. J. Electron. Commun. (AEÜ) 86 (2018) 1–7
T. Kaya, H. Guler
Fig. 2. The flowchart for the developed HGA.
2.4. The developed LabVIEW-based HGA
without decreasing the objective function value during the searching process [21,22]. TS consists of several parts such as the neighborhood structure, the move attributes, the Tabu list, the aspiration criteria and the termination criteria [21]. The fundamental flowchart for TS is demonstrated in Fig. 3.
In this study, LabVIEW is used to develop the HGA structure. There are many steps and sub-VIs (Virtual Instruments subroutines) in the process. The sub-VIs created for the initial population and selection, and the crossover and mutation stages, are shown in Figs. 4 and 5, respectively. Fig. 3. The flowchart for the TS algorithm.
3
Int. J. Electron. Commun. (AEÜ) 86 (2018) 1–7
T. Kaya, H. Guler
Fig. 4. The developed sub-VI for initial population.
Fig. 5. The developed sub-VI for selection, crossover and mutation.
R2-1
R2-2 R2-3
R1-1
0.01 R1-2
+
0.01 0.01
Opamp
-
0.01
0.01
RB
Opamp -
R3-2
RA
218
+
-
R3-1
Vin
R1-3
+
Opamp
0.01 RA
R3-3 10.5
RB RA
RB
Vout
Fig. 6. The 6th degree Sallen-Key bandpass active filter circuit.
3. Results In this study, an HGA-based active filter value extraction process was designed. The Intelligent Control Toolkit was used to achieve this. The 6th degree Sallen-Key bandpass active filter circuit design is given in Fig. 6. In Fig. 6, there are three stages in the circuit, and the aim is to find
Table 3 The average fitness function of the initial population for performances with different values. Parameters
HGA1
HGA2
HGA3
Average fitness Iteration numbers CPU time (sec)
0.23 207 116.45
0.2 218 120.83
0.17 230 140.41
Fig. 7. The performance of each HGAs for average fitness, iteration numbers, and CPU time.
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Int. J. Electron. Commun. (AEÜ) 86 (2018) 1–7
T. Kaya, H. Guler
implemented to obtain the resistance values. These algorithms were HGA1 that consists of GA-TS, HGA2 that combines GA-ABC, and HGA3 that contains GA-DE. The performance of each HGA was compared with regard to average fitness, iteration numbers, and CPU time in Table 3 and Fig. 7. Fig. 8 represents logarithmic error versus iteration number for each of the algorithms for the 6th degree Sallen-Key band-pass active filter (see Table 4). In this paper, the developed block diagram for active filter component selection was illustrated in Fig. 9. The filter amplitude responses for different algorithms are given in Fig. 10 and the obtained resistance values are given in Table 5. When the amplitude responses in Fig. 10 are examined-plotted using the values in Table 5, HGA 1 showed the nearest performance to the amplitude responses meeting the desired characteristics. The worst amplitude response performance belongs to HGA 3. At the lower and upper cut-off frequency, the performance of HGA1 will be best and will give the best response in filtering the signals. The other two algorithms
Table 4 Performance parameter of the resulting active filter.
HGA1 HGA2 HGA3
Error value for average deviation
Error value for maximum deviation
CPU time
Iteration
0.00105 0.00206 0.00301
0.0092 0.01 0.075
0.17 230 140.41
198 205 213
the optimum resistances values at each stages. The resistances to be found by HGA are R1-1, R2-1 and R3-1 in the first stage, R1-2, R2-2 and R3-2 in the second stage and R1-3, R2-3 and R3-3 in the last stage. In addition, in this circuit, all capacitor values are 0.01µf, and the RA and RB values for gain in the first and second stages are 10 kΩ and 24.5 kΩ, respectively, while those for the last stage are 10 kΩ and 18.4 kΩ, respectively. In this study, three different local search algorithms were
Fig. 8. Logarithmic error versus iteration number for each of the algorithm for the 6th degree Sallen-Key band-pass active filter.
Fig. 9. The developed block diagram for active filter value extraction.
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Fig. 10. The filter response for different algorithms.
allow such optimization to be calculated in a uniform manner and will help to ease the determination of passive component values in analog active filters.
Table 5 Performances for different values of the average fitness function of the initial population. Resistance (kΩ)
HGA1
HGA2
HGA3
R1-1 R2-1 R3-1 R1-2 R2-2 R3-2 R1-3 R2-3 R3-3
1.4111 6.6466 4.4445 5.1511 5.5888 7.0241 2.2212 2.1202 2.2222
19.9929 11.1112 11.1111 9.1196 26.4221 23.1411 19.8889 22.7222 33.8123
19.1969 11.6142 11.2131 9.5196 25.2221 23.7411 9.8881 23.6292 32.1121
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.aeue.2018.01.015. References [1] Zebulum RS, Pacheco MA, Vellasco M. Comparison of different evolutionary methodologies applied to electronic filter design. IEEE Conf Evol Comput 1998:434–9. [2] Das A, Vemuri R. An automated passive analog circuit synthesis framework using genetic algorithms. In: IEEE Computer Society annual symposium on VLSI; 2007. p. 145–52. [3] Koza JR, Bennett FH, Andre D, Keane MA, Dunlap F. Automated synthesis of analog electrical circuit by means of genetic programming. IEEE Trans Evol Comput 1997;1(2):109–28. [4] Chang S-J, Hou H-S, Su Y-K. Automated passive filter synthesis using a novel tree representation and genetic programming. IEEE Trans Evol Comput 2006;10(1):93–100. [5] Hu J, Zhong X, Goodman E. Open-ended robust design of analog filters using genetic programming. Genet Evolut Comput Conf 2005:1619–26. [6] Goh C, Li Y. GA automated design and synthesis of analog circuits with practical constraints. IEEE Congr Evol Comput 2001:170–7. [7] Sheta AF. Analogue filter design using differential evolution. Int J Bio-Inspired Comput 2010;2(3/4):233–41. [8] Vural RA, Bozkurt U, Yildirim T. Analog active filter component selection with nature inspired metaheuristics. Int J Electron Commun (AEÜ) 2013;67:197–205. [9] Ning Z, Kole M, Mouthaan T, Willings H. Analog circuits design automation for performance. In: Proceedings of the 14th CICC, New York, I1 Press, 8.2.1.–8.2.4; 1992. [10] Kalinli A. Component value selection for active filters using parallel tabu search algorithm. Int J Electron Commun (AEU) 2006;60(1):85–92. [11] Horrocks DH, Khalifa YMA. Genetically evolved FDNR and leap-frog active filters using preferred component values. In: Proc European conference on circuits theory and design, Turkey; 1995. p. 359–62. [12] D.H. Horrocks, Y.M.A. Khalifa, “Genetic algorithm design of electronic analogue circuits including parasitic effects”. Proc. First On-Line Workshop on Soft Computing (WSC1), Nagoya University, Japan, 1996, 71–78. [13] Vural RA, Yildirim T. Component value selection for analog active filter using particle swarm optimization. Computer and Automation Engineering (ICCAE), 2010 The 2nd International Conference on, vol. 1; 2010. p. 25–8. [14] Kaya T, Ince MC. The design of analog active filter with different component value using genetic algorithm. Int J Comp Appl 2012;45(8):45–7. [15] Guler H, Turkoglu I, Ata F. Designing intelligent mechanical ventilator and user interface using LabVIEW (R). Arab J Sci Eng 2014;39(6):4805–13. [16] Guler H, Ata F. Design of a Fuzzy-Labview-based mechanical ventilator. Comput Syst Sci Eng 2014;29(3):219–29.
(HGA2 and HGA3) perform poorly, especially at the upper cut-off frequency. 4. Conclusion Resistors, capacitors and op-amps are generally used in active filters. These kinds of filters are small, lightweight, have high reliability and produce low noise signals. The choice of passive circuit components such as resistors and capacitors in active filter design is important to obtain the desired amplitude response. In a circuit design implemented by using equal component values, the design does not provide for different component values that the user may have. This problem has been removed with the help of the improved method. This study tried to choose the values of passive circuit components by using LabVIEW-based GA-TS. The extraction of filter values with HGA in LabVIEW is an easy calculation and offers easier circuit design possibilities for users. The component values of the 6th order band-pass Sallen Key active filter were estimated by the developed algorithm. The obtained values for resistors used in the active filter are presented in Tables. The amplitude response for GA-TS, GA-ABC and GA-DE algorithms were plotted. According to the amplitude response, GA-TS gave better results than the other algorithms. It can be seen from these figures that even the worst amplitude response obtained from the developed algorithm gave close to the desired amplitude response. Although a 6th order band-pass filter was used, the developed algorithm can be easily generalized for low-pass, high-pass and band-stop filters with different circuit models. This will
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