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The optimal design and analysis of wideband second-order microwave integrator

  • Usha Gautam (a1) and Tarun Kumar Rawat (a1)


The implementation of stable, accurate, and wideband second-order microwave integrators (SOMIs) is presented in this paper. These designs of SOMIs are obtained by using different combinations of transmission line sections and shunt stubs in cascading. Particle swarm optimization (PSO), cuckoo search algorithm (CSA), and gravitational search algorithm (GSA) are applied to obtain the optimal values of the characteristic impedances of these line elements to approximate the magnitude response of ideal second-order integrator (SOI). The performance measure criteria for the proposed SOMIs are carried out based on magnitude response, absolute magnitude error, phase response, convergence rate, pole-zero plot, and improvement graph. The simulation results and statistical analysis demonstrate that GSA surpasses the PSO and CSA to approximate the ideal SOI in all state-of-the-art, that is eligible for wide-band microwave integrator. The designed SOMI is compact in size and suitable to cover microwave applications. The magnitude errors for the proposed SOMIs GSA based are as low as 4.9954 and 3.6573, respectively. The structure of the designed SOMI is implemented in the form of microstrip line on RT/Duroid substrate with dielectric constant 2.2 and having height 0.762 mm. The simulated and measured magnitude result agrees well with the ideal one in the frequency range of 3–15 GHz.


Corresponding author

Author for correspondence: Email: Usha Gautam,


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1.Oppenheim, AV and Shafer, RW (1989) Discrete-Time Signal Processing. New Jersey: Prentice-Hall.
2.Ngo, NQ (2006) A new approach for the design of wideband digital integrator and differentiator. IEEE Transactions on Circuits and Systems II: Express Briefs 53, 936940.
3.Gupta, M, Jain, M and Kumar, B (2010) Novel class of stable wideband recursive digital integrators and differentiators. IET Signal Processing 4, 560566.
4.Upadhyay, DK and Singh, RK (2011) Recursive wideband digital differentiator and integrator. Electronics Letters 47, 647648.
5.Upadhyay, DK (2012) Class of recursive wideband digital differentiators and integrators. Radioengineering 21, 904910.
6.Garg, K and Upadhyay, DK (2017) Design of second-order recursive digital integrators with matching phase and magnitude response. Radioengineering 26, 376386.
7.Skolink, MI (1980) Introduction to Radar Systems. New York: McGraw-Hill.
8.Hsue, CW, Tsai, LC and Kan, ST (2006) Implementation of a trapezoidal rule microwave integrator. Microwave and Optical Technology Letters 48, 822825.
9.Hsue, C -W, Tsai, L -C, Tsai, Y-H. (2006) Time-constant control of microwave integrators using transmission lines. IEEE Transactions on Microwave Theory and Techniques 54, 10431047.
10.Tsai, L-C and Wu, Y-T (2008) Time-constant control analysis of microwave differentiators. IET Microwaves, Antennas & Propagation 3, 10441050.
11.Tsai, LC and Fang, HS (2011) Design and implementation of second-order microwave integrators. Microwave and Optical Technology Letters 53, 19831986.
12.Upadhyay, DK and Singh, RK (2013) A simple approach to control the time constant of microwave integrator. IJMOT 8, 2327.
13.Gautam, U, Upadhyay, DK and Rawat, TK (2016) New designs of first order microwave integrator. IEEE International Conference on Signal Processing (SPIN), India, 285–289.
14.Gupta, M and Upadhyay, DK (2017) New design of second order microwave integrator. IEEE International Conference on Innovative Mechanisms for Industry Applications (ICIMIA), India, 556–560.
15.Kennedy, J and Eberhart, R (1995) Particle Swarm optimization. Proceedings of IEEE International Conference Neural Network, 4, 1942–48.
16.Shi, JY and Eberhart, RC (1999) Empirical study of particle swarm optimization. Proceedings of the Congress on Evolutionary Computation (CEC99), Washington, DC, USA, 3, 1945–1950.
17.Yang, XS and Deb, S (2009) Cuckoo search via Lvy flights. Proceedings of world congress on nature and biologically inspired computing, USA IEEE Publications, 210–214.
18.Yang, XS and Deb, S (2014) Cuckoo search: recent advances and applications. Neural Computing & Applications 24, 169–74.
19.Kumar, M and Rawat, TK (2015) Optimal fractional delay-IIR filter design using cuckoo search algorithm. ISA Transaction 59, 3954.
20.Aggarwal, A, Rawat, TK, Kumar, M and Upadhyay, DK (2016) Efficient design of digital FIR differentiator using L 1-method. Radioengineering 25, 8692.
21.Aggarwal, A, Kumar, M, Rawat, TK and Upadhyay, DK (2017) Optimal design of 2-D FIR digital differentiator uing L1-norm based cuckoo-search algorithm. Multidimensional Systems and Signals Processing 28, 1569–87.
22.Dhabal, S and Venkateswaran, P (2017) An efficient gbest-guided Cuckoo Search algorithm for higher order two channel filter bank design. Swarm and Evolutionary Computation 33, 6884.
23.Barsainya, R, Aggarwal, A and Rawat, T (2018) Optimal design of minimum multiplier lattice wave digital lowpass filter using metaheuristic techniques. IET Signal Processing 12, 700712.
24.Hong, JS and Lancanter, MJ (2001) Microstrip Filters for RF/Microwave Applications. NewYork: Wiley.
25.Rashedi, E, Nezamabadi, S and Saryazdi, S (2009) GSA: a gravitational search algorithm. Information Sciences 179, 2232–48.
26.Newton Isaac, . In Experimental Philosophy Particular Propositions are Inferred from The Phenomena and Afterwards Rendered General by Induction, 3rd ed.: Andrew Motte's English Translation published 1729.
27.Rashedi, E, Nezamabadi, S and Saryazdi, S (2011) Filter modelling using gravitational search algorithm. Engineering Applications of Artificial Intelligence's 24, 117122.
28.Saha, SK, Kar, R, Mandal, D and Ghoshal, SP (2014) Gravitation search algorithm: application to the optimal IIR filter design. Journal of King Saud university-Engineering Sciences 26, 6981.
29.Siddiquea, N and Adelib, H (2016) Application of gravitational search algorithm in engineering. Journal of Civil Engineering and Management 22, 981990.
30.Bahl, I. (2003) Lumped Elements for RF and Microwave Circuits. London: Boston.


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The optimal design and analysis of wideband second-order microwave integrator

  • Usha Gautam (a1) and Tarun Kumar Rawat (a1)


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