Abstract

The re-configurable filter allows independent tuning of frequency and changes the frequency response of the filter without switching the circuit components. Here, fractional-capacitors and fractional-inductors are used to design a re-configurable fractional order band-stop and all-pass filter to replicate the frequency domain behavior of each other. The proposed filter has been tested in the frequency range of 10 Hz to 10 MHz. The primary aim of this article is to realize, the design parameters (center frequency and bandwidth) of re-configurable filters using fractional order topology, where tunability of filter components is not reliable. To explore the dependence of notches and all-pass characteristics with the variation of fractional exponents of both the proposed filters, the simulation studies have been carried out by varying the exponents (α, β) from 0.1 to 1.0 with a step of 0.1 maintaining one exponent fixed and vice-versa. It is observed experimentally that a re-configurable integer order (IO) band-stop filter can be designed by using fractional value of order (i.e., α=0.5 and β=0.7) of all-pass filter. The stability of the proposed filters has also been investigated by observing the step response of the filter. Finally, the Python software was used to characterize the design parameters of the suggested filters and it was observed that the frequency response of the proposed filters shifts to their IO counterpart at those orders (i.e., α=0.5 and β=0.7). Hence, the flexibility in obtaining the notch frequency in fractional-order all-pass filter using the exponents α and β helps the researchers to realize a band-stop filter with desired specifications.

Keyword

All-pass filter, Band-stop filter, Fractional capacitors, Fractional inductor, Fractional orders, Step response.

Cite this article

Biswal K, Swain S, Tripathy MC, Kar SK

Refference

[1][1]Moshrefi-torbati M, Hammond JK. Physical and geometrical interpretation of fractional operators. Journal of the Franklin Institute. 1998; 335(6):1077-86.

[2][2]Caponetto R. Fractional order systems: modeling and control applications. World Scientific; 2010.

[3][3]Radwan AG, Soliman AM, Elwakil AS. First-order filters generalized to the fractional domain. Journal of Circuits, Systems, and Computers. 2008; 17(1):55-66.

[4][4]Biswal K, Swain S, Tripathy MC, Kar SK. Modeling and performance improvement of fractional-order band-pass filter using fractional elements. IETE Journal of Research. 2021:1-10.

[5][5]Swain S, Mohapatra D, Tripathy MC, Behera S. Design study of DC-DC fractional-order boost-converter using fractional-capacitor. In 7th international conference for convergence in technology 2022 (pp. 1-5). IEEE.

[6][6]Yadav R, Kumari U. Design an optimal digital phase lock loop with current-starved ring VCO using CMOS technology. International Journal of Information Technology. 2021; 13(4):1625-31.

[7][7]Naglich EJ, Lee J, Peroulis D, Chappell WJ. Switchless tunable bandstop-to-all-pass reconfigurable filter. IEEE Transactions on Microwave Theory and Techniques. 2012; 60(5):1258-65.

[8][8]Soltan A, Radwan AG, Soliman AM. Fractional order sallen–key and KHN filters: stability and poles allocation. Circuits, Systems, and Signal Processing. 2015; 34(5):1461-80.

[9][9]Saising E, Prommee P. Fully tunable all-pass filter using OTA and its application. In 39th international conference on telecommunications and signal processing 2016 (pp. 287-90). IEEE.

[10][10]Chattopadhyay T, Majumder SD, Bhattacharyya P, Mondal BJ. Design and analysis of a microwave band reject filter using a double magic tee. In international conference on signal processing and communications 2014 (pp. 1-5). IEEE.

[11][11]Freeborn T, Maundy B, Elwakil AS. Approximated fractional order Chebyshev lowpass filters. Mathematical Problems in Engineering. 2015; 2015:1-8.

[12][12]Freeborn TJ, Maundy B, Elwakil AS. Cole impedance extractions from the step-response of a current excited fruit sample. Computers and Electronics in Agriculture. 2013; 98:100-8.

[13][13]Domansky O, Sotner R, Langhammer L, Polak L. Electronically reconfigurable and tunable fractional-order filter using resonator concept and feedforward path for low-frequency tone signalization. IEEE Access. 2021; 9:138026-41.

[14][14]Soltan A, Radwan AG, Soliman AM. Fractional order filter with two fractional elements of dependant orders. Microelectronics Journal. 2012; 43(11):818-27.

[15][15]Boukal Y, Darouach M, Zasadzinski M, Radhy NE. Design of functional fractional-order observers for linear time-delay fractional-order systems in the time domain. In ICFDA14 international conference on fractional differentiation and its applications 2014 (pp. 1-6). IEEE.

[16][16]Sotner R, Petrzela J, Jerabek J, Dostal T. Reconnection-less OTA-based biquad filter with electronically reconfigurable transfers. Elektronika IR Elektrotechnika. 2015; 21(3):33-7.

[17][17]Freeborn TJ. Comparison of (1+ α) fractional-order transfer functions to approximate lowpass Butterworth magnitude responses. Circuits, Systems, and Signal Processing. 2016; 35(6):1983-2002.

[18][18]Adoum BA, Wen WP. Investigation of band-stop to all pass reconfigurable filter. In 4th international conference on intelligent and advanced systems 2012 (pp. 190-3). IEEE.

[19][19]Chen YM, Chang SF, Chou CY, Liu KH. A reconfigurable bandpass-bandstop filter based on varactor-loaded closed-ring resonators. IEEE Microwave Magazine. 2009; 10(1):138-40.

[20][20]Tsirimokou G, Psychalinos C, Elwakil AS, Salama KN. Experimental behavior evaluation of series and parallel connected constant phase elements. AEU-International Journal of Electronics and Communications. 2017; 74:5-12.

[21][21]Biswal K, Kar SK, Tripathy MC. Stability analysis of fractional-order filters realized with PMMA coated elements. In international conference in advances in power, signal, and information technology 2021 (pp. 1-5). IEEE.

[22][22]Lee TH, Lee B, Nam S, Kim YS, Lee J. Frequency-tunable tri-function filter. IEEE Transactions on Microwave Theory and Techniques. 2017; 65(11):4584-92.

[23][23]Mondal D, Biswas K. Performance study of fractional order integrator using single-component fractional order element. IET Circuits, Devices & Systems. 2011; 5(4):334-42.

[24][24]Tsirimokou G, Psychalinos C, Elwakil AS. Fractional‐order electronically controlled generalized filters. International Journal of Circuit Theory and Applications. 2017; 45(5):595-612.

[25][25]Zhao KY, Li L, Wu QH, Xu W, Wang YM. Reconfigurable bandstop filter with adjustable bandwidth and center frequency. Progress in Electromagnetics Research Letters. 2012; 35:125-33.

[26][26]Comer DT, Comer DJ, Gonzalez JR. A high-frequency integrable bandpass filter configuration. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing. 1997; 44(10):856-61.

[27][27]Ahmad BH, Zahari MK, Wong PW. Design and comparison of reconfigurable perfectly matched bandstop filters. International Journal of Electronics and Computer Science Engineering. 2013; 2(1):360-9.

[28][28]Khoder K, Pérennec A, Le RM. A 180° tunable analog phase shifter based on a single all‐pass unit cell. Microwave and Optical Technology Letters. 2013; 55(12):2915-8.

[29][29]Fan M, Song K, Zhu Y, Fan Y. Compact bandpass-to-bandstop reconfigurable filter with wide tuning range. IEEE Microwave and Wireless Components Letters. 2019; 29(3):198-200.

[30][30]Dvorak J, Jerabek J, Polesakova Z, Kubanek D, Blazek P. Multifunctional electronically reconfigurable and tunable fractional-order filter. Elektronika IR Elektrotechnika. 2019; 25(1):26-30.

[31][31]Lee J, Naglich EJ, Chappell WJ. Frequency response control in frequency-tunable bandstop filters. IEEE Microwave and Wireless Components Letters. 2010; 20(12):669-71.

[32][32]Golestan S, Guerrero JM, Vasquez JC, Abusorrah AM, Al-turki Y. All-pass-filter-based PLL systems: linear modeling, analysis, and comparative evaluation. IEEE Transactions on Power Electronics. 2019; 35(4):3558-72.

[33][33]Jerabek J, Sotner R, Dvorak J, Polak J, Kubanek D, Herencsar N, et al. Reconfigurable fractional-order filter with electronically controllable slope of attenuation, pole frequency and type of approximation. Journal of Circuits, Systems and Computers. 2017; 26(10):1-21.

[34][34]Mohapatra AS, Biswas K. A fractional order notch filter to compensate the attenuation-loss due to change in order of the circuit. IEEE Transactions on Circuits and Systems I: Regular Papers. 2020; 68(2):655-66.

[35][35]Sladok O, Koton J, Kubanek D, Dvorak J, Psychalinos C. Pseudo-differential (2+ α)-order Butterworth frequency filter. IEEE Access. 2021; 9:92178-88.

[36][36]Adhikary A, Sen S, Biswas K. Practical realization of tunable fractional order parallel resonator and fractional order filters. IEEE Transactions on Circuits and Systems I: Regular Papers. 2016; 63(8):1142-51.

[37][37]Adhikary A, Shil A, Biswas K. Realization of foster structure-based ladder fractor with phase band specification. Circuits, Systems, and Signal Processing. 2020; 39(5):2272-92.

[38][38]Saeedi S, Lee J, Sigmarsson HH. Tunable, high-Q, substrate-integrated, evanescent-mode cavity bandpass-bandstop filter cascade. IEEE Microwave and Wireless Components Letters. 2016; 26(4):240-2.

[39][39]Singh B, Maheshwari S. All pass filter using DTMOS technique. In international conference on smart electronics and communication 2020 (pp. 1301-5). IEEE.

[40][40]Sotner R, Jerabek J, Polak L, Langhammer L, Stolarova H, Petrzela J, et al. On the performance of electronically tunable fractional-order oscillator using grounded resonator concept. AEU-International Journal of Electronics and Communications. 2021; 129:1-17.

[41][41]Lababidi R, Al SM, Le RM, Le JD, Khoder K, Pérennec A. Tunable channelised bandstop passive filter using reconfigurable phase shifter. IET Microwaves, Antennas & Propagation. 2019; 13(5):591-6.

[42][42]Pakhira A, Das S, Acharya A, Pan I, Saha S. Optimized quality factor of fractional order analog filters with band-pass and band-stop characteristics. In third international conference on computing, communication and networking technologies 2012 (pp. 1-6). IEEE.

[43][43]Chen R, Sheng Q, Zhou L, Chen C, Zhang H. High-Q bandpass-to-bandstop reconfigurable filter based on SAW resonators. In IEEE/MTT-S international microwave symposium 2020 (pp. 123-6). IEEE.

[44][44]Zhu Y, Dong Y. Novel dual-band bandpass-to-bandstop filter using shunt PIN switches loaded on the transmission line. In IEEE/MTT-S international microwave symposium 2020 (pp. 924-7). IEEE.

[45][45]Langhammer L, Sotner R, Dvorak J, Jerabek J, Andriukaitis D. Reconnection–less reconfigurable fractional–order current–mode integrator design with simple control. IEEE Access. 2021; 9:136395-405.

[46][46]Verma R, Pandey N, Pandey R. Realization of a higher fractional order element based on novel OTA based IIMC and its application in filter. Analog Integrated Circuits and Signal Processing. 2018; 97(1):177-91.

[47][47]Sotner R, Jerabek J, Herencsar N, Vrba K, Dostal T. Features of multi-loop structures with OTAs and adjustable current amplifier for second-order multiphase/quadrature oscillators. AEU-International Journal of Electronics and Communications. 2015; 69(5):814-22.

[48][48]Koton J, Kubanek D, Sladok O, Vrba K, Shadrin A, Ushakov P. Fractional-order low-and high-pass filters using UVCs. Journal of Circuits, Systems and Computers. 2017; 26(12):1-23.

[49][49]Keskin AÜ, Pal K, Hancioglu E. Resistorless first-order all-pass filter with electronic tuning. AEU-International Journal of Electronics and Communications. 2008; 62(4):304-6.

[50][50]Bhaskar DR, Kumar M, Kumar P. Minimal realization of fractional-order inverse filters. IETE Journal of Research. 2020:1-4.

[51][51]Banerjee S, Borah SS, Ghosh M, Mondal P. Three novel configurations of second order inverse band reject filter using a single operational transresistance amplifier. In TENCON 2019 (pp. 2173-8). IEEE.