Current mode fractional order filters using VDTAs with Grounded capacitors


  • Dinesh Prasad Jamia Millia Islamia
  • Mayank Kumar
  • Md Waseem Akram


In this work, the design of current mode Fractional order filter using VDTAs (Voltage differencing trans-conductance amplifier) as an active element with grounded capacitors has been proposed. The approximate transfer functions of low and high pass filters of fractional order on the basis of the integer order transfer has been shown and the form of those functions of filters is also implemented using VDTA as an active building block. In this work, filters of the different sequence have been realized. The frequency domain simulation results of the proposed filters are obtained on Matlab and PSPICE with TSMC CMOS 180 nm technology parameters. Stability and sensitivity is also verified

Author Biography

Dinesh Prasad, Jamia Millia Islamia

Associate Professor


K. Miller and B. Ross, “An Introduction to the Fractional Calculus and Fractional Differential Equations”. First Edition New York: Wiley,1993.

B. T. Krishna, “Studies on fractional order differentiators and integrators: A survey”, Signal Processing, vol 91, pp. 386–426, March 2011.

J. Sabatier, O. P. Agarwal and J. A. T. Machado, “Advances in fractional calculus”, First Edition, Springer 2007.

Y. Chen, B. M. Vinagre and I. Podlubny, “Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives—an Expository Review”, Springer Nonlinear Dynamics, vol. 38(1-4), pp.155–170, December 2004.

A. Soltan, A. G. Radwan, A. M. Soliman, “CCII based fractional filters of different orders”, Journal of Advanced Research, vol. 5, pp157-164, March 2014.

A. Soltan, A. G. Radwan and A. M. Soliman, “Fractional order butterworth filter: active and passive realizations” IEEE journal on emerging and selected topics in circuits and systems, vol. 3 (3),pp. 346-354 September 2013.

H. Li, Y. Luo and Y. Q. Chen, “A fractional-order proportional and derivative (FOPD) motion controller: Tuning rule and experiments”, IEEE Trans. Control Syst. Tech., vol 18(2), pp 516–520, March 2010.

A. Soltan, A. G. Radwan and A. M. Soliman, “Fractional order filter with two fractional elements of dependant orders”, Microelectronics. Journal, 43(11) 818–827, November 2012).

E. A. Sobhy and A. M. Soliman, “Novel CMOS realizations of the inverting second-generation current conveyor and applications”, Analog Integrated Circuit, vol. 52, pp. 57–64 August 2007.

G. Tsirimokou, C. Psychalinos and A. S. Elwakil, “Fractional‐ order electronically controlled generalized filters” International Journal of Circuit Theory and Applications, vol. 45(5), pp. 595-612, September 2017.

A. G. Radwan, A. Gomaa, A. S. Elwakil and A. M. Soliman ,“Fractional-order sinusoidal oscillators: design procedure and practical examples”, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 55(7), pp. 2051-2063, February 2008.

C. C. Tseng, “Design of FIR and IIR fractional order Simpson digital integrators”, Signal Processing, vol. 87 (5), pp.1045-1057, May 2007.

Mayank kumar et. al.,” current mode fractional order band pass and band stop filters using VDTA”, Indian journal of pure and applied physics, vol.56, pp. 533-537, July 2018.

M. Bhushan and R. Newcomb, “Grounding of capacitors in integrated circuits”, Electronics Letters, vol. 3, pp 148-149, April 1967.

G. Tsirimokou, S. Koumousi and C. Psychalinos, “Design of Fractional-Order Filters Using Current Feedback Operational Amplifiers”, Journal of Engineering Science and Technology Review, vol. 9(4), pp. 71-81, January 2016.

G. Tsirimokou, C. Psychalinos and A. S. Elwakil, “Design of CMOS Analog Integrated Fractional-Order Circuits”, Springer Briefs in Electrical and Computer Engineering, 2017.

A. Soltan, A. G. Radwan and A. M. Soliman, “Fractional order Sallen–Key and KHN filters: stability and poles allocation”, Circuits Systems and Signal Processing, vol. 34(5), pp. 1461–1480, November 2014.

D. Matignon, “Stability results for fractional differential equations with applications to control processing”, Computational Engineering in Systems Applications, vol. 2, pp. 963–968, March 1997.

A. G. Radwan, A. M. Soliman, A. S. Elwakil and A. Sedeek, “on the stability of linear systems with fractional-order elements”, Chaos, Solitons & Fractals, vol. 40(5),pp. 2317–2328, June 2009.

A. Yesil, F. Kacar and H. Kuntman, “New simple CMOS realization of voltage differencing transconductance amplifier and its RF filter application”, Radioengineering, vol. 20(3), pp. 632-637, September 2011).

D. Prasad, D. R. Bhaskar and M. Srivastava, “Universal Current Mode Biquad Filter using a VDTA”, Circuits and Systems, vol. 4(1), pp. 32-36, January 2013.

D. Prasad, D. R. Bhaskar and M. Srivastava, “Universal voltage mode biquad filter using voltage differencing transconductance amplifier”, Indian Journal of Pure and Applied Physics, vol. 51(12), pp. 864-868, December 2013.

D. Prasad, M. Srivastava and D. R. Bhaskar, “Transadmittance – type universal current-mode biquad filter using voltage differencing transconductance amplifiers”, International Scholarly Research Network, doi: 10.1155/2014/762845, 2014.

D. Prasad, M. Srivastava and D. R. Bhaskar, “Electronically controllable fully uncoupled explicit current mode quadrature oscillator using VDTA and grounded capacitors”, Circuits and Systems, vol. 4(2), pp. 169-172, April 2013.

M. C. Tripathy, K. Biswas and S. Sen, “A design example of a fractional-order Kerwin– Huelsman–Newcomb biquad filter with two fractional capacitors of different order”, Circuits,Systems, and Signal Processing, vol. 32(4), pp. 1523-1536 , August 2013.

A. Adhikary, S. Sen, and K. Biswas, “Practical realization of tunable fractional order parallel resonator and fractional order filters”, IEEE Transactions on Circuits and Systems I: Regular Papers vol. 63(8),pp. 1142-1151, July 2016.

G. Kaur, A. Q. Ansari and M. S. Hashmi, “Fractional order multifunction filter with 3 degrees of freedom”, AEU – Intern ational Journal of Electronics and Communications, vol. 82, pp. 127-135, December 2017.