A Design Example of a Fractional-Order Kerwin–Huelsman–Newcomb Biquad Filter with Two Fractional Capacitors of Different Order
First Online: 03 January 2013 Received: 03 September 2012 Revised: 04 December 2012 DOI:
Cite this article as: Tripathy, M.C., Biswas, K. & Sen, S. Circuits Syst Signal Process (2013) 32: 1523. doi:10.1007/s00034-012-9539-2 Abstract
Design, realization and performance studies of continuous-time fractional order Kerwin–Huelsman–Newcomb (KHN) biquad filters have been presented. The filters are constructed using two fractional order capacitors (FC) of orders
α and β (0< α, β≤1). The frequency responses of the filters, obtained experimentally have been compared with simulated results using MATLAB/SIMULINK and also with PSpice (Cadence PSD 14.2), where the fractional order capacitor is approximated by a domino ladder circuit. It has been observed that fractional order filters can give better performance in certain aspects compared to integer order filters. The effects of the exponents ( α and β) on bandwidth and stability of the realized filter have been examined. Sensitivity analysis of the realized fractional order filter has also been carried out to investigate the deviation of the performance due to the parameter variation. Keywords Fractional order capacitor KHN biquad filter Constant phase angle Domino ladder circuit Fractional order filter References
W. Ahmad, R. El-Khazali, Fractional order passive low-pass filters, in
Proceedings of the ICECS, (2003), pp. 160–163
P. Ahmadi, B. Maundy, A.S. Elwakil, L. Belostotski, Band-pass filters with high quality factors and asymmetric-slope characteristics, in
IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS), August 2011, pp. 1–4
K. Biswas, S. Sen, P.K. Dutta, Realization of a constant phase element and its performance study in a differentiator circuit. IEEE Trans. Circuits Syst. II
, 802–806 (2006)
R. Caponetto, G. Dongola, L. Fortuna, I. Petras,
Fractional Order Systems: Modeling and Control Applications (World Scientific, Singapore, 2010)
R. Caponetto, L. Fortuna, D. Porto, A new tuning strategy for a non-integer order pid controller, in
First IFAC Workshop on Fractional Differentiation and Its Application, vol. 40, (2004), pp. 168–173
G. Carlson, C. Halijak, Approximation of fractional capacitors (1/
s) (1/ by regular Newton process. IEEE Trans. Circuits Syst. n) 11, 213–214 (1964)
R.C. Dorf, R.H. Bishop,
Modern Control Systems (Addison-Wesley, New York, 1990)
S.A.A. El-Salam, A.M.A. El-Sayed, On the stability of some fractional-order nonautonomous systems. Electron. J. Qual. Theory Differ. Equ.
6, 1–14 (2007)
Design with Operational Amplifier and Analog Integrated Circuits (Tata McGraw-Hill, New Delhi, 2002)
T. Freeborn, B. Maundy, A. Elwakil, Field programmable analogue array implementation of fractional step filters.
IET Circuits Devices Syst.
, 548–561 (2010). doi:
T. Freeborn, B. Maundy, A. Elwakil, Towards the realization of fractional step filters, in
IEEE International Symposium on Circuits and Systems, June 2010, pp. 1037–1040
M. Gupta, P. Varshney, G.S. Visweswaran, Digital fractional-order differentiator and integrator models based on first-order and higher order operators. Int. J. Circuit Theory Appl.
(5), 461–474 (2011)
B.T. Krishna, Studies on fractional order differentiators and integrators: a survey. Signal Process.
(3), 386–426 (2011)
B.T. Krishna, K.V.V.S. Reddy, Active and passive realization of fractance device of order 1/2. Act. Passive Electron. Compon.
, 1–5 (2008)
B. Maundy, A.S. Elwakil, T.J. Freeborn, On the practical realization of higher order filters with a fractional stepping. Signal Process.
, 484–491 (2011)
D. Mondal, K. Biswas, Performance study of fractional order integrator using single component fractional order element. IET Circuits Devices Syst.
, 334–342 (2011)
M. Moshrefi, J.K. Hammond, Physical and geometrical interpretation of fractional operator. Int. J. Appl. Math. Comput. Sci.
(6), 1077–1086 (1998)
K.B. Oldham, C.G. Zoski, Analogue instrumentation for processing polarographic data. J. Electroanal. Chem.
, 27–51 (1983)
I. Podlubny, Fractional-order system and
controller. IEEE Trans. Autom. Control
(1), 708–719 (1999)
A.G. Radwan, A.S. Elwakil, A. Soliman, First-order filter generalized to the fractional domain. J. Circuits Syst. Comput.
(4), 55–66 (2008)
A.G. Radwan, A. Soliman, A.S. Elwakil, Design equations for fractional-order sinusoidal oscillators: four practical circuit examples. Int. J. Circuit Theory Appl.
, 473–492 (2008)
A.G. Radwan, A.S. Elwakil, A. Soliman, On the generalization of second-order filters to the fractional-order domain. J. Circuits Syst. Comput.
(2), 361–386 (2009)
A.G. Radwan, A. Soliman, A.S. Elwakil, A. Sedeek, On the stability of linear system with fractional order elements. Chaos Solitons Fractals
, 2317–2328 (2009)
A.S. Sedra, K.C. Smith,
Microelectronic Circuits, 5th edn. (Oxford University Press, London, 2007)
© Springer Science+Business Media New York 2012