This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which is unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples for the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.<\/p>\r\n","references":"[1]\tB. T. Krishna, \"Studies on fractional order differentiators and integrators: A survey,\" Signal Processing, vol. 91, no. 3, pp. 386-426, 2011.\r\n[2]\tA. G. Radwan, A. M. Soliman, and A. S. Elwakil, \"First-order filters generalized to the fractional domain,\" Journal of Circuits, Systems, and Computers, vol. 17, no. 01, pp. 55-66, 2008.\r\n[3]\tR.P. Sallen and E.L. Key, \"A practical method of designing RC active filters,\" Circuit Theory, IRE Transactions on, vol. 2, no. 1, pp. 74-85, 1955.\r\n[4]\tA. Soltan, A. G. Radwan, and A.M. Soliman, \"Butterworth passive filter in the fractional-order,\" in Microelectronics (ICM), 2011 International Conference on, 2011, pp. 1-5.\r\n[5]\tA. S. Ali, A. G. Radwan, and A. M. Soliman, \"Fractional Order Butterworth Filter: Active and Passive Realizations\", Emerging and Selected Topics in Circuits and Systems, IEEE Journal on , vol.3, no.3, pp.346 - 354, 2013\r\n[6]\tA. G. Radwan, A. S. Elwakil, and A. M. Soliman, \"On the generalization of second-order filters to the fractional-order domain,\" Journal of Circuits, Systems, and Computers, vol. 18, no. 02, pp. 361-386, 2009.\r\n[7]\tA. Soltan, A. G. Radwan, and A. M. Soliman, \"Fractional order filter with two fractional elements of dependant orders,\" Microelectronics Journal, vol. 43, pp. 818 \u2013 827, 2012.\r\n[8]\tA. Soltan, A. G. Radwan, A. M. Soliman, \"CCII based fractional filters of different orders\", J Adv Res, DOI: 10.1016\/ j.jare. 2013.01.007, 2013\r\n[9]\tA.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, no. 5, pp. 2317-2328, 2009.\r\n[10]\tK. Biswas, S. Sen, and P. K. Dutta, \"A constant phase element sensor for monitoring microbial growth ,\" Sensors and Actuators B: Chemical , vol. 119, no. 1, pp. 186-191, 2006. \r\n[11]\tT. C. Haba, G. Ablart, T. Camps, and F. Olivie, \"Influence of the electrical parameters on the input impedance of a fractal structure realised on silicon ,\" Chaos, Solitons & Fractals , vol. 24, no. 2, pp. 479-490, 2005. \r\n[12]\tA. M. Elshurafa, M. N. Almadhoun, K. N. Salama, and H. N. Alshareef, \"Microscale electrostatic fractional capacitors using reduced graphene oxide percolated polymer composites,\" Applied Physics Letters, vol. 102, no. 23, p. 232901, 2013. \r\n[13]\tM. Nakagawa and K. Sorimachi, \"Basic characteristics of a fractance device,\" IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. 75, no. 12, pp. 1814-1819, 1992.\r\n[14]\tS. Michio, Y. Hirano, Y. F. Miura, and K. Saito, \"Simulation of fractal immittance by analog circuits: an approach to the optimized circuits,\" IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. 82, no. 8, pp. 1627-1635, 1999.\r\n","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 84, 2013"}