This paper introduces the general fundamentals of the fractional order RL?C? circuit, where ? is the order of the elements. The generalized complex impedance of the RL?C? circuit can be purely real, imaginary, or short circuit. The stability analyses where two regions have been classified are introduced with many numerical examples. General maps for transient and frequency responses are investigated showing the damping parameters for each case. The resonance, 3 dB frequencies, bandwidth, and quality factor for all possible cases have been investigated with detailed analytical formulas. Numerical and PSpice simulations are provided using different examples to validate these concepts. © 2011 IEEE.
Bandwidth; damping ratios; distortion; fractional calculus; fractional-order filter; quality factor; resonance; RL?C? circuit; stability analysis
IEEE Journal on Emerging and Selected Topics in Circuits and Systems, Vol. 3, Art. No. 6564463, PP. 377 to 385, Doi: 10.1109/JETCAS.2013.2272838