Fractional-step Tow-Thomas biquad filters

Abstract

Abstract:In this paper we propose the use of fractional capacitors in the Tow-Thomas biquad to realize both fractional lowpass and asymmetric bandpass filters of order 0 < α 1 + α 2 ≤ 2, where α 1 and α 2 are the orders of the fractional capacitors and 0 < α 1,2 ≤ 1. We show how these filters can be designed using an integer-order transfer function approximation of the fractional capacitors. MATLAB and PSPICE simulations of first order fractional-step low and bandpass filters of order 1.1, 1.5, and 1.9 are given as examples. Experimental results of fractional low pass filters of order 1.5 implemented with silicon-fabricated fractional capacitors verify the operation of the fractional Tow-Thomas biquad.

Fractional-order low-pass filter with electronic tunability of its order and pole frequency

“…OA -Operational Amplifier, DDCC -Differential Difference Current Conveyor, CFOA -Current Feedback Operational Amplifier, VCVS -Voltage Controlled Voltage Source, OTA -Operational Transconductance Amplifier, MOTA -Multi-Output Transconductance Amplifier, ACA -Adjustable Current Amplifier, DO-CF -Dual-Output Current Follower, MO-CF -Multi-Output Current Follower, LP -Low Pass, BP -Band Pass, HP -High Pass, VM -Voltage Mode, CM -Current Mode. feedback) [11], or SAB (single amplifier biquad) in combination with a 1st-order filter [4,8]. For the design of a fractional-order filter, a wide variety of commercially available types of active elements such as operational amplifiers (Op Amps) [2,4,8,9,12,15,21], differential difference current conveyors (DDCCs) [11], current feedback operational amplifiers (CFOAs) [30], second generation current conveyors (CCIIs) [34], transconductance amplifiers (OTAs) [35,36], or current amplifiers (CAs) [37,38] can be used.…”

“…feedback) [11], or SAB (single amplifier biquad) in combination with a 1st-order filter [4,8]. For the design of a fractional-order filter, a wide variety of commercially available types of active elements such as operational amplifiers (Op Amps) [2,4,8,9,12,15,21], differential difference current conveyors (DDCCs) [11], current feedback operational amplifiers (CFOAs) [30], second generation current conveyors (CCIIs) [34], transconductance amplifiers (OTAs) [35,36], or current amplifiers (CAs) [37,38] can be used. Based on the type of elements used in the topology, some researchers try to control not only pole frequency or quality factor of the filter, but also the order of the filter itself [10,27,28].…”

“…Most of the papers describe the design of a fractionalorder low-pass filter [2, 4-11, 15, 21, 27, 28], other also proposed transfer function of fractional-order high-pass filter [6,7]. Some papers present a proposal of a fractional-order band-pass filter [4,8,15]. The disadvantage is that a filter structure providing more transfer functions at once cannot be simply created since each filter function requires different values of parameters, or topology modifications [4,6,7,8].…”

“…The fractional order circuits can find practical use in precision measurement, or modelling of various biological signals [3,13,26]. Another use may be in electrical engineering [2][3][4][5][6][7][8][9][10][11][12][13][14][15]32], telecommunications [2] and also agriculture [16].…”

On Digital Realizations of Non-integer Order Filters

“…The result was a filter with more degrees of freedom than classical filter and therefore with better design flexibility. In [17], Freeborn et al presented fractional two-step Tow-Thomas biquad filter. They used an approximation of fractional-order capacitors in form of integer order transfer function.…”