Generalization of shadow filters in fractional domain

Abstract

This work is intended to generalize the design of shadow filters to the fractional-order domain. Shadow filters, in integer-order domain, introduced by Lakys and Fabre, consist of an external amplifier in the feedback loop of the basic filter cell and by varying the gain of this amplifier the parameters of the resulting filter are modified without disturbing the active and passive components of the filter itself. In particular, we consider here the case where a basic 2α order filter is constructed using two fractional-order capacitors both of the same order α. Mathematical formulations are drafted for pole frequency and pole quality factor for different feedback signals with various cases of stability and demonstrated using MATLAB simulations. Functional verification of the proposed theory is verified using an active filter example, designed around operational transconductance amplifier (OTA), through SPICE using 180 nm CMOS technology model parameters.

Shadow Filters Using Multiple-Input Differential Difference Transconductance Amplifiers

“…Finally, Table 2 provides a comparison of the proposed filters with previously published shadow filters in [ 22 , 23 , 26 , 29 , 30 ]. The proposed filters provide lower power consumption, as compared with [ 22 , 23 ], lower output impedance, as compared with [ 26 , 30 ] (except the output impedance of the LP filter in Figure 3 b), larger number of low-impedance nodes, as compared with [ 29 ], and lower supply voltage, as compared with [ 23 , 26 , 29 , 30 ].…”

“…There are many shadow filters (also known as frequency-agile filters) realized using variant active elements available in the literature [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. In [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 ], current-mode (CM) shadow filters have been reported whereas in [ 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ] voltage-mode (VM) shadow filters have been introduced. This paper is focused on the VM filters which offer high-input and low-output impedances, electronic tuning ability, and use grounded passive components.…”

“…However, the circuits in [ 19 , 20 , 21 , 22 ] don’t provide an electronic tuning ability of the natural frequency and the quality factor. The shadow filters employing voltage differencing transconductance amplifier (VDTA) [ 23 , 24 , 25 , 26 , 27 ], voltage differencing gain amplifier (VDGA) [ 28 ], voltage differencing differential difference amplifier (VDDDA) [ 29 ], and operational transconductance amplifier (OTA) [ 30 ] offer an electronic tuning ability and high-input impedance, which is advantageous for VM circuits. However, these active filters were supplied with relatively high voltages, namely, ±0.9 V in [ 23 , 29 ], ±1 V in [ 24 , 25 , 27 ], ±1.5 V in [ 26 ], and ±1.8 V in [ 30 ].…”

Electronically Reconfigurable and Tunable Fractional-Order Filter Using Resonator Concept and Feedforward Path for Low-Frequency Tone Signalization

“…The sum of both branches creates the target reconfiguration. This technique is similar to the socalled Shadow filter operation [35] (difference is in the orientation of loop transfer) and it represents certain alternative targeting on the reconfiguration of transfer responses more than on quality factor adjustment in Shadow filter design [35]. However, to the best of authors' knowledge, this approach was not presented with advantages that are discussed in this paper.…”

Further Generalization and Approximation of Fractional-Order Filters and Their Inverse Functions of the Second-Order Limiting Form

“…In contrast, the minimum slope yielded for the classical band-pass filter, which always exhibits a symmetric magnitude-frequency behavior about the center frequency, is ±20 dB/dec. Generalization of the traditional filters, such as the Butterworth [6], Chebyshev [7], shadow filter [8], etc., exploits the afore-mentioned advantages; (ii) various filter characteristics such as bandwidth, center frequency, quality factor, etc., are dependent on α which provides an additional design parameter to the circuit designer, and, hence, better flexibility [9]; and (iii) FO filters (for example, the FO Sallen-Key filter [10]) may achieve improved stability range compared to their classical counterparts.…”