Design of Sinh‐Domain filters using complementary operators

Abstract

SUMMARYA new systematic method for designing Sinh-Domain filters is introduced in this paper. This is achieved by employing an appropriate set of complementary operators, in order to transpose the conventional functional block diagram representation of each linear operation to the corresponding one into the Sinh-Domain. The proposed method offers the benefits of facilitating the design procedure of high-order Sinh-Domain filters and of the absence of any restriction concerning the type and/or the order of the realized filter function. As an example, a third-order Sinh-Domain leapfrog filter is designed by employing the proposed set of operators. Two possible realizations are given and their performance has been evaluated and compared through simulation results.

A low-voltage and low-power sinh-domain universal biquadratic filter for low-frequency applications

“…The derivation of the proposed universal biquadratic filter has been achieved by employing the following set of complementary SINH −1 and SINH operators [15], which are described by Eqs. (1) and (2) as:…”

“…Sinh filters are inherently class-AB [11][12][13] and, as such, possess the potential for a high dynamic range and possible biomedical applications (e.g., electroencephalography (EEG) or ultrasound, [9,14]). In applications with low frequency and * Correspondence: farooqsnn20@yahoo.co.in large number of filter stages, where the relative increase in power does not compromise the overall system's power budget, the sinh paradigm might have a comparative advantage in terms of minimizing the chip area cost [15].…”

1.2 V BiCMOS Sinh-Domain Filters

“…In order to facilitate the derivation of these blocks, a set of complementary operators, denoted as SINH −1 and SINH, is introduced at this point. Their definitions are slightly modified in comparison with those introduced in [7], and they are given by (6) and (7), respectively, asυ…”

“…4b must be added at the input and output of the topology in Fig. 4c, respectively [7]. The derived circuit could be further simplified through the following steps: (a) by substituting (6) in the right side of (10) the nominator takes the form of the difference i I N1 − i I N2 , and (b) employing an S/C cell instead of a C cell the derived hyperbolic sine output is actually the required expansion of the compressed output voltage according to (7).…”

Sinh-Domain linear transformation filters

“…The compression of the input current can be performed by the following ways: (a) through the logarithmic V-I relationship of bipolar transistor in active region or MOS transistor in weak inversion -the derived filters are known in the literature as log-domain filters Frey, 1993;Kontogiannopoulos & Psychalinos, 2005;Mahattanakul & Toumazou, 1999;Perry & Roberts, 1996;Psychalinos, 2006;Shah & Khanday, 2009a, 2009b;. (b) through the square-root V-I relationship of MOS transistor in strong inversion -the derived filters are known as square-root domain filters (Lopez-Martin & Carlosena, 2001;Psychalinos, 2007aPsychalinos, , 2007bPsychalinos, 2008a;Psychalinos & Vlassis, 2002a;Stoumpou, Khanday, Psychalinos, & Shah, 2009) and (c) through the inverse of the hyperbolic sine function realised by translinear loops formed by bipolar transistors in active region or MOS transistors in weak inversion -the derived filters are known as Sinh-Domain filters (Frey, 1999;Frey & Tola, 1999;Haddad & Serdijn, 2006;Kasimis & Psychalinos, 2012a, 2012bKatsiamis & Drakakis, 2005;Katsiamis, Glaros, & Drakakis, 2008;Lopez-Martin & Carlosena, 1999a, 1999bPoort, Serdijn, Mulder, & van der Woerd, 1999;Serdijn, Kouwenhoven, Mulder, & van Roermund, 1999). This type of companding filters offers an inherent class-AB operation, while in the cases of square-root domain and log-domain filters a class-AB pseudo-operation is achieved by utilising an input current splitter, two identical class-A signal paths and subtracting the intermediate output currents.…”