Synthesis of active inductors using SFG stamps Mourad Fakhfakh a , Marian Pierzchala b a University of Sfax, Tunisia b Wroclaw University of Technology, Poland article info Article history: Received 22 January 2013 Received in revised form 18 June 2013 Accepted 21 June 2013 Available online 11 July 2013 Keywords: Analog circuit synthesis Active inductors Signal-flow graph CC CCII-TA CFOA OTRA CBTA CFTA VDIBA CMOS abstract This paper proposes a new approach for the systematic synthesis of active inductors via signal-flow graphs (SFGs). The basic idea consists of proposing and using SFG stamps of active basic building blocks (ABBs) to construct the equivalent SFG of a classical inductor. We show that a large number of active inductors can be thus synthesized; twelve are proposed, most of them are novel. Known ABBs, as well as newly proposed ones are used, namely current conveyors (CC), operational transconductance amplifiers (OTA), current conveyor transconductance amplifiers (CCII-TA), current feedback operational amplifiers (CFOA), operational transresistance amplifiers (OTRA), current backward transconductance amplifiers (CBTA), current feedback transconductance amplifiers (CFTA) and voltage differencing inverting buffered amplifiers (VDIBA). SPICE simulations are given to show the viability of the proposed technique. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction Active filter design continues to be deeply investigated by analog designers [1–4]. The literature offers a large plethora of techniques for the design of such active circuits, such as the gm-C technique [5,6], the NAME approach [7–9], the two-graph techni- que [10–12], to name a few. Similar techniques mainly consist of either the use of the symbolic transfer function of the active network to synthesize the corresponding circuit, or the transformation of passive RLC networks into active RC ones. However, there is no systematic method that allows in an easy manner the design of such networks, particularly the simulated inductors. The method proposed in this paper is based on a new approach that consists of the use of signal-flow graph (SFG) stamps of active basic building blocks (ABBs), e.g. CC [13–16], OTA [6], CCII-TA [17], CFOA [18], OTRA [11], CBTA [19,20], CFTA [21–23] and VDIBA [24]. where CC, OTA, CCII-TA, CFOA, OTRA, CBTA, CFTA and VDIBA, stand for current conveyors, operational transconductance amplifiers, current conveyor transconductance amplifiers, current feedback operational amplifiers, operational transresistance amplifiers, current backward transconductance amplifier, current feedback transconductance amplifiers and voltage differencing inverting buffered amplifier, respectively. The basic idea consists of the following: 1- Building a signal-flow graph the transfer function of which is equivalent to the impedance (admittance) of the ideal inductor, 2- identifying the ABB SFG from the SFG built in (1-), 3- constructing the equivalent active inductor by replacing each ABB SFG by its transistor level circuit. The rest of the paper is structured as follows. Signal-flow graphs equivalent to the primitive SFG of a classical inductor are presented in Section II. SFGs of active basic building blocks are proposed in Section III, and the synthesis of active inductors using these ABBs' SFGs is detailed in Section IV. Finally, Section V presents the concluding remarks. 2. Equivalent SFG of an active inductor An immitance can be represented in two different ways by a SFG: (i) as an impedance, or (ii) as an admittance [25], as it is shown in Table 1. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/mejo Microelectronics Journal 0026-2692/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mejo.2013.06.011 E-mail addresses: mourad.fakhfakh@ieee.org, fakhfakhmourad@gmail.com (M. Fakhfakh), marian.pierzchala@pwr.wroc.pl (M. Pierzchala). Microelectronics Journal 44 (2013) 1107–1122