Int. J. Electron. Commun. (AEÜ) 64 (2010) 443 – 449 www.elsevier.de/aeue Current-mode squaring, square-rooting and vector summation circuits Wijittra Petchakit a , ∗ , Anuree Lorsawatsiri a , Wiwat Kiranon a , Chariya Wongtaychathum b , Paramote Wardkein a a Department of Telecommunication Engineering, Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang (KMITL), Ladkrabang, Bangkok 10520, Thailand b Department of Electronic Engineering, Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang (KMITL), Ladkrabang, Bangkok 10520, Thailand Received 24 July 2008; accepted 27 February 2009 Abstract This paper presents new current-mode squaring, square-rooting and vector summation circuits based on the second genera- tion current controlled conveyor (CCCII). Consisting of only CCCIIs as active elements not requiring any external passive elements, all of the proposed circuits are capable of high frequency operation and well suited for IC fabrication. Moreover, the circuits performances are insensitive to temperature and their gains can be easily adjusted by varying the input bias current of CCCII. Finally, the simulation results of the proposed squaring, square-rooting and a two-input vector summation circuits are depicted to confirm the theoretical analysis.  2009 Elsevier GmbH. All rights reserved. Keywords: Current controlled conveyor; Squarer; Square-rooter; Vector summation circuit 1. Introduction Current-mode techniques have been very attractive re- search fields for decades. Many advantages over their volt- age mode counterpart are well known, for example wider dynamic range, extended signal bandwidth, improved linear- ity, simpler circuitry, and lower power consumption [1,2]. One of the essential active building blocks in the de- sign and implementation of current-mode analogue signal processing circuits is the second generation current con- trolled conveyor (CCCII) [2]. Using CCCII for circuit implementation, a broad range of applications can be easily obtained by making use of the serial resistance on port X electronically controlled by the bias current [3–6]. Opera- tional transconductance amplifier (OTA) is another active ∗ Corresponding author. Tel.: +66 7567 2304; fax: +66 7567 2399. E-mail address: pwijittr@wu.ac.th (W. Petchakit). 1434-8411/$ - see front matter  2009 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2009.02.007 element employed in current-mode. However dynamic range of the circuits based on OTA is very limited [7]. Among various applications in signal processing squaring and square-rooting are common circuit realization [8,9] and many techniques have been proposed. In [10], a squarer and a square-rooter are designed using OTA as the main active element. An improved version based on integrators as the basic elements is proposed in [11], while [12] presents the design using CMOS. Current conveyors are also used in the designs of a square-rooter [13,14]. Notice that those cited in [10–14] operate in voltage mode. In order to work in current-mode, current-to-voltage and voltage-to-current converting circuits are required; resulting in increasingly complicated configuration. In this paper, true current-mode operating circuit design of a squarer and a square-rooter is presented. Typically, a squarer is implemented by simply using a multiplier injected with identical inputs. The scheme suffers from distortions resulting mainly from the nonlinearity of the