SYNTHESIS OF CONTROLLED SOURCES BY ADMITTANCE MATRIX EXPANSION ¤ AHMED M. SOLIMAN Electronics and Communications Engineering Department, Faculty of Engineering Cairo University, Egypt asoliman@ieee.org Received 3 April 2009 Accepted 4 November 2009 The admittance matrix expansion method based on using nullors and pathological mirror elements is used to provide a systematic synthesis method of controlled sources. Four new realizations of the current controlled voltage source (CCVS) using a single grounded resistor are given. Three new nodal admittance matrix expansions (NAM) for the voltage controlled voltage source (VCVS) are introduced in this paper. The voltage mirror current mirror pair is used as intrinsic element in the NAM expansion. Eight new realizations for the noninverting VCVS using two grounded resistors are given. Eight realizations for the inverting VCVS using two grounded resistors are also given. Two new NAM expansions for the current controlled current source (CCCS) are introduced in this paper. The voltage mirror current mirror pair is used as an intrinsic element in the NAM expansion. Eight realizations for the CCCS using two grounded resistors are given. The generation of the controlled sources using a single building block is also discussed and the adjoint relations between VCVS and CCCS are summarized. Keywords: Admittance matrix expansion; VCVS; CCCS; VCCS; nullors; current conveyor; inverting current conveyor. 1. Introduction A symbolic framework for systematic synthesis of controlled sources based on nodal admittance matrix (NAM) expansion was presented in Ref. 1. The matrix expansion process begins by introducing blank rows and columns, representing new internal nodes, in the admittance matrix. Then, nullators and norators are used to move the resulting admittance matrix elements to their ¯nal locations, properly describing either °oating or grounded passive elements. Thus, the ¯nal NAM is obtained including ¯nite elements representing passive circuit components and unbounded elements, so called in¯nity-variables, representing nullators and norators. In this framework, nullators and norators 2À4 shown in Fig. 1 ideally describe active elements in the circuit are used. The nullator and norator are pathological elements * This paper was recommended by Regional Editor Piero Malcovati. Journal of Circuits, Systems, and Computers Vol. 19, No. 3 (2010) 597À634 # . c World Scienti¯c Publishing Company DOI: 10.1142/S0218126610006323 597