A systematic approach to circuit design and analysis: classification of two-VCCS circuits

This paper discusses a systematic approach to the design and analysis of circuits, using a transconductor or voltage controlled current source (VCCS) as a building block. It is shown that two independent Kirchhoff relations among the VCCS voltages and currents play a crucial role in establishing a unique transfer function in two-port circuits with two VCCSs. A class of two VCCS circuits is defined, which can be subdivided into three main classes and 14 subclasses, based on different imposable sets of two Kirchhoff relations. The classification is useful for circuit synthesis and analysis, as it reveals all the basically different ways to exploit two VCCS's, and allows for a unified analysis of classes of circuits. To exemplify this, all complementary metal-oxide-semiconductor (CMOS) V-I converter kernels, based on two matched MOS transistor (MOST)-VCCSs, are generated and analyzed with respect to distortion. It is shown that dozens of published transconductor circuits can be classified in only four classes, with essentially different distortion behavior.