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

Abstract

Abstract-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 VCCS's. A class of two-VCCS circuits is defined, which can be subdivided into three main classes and 14 subclasses, based on different imposeable 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-semiconducter (CMOS) V 0 I converter kernels, based on two matched MOS transistor (MOST)-VCCS's, 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.

Systematic comparison of hf cmos transconductors

“…In the well-known differential pair, this is often done by adding a bias current source ("long-tailed pair") or by grounding the low-ohmic node. Actually, there are more ways of implementing 4-terminal transconductor starting from 3-terminal ones [9], and we will return to this subject later when we discuss composite V-I kernels in Section VI. For now it suffices to state that it is possible to realize a 4-terminal transconductor starting from 3-terminal transconductors and we focus on the question how we can make 3-terminal transconductors.…”

“…We will now calculate and compare the NSNR of the basic V-I kernels. Using (7) and (4), NSNR can be rewritten as (9) The equations in Table II and the biasing ranges of Table III were used to calculate NSNR and the results are shown in Fig. 8.…”

“…Taking this scalability into account, we propose a "normalized signal to noise ratio" (NSNR) as a figure of merit for transconductor comparison. We will then compare the NSNR of virtually all V-I kernels that we are aware of, generated based on [7]- [9] and partly on [10]. First, simple 3-terminal kernels are introduced in Section IV and compared in Section V. Then all five different classes of "composite V-I kernels" [9] combining two 3-terminal V-I kernels are discussed in Section VI and compared in Section I.…”

Finding all elementary circuits exploiting transconductance

“…Only these graphs have all branches connected in loops and are potentially useful. This is because unconnected graph branches do not serve any function in a circuit (open -branch: undetermined voltage and related current; open -or -branch: zero current; open -branch: input not sensed; so none of them contribute to Kirchhoff relations to force a finite transactance 9 (see also [8]). 2) Graphs are then labeled in all different possible ways (step 2 in Fig.…”

“…For simplicity, only the main functional dependence on transconductance is shown. For this purpose a transconductance is introduced, being an arbitrary index, that represents one of the following expressions: (10) These expressions can also be derived in a systematic way from considerations regarding different possible sets of Kirchhoff relations that can be forced in circuits with two VCCSs [8]. As expected from considerations of dimension, the voltage gain and current gain of the two-port described in Table II are either 0, 1 or a ratio of transconductance expression .…”