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

A systematic approach to circuit design and analysis: classification of two-VCCS circuits,10.1109/81.774226,IEEE Transactions on Circuits and Systems

A systematic approach to circuit design and analysis: classification of two-VCCS circuits   (Citations: 4)
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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
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    • ...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. Section VIII presents conclusions...
    • ...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...
    • ...It can be shown that there exist only a limited number of different ways to combine two VCCS blocks to create a two-port network with a well-defined transfer function [9]...
    • ...The circuit can be classified in 12 classes of circuits [9], based on the set of two Kirchhoff relations that is forced by the interconnection pattern of the VCCSs, and their connection to the signal source and load...
    • ...In case of transconductors, five classes with useful behavior result5 [9], represented in Fig. 10. The name of each class refers to the two variables that are being forced by Kirchhoff equations (e.g., means that a sum-voltage and difference-voltage is forced)...
    • ...For other options see [7] and [9] Fig. 10. Five different ways of combining two transconductors by forcing a different set of two Kirchhoff relations, indicated in the class name...
    • ...Fig. 10(b) shows a circuit, in which the input voltage source forces a so-called “primary” VCCS voltage [9], while the sum of the VCCS-voltages is forced equal to . This class is strongly related to the previous one, but the full input voltage swing is now applied to both VCCSs, and it has a single-ended input...
    • ...For some well-known transconductors, e.g., [34]‐[46], examples of the decomposition are given in [9] and a more extensive discussion can be found in [7]...

    Eric A. M. Klumperinket al. Systematic comparison of HF CMOS transconductors

    • ...So called “tree-graphs” [4] are used as a starting point...

    Eric A. M. Klumperinket al. Finding all elementary circuits exploiting transconductance

    • ...This is because unconnected graph branches do not serve any function in a circuit (open -branch: undetermined voltage and related current; open -o r -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])...
    • ...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]...

    Eric A. M. Klumperinket al. Finding all elementary circuits exploiting transconductance

    • ...First a generalization step is made: a MOS transistor is considered as a Voltage Controlled Current Source [4] (VCCS, see fig. 1)...

    F. Bruccoleriet al. Generating all 2-transistor circuits leads to new wide-band CMOS LNAs

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