A signal‐flow graph representation for switched‐capacitor networks and its application to SC circuit design

Abstract

AbstractThe n‐phase switched‐capacitor (SC) circuit operates by taking successively connection configurations. Consequently, even if the same edge voltage is considered, it takes n different kinds of voltages in general in a period. This makes it difficult to describe the operation of the SC circuit. Although several methods have already been proposed for representing the operation of the SC circuit, the representation by equivalent active RC circuit, which is presently used most widely, cannot provide a clear‐cut description of this essential point. From such a viewpoint, this paper first derives the primitive signal‐flow graph (SFG) representation for adequate representation of the SC circuit, which is formulated based on the common tree in the SC circuit. Then the simplified SFG representation is derived which is obtained by simplifying the representation, eliminating the cotree‐edge variables from the primitive SFG representation. The simplified SFG representation is a network representation, in which only the tree‐edge voltage and the tree‐edge stored‐charge in each phase are used as the variable‐node. It can adequately provide an intuitively clear representation of the relation between the variables in each phase and the relation between the timing of the switch connection and the operation of the circuit. The condition for the structure of SFG is derived, which corresponds to Hasler's structure condition in order that the stray capacitance does not affect the operation. By this method, the problem of constructing an SC circuit insensitive to the stray capacitance is reduced to the problem of constructing an SFG satisfying a certain condition.