Graph Method for Solving Switched Capacitors Circuits

摘要

Circuits with switched capacitors are described by a capacitance matrix and seeking voltage transfers then means calculating the ratio of algebraic supplements of this matrix. As there are also graph methods of circuit analysis in addition to algebraic methods, it is clearly possible in theory to carry out an analysis of the whole switched circuit in two-phase switching exclusively by the graph method as well. For this purpose it is possible to plot a Mason graph of a circuit, use transformation graphs to reduce Mason graphs for all the four phases of switching, and then plot a summary graph from the transformed graphs obtained this way. First we draw nodes and possible branches, obtained by transformation graphs for transfers of EE (even-even) and OO (odd-odd) phases. In the next step, branches obtained by transformation graphs for EO and OE phase are drawn between these nodes, while their resulting transfer is multiplied by z~(1/2). This summary graph can then be interpreted by the Mason's relation to provide transparent voltage transfers. Therefore it is not necessary to compose a sum capacitance matrix and to express this consequently in numbers, and so it is possible to reach the final result in a graphical.