Automatic Symbolic Analysis of Switched-Capacitor Filtering Networks Using Signal Flow Graphs

Signal flow graphs (SFG’s) are a powerful technique to analyze switched-capacitor (SC) circuits in a way that provides in-depth information about their operation and direct access to the corresponding symbolic z-transfer functions. Due to lengthy and error-prone symbolic manipulations this is manually manageable for simple first- or second-order circuits, but becomes unpractical for manipulating higher-order circuits which can not be decomposed into first- and second-order ones. Hence, there is an important need to provide designers with a computer-aided tool for the SFG symbolic analysis of a broad class of SC filtering networks, as described in this paper. Rule-based techniques are employed to capture from arbitrary circuit schematic and timing diagrams the corresponding symbolic SFG leading to the automatic generation of the associated z-transfer function. Symbols can then be instantiated to numerical values to obtain measurable data on a variety of performance indicators such as total capacitor area and capacitance spread as well as the resulting nominal frequency response and its variability against component errors. This is illustrated considering a variety of examples of SC filtering networks including, besides the more traditional filters, both finite and infinite impulse response decimators.