Tree/link method for transfer function and stability analysis of switched‐capacitor circuits

Summary The wide spread application of switched‐capacitor circuits has resulted in complex structures wherein the derivation of transfer function in discrete form is not quite straight forward. A computer‐aided tool for direct transfer function analysis of switched‐capacitor circuits using state formulation method is proposed in this paper. The state equation matrices are directly constructed from the circuit topology using tree/link analysis. The entire topology is formulated only using cutset equations to obtain the state matrices without any modifications. The discretized topological state matrices are used to generate the transfer function in z form by forward substitution of state equation in successive clock phase. Lyapunov criteria‐based matrix equation constructed using the same state matrix is used to investigate the circuit stability. The formulation is also suitable in addressing the effect of non‐idealities like switch resistance and finite gain of operational amplifiers, on the location of poles and zeros. Various numerical examples have been presented to demonstrate the performance of the simulator. The work explains the development of a CAD tool for direct computation of z domain transfer function for switched‐capacitor circuits using topological approach. Tree/link‐based systematic approach is preferred for state space formulation of SC circuits by constructing the state matrices directly from the circuit structure. Such construction of state matrices is achieved using single cut‐set computation without any circuit partition or source transformation. The computed state matrices also helps in stability investigation of SC circuits.