A systematic design flow for optimal capacitance assignment in switched-capacitor biquads

This paper presents a systematic design flow for optimal capacitance assignment in switched-capacitor biquad circuits. The proposed design flow starts with a biquad template configuration, which is defined based on circuit regularity. Then, the symbolic transfer function in the z-domain is derived for the biquad template. Given the desired transfer function to be realized, a set of equality constraints can be obtained from coefficient matching of the symbolic transfer function and the desired one. In addition, we also formulate an exact closed-form expression for the output swing constraint so that output swings for the biquad are equalized. Other constraints, such as direct charge coupling, are also formulated. Finally, a nonlinear programming technique is used to solve for capacitance variables subject to optimal capacitance assignment, which is defined as minimizing total capacitance, total number of capacitors and circuit sensitivity. The main advantage of the proposed design flow is that an optimal biquad configuration can be obtained in an automated and accurate way. Experiments confirmed the flexibility of the design flow on obtaining optimal biquad configurations under various design tradeoffs.