Optimal realization of switched-capacitor circuits by symbolic analysis

Abstract

In modern systems-on-chip (SOC) technology analog modules are costly to design. This paper studies an optimal realization of switched-capacitor (SC) circuit given a transfer function (TF) in the z-domain. Among the multiple possibilities of capacitance assignments, the proposed method is more controllable in arriving at a desirable SC realization. The underlying technique applies a symbolic method to derive a cancellation-free symbolic representation for a given SC circuit topology, then uses the automatically generated symbolic coefficient expressions to synthesize a set of numerical capacitance values suitable for physical implementation. Examples demonstrate the effectiveness of the proposal.

A comparative study on using linear programming and simulated annealing in the optimal realization of a SC filter

“…The coefficient expressions in terms of the capacitor values for the Fleischer-Laker biquad can be produced by a symbolic tool as follows [6]: The realization parameters consist of the 12 capacitor values.…”

“…In practice, heuristic method is most frequently applied for solving a nonlinear circuit realization problem, such as SA or genetic algorithms [4][5][6]8]. Hence, we may view these six equations as constraints, and based on them, an optimization problem can be formulated.…”

“…The realization parameters consist of the 12 capacitor values. The coefficient expressions in terms of the capacitor values for the Fleischer-Laker biquad can be produced by a symbolic tool as follows [6]:…”

“…In general, finding the global minimum of a nonlinear optimization problem is uneasy if it is unknown whether the optimization problem is convex. In practice, heuristic method is most frequently applied for solving a nonlinear circuit realization problem, such as SA or genetic algorithms [4][5][6]8]. Heuristic algorithms are often stochastic and only capable of finding suboptimal solutions.…”

“…However, its realization is subject to many constraints, such as area, spread, dynamic range, and power [1]. In the literature, most optimization methods are based on heuristic algorithms; among them, the algorithm of simulated annealing (SA) is the most frequently used [2][3][4][5][6]. However, an unsatisfactory issue with a heuristic search algorithm is the uncertainty of result in each run and the lengthy runtime.…”