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

Abstract

The switched-capacitor (SC) circuit realization problem is traditionally solved by heuristic algorithms. However, an algorithm-like simulated annealing (SA) is stochastic, and its behavior in solving a non-convex optimization problem is unpredictable. In this paper, we make an investigation on using a deterministic and a stochastic optimization algorithm for solving the realization problem of the classical Fleischer-Laker SC filter. By considering minimum area as the design goal, we prove that the a linear programming-based deterministic algorithm is capable of finding a global minimum. With the global optimality established, we then use an SA algorithm to solve the same problem in purpose of investigating the search capability of the SA algorithm. We find that the stochastic SA algorithm cannot always reach a suboptimal solution with quality comparable with the linear programming result. Other issues like convergence speed and the percentage of arriving at the global minimum are examined as well. This research exposes that understanding the underlying optimization problem structure for the realization of SC circuits is of fundamental meaning for developing more efficient heuristic algorithms.

Noise and sensitivity comparison for different BP filter designs

“…The forward Euler transformation (s = > (z-1)/T s ) has been implemented for the calculation of the discrete transfer function [10]. The sampling time T s has been calculated as T s = 1/f s where f s = 4900f c .…”

Transistor‐level optimization methodology for the complete design of switched‐capacitor filter circuits

“…Commonly used algorithms for the design and optimization of SC filters include gradient descent, 9 simulated annealing, 4,8,18 differential evolution, 10 linear programming, 8 GAs, 7,19 among others. Gradient descent algorithms are not guaranteed to find the global minimum, since the algorithm can, depending on the step size, get stuck when a first‐order critical point is found.…”

“…Similarly, simulated annealing algorithms can also get stuck on local minima, however, the algorithm may discard suboptimal solutions, with a given probability, when a better solution is not found, in an attempt to find other suboptimal solutions with better performance. On the other hand, linear programming is always capable of finding the global minimum, unlike the previous algorithms, and in a shorter amount of time, however, in most cases the optimization problem is nonlinear in nature and requires some reformulation, if possible, to transform it into a linear problem 8 . GAs are well suited to find the global minimum in optimization problems where the cost function has many local minima and is capable of storing several good solutions.…”

“…Most methods found in the literature either optimize the circuit from an ideal standpoint [3][4][5][6][7][8] (i.e., consider the switches and the amplifiers as ideal elements) or use simplified models [9][10][11] to predict the behavior of the real SC circuit, which can limit the accuracy of the optimized frequency response. In Ruiz-Amaya et al, 11 a method to model the settling-time of SC circuits, implemented using the two-stage Miller-compensated amplifier, is described.…”

“…On the other hand, linear programming is always capable of finding the global minimum, unlike the previous algorithms, and in a shorter amount of time, however, in most cases the optimization problem is nonlinear in nature and requires some reformulation, if possible, to transform it into a linear problem. 8 GAs are well suited to find the global minimum in optimization problems where the cost function has many local minima and is capable of storing several good solutions.…”