Designing globally optimal delta–sigma modulator topologies via signomial programming

We present a design methodology for globally optimizing the topologies of delta–sigma modulators (DSMs). Previous work cast the design task into a general non-convex, nonlinear programming problem, whereas we propose to recast it as a signomial programming problem. Convexification strategies are presented for transforming the signomial programming problem into its equivalent convex counterpart, thereby enabling the solution of globally optimal design parameters. It is also possible to include circuit non-ideal effects that affect the transfer function of the modulator into the formulation without affecting the computational efficiency. The proposed framework has been applied to topology synthesis problems of single-loop and multi-loop low-pass DSMs based on discrete-time circuitry. Numerical results confirm the effectiveness of the proposed approach over conventional nonlinear programming techniques. Copyright © 2008 John Wiley & Sons, Ltd.