Excess Loop Delay Compensation in Continuous-Time Delta-Sigma Modulators

Abstract

We present a simple, intuitive technique to compensate the loop filter transfer function for excess delay in low-pass continuous-time DeltaSigma modulators. Conventional methods of finding the appropriate filter coefficients to account for loop delay work in the z-domain, leading to cumbersome algebra. We show that the same objective can be accomplished entirely in the continuous-time domain, resulting in a procedure that lends itself to hand calculations, even for high order modulators. We derive closed-form expressions for the loop filter coefficients in modulators using nonreturn-to-zero and return-to-zero digital-to-analog converters. Simulation results confirming the theory are given.