Resonators in Open-Loop Sigma–Delta Modulators

In this paper, we introduce the modulo resonator for use in analog-to-digital
open-loop sigma-delta modulators
(OLSDMs). The OLSDM presented in this paper is intended for use in high-accuracy (14-bit) high-speed analog-to-digital converters. The modulo resonator is used with a modulo notch filter to insert a zero in the noise transfer function at a nonzero frequency. The effect of finite gain in modulo integrators and resonators is described and verified through simulation. The modulo resonator and a previously published modulo integrator are used in a behavioral model of a switched-capacitor fifth-order OLSDM with more than 13-bit effective number of bits for an oversampling ratio of four. We prove for the
N
-order OLSDM that the number of bits in the quantizer (
B
) must be larger than
N
to ensure equivalence between open-loop sigma-delta modulation and sigma-delta modulation.