Study of non-ideal effects in a CT ΣΔ modulator with decaying exponential feedback waveforms

Abstract

In this article, a detailed theoretical analysis of the impact of finite gain-bandwidth product (GBW) in amplifiers, excess loop delay, and a hysteretic quantiser on a second order, 3-bit, continuous-time sigma-delta (CT ) modulator with decaying exponential feedback pulses has been accomplished. A “short” exponential pulse – namely, an exponential pulse whose time constant is lower than the pulse width – was used in order to improve jitter rejection. An overall noise transfer function (NTF) that includes the effect of the three non-ideal effects was analytically calculated using the modified Z-transform method. The evolution of the NTF poles and zeroes locus in the z-plane is obtained when these effects are taken into account separately or combined. System-level simulations have been also carried out in order to validate the proposed theoretical study. The stability of a modulator with “short” exponential feedback pulses is higher than that of a modulator with rectangular ones when finite GBW or excess loop delay are included. Finally “short” exponential pulses and “narrow” rectangular ones are proved to be equivalent from the stability viewpoint.