Analyzing distortion in ASDMs with loop delay

Recently nearly exact expressions for the distortion in a commonly used family of Pulse Width Modulators (PWMs) known as Asynchronous Sigma Delta Modulators (ASDMs) were presented. Such an ASDM consists of a feedback loop with a schmitt-trigger (or a comparator), and a continuous time loop filter. However these previous results are not yet practically applicable because the effect of unavoidable loop delay (e.g. in the schmitt trigger) was not taken into account. Therefore we now present a more general theory that is also valid when there is a nonzero loop delay. A comparison of the resulting equations with computer simulations demonstrated a very good matching, confirming the validness of the theory. This way, a designer can now easily understand the relationship between the loop filter dynamics and the linearity of an ASDM.