The Effect of Integrator Leak in

versampled sigma-delta modulators are finding widespread use in audio and other signal processing applica- tions, due to their simple structure and robustness against circuit imperfections. Exact analyses of the system are compli- cated by the presence of a discontinuous nonlinear element. The response of most researchers who have studied the system analytically has been to linearize the system and apply standard linear theory, but this approach in general does not yield correct results. In this paper we apply theory from the field of nonlinear dynamics to provide an analytical description of the behavior of the single-loop modulator with leaky integrators. Integrator leak is inevitable in any practical circuit implementation due to finite op-amp gain. The results obtained allow us to discuss in quanti- tative rather than qualitative terms the robustness of the sigma-delta system to this circuit imperfection.