The effect of integrator leak in Sigma - Delta modulation

A method is presented which makes it possible to determine exactly the effect of integrator leak on the performance of the single-loop Sigma - Delta modulator with DC input. Theory from the field of nonlinear dynamics is used 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 make it possible to discuss in quantitative rather than qualitative terms the robustness of the sigma-delta system to this circuit imperfection.< >