Qualification and quantification of the nonlinear distortions in discrete-time sigma-delta ADCs

Sigma-delta modulators are becoming increasingly popular in electronic circuits, pushing these circuits to higher sampling frequencies, higher bandwidths, complex feedback/feedforward structures and even complex-valued loop filters. The top-down refinement during a sigma-delta modulator design gradually introduces and verifies circuit non-idealities such as the finite gain-bandwidth or the finite slew-rate of the amplifiers. However, a bottom-up analysis is more difficult: The complex feedback structure and the quantization noise shaped by the feedback loop makes it hard to pinpoint the nonlinear contributors. This paper(1) shows how to qualify and quantify the sources of distortion within a sigma-delta loop starting from SPICE-like transient simulations with a random-phase multisine excitation. The linear and nonlinear distortions are then analyzed using the concept of the Best Linear Approximation. This technique is demonstrated on SPICE-like transient simulations of a discrete-time sigma-delta ADC.