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 paper¹ 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.