On the characterization of limit cycle modes in oversampled data converters

This paper studies the appearance of periodic and quazi-periodic modes, denoted as limit cycles, in the operation of closed-loop oversampled data converters. It demonstrates that the properties of these limit cycles are largely determined by the parameterization of the system loop filter, the amplitudes and the frequencies of the applied input signals, and the applied sampling frequency. For the analysis, quantization in amplitude and quantization in time are seen as separate functions. The quantizer is represented with sampled describing functions and a quazi-linear time-variant model for the loop operation is introduced and illustrated with simulation examples.