Amplitude bounds on oscillations from a sigma-delta modulator structure

Sufficient conditions are given for the zero-input nonlinear oscillations of a Σδ modulator containing a 3rd order digital-filter to be bounded to a specified cube in the state-space. These oscillations have an adverse effect upon performance in many applications, so knowledge of amplitude bounds may be of practical significance. Short-period oscillations give rise to narrowband spectral `tones´ which are typically more objectionable than the spectral content of long-period oscillations so conversion of oscillations from short-period into longer period can be useful. Some discussion is included of the effect of a `deterministic bit flipping´ method for breaking up short period oscillations on the amplitude bounds