Periodic non-linear oscillations from bandpass ΣΔ modulators

A bandpass ΣΔ modulator incorporating a 2nd order resonator shows close similarities in behaviour to such a resonator alone but with a two´s complement overflow characteristic. The paper shows that an analysis method used previously for the two´s complement non-linearity leads to a geometrical construction for zero-input short-period non-linear oscillations of the ΣΔ modulator. The initial states which result in commonly-observed zero-input oscillations are derived analytically