On the stability of third-order sigma-delta modulation

The geometric methods introduced in H. Wong, `A geometric view of Σ-Δ modulation,´ IEEE Trans. Circ. Sys., Vol. 39, no. 6, pp. 402-405, are applied to the basic architecture of third-order, single-path sigma-delta modulation. An attempt is made to answer the fundamental questions on the stability problem of the third-order system, i.e., can such a modulation be stable, and if so, under what conditions? Combined with the application of bifurcation theory, the stability and other dynamical properties of the modulation are revealed, and certain guidelines directly applicable to the design are provided