Analysis of tones in the double loop ΣΔ modulator with unstable filter dynamics

In this paper we analyze the tone behavior of the double loop ΣΔ modulator with unstable filter dynamics. We show that some unstable limit cycles have an attractor region in their neighborhood which results in tones in the spectrum corresponding to the fundamental or harmonics of these limit cycles. We develop the tools to determine whether or not an unstable limit cycle has an attractor in its neighborhood and obtain a method to approximate the boundaries of these attractors