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Hein and Zakhor analyzed the limit-cycle behavior of the low-pass double-loop converter. This brief demonstrates that the limit cycles in a bandpass Σ-Δ double-loop converter are identical to the low-pass case. It is shown that the double-loop converter can have two independent limit cycles occurring simultaneously. Simulations confirm that the bandpass converter state variables can be designed to stay within designed bounds, as in the low-pass (baseband) case, Hence, stability is improved as the likelihood of stages saturating and clipping is significantly reduced.