EXPLOITING CHAOS TO SUPPRESS SPURIOUS TONES IN GENERAL DOUBLE-LOOP SIGMA-DELTA-MODULATORS

Conventional SIGMADELTA modulators are operated exclusively in the non chaotic regime in which the internal integrators are stable. Theoretic al interest in chaotic SIGMADELTA modulators recently arose, mainly be cause the circuits are simple and strongly nonlinear systems with rich behavior, not unlike Chua's circuit [1], [2]. It has since been recog nized that the application of conventional SIGMADELTA modulators to A/ D and D/A conversion may be haunted by spurious ''tones'' in the outpu t, and it has been proposed use chaotic modulators to overcome that pr oblem. This paper employs a semi-analytical technique to solve the des ign problem for general chaotic double-loop modulators with constant i nputs Using the results, optimized scaling factors are easily for give n integrator pole locations, such that an approximate performance meas ure is maximized subject to bounds on internal state variables. The cl arification of this explicit tradeoff between tone rejection through c haos, system stability, and practical performance may help to overcome some understandable skepticism in the community of SIGMADELTA designe rs.