Nonlinear dynamics of chaotic double-loop sigma-delta modulation

The double-loop sigma-delta modulator is playing an increasingly important role in signal-processing applications, but this role is often hampered by the appearance of unwanted periodic signals in the modulator output. Operation in a chaotic regime has been suggested as a possible means of overcoming this disadvantage. For some parameter values, however, chaotic operation can lead to unbounded state variables, destroying the functionality of the modulator. State variables that, though bounded, exceed implementation-dependent limits can also destroy functionality. The aim of this paper is to show how established methods of nonlinear dynamics can be applied to the zero-input system to study the steady-state location of the state variables and to determine parameter values for which rounded behaviour is possible