Design techniques for sigma-delta modulators in communications applications
Specialised design techniques for sigma-delta modulators are described in this thesis with all of the examples coming from modern communications systems. The noise shaping and the signal transfer functions can be optimised using a weighted least squares approach. Numerical problems arising in the optimisation as a result of high oversampling rates are overcome through the use a simple transformation. The application to digitising audio is discussed, with the conclusion that Butterworth response noise shaping is preferable to inverse Chebyshev noise shaping for audio applications. An example of optimising the signal transfer function to provide immunity to instability brought about by large out-of-band signals is also presented. The use of redundant arithmetic in the implementation of very high speed sigma-delta modulators is introduced, together with a DAC / filter combination suitable for reconstructing an analogue signal from the redundant arithmetic SDM. An improved topology for a speech compander is described which offers a number of significant advantages over existing published methods. This uses no external components for ac coupling or setting the response time-constant, yet is robust and insensitive to parasitic components and process variations. This has been integrated on a CMOS IC process and the results are compared with the high level simulations. A simulation method which allows the verification of switched-capacitor schematics with several orders of magnitude speed improvements over commercially available simulation tools is discussed. The method assumes ideal components, with internally controllable switches and reduces the schematic netlist to the few key equations that an experienced designer would derive manually. This process is fully automated and consequently is useful for providing confidence in implementations of complex SC systems.