Slope overload noise in linear delta modulators with Gaussian inputs

This paper derives a slope overload noise power formula for linear delta modulators having ideal integrators and Gaussian random inputs. Although the same problem has been treated by others, the present result is the only one applicable to all slope-following capacities and input spectra. Despite its singleness of purpose, the paper divides logically into two parts. In Part 1, a common element in all previously published results is used to derive a new slope overload noise power formula. This derivation is analytically rigorous and provides some useful insights, but pertains to a particular kind of spectrum and so is incomplete. The more universal result we seek is derived in Part 2. The approach here is far less rigorous and amounts to approximating the influences of other kinds of spectra by modifying the result of Part 1. The final expression contains four spectrum-related coefficients, for which simple formulas are given, and has an estimated accuracy of 1 dB for all cases of practical interest. Computed results are given for two important families of spectra and comparisons are made with previously published results.