Exact analysis of second order bandpass delta-sigma modulator with sinusoidal inputs

The nonlinear recursive difference equations of second order bandpass delta-sigma modulator with sinusoidal inputs are solved. The results indicate that quantization error is neither uniformly distributed nor white. The autocorrelation of quantization error is symmetric but does not vanish as correlation index increased. The study of crosscorrelation between quantization error and sinusoidal input shows it indeed exists which also contradicts the assumption of linear model.