The effects of finite switch resistance and finite op-amp bandwidth on first-order ΣΔ modulators with sinusoidal inputs

Nonideal component effects on the performance of first order ΣΔ modulators are investigated. An exact methodology for analyzing the moments and spectra of the quantization noise sequence has been published. It was shown that the quantization noise approaches white noise only when the number of levels in the quantizer is large compared to the amplitude of the input sequence. This result was shown for an ideal oversampled ΣΔ modulator. The authors extend this work to obtain an exact discrete-time representation of the moments of the quantization noise sequence for a first-order oversampled ΣΔ modulator including the effects of the time constants associated with the switches and the op-amp of the integrator. The emphasis is on obtaining the moments in terms of the component values such that they may be used as design equations. These equations, therefore, allow the designer to trade off overall system performance and component values. Results are presented for finite switch resistance and finite op-amp bandwidth