The basic principle of a first-order noise shaping sigma-delta ADC
is shown in Fig. B.1. The input signal *x*(*t*) is fed
through an integrator and is then quantized, usually with only one
bit resolution. The quantizer
output is then sampled at a high frequency
and subtracted from the input. Thus, average of the digital output
equals the input *x*(*t*).
As a consequence of the oversampling and of the integration
most of the noise contained in the digital output *y* lies outside of
the signal band and is eliminated by a subsequent digital low-pass
filter (usually a decimation filter to reduce the sampling frequency
from
to
[38]) which is not shown in
Fig. B.1.

An improvement of the signal-to-noise (SNR) ratio can be achieved by
increasing the order of the integrating filter as shown in
Fig. B.2. The resulting SNR at full-range input is
given by

where is the oversampling rate, which spreads the noise over a wider band, and

G. Schrom