Maxim > Design Support > Technical Documents > Tutorials > A/D and D/A Conversion/Sampling Circuits > APP 1870
Maxim > Design Support > Technical Documents > Tutorials > Sensors and Sensor Interface > APP 1870
Keywords: Delta-Sigma, analog to digital converters, ADCs, A to D, A/D, oversampling, noise shaping, decimation,
decimation filters, MAX1402, thermocouple measurement, RTD, resistance temperature detectors, 4-20mA, 4-20mA
trnasmitter, 24-bit sigma delta ADC
TUTORIAL 1870
Demystifying Delta-Sigma ADCs
Jan 31, 2003
Abstract:
This
in-depth article covers the theory behind a Delta-Sigma analog-to-digital converter (ADC). It specifically
focuses on the difficult to understand key digital concepts of over-sampling, noise shaping, and decimation filtering.
Several applications for Delta-Sigma converters are included.
Modern Sigma-delta converters offer high resolution, high integration, low power consumption, and low cost, making
them a good ADC choice for applications such as process control, precision temperature measurements, and weighing
scales. Designers often choose a classic SAR ADC instead, because they don't understand the sigma-delta types.
The analog side of a sigma-delta converter (a 1-bit ADC) is very simple. The digital side, which is what makes the
sigma-delta ADC inexpensive to produce, is more complex. It performs filtering and decimation. To understand how it
works, you must become familiar with the concepts of oversampling, noise shaping, digital filtering, and decimation.
This application note covers these topics.
Oversampling
First, consider the frequency-domain transfer function of a traditional multi-bit ADC with a sine-wave input signal. This
input is sampled at a frequency F
s
. According to Nyquist theory, F
s
must be at least twice the bandwidth of the input
signal.
When observing the result of an FFT analysis on the digital output, we see a single tone and lots of random noise
extending from DC to F
s
/2 (Figure 1). Known as quantization noise, this effect results from the following consideration:
the ADC input is a continuous signal with an infinite number of possible states, but the digital output is a discrete
function whose number of different states is determined by the converter's resolution. So, the conversion from analog
to digital loses some information and introduces some distortion into the signal. The magnitude of this error is random,
with values up to ±LSB.
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