# sigma delta converter

Sigma-Delta converters use a 1-bit converter for analog-to- digital conversion; in addition, the techniques of oversampling, noise shaping and digital filters are used. The sigma-delta process is characterized by a very high resolution of up to 24 bits and is used in audio technology, consumer electronics and communications technology, among others.

In principle, the sigma-delta converter is a very simple A/D conversion principle, the 1-bit conversion, which knows only a single bit. In delta modulation, only the changes in the signal level are converted digitally. In the simplest case, the digital "1" represents a rising voltage, the "0" a falling voltage. Each bit represents a fixed change value. If the voltage remains constant, there is a constant change between "1" and "0". This modulation technique can be used with changing input voltage, as in audio, but is not suitable for DC voltage.

## The technique of oversampling

The n-fold sampling frequency used in oversampling increases the resolution and accuracy of the delta converter. This results from the fact that the depth of information depends on both the sampling depth and the sampling rate. A lower sample rate and a high sample depth have the same depth of information as a high sample rate and a low sample depth. Thus, a 1-bit converter with a high sampling rate can have the same depth of information as a 16-bit converter with a low sampling rate. This basic principle is exploited with oversampling.

In addition, the effective quantization noise is distributed over a wider frequency range. At n times the sampling frequency, the noise energy is distributed over n times the frequency range, so the noise component decreases compared to the single sampling frequency, which translates into a higher dynamic range. For example, an eight-fold oversampling ratio( OSR) increases the bit number by 3, while a 256-fold increases it by 8.

According to the procedure, the binary signal is sampled with a high sampling frequency. This is many times higher than the sampling frequency resulting from the sampling theorem. For a compact disc operating at a sampling frequency of 44.1 kHz, the oversampling ratio (OSR) may well be well over 10 MHz, which would correspond to over 200 times oversampling.

The delta sigma modulator converts a binary input signal of arbitrary bit width into a serial bit stream. For this purpose, the input signal is fed to a differential amplifier followed by an integrator. The output level of the integrator is fed to a comparator, which evaluates it with "0" or "1". The number of "ones" at the modulator output is proportional to the input signal. The comparator output is fed through a 1-bit converter, which converts the 1-bit data stream into a positive or negative voltage, which is then fed to the integrator as a control voltage via the differential amplifier. The analog output signal is generated by passing the comparator signal through a low-pass filter.