# Delta-Sigma-Modulation

The delta-sigma ( ΔΣ ) modulation is a form of analog-to- digital conversion or digital-to- analog conversion, which is derived from the delta modulation. Despite the development of ΔΣ technology in the early 1960s, this technique can only since the 1990s produced inexpensively with the advances in CMOS technology. Delta-sigma modulators are offered by many large semiconductor manufacturers as a finished integrated circuit.

## Principle

The principle of the delta-sigma modulation is based on a first rough measurement of the signal ( the quantizer in the image Engl. " Quantizer "). The resulting measurement error is integrated (in the picture engl. " Integrator " ) and compensated gradually over a negative feedback. Depending on whether an analog - to-digital conversion (ADC ), a digital-to- analog conversion (DAC ), an analog-to- analog conversion is to be ( in the SACD) and digital-to- digital conversion carried out ( also conceivable for sampling rate conversion), the individual blocks of the delta -sigma modulator are implemented in digital or analog. ( Under the " 1 -bit DAC " shown in the block diagrams you have to imagine an allocator which a " 1" bit of the greatest and a " 0" bit assigns the smallest possible input value - whether this is voltages ( analog input) or PCM data ( digital input) are. ) the said steps are carried out very frequently, for example, with 128 times the rate of the PCM data underlying sampling rate ( oversampling ).

The average output signal is the input signal. The delta-sigma modulation has the property that the spectral power density reduces the undesired quantization noise at low frequencies and at high frequencies ( which are outside of the detected frequency band ) is increased - Illustratively stated, the noise power is shifted to higher frequencies; this fact is called " noise shaping " or English. " Noise Shaping " means. Thus, the low-frequency signal components can be detected with a high signal to noise ratio.

Higher frequencies are not used due to the poor signal to noise ratio, and through a filter (a digital filter for a digital output ( ADC ) or an analog filter for an analog output ( DAC ). Pictured eng " digital filter " ) away. In the case of a digital output of this filter simultaneously performs a sample rate conversion to the desired output bandwidth and extends the word width of the quantizer for a suitable dynamic range.

The number of integrators or the number of negative feedback loops characterize the order of the ΔΣ modulator. The higher the order, the more the displacement of the noise, the higher frequencies can be used. A disadvantage is the in principle possible occurrence of oscillations and instabilities in the modulator circuit at higher orders.

The ratio of sample rate conversion (English oversampling ratio, OSR) and the order N determine the possible dynamic range of a delta-sigma converter. The dynamic range of the ratio between the power of a just undistorted digitalizeable sine tones and noise power yields to:

The higher the oversampling and the higher the order is, the larger the dynamic range of the converter.

Advantageous over other AD conversion principles is the high sampling rate of the analog signal, compared to the bandwidth of the useful signal. Through this scanning requires an analog band limiting filter, which is required for maintaining the Nyquist -Shannon sampling theorem, only a small slope, and may be easily constructed. See also section order the article Filter.

## Application

Due to its properties it finds in a number of applications advantageous application:

- In the field of audio signal processing he has other converter techniques almost completely displaced. Versions with a signal bandwidth of 100 kHz and a signal -to-noise ratio of 120 dB are commercially available since 2005. In particular, the sigma-delta modulator forms the basis referred to in the Super Audio Compact Disc used Direct Stream Digital encoding method. This is in principle a "distributed " Analog -to-analog modulation carried out, wherein when recording the coming from the 1-bit quantizer signal is recorded (pre- filter) to the SACD. Only during the playback of the data stream is processed by an analog filter to the output signal.
- In the low-frequency data acquisition special versions come with bandwidths of less than 50 Hz seismometers, electronic scales and similar appliances. These converters usually also have a dedicated digital filter, which suppresses the power line frequencies of 50 Hz and 60 Hz and their harmonics.
- In PLL circuits for clock generation fractional-rational ( fractional- N PLLs ) sigma- delta modulators can be used in the feedback loop to switch between the divider ratios alternately used in fractional- N PLLs. Advantage of fractional-N PLLs is the lower phase noise and the higher for a constant frequency output of the maximum loop bandwidth, as a higher reference clock can be used than in conventional PLLs. However, the continuous change of the divider ratio is an additional source of noise. By controlling the switching of the division ratio by means of a sigma -delta modulator, however, the property of the noise shapings can be used to route to move the additional phase noise of the output frequency of the fractional- N- PLL, where it is filtered by the low-pass effect of the PLL can be.