The rate of change of the output is following that of the input. Figure 4. Using a linear model to describe this single bit modulator Mod 1 the system is shown as a control system with negative feedback. The quantization noise is the difference between the input and the output of the quantizer.
A low-pass filter follows the input delta node. In Figure 5b, the quantization noise is described by the term N. Figure 5. H f is the function of the loop filter and it defines both the noise and signal transfer functions. H f is a low-pass filter function with very high gain at low frequencies within the bandwidth of interest and attenuation of higher frequency signals.
The loop filter can be implemented as a simple integrator or a cascade of integrators. In practice a DAC is placed in the feedback path to take the digital output signal and feed it back to the analog input delta node.
Solving the equations shown in Figure 5 gives the signal and noise transfer functions. The signal transfer function operates as a low-pass filter, with a gain of 1 in the bandwidth of interest. The noise transfer function is a high- pass filter function, providing the noise shaping. There is strong suppression of the quantization noise at low frequencies around dc. The quantization noise signal seen at high frequencies outside the bandwidth of interest is increased.
A common method to increase the resolution of the system is to increase the loop filter order by cascading two loop filters. The quantization noise is shaped more aggressively, with much lower frequency noise. Click the Next Step button to move the tutorial forward a step. At each step the diagram is updated to show the current output of each block.
To see the outputs at the previous step of the tutorial, click the Previous Step button. To advance the tutorial complete loops of the modulator, click the Next Loops button. The outputs from the comparator will be: 1, 0, 1, 1, 1, 0, 1, 1. This means 6 of the 8 outputs have been a 1; i.
The allowed input range is With a 1. The digital filter does a much better job at detecting this trend then our simple count ones method. Instructions Related Information Instructions The diagram inside the applet shows a basic first order sigma-delta modulator. How to use this tool Enter an ADC reference voltage in the lower input field.
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