Analog to digital conversion[edit]
Description[edit]
The ADC generates a pulse stream in which the frequency of pulses in the stream is proportional to the analog voltage input, , so that the frequency, where k is a constant for the particular implementation.
A counter sums the number of pulses that occur in a predetermined period, so that the sum, , is .
is chosen so that a digital display of the count, , is a display of with a predetermined scaling factor. Because may take any designed value it may be made large enough to give any desired resolution or accuracy.
Each pulse of the pulse stream has a known, constant amplitude and duration , and thus has a known integral but variable separating interval.
In a formal analysis an impulse such as integral is treated as the Dirac δ (delta) function and is specified by the step produced on integration. Here we indicate that step as .
The interval between pulses, p, is determined by a feedback loop arranged so that .
The action of the feedback loop is to monitor the integral of v and when that integral has incremented by , which is indicated by the integral waveform crossing a threshold, then subtracting from the integral of v so that the combined waveform sawtooths between the threshold and ( threshold - ). At each step a pulse is added to the pulse stream.
Between impulses the slope of the integral is proportional to . Whence .
It is the pulse stream which is transmitted for delta-sigma modulation but the pulses are counted to form sigma in the case of analogue to digital conversion.