## Thoughts on Digital Modulators

The purpose of a digital modulator is to generate a digital stream that has a particular percentage high value.  For pulse width modulators (PWM) this is called Duty Cycle , but the more generic term is Density (D).  A digital stream can have a density ranging from 0% (all low) to 100% (all high).  There are three basic types you should know about.

• Pulse Width Modulation (PWM)
• Delta Sigma Modulation (DSM)
• Pseudo Random Modulation (PRM)

Pulse Width Modulation

PWM generate the smallest possible frequency transition.  They go high once and low once and have a constant output frequency of   fs/(Counter size).  If the cost of switching is high (Lets stay a switching power supply) then this is the modulation to use.  Because the frequency is constant, they generate a lot of harmonics.

Delta Sigma Modulation

If PWMs generate the lowest possible frequency, then DSMs generate the highest possible frequency.  For a density if 50% (128/256) there are 128 raising and falling edges for an output frequency of ½fs.  For a density of 25% (64/256) or 75% (192/256) there are 64 rising and falling edges for an output frequency ¼fs.  The output frequency is a function of the clock and density and is fs*min(D, D-1).  This type of modulation makes the signal easy to filter.  That makes it the preferred modulator for single bit DACs.

Pseudo Random Modulation

Here the output has a probability, for each cycle, of being high that is equal to the density value.  An example is to take a die and repeatedly toss it.  Make the output high when ever the die is two or less.  On the average it will be high one third of the type.  For this type of modulation the output frequency works out to fs* ½min(D,D-1).  IT key advance is that there are no harmonics.  If I was building a battery charger I would most likely use a PWM.  But if the charger was to be placed next to a radio receiver, I would use a PRM.

Summary

For the lowest possible output frequency, use a PWM

For the highest possible output frequency, use a DSM

For something in the middle, with no harmonics, use a PRM

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