Notes on pulse-width modulation appropriate for a sophomore-level electronics or programming class

Abstract

Pulse-width modulation is a nice way to create pseudo analog outputs from a microcontroller (eg, an Arduino), which is limited to digital output signals. The quality of the analog output signal depends on the filter one uses to average out the digital outputs, and this filter can be analyzed with sophomore-level knowledge of resistor-capacitor circuits in charging and discharging state. These notes were used as a text supplement in a sophomore/junior level Microcontroller programming class for second and third-year Physics majors. I don't know where this material is normally treated in the Physics curriculum and figured others might find the resource useful. Comments welcome!