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

TL;DR

This paper explains how pulse-width modulation (PWM) can be used to generate analog signals from microcontrollers, using simple resistor-capacitor filters, suitable for teaching sophomore-level physics and electronics students.

Contribution

It provides a clear, accessible explanation of PWM and filter analysis tailored for undergraduate physics and electronics education, filling a gap in typical curriculum resources.

Findings

PWM effectively creates pseudo-analog signals from digital outputs.

Resistor-capacitor filters can be analyzed with basic physics knowledge.

The notes serve as a useful teaching supplement for undergraduates.

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!