Buck Converter Concepts Part 1 of 3: Frequency Content of Square Waves

Take a square wave with a duty cycle of 0<x<1, a frequency of f, and an amplitude of A. (The minimum value of this square wave is 0.) This signal can be decomposed into its frequency components by Fourier analysis. The frequency components of a signal are just the collection of sine waves that when added together give you the original signal.


"SquareWave" by Peretuset - Own work. Licensed under CC BY 3.0 via Wikimedia Commons.

The first sine wave of interest in our square wave is the 0 Hz sine wave. It's not really a sine wave, it's just the average value of the signal over one period. For our square wave, the average value over one period is A*x + 0*(1-x) = A*x. This frequency component is the "DC value" of the signal.

The next sine wave of interest is the one at the fundamental frequency of our signal. The fundamental frequency of our signal is the lowest frequency component of the signal. It's determined by the period of the signal and is known as f_1: f_1 = 1/T. In the case of our square wave, the fundamental frequency is f.

The rest of the frequency components of our square wave all have frequencies that are greater than the fundamental frequency. In fact, all the other components are known as "harmonics" and have frequencies that are integer multiples of the fundamental. This is all true regardless of the duty cycle of our square wave.

This means that our square wave will have some power at 0 Hz and f HZ, but no power in between. Were we able to somehow remove all frequencies above n Hz where 0<n<f then we'd be left with a simple DC waveform. This is the basic concept behind a DC-DC buck regulator.

This entry is part two of a three-part series explaining how DC-DC buck regulators work.

Photo by Rising Damp