# Sawtooth to sinusoid

Discussion in 'The Projects Forum' started by iflabs, Nov 25, 2009.

1. ### iflabs Thread Starter New Member

Sep 14, 2006
6
0
Before we start, I would like to state that we have not been introduced to Fourier series yet, but somehow ended up with a project involving it.

The goal of this project is to convert a sawtooth signal to a pure sinusoid signal. The sawtooth has a frequency of 50hz with a 5v amplitude and we want a sinusoid with a period of 250Khz. We are to build a filter circuit with only inductors, resistors, and capacitors to perform as asked.

After researching, it turns out that a sawtooth signal is merely a superposition of sinusoid with varying signals.

So the question/s are:

-To achieve a 250khz sinusoid, all we need to do is create a 2nd order bandpass filter to filter all signals below and above 250khz, am I correct? Or am I missing a piece of the equation to get the desired result?

-But then as I look at the Fourier equation for a sawtooth again, it says there is a "fundamental" frequency and a term called "harmonic". In this case, I believe the fundamental frequency is 50hz. So at 250khz, it would be the 5000th harmonic. What am I suppose to do with this? lol

2. ### Wendy Moderator

Mar 24, 2008
21,470
2,959
You have some terms mixed up, period should be in seconds (milliseconds, microseconds). You 're giving it in frequency units.

Are you really wanting 250Khz from a 50Hz fundamental frequency? If so it is doable, but the amplitude will be in microvolts or smaller. Amplitude drops off fast, and you are talking the 5,000 harmonic.

3. ### iflabs Thread Starter New Member

Sep 14, 2006
6
0
I meant a "frequency of 250khz", not period.

The project didn't specify any limitations to sinusoidal amplitude so I assume any amplitude is fine. But the project did specifically state that a 50hz sawtooth conversion to a 250khz is required. Since the sawtooth is a 50hz signal, I assumed 50hz is the fundamental frequency. And being that 5000 is the multiplier of the fundamental frequency to obtain 250khz, it is the harmonic.

I'll go ahead and post up spice simulations later for feedback.

4. ### Wendy Moderator

Mar 24, 2008
21,470
2,959
A simple LC bandpass filter will work, in other words, a LC tank. Again, this signal will be so small as to be almost undetectable, but it will be there.