Re: How much scope is too much scope

by adafruit_support_mike on Fri May 04, 2012 7:33 pm

There's no hard rule for this, but the Nyquist theorem and Fourier wave theory help you make some basic decisions.

Nyquist says you can recover everything you need to know about a sine wave (its frequency and amplitude) if you sample it at more than twice its frequency. If you need to measure a 1000 Hz sine wave, your sampling rate needs to be at least 2001 Hz to get everything you need to know. If you sample at 2000 Hz, you'll get the frequency, but can't be sure you've got the right amplitude. Below 2000 Hz, you'll get what's called 'aliasing', which is what used to make it look like a car's wheels were spinning backwards in old movies.

To state Nyquist another way, the information you can learn is 'bandlimited' (meaning you don't get any more useful information) above half your sampling frequency.

Now we turn to M. Fourier, who proved that you can break any periodic function into an infinite sum of sine waves of different frequencies. The sum:

sinx + (sin 2x)/2 + (sin 3x)/3 + (sin 4x)/4 + ...

gives you better and better approximations of a sawtooth wave, for instance. If you add the odd multiples of x, you get a square wave.

We use integer multiples of the base frequency because it works, and it makes the calculations easier. Each multiple is called a 'harmonic', and the harmonic number equals the multiplier.. 2x = second harmonic, 3x = third harmonic, etc.

So.. the closer you get to the Nyquist frequency of your basic signal, the less you can know about the shape of the wave. At a sampling rate of 2001 Hz, you can't tell a 1000 Hz square wave from a 1000Hz triangle wave from a 1000 Hz sine wave, because all you'll get is the 1000 Hz sine wave component from all three.

The more you want to know about the shape of your wave, the more harmonics you need to be able to measure. That means you want a scope that can sample twice as fast as the highest harmonic you need.

As a general rule of thumb, sampling up to the 7th harmonic is pretty good. That means you want a scope whose sampling rate is about 15 times the highest base frequency you want to measure. A scope with a 30 MHz sampling rate will give you decent information about signals running up to around 2 MHz. A scope with a 1 MHz sampling rate will give you decent information about signals up to around 70 KHz.

From there, you make tradeoffs between what you want to measure and what you can afford.

If you're just starting out, a 1 MHz sampling rate will serve you well for circuits that work in the audio range. A 30 MHz scope will allow you to tweak digital circuits running at up to a couple megahertz. Beyond that, when you need it, you'll know it.

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