# Computing stuff tied to the physical world

## Lissajous is tea for two!

In Hardware on Mar 26, 2012 at 00:01

When you have two nearly identical sine wave signals and you want to compare them, one technique is to plot one against the other, creating what is known as a Lissajous curve.

Lissajous curves make nice images, and even nicer videos because of the phase shifts.

So let’s take two signal generators and try it out, eh?

On the X-axis, I’m going to plot a 10 MHz sine wave from the new AWG, described on this weblog a few days ago. The frequency accuracy and stability of its output signal is within 1 or 2 ppm, according to the TG2511 specs.

On the Y-axis, let’s connect a second 10 MHz sine wave from a cheap DDS, also described on this weblog a few months back. This has a simple crystal so I’d expect 50 to 100 ppm frequency accuracy, i.e. within ≤ 1000 Hz.

When you connect these to an oscilloscope and put it in X-Y mode, you get pictures like these:

The more the two signals are in phase, the more the result will look like a straight line, slanted at 45° (from the bottom left to the top right). When exactly 180° out of phase, it will show a straight line from top left to bottom right. Everything in between create ovals, and when the signals are 90° out of phase (either lagging or leading), the result is a perfect circle.

So the big thing about Lissajous curves is that they let you compare the relative phase of two sine waves.

In practice, signals from different sources will tend to change phase over time, i.e. “drift” as one sine wave is slightly slower or faster than the other. This creates a way to precisely compare two frequency generators: measure how long it takes for the phase to go from 0° to 180° (or 360°, which is 0° again), and you get an idea how long it takes for one signal to catch up (or lag) one full sine wave over the other. Trouble with this approach is that sometimes these cycles are too fast to see, let alone time manually.

With an adjustable frequency source, there’s also another way: adjust a known frequency until the shape stays the same, and you’ll have “measured” the frequency of the other signal in terms of the adjusted one since they must now be equal. It’s very much like tuning a musical instrument by ear and adjusting for a “zero beat”.

That’s what I did, and I ended up with the following result for this test setup:

IOW, the cheap DDS is running 0.03% slow – i.e. about 300 ppm! And it’s not even very stable, because very soon the DDS starts drifting again: an indication that it’s not holding its frequency really accurately either. This is not really surprising for such a low-cost unit off eBay – it’s still a useful signal source: lots of useful experiments and measurements can be done with such a fairly decent 0.03 % accuracy level, after all.

Ok, this concludes my first exploration into signal-processing – enough signal theory for now!

1. The thermal performance of the DDS-60 is limited since the crystal reference oscillator is placed close to the AD9581 and voltage regulator – both of which are running hot in this design.

This reflects as a slow drift of output frequency from power up – by the time it has stabilised, the crystal package is running well away from the standard calibration temperature of 21ºC, so you get bitten twice.

Nevertheless, this won’t get in the way of many uses – just don’t try to calibrate your RFM12B’s with this as the reference.

2. Hi

It woud be interesting to compare the AWG against the Rubidium source.I am waiting for the arrival of an Agilent 33120A I recently bought and can’t await to compare it.

Cheers Michael

3. Is there a way to electronically determine the phase difference ? i.e. to translate the lissajous pictures into something of a voltage ? or is the humble capacitor/resistor integrator the only way ? (in my case both signals are not under my control, or more exactly not directly under my control)

• That would be a phase locked loop aka PLL.

4. For some reason, those first few photographs take me back to my youth…