Understanding Lissajous Figures with Oscilloscopes

This page covers Lissajous figures and how to create them using a CRO (Cathode Ray Oscilloscope). As you probably know, an oscilloscope is a fundamental instrument used for studying different types of waveforms.

It can generate graphs of:

• Input Signal versus time (i.e., Voltage-Time Mode)
• X-Y Mode

Oscilloscopes come in different types. Let’s delve into the XY mode and how it helps generate Lissajous figures.

X-Y Mode on an Oscilloscope

Besides displaying time-varying signals, a CRO can display an input signal on the horizontal axis instead of a time base.

This setup is known as XY mode. The reason being that both the X-axis and Y-axis trace the input voltage. The waveform that results from this XY arrangement of two periodic signals (having different periods) is called a Lissajous Pattern.

By observing the shape of the Lissajous pattern displayed on the CRO screen, we can figure out information about the relative phases of the signals and, importantly, the frequency ratio of the signals.

Figure 1: Lissajous figure obtained on CRO using two sinusoidal voltages having a frequency ratio of 2:1.