# Lissajous figures phase difference equation

This article includes a list of referencesbut its sources remain unclear because it has insufficient inline citations. Obviously, a suitable function generator will work. The number of intersections of the horizontal and the vertical lines with the Lissajous pattern curve is individually counted. The most common use of an oscilloscope is to display one or more signals in the time domain. The menu appears to the right of the display, and XY Display is currently off.

So, by substituting the values of nH, nV and fH in Equation 1, we will get the If the Lissajous figure is in circular shape, then the phase difference between the.

### Observing phase shift with Lissajous patterns

In mathematics, a Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch Finally, the value of δ determines the apparent "rotation" angle of the figure, viewed as if it were actually a three-dimensional curve. in X-Y mode and the phase relationship between the signals is presented as a Lissajous figure.

Lissajous curves (sometimes also known as Lissajous figures or Bowditch curves ), are Liassajou curves are described by the parametric equations below: the two waves is 3/2, and the amplitude ratio is (with a phase difference of π/2).

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Regardless of the two amplitudes of the applied voltages, the ellipse provides a simple means of measuring phase difference between two voltages.

Video: Lissajous figures phase difference equation How to measure phase shift with a RC circuit

NDL : An ellipse signifies a capacitor or inductor. The default waveform is sine, which is what we want. Lissajous pattern with equal frequency voltages and zero phase shift.

## Lissajou Curves

Crossing. FIGURE Two signals with a relative phase difference of φ between them. The time scale From Equations andit follows that this filter has impulse response. Shape of these Lissajous pattern changes with changes of phase difference between signal and ration of frequencies applied to the deflection.

There are a number of ways to measure the phase difference between two voltage waveforms using an oscilloscope.

## Lissajous Patterns of CRO or Cathode Ray Oscilloscope Electrical4U

. dual-channel trace. Figure 2. Lissajous figure.

Video: Lissajous figures phase difference equation How X/Y Mode Works on an Oscilloscope

(by Paul Kavan) . Substracting the lower equation from the upper.

## Lissajous patterns using a scope for display signals

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When two sinusoidal voltages of the same frequency are applied :. November Learn how and when to remove this template message. The simple rule mentioned above needs the following modifications :. In all cases when the frequency ratio iswhat displays is an ellipse, of which the straight line and circle are limiting cases.

### Lissajous Patterns in CRO for Measurement of Phase & Frequency

But there are other alternatives. The ratio of frequencies when open-ended Lissajous patterns are obtained can also be found by treating the open ends as half tangencies as shown in the below figure b. It consisted of a vibrating tuning fork to which a mirror was attached.

Lissajous figures phase difference equation |
Light reflected from this mirror and then, in turn, reflected from another mirror attached to a second tuning fork.
An ellipse is also obtained when unequal voltages of the same frequency are applied to the CRO. If the Y voltage is larger, an ellipse with vertical major axis is formed while if the X plate voltage has a greater magnitude, the major axis of the ellipse lies along the horizontal axis. Channel One is the default selection. Lissajous patterns get their name from Jules Antoine Lissajous, who investigated, wrote and lectured about them in Lissajous patterns may be used for accurate measurement of frequency. Where it is not possible to adjust the standard signal frequency to the exact frequency of the unknown signal, the standard if adjusted to multiple or a submultiple of the frequency of the unknown source so that the pattern appears stationary. |

About Us. The simplest Lissajous patterns appear in the oscilloscope display when the frequencies of the signals are the same, i.

A slanted line going from the lower left to the upper right is displayed when the device hooked to the octopus tester is a resistor. By adjusting the frequency of each wave, the phase between them, and their relative amplitudes, interesting patterns emerge.

This article includes a list of referencesbut its sources remain unclear because it has insufficient inline citations. In most oscilloscopes that have this capability, the frequency domain is accessed by pressing a button labeled Math.

Chand " is the best in industry. You can imagine sweeping a pencil side-to-side in a sinusoidal motion adjusting just the x-axisand what you would get is a straight line.

Suppose sine waves are applied to X and Y plates as shown in the figure below. In automatic mode, the frequencies slowly change in phase to animate the shapes.