We can connect a function generator to both the x and y axis and begin to draw lissajous patterns. Finally, if the two ac signals are directly opposing one another in phase 180 shift, we will end up with a line again, only this time it will be oriented in the opposite direction. If the ratio of the frequencies is rational, the curve will always eventually close. A labview based simulation of lissajous pattern using daq. The metrics of interest are frequency, ratio, relative amplitude and phase shift. Measuring relative phase between oscilloscope traces using the lissajous ellipse method requirements. To estimate the phase relation of thoracoabdominal motions i. N2 this paper presents a novel analysis of nonlinear circuits useful for the computation of the reactive power from only terminal. At each instant, the scope plots a dot with the input x sample as the horizontal coordinate and the output. Such figures are widely used in frequency and phase measurements see illustration.
Two phaseshifted sinusoid inputs are applied to the. This family of curves was investigated by nathaniel bowditch in 1815, and later in more detail by jules antoine lissajous in 1857. Here is the 2d lissajous pattern of the pure ratio major chord 11 54 32, from tune smithy. A modification to the conventional method of phase measurement on an oscilloscope based on the lissajous pattern is suggested and its advantages presented. The original lissajous patterns were based on diads two note chords. We can tell that oscilloscope can measure the phase and thefrequency of two frequency.
A much wider range of lissajous figures can be created by manually adjusting the amplitude, frequency, andor phase of one or both of the voltages via the designated sliders. Phase shift lissajous on old eico 427 oscilloscope. Lissajous is a complex audiovideo signal generator built in maxmsp and inspired by the work of jules antoine lissajous. Note that at every time t, each x value is identical to each y value.
Two phase shifted interferograms can be represented as the lissajous figure by plotting their pixelwise corresponding intensities, see fig. The australian broadcasting corporation is a mostly. Shape of these lissajous pattern changes with changes of phase difference between signal and ration of frequencies applied to the deflection. Lissajous curves can also be generated using an oscilloscope as illustrated. If it is irrational, the curve will never close and eventually fill a region. Geometrical and graphical representations analysis of.
We can calculate the phase difference between the two sinusoidal signals by using formulae, when the lissajous figures are of elliptical shape. Measuring relative phase between oscilloscope traces using the lissajous. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal. However, most oscilloscope will allow you to supply an external input that will allow you to directly control the x axis. The lissajous pattern indicates the phase difference by the shape of the xy plot. T1 lissajous curve methods for the identification of nonlinear circuits. Through theoretical analysis, software simulation and experimental test, we conclude that the central angles of lissajous figure have a linear relationship with phase modulation coefficients and microvibration displacements, and the experimental results have a good agreement. Nv6543 lissajous pattern traineri is a unique product designed to explain the measurement of unknown frequency, phase difference and resonance frequency using lissajous pattern. A classic phase measurement, the lissajous pattern blogs. Phase shifting interferometry is widely used to obtain the phase distribution in interferometric measurements. Block diagram of the system this block diagram shows the combination of software and hardware.
An octopus circuit can be used to demonstrate the waveform images on an oscilloscope. Instantaneous phase difference analysis between thoracic and. Named after jules antoine lissajous, a lissajous curve. The phase shift equation is ps 360 td p, where ps is the. The spreadsheet or other software must then calculate voltage v. For example, an electronic oscillator may produce sine waves at a frequency of 100 hz. But musicians often play triads three note chords or tetrads four notes or more. So the steps would be to get an expression for the curve, and then the two zero crossings would be the displacement. I have read somewhere that it is the least common multiple lcm of v and w but i do not understand what this means.
The maximum period of a lissajous curve is 2 pi, and i do not understand how lcmv,w would yield a value less than 2 pi. On an oscilloscope, we suppose x is ch1 and y is ch2, a is amplitude of ch1 and b is amplitude of ch2, a is frequency of ch1 and b is frequency of ch2, so a b is a ratio of frequency. Lissajous figures introduction lissajous figures displayed on an oscilloscope can be used to give a quick estimate of the relative phase of two signals at the same frequency. We present the simplified lissajous ellipse fitting slef method for the calculation of the random phase step and the phase distribution from two phaseshifted interferograms. Two phase shifted sinusoid inputs are applied to the.
This is an article about lissajous curves lissajous curves sometimes also known as lissajous figures or bowditch curves, are pretty shapes first investigated by nathaniel bowditch in 1815, and later and in much more detail by jules antoine lissajou in 1857. The phase results in a kind of rotation of the figure. The same lissajous pattern is displayed when the phase shift is 360, illustrating that these two phase shifts are equivalent. But if we apply these input and output channels to daq then the lissajous pattern can be seen in labview. When both pairs of the deflection plates horizontal deflection plates and vertical deflection plates of cro cathode ray oscilloscope are connected to two sinusoidal voltages, the patterns appear at cro screen are called the lissajous pattern. The simplest lissajous patterns appear in the oscilloscope display when the frequencies of the signals are the same, i. Phase angle calculation time delay frequency calculate. In the quiet tidal breathing of a healthy human, the thoracic wall movement twm and abdominal wall movement awm occur nearly simultaneously and move synchronously i. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Lissajous knots are highly symmetric, and for this reason, not all knots are lissajous.
See harmonic motion typical lissajous figures for ratios of vertical frequency. A lissajous curve, named after jules antoine lissajous is a graph of the following two parametric equations. Breathing is one of the most essential processes for sustaining human life 1, 2. This phase shift can be measured as the fraction of a cycle delayed times 360. It includes two sine wave generators for ease of operation. This is because when we want measure usingequation 1. The oscilloscope will help us to calculate the phase or thefrequency by his formed lissajous figure. Using a scope to display lissajous patterns electrical. Lissajous figures in the application of microvibration. A circle can be formed only when the magnitude of the two signals are equal and the phase difference between them is either 90 or 270. There are a number of ways to measure the phase difference between two voltage waveforms using an oscilloscope.
A labview based simulation of lissajous pattern using daq card. Click on the figure 4 to see a dynamic display as the second functions phase moves through a full cycle from 0 through 2. Twostep phase estimation using the simplified lissajous. Trigonometryfor enthusiastslissajous figures wikibooks. In this video, we demonstrate how to make quick and simple phase shift measurements based on the lissajous patterns using an oscilloscope with xy mode. Even though the calculation can be performed in a single shot, the use of several phase shifted interferograms proved to make the measurement more robust to environmental variations.
Stuart yaniger provides an indepth look at the virtins multiinstrument software, for data acquisition and measurements. When the two sine waves are of equal frequency and inphase, you get a. When we are faced with signal frequencies that are not the same, lissajous figures get quite a bit more. So this is an example of the an initial application of the lissajous figure to determine that phase relationship between two signals. Lissajous figures where a 1, b n n is a natural number and 2 1 s g n n 3 lissajous curves can also be generated using an oscilloscope as illustrated. Triads, harmonic polyrhythms and 3d lissajous patterns. For example after selecting move lissajous curve choose m5 n6 and change the phase via the slider. The multiinstrument package from virtins technology a singaporebased company is one of the most powerful and versatile.
By shifting the frequency and phase of the signals, you can get different shapes. When this condition is met and when the phase shift is 0, the display consists of a straight line sloping upward from the left side of the screen to the right side. In the old days, whenever they showed an engineer working, there was usually an oscilloscope nearby with a pattern on the screen. An equilibrium phase diagram is usually a diagram with axes for temperature and composition of a chemical system. Able to display the voltage of one channel vertically and the other channel horizontally. Therefore, the two signals form the lissajous figure of a straight line between 1,1 and 1,1.
Lissajous curves in vivo to get a better understanding of the lissajous curves the choice move lissajous curve was introduced. Aug 25, 2016 the simplest lissajous patterns appear in the oscilloscope display when the frequencies of the signals are the same, i. Robust twostep phase estimation using the simplified. This allows you to see a continuous change of a lissajous curve, while you alter m,n or the phase. Nowadays, the tendency has been to reduce the number of steps in order to. Frequency and phase measurement ac metering circuits. It turns out that the complex harmonic oscillation only truly begins when the frequency of oscillation in both directions are different.
Phase measurements using lissajous figures lissajous figures are sometimes used for the measurement of phase. The user interface above allows you to modify each of these five parameters and see how the graph. Note that signal across the capacitor lags the signal across the function generator. Phase angle deg time shift time difference frequency. In the example in curvilinear motion, the lissajous figure is a circle. Lissajous pattern trainer experiment setup electronics lab. On the research path of thoracoabdominal motions, the lissajous figure analysis also called loop analysis technique is a conventional.
The lissajous pattern, a classic phase measurement. The clinical background of phase difference estimation in breathing. One can conclude from this that the two signals are of the same amplitude and phase or delay. From here we know that oscilloscope has very many function notlimited only to display waveform.
A classic phase measurement, the lissajous pattern. Before the days of digital frequency meters and phaselocked loops, lissajous figures were used to determine the frequencies of sounds or radio signals. Various fixed geometric shapes and patterns can be produced on the oscilloscope screen by selecting the desired option from the choose a preset pulldown menu. Lissajous figures plane curves traced by a point which executes two independent harmonic motions in perpendicular directions, the frequencies of the motion being in the ratio of two integers. Calphad stands for calculation of phase diagrams, a methodology introduced in the 1960s by larry kaufman. The eight lissajous figures ah, simulated by using the software matlab when a 1 and the phase modulation coefficients are. Measuring relative phase between two waveforms using an. Oct 31, 2012 in this video, we demonstrate how to make quick and simple phase shift measurements based on the lissajous patterns using an oscilloscope with xy mode. Aug 07, 2018 calculation of the phase difference between two sinusoidal signals having same frequency when two sinusoidal signals of same frequency and magnitude are applied two both pairs of deflecting plates of cro, the lissajous pattern changes with change of phase difference between signals applied to the cro. Phase angle calculation time delay frequency calculate phase. Maths geometry polar plot parametric a lissajous curve, named after jules antoine lissajous is a graph of the following two parametric equations. In mathematical 29 terminology, a lissajous curve is a simple system of two 35 curve is highly dependent on the ratio ba, and also on the 36 phase angles. Lissajous patterns at the dawn of the technological revolution.
This document covers four methods and summarizes the advantages and limitations of each. The signal processing required for phase difference estimation. In mathematics, a lissajous curve lissajous figure or bowditch curve is the graph of a system of parametric equations. To calculate the phase shift, you need the frequency and period of the waves.
Lissajous a simple example of 2d line plot in matlab, and creating a gui without guide. The lissajous ellipse fitting lef method consists on using the lissajous figure to detect the phase step between two interferograms and estimate the phase. Another problems is when we calculated the phase angle for the 1stcalculation is not same as the 2nd calculation. Instantaneous phase difference analysis between thoracic. How to make phase shift measurements using xy mode on a. A well known and readily applied method of measure ment of phase difference 8 between two sinusoidal signals with a singletrace oscilloscope is based on the elliptic. In this paper, we have proposed a new technique to realize microvibration displacement measurement. The angle of the line depends on the difference in amplitude between the two signals, a line at 45.
Dividing the frequency into 1 gives the period, or duration of each cycle, so 1100 gives a period of 0. Lissajous patterns of cro or cathode ray oscilloscope. Lissajous 3d pattern for a harmonic polyrhythmic triad 11 54 32. That means, those two sinusoidal signals are out of phase. Two phase shifted sinusoid inputs are applied to the oscilloscope in xy mode and the phase relationship between the signals is presented as a lissajous figure. Method oscilloscope requirements waveform requirements advantages limitations timedifference 2 channels b a lissajous 1 v. The software scans the waveforms looking for the time points where they cross their average value zero crossing with dc offset removed. If you increase the phase difference, the circle transforms to a diagonal line as if you would look at the circle from the side where its flat.
Lissajous setup was similar to the apparatus which is used today to project laser light shows. The time measurement capabilities of most any oscilloscope, the adalm and the alice software included, can display the relative phase. T2 calculation of a physical consistent reactive power. You surely have needed to calculate a signals phase change when it passes through a circuit. It shows the regions where substances or solutions i. Jun 19, 2018 stuart yaniger provides an indepth look at the virtins multiinstrument software, for data acquisition and measurements. It explores the field of harmony and disorder and let the user dip into an elegant, dreamlike.