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- 1. LISSAJOUS PATTERNS (INTRODUCTION)OBJECTIVE 1. To use Lissajous figures to take phase measurements. 2. To use Lissajous figures to take frequency measurements.LIST OF REQUIREMENTSEquipment 1. General purpose oscilloscope (10MHz) 2. Function generators (1 Hz to 1 MHz) 3. Digital multimeter 1
- 2. THEORY Lissajous patterns are formed when you combined periodic waves moving back andforth with periodic waves moving up and down. This exhibit does this electronically allowingthe visitor to control the frequency of the X and Y motions independently. The resultingpattern can be observed on an oscilloscope and viewed on moving speakers. If thefrequencies are high enough, the speakers produce sound. The combination of tones can becorrelated with the scope pictures. The oscilloscope can measure voltage, frequency, and phase angle. Two-channelmeasurements are very useful and are presented.We also can get lissajous figures inoscilloscope other than to get the waveform figures. In electronic applications we can generate Lissajous patterns by applying differentsignals to the horizontal and vertical inputs of an oscilloscope. In facts, this techniques wasoften to used to measure frequencies in the days before frequency meters. A signal of aknown frequency was applied to the vertical input. The resulting pattern was a function of theratio of the two frequencies.Lissajous Figures A lissajous figure is produced by taking two sine waves and displaying them at rightangles to each other. This easily done on an oscilloscope in XY mode.If the oscilloscope hasthe x-versus-y capability, one can apply one signal to the vertical deflection plates whileapplying a second signal to the horizontal deflection plates. The horizontal sweep section isautomatically disengaged at this time. The resulting waveform is called Lissajous figure. Thismode can be used to measure phase or frequency relationships between two signals. When the two sine waves are of equal frequency and in-phase, diagonal line to theright will produced. When the two sine waves are of equal frequency and 180 degrees out-of-phase a diagonal line to the left will produced. When the two sine waves are of equalfrequency and 90 degrees out-of-phase a circle will produced. When the horizontal andvertical sine wave frequencies differ by a fixed amount, this is equivalent to constantlyrotating the phase between them 2
- 3. Phase Measurements Using Lissajous Figures Lissajous figures are sometimes used for the measurement of phase. They areproduced in an oscilloscope by connecting one signal to the vertical trace and the other tothe horizontal trace. If the ratio of the first frequency to the second is a rational number, thena closed curve will be observed on the CRO. If the two frequencies are unrelated, then therewill be only a patch of light observed because of the persistence of the oscilloscope screen. If the two signals have the same frequency, then the Lissajous figure will assume theshape of an ellipse. The ellipse’s shape will vary according to the phase difference betweenthe two signals, and according to the ratio of the amplitude of the two signals. Below shownsome figures for two signals with synchronized frequency and equal amplitudes, but differentphase relationships. The formula used for determining the phase is: sin(θ)=± (equation 1.1) Where Ymax is half the maximum vertical height of the ellipse and Yo is the intercepton the y-axis. Two signals that are identical in frequency and have a phase difference of 450,but with different amplitude ratios. Note that is necessary to know the direction that theLissajous trace is moving in order to determine the sign of the phase difference. In practice,if this is not known a priori, then it can be determined by testing with a variable frequencysignal generator. In the case, one of the signals under consideration is replaced with thevariable frequency signal. The signal generator is adjusted until its frequency and phaseequal that of the other signal input the CRO. When this happens, a straight line will exist.The signal generator frequency is then increased a little with the relative phase thus beingeffectively changed in a known direction. This can be used to determine the correct sign inthe equation above. Lissajous figure methods are a little more robust to noise than direct oscilloscopemethods. This is because there are no triggering problems due to random noise fluctuations.Direct methods are, however, much easier to interpret when harmonics are present. Theaccuracy of oscilloscope methods is comparatively poor. The uncertainly of themeasurement is typically in excess of 10. 3
- 4. Frequency Measurements Using Lissajous Figures Lissajous pattern also helps to measure frequency. The signal whose frequency is tobe measured is given 1 F plates or vertical plates and the signal whose frequency is given toX-plates or horizontal plates. Now the know frequency or standard frequency is a adjustedso Lissajous patterns can be obtained on the screen which depends on the ratio of twofrequencies. In the given figure,Let, fy – Unknown frequency signal applied to vertical plates. Fh – Known frequency signalapplied to horizontal plates. Two lines are drawn, one vertical and one horizontal so that they do not pass throughany intersection on Lissajous pattern. Then the number of intersections of the horizontal andvertical lines with the Lissajous patterns and counted separately. So after finding thetangencies if we know we can easily calculate the unknown frequency applied to verticalplate. All electronic circuits in the oscilloscope like attenuators, time base generators,amplifiers cause some amount of time delay while transmitting signal voltage to deflectionplates. We also know that horizontal signal is initiated or triggered by some portion of outputsignal applied to vertical plates of CRT. So the delay line is used to delay the signal for sometime in the vertical section of CRT. 4
- 5. PROCEDURESPART A : FREQUENCY MEASUREMENT USING LISSAJOUS FIGURES 1. Two signal generators was used and the first generator (generator 1) was considered as the known or standard frequency source. Assumed that it has correct dial markings. Generator 2 will be the variable (unknown) source. 2. Generator 1 was set at 1 kHz. The signal voltage was set at 4V peak-to-peak. Vary the frequency of generator 2 until a circular pattern occurs on the scope. 3. This pattern was recorded in table 3.2. The number of vertical and horizontal tangencies was recorded and the frequency of the generator 2 was calculated(A vertical tangencies is a point where the figure is tangent to the vertical axis). 4. These procedures was repeated for other convenient ratios and complete Table 3.2. Used at least one other standard frequency for the last three entries ( e.g., 3 kHz).PART B : PHASE MEASUREMENTS USING OSCILLOSCOPE AND LISSAJOUS FIGURES 1. The circuit was connected as in Figure 3.8. 2. The frequency of Ein was set at 1 kHz. R was set at 0 Ω. The signal voltage was set at 4 V peak-to-peak. The display was centered. R was changed to 10 kΩ and the pattern in was recorded in Table 3.3. The measured and calculated values was recorded in Table 3.3, for different values of R. Figure 3.8 5
- 6. RESULT(Part A)Lissajous No.Of Vertical No. Of Frequency of Frequency ofFigure Tangencies Horizontal Generator Generator Tangencies 1(Hz) 2(Hz) 1 2 500Hz 1kHz 2 1 3kHz 1.5kHz 1 3 500Hz 1.5kHz 2 3 1kHz 1.5kHz 3 2 3kHz 2kHz 1 2 1kHz 2kHz 1 4 500 2kHz 6
- 7. RESULT(Part B)Resistance Lissajous Figure Measure Values Calculated(kΩ) Values10 2.4 2.8 58.99 57.8615 2.8 3.8 47.46 46.722 1.2 2.0 36.87 35.8830 2.2 4.8 27.28 27.9550 0.8 2.6 17.92 17.66 7
- 8. Discussion In this experiment we was exposed to another function of oscilloscope which are tomeasure frequency and to measure phase angle and also to display lissajous pattern. From the experiment part A.We can tell that the lissajous pattern are formed by twofrequency that was given.Based on our result we can tell that the No. Of HorizontalTangencies and No.of Vertical Tangencies are the ratio of the two input frequency.So wecan tell here that Lissajous Figures are affected by the ratio and the value of the two inputfrequency.We also know when high frequency given the pattern will move faster. From experiment part B.we conducted an experiment to calculated phase angle bythe help of figure in oscilloscope.We can measure the phase angle using the equation 1.1.Inthis experiment we also get the info how the pattern when we want to find the phase anglewhich is in a circle type.The circle become thinner when it nearly to the 0° angle. The problem that we get in this experiment is when we get unstable lissahouspattern.After we tracking the source of this problem,we found that the problem is on theconnecting wire probe which maybe already broken .So we replace it with another ,then weget a stable result.Another problems is when we calculated the phase angle for the 1stcalculation is not same as the 2nd calculation.This is because when we want measure usingequation 1.1.Our Eyes does not perpendicular with the scale on the oscilloscope whichknow as parallax error.So we corrected it by making our eyes perpendicular with the scaleon the oscilloscope.Then we get same calculated value.Other problem is when we want totake the displayed lissajous pattern .It moving too fast .To take it we need to press stopbutton at the oscilloscope to see the clear lissajous pattern. 8
- 9. CONCLUSION As our conclusion .We can tell that oscilloscope can measure the phase and thefrequency of two frequency.From here we know that oscilloscope has very many function notlimited only to display waveform.The oscilloscope will help us to calculate the phase or thefrequency by his formed lissajous figure.We can conclude that experiment part A show usthat lissajous patern are affected by the ratio of two input frequency while for the experimentpart B that the phase angle below 90° will produce a thinner curve . When achieve to 0° , thecurve become straight line.The calculated phase angle and the calculated phase angle bythe help of oscilloscope is slightly difference.This is because when we calculated phaseangle roughly we round off the number to have a easier measurement.While we taking theresult we need to press stop button in oscilloscope because the figures is moving toofast.From here we can conclude that the more the frequency the faster the figures move. . 9
- 10. REFERENCE 1. Rusnani Ariffin & Mohd Aminudin Murad (2011).Laboratory Manual Electrical Engineering Laboratory 1:University Publication Center (UPENA). 2. Charles K.Alexander & Mattgew N.O.Sadiku (2009).Fundamentals Of Electrical Circuit Fourth Edition:McGRAW HILL. 3. http://www.jmargolin.com/mtest/LJfigs.htm 4. http://www.allaboutcircuits.com/vol_2/chpt_12/2.html 5. http://ei-notes.blogspot.com/2012/03/method-of-finding-phase-frequency.html 10

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