EEE 125 LAB 4
Universiti Sains Malaysia Electrical & Electronic Engineering Department Basic Circuits Laboratory EEE125
Oscilloscope X-Y Mode, Function (Audio) Generator, Phase Difference and Lissajous Polar OBJECTIVE
To become familiar with using an oscilloscope and function generator. To measure phase angle using automated time difference measurement and Lissajous Polar.
INTRODUCTION Function Generator The front panel of your function generator is shown in Figure 1. This is one of the older units we have in the lab, and as such uses banana plug outputs. This instrument outputs a time-varying periodic voltage signal (sinusoidal and square wave). By using the appropriate buttons on the front panel, the user can specify various characteristics of the signal.
Figure 1: GW Function Generator model GAG-809 Most of the features are self-explanatory. The power switch is (1). The main output is taken from (2). The amplitude of signal is controlled by (3). Waveform type is determined by the position of switch (4). The frequency of the output signal is controlled by the frequency selection switch (5) and the variable control (6). The attenuation signal in decibel (dB) is selected using (7).
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EEE 125 LAB 4
The GAG-809 provides a convenient solution for low frequency (< 1MHz) signal generation, specifically for audio bandwidth. Intuitive and simple panel interface provides quick frequency and amplitude adjustment, with dial/key shortcuts to different ranges. Square wave generation covers digital application in addition to the traditional analog using sine waves. Attenuation in Function Generator The attenuation buttons are used to attenuate (decrease) the amplitude of the signal by a factor measured in decibels. The following relationship will assist in working with the attenuation buttons: (dB) = -10 * log10 (P out / Pin) (if power is the unit of measurement) or (dB) = -20 * log10 (V out / Vin) (if voltage is the unit of measurement) Example: Given a 1 volt input signal, what is the change in voltage amplitude if the 10 dB attenuation button is depressed? Beginning with the equation defined above: (dB) = -20 * log10 (V out / Vin) 10dB = -20 * log10 (V out / Vin) -0.5 dB = log10 (V out / Vin) 10-.5 = Vout / Vin Vout / Vin = 0.3162 or Vout = Vin * 0.3162 Since the initial input voltage (Vin) was 1 volt the output voltage (Vout) must be 0.3162V.
Phase Angle Measurement using time difference The difference in phase angle (phase shift) between two waveforms may be measured directly on the oscilloscope with little difficulty. Generally, phase difference is the ratio of voltage at the time reference to the maximum voltage is equal to the sine of the phase difference between the two waves. This relation is shown below. Phase angle, φ = arcsin (A/B) in degrees
Figure 2: Phase angle between the two waves using magnitude
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For an oscilloscope with two inputs probes, the phase angle can be calculated by the following formula.
Figure 3: Phase angle between the two waves using time difference Phase angle = Δt = Δt * f * 360° * 360° in degrees or Phase angle = Δt = Δt * f * 2π * 2π in radians. Where f is the frequency and Δt is the time difference between the two waveforms. Many new digital scopes have cursors that allow directly marking, calculating, and displaying the time difference and perhaps even the phase shift. The [cursors] button for DSO-X 2002A Oscilloscopes can be found in the Measurement Menu of the oscilloscope. Phase Angle and Frequency Measurement using Lissajous Polar The oscilloscope may be used to compare simultaneously two separate waveforms. When two voltages of the same frequency are impressed on the oscilloscope, one on the vertical and one on the horizontal plates, a straight line results on the screen if the voltages are in phase or 180° out of phase (see Figure 6). An ellipse is obtained for other phase angles. The pattern which results when two sine waves are applied to the oscilloscope in this way are called Lissajous polar or patterns. They can take many forms, depending on the frequencies involved.
Figure 4: Lissajous Polar for the same frequency
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Phase shift (the phase angle between two waves of equal frequency) may be calculated from the pattern on the oscilloscope screen. If the voltage applied to the vertical plates leads the voltage applied to the horizontal plates by an angle φ, a pattern such as in Figure 4 results. The phase difference can be found by taking the ratio of the horizontal intercept to the maximum horizontal deflection. However, twice the values provide more accuracy. The phase shift is now calculated. Phase angle, φ = arcsin (a/b) in degrees or Phase angle, φ = arcsin (a 1 /b1) in degrees Note that if the phase difference exceeds 90° the Lissajous ellipse is tilted the other way (\), and the formula must be modified to φ = 180° - arcsin (a/b). Lissajous polar may be used to measure and compare the frequencies of voltages from two separate signal sources. If these are close to the same frequency, the pattern will slowly change back and forth from an ellipse to a straight line each half cycle of difference in frequency. For any stationary pattern, the ratio between the two frequencies may be determined by counting the number of pattern tangencies along the horizontal and vertical axis. The ratio of vertical to horizontal frequency (Y:X) equals the number of horizontal tangencies divided by the number of vertical tangencies. Lissajous polar for three frequency ratios are as follow.
Figure 5: Lissajous Polar for different frequencies
Be warned that many presentations of Lissajous patterns report (X frequency) : (Y frequency), which would be the inverse of the ratios shown here. To measure frequency by Lissajous patterns, the unknown signal is applied to the vertical input terminals. Then, a variable signal of known frequency is applied to the horizontal input. The known signal is varied until a stable pattern is obtained, and the unknown frequency is calculated. The simplest way to do this, however, is just to obtain a pattern in a 1:1 ratio. Then the unknown can be read directly off the dial of the known source. These patterns, named in honor of the French mathematician Lissajous (pronounced LEE´-ZASHOO´ SHOO´).
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Figure 6: Lissajous Polar for the same frequency but difference phase angle
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Oscilloscope XY Mode The oscilloscope also lets you display an input signal rather than the time base on the horizontal axis. This setup is called XY mode because both the X and Y axes are tracing input voltages. As a note of interest, the waveform resulting from the XY arrangement of two periodic signals of different periods is called a Lissajous pattern. From the shape of the Lissajous pattern, you can determine information about the relative phases of the signals, as well as their frequency ratio. For example, if you were to input the signal sin(ωt) into both channel 1 and 2. Using the XY mode you would see a straight line of unit slope displayed on the screen (because at every instant the voltages on channel 1 and 2 are identical, ie. X=Y). Now imagine that you input the function sin(ωt) in channel 1, but this time you decide to input sin(ωt -π/2) = cos(ωt) into channel 2. In this case y=sin(ωt) and x=cos(ωt), which as you might remember from trigonometry correspond to the parameterization of the points on a circle. The XY time mode converts the oscilloscope from a volt- versus- time display to a volt- versusvolt display using two input channels. . The time base is turned off. Channel 1 amplitude is plotted on the X axis and Channel 2 amplitude is plotted on the Y axis. You can use various transducers so the display could show strain versus displacement, flow versus pressure, volts versus current, or voltage versus frequency. Use the cursors to make measurements on XY mode waveforms. About using XY mode for measurements, again, the [Cursors] button for DSO-X 2002A Oscilloscopes can be found in the Measurement Menu of the oscilloscope.
EQUIPMENTS
Resistors 4.7k X 1 Electrolytic capacitor 1uF X 1 Breadboard Digital multimeter GW Function Generator GAG-809 X 2 DSO-X 2002A Oscilloscopes Crocodile clips, BNC Connectors, Connection wires (single core)
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EEE 125 LAB 4
Experiment: Part I Function Generator
1.
In this part of the lab, you will use the function generator to generate a signal and then use a digital oscilloscope and a digital multimeter to make some measurements of the data.
2.
Turn on the function generator. The power switch is on the bottom right-hand corner of the unit. The red LED will indicate that the unit is on. Select the waveform type to sinusoidal mode and set the attenuator switch to 0 dB.
3.
The function generator consists of the frequency control knob and the five frequency multiplier selection buttons. For example, to set the function generator to an operating frequency of 2000 Hz (2 kHz). Rotate the frequency control knob to 20. Select the X100 frequency multiplier button. With the result that: 20 * 100 Hz = 2.0 kHz.
4.
Adjust the function generator to have the maximum output voltage by turning the amplitude knob to fully clockwise (CW). Press [Auto Scale] and use the automated measurement of the oscilloscope to measure the frequency, peak to peak voltage and AC RMS-FS voltage generated by the function generator and record the r esults. Frequency, f = __________ Hz (measured) Pk-Pk voltage, Vp-p = __________ V (measured) AC RMS-FS voltage, V ac,rms = __________ V (measured)
5.
Take a digital digital multimeter and measure the AC RMS output voltage directly from the function generator’s output port. AC RMS voltage, V ac,rms = __________ V (measured using digital multimeter)
6.
Compare the AC RMS output voltage measured by the multimeter and the oscilloscope. Are they almost the same? Explain.
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Experiment: Part II Effect of Attenuation in Function Generator 1.
In this part of the lab, you will use the function generator to generate a signal and then use the attenuator button to attenuate the signal.
2.
Generate a 1.4 kHz sine wave with the function generator; setting the amplitude knob all the way to its maximum value. Then display the signal on the oscilloscope. Draw the displayed signal on Figure 2a. Be neat, to scale, and concise. Write the scale (Volt/div and Time/div settings) on the graph. Record the frequency and peak-to-peak voltage.
Figure 2a: 1.4 kHz Function Generator’s output Frequency, f = __________ Hz (measured) Pk-Pk voltage, Vp-p = __________ V (measured) 3.
On the function generator, select the 10 dB attenuation button. It's a delicate adjustment, so watch the screen carefully while you turn the attenuation button to the left. What happen to the signal? You may need to change the Volt/div setting of the oscilloscope, what is the new frequency and peak-to-peak voltage?
Figure 2b: 1.4 kHz Function Generator’s output with 10dB attenuation
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Frequency, f = __________ Hz (with 10dB attenuation) Pk-Pk voltage, Vp-p = __________ V (with 10dB attenuation) 4.
Using the obtained peak to peak voltage and the given formula, what is the attenuation in dB? Show the calculation. Is the value almost the same with the one you set on the function generator? Does the attenuation affect the frequency of the signal? Explain. Attenuation,dB = __________ dB (calculat ed)
5.
Repeat step 3 to 4 but now change the dB setting as in Table 2a. Fill up the table. Table 2a: dB and output voltage Attenuation,dB
Peak to peak voltage Vp-p, V
dB Calculated
20 30 40 50
6.
Return back the setting of attenuator to 0 dB. dB.
7.
Disconnect the digital oscilloscope from the function generator and turn off the power.
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Experiment: Part III Phase Angle Measurement Using Time Difference 1.
One way to measure the phase difference between two signals with with the same frequency is to set the oscilloscope for dual trace operation (Channel 1 and 2) and observe the time difference between the reference waveform and the waveform measured at the desired node in the circuit. This is depicted in Figure 3a. Set up the following circuit, using a function generator as an input signal. Please note the right polarity of capacitor.
Figure 3a: Measuring phase shift through capacitor. 2.
Connect the input reference voltage to Channel 1 of the oscilloscope and connect the second voltage to Channel 2. Set both coupling mode to AC on the oscilloscope.
3.
Adjust the amplitudes to maximum and the frequency of 50 Hz. Press [Auto Scale] so that the overlapping signals look something like the Figure 3b below. On channel 1 and 2, press the “Push to Zero” button to set the AC level at the center of the screen. The Channel 1 is the reference (yellow) and the Channel 2 (green). In this figure, the Channel 2 is lagging the Channel 1.
Figure 3b: Phase angle measurement using time difference and ΔX cursors 4.
Use the cursors to make measurements of the waveforms. The [Cursors] button for DSOX 2002A Oscilloscopes can be found in the Measurement Menu of the oscilloscope. Measure Δt, Δt, frequency and calculate the phase angle. Δt = __________ ms Frequency, f = __________ Hz Phase angle, φ = __________ ° (in degrees using time difference) Phase angle, φ = __________ rad (in radians)
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EEE 125 LAB 4
Experiment: Part IV Phase Angle Measurement Using Lissajous Polar 1.
Another way to determine the phase difference between two sinusoids is to make use of the X-Y capability of the oscilloscope. In this technique, the reference sinusoid is applied to the horizontal (X) deflection of the ’scope display while the other sinusoid sinusoid is applied to the vertical (Y) deflection.
2.
Since the two waveforms have the same frequency but possibly differing phases, the resulting display will be an ellipse. ellipse. For example, if the two waveforms are in phase they will both reach their maxima and minima at the same time, giving a straight diagonal line (a "squashed" ellipse).
3.
If, on the other hand, the two waveforms are 90° out of phase, the maxima and minima of one waveform always occur when the other waveform is zero, giving an ellipse with its primary axis running either horizontally or vertically depending upon the amplitude relationship of the two signals. Other phase differences give elliptical displays with various orientations.
4.
This exercise shows a common use of the XY display mode by measuring the phase difference between two signals of the same frequency with the Lissajous method. Use the same circuit as in Figure 3a. Connect a sine wave signal to Channel 1, and a sine wave signal of the same frequency but out of phase to Channel 2. Press the [AutoScale] key, press the [Horiz] key, then press Time Mode and select "XY".
5.
Again, on channel 1 and 2, press the “Push to Zero” button to set the display at the center of the screen. Use the channel 1 and 2 volts/div knobs to expand the signal for convenient viewing. Press the [Cursors] key. Set the Y2 cursor to the top of the signal, and set Y1 to the bottom of the signal. Note the ΔY ΔY value at the bottom of the display. In this example, we are using the Y cursors, but you could have used the X cursors instead. Move the Y1 and Y2 cursors to the intersection of the signal and the Y axis. Again, note the Δ the ΔY Y value. You will get signals look something like the Figure 4a below.
Figure 4a: Phase angle measurement using Lissajous polar and ΔY cursors 6.
The phase difference angle (φ) can be calculated using the given formula (assuming the amplitude is the same on both channels). Calculate the phase difference angle (φ) and compare this value with the one you have calculated in Part III of the experiment. Are they almost the same? Explain. Phase angle, φ = __________ ° (in degrees using Lissajous Polar)
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Experiment: Part V Frequency Measurement Using Lissajous Polar 1.
Oscilloscope can be used to determine the frequency of a signal by using the Lissajous polar.
2.
Connect the Channel 1 input to a signal of a known frequency, FY = 1 kHz, taken from a function generator. Connect the Channel 2 input to a signal of an unknown frequency F X, taken from second function generator. F X is the frequency that we would like to determine. The magnitude of both both signals should be approximately the same.
3.
The polar shown on the screen can be a straight line, a circle or a varying ellipse. The polar depends on the FY and F X as well as the phase shift between the two signals. To get a stable and constant polar, the frequency of the unknown signal may need to be adjusted slowly. Sketch the Lissajous polar in Table 5a. Table 5a: Lissajous polars F Y : FX
Lissajous Polar
1:1
1:2
2:1
1:5
5:1
3:2
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REVIEW QUESTIONS 1.
List the uses of signal generator.
2.
Describe the appearance of attenuation signal in practice and modern electronic circuit.
3.
Why it is important to measure the phase angle and frequency of an an electrical power circuit.
4.
An attenuated output voltage from a resonance resonance circuit consist of resistor and capacitor in series is represented by V(t) = 24 sin 314t - 45°. Determine the expression of the input voltage fed into the circuit if a 20dB attenuation signal is applied to the circuit.
5.
How do you expect the Lissajous polar will look like if FY : FX is equal to 2 : 3.
TURN IN ONE REPORT PER GROUP AT THE END OF YOUR LAB SESSION. THERE IS NO TAKE HOME REPORT.
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