EXPERIMENT 6

The Oscilloscope

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University Physics II, Exp 6: The Oscilloscope

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Purpose You will use the Scope display in Data Studio to gain some experience in the use of this versatile laboratory tool for measuring AC voltage, frequency, and comparing AC signals through the use of Lissajous figures.

Equipment • •

Voltage Sensor Function Generator

•

Digital Multimeter

Introduction The oscilloscope is a versatile measurement tool that can display real-time plots of voltage vs. time or voltage vs. voltage. A typical model of an oscilloscope is shown schematically in Figure 6.1. Its main component is the cathode ray tube (CRT), shown in Figure 6.2. The CRT is also commonly used to produce a visual display of electronic information in other applications, including radar and television receivers and computer monitors.

Figure 6.1

Figure 6.2

A hundred years ago, the cathode ray tube was the last word in advanced laboratory research instruments. In appearance, the early CRTs looked much like the tubes now used in “neon” signs. Originally, the rays that cause the glass walls of such tubes to glow were thought to be a new kind of light called a cathode ray which was emitted by a hot wire, called a cathode, located inside the tube.

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In 1897, Cambridge physicist J. J. Thompson, using a tube much like the one in Figure 6.2, showed that cathode rays were simply streams of tiny negatively-charged particles, which he called corpuscles. Thompson won the 1906 Nobel Prize in Physics for discovering what we now call the electron. The interior of a cathode ray tube is evacuated to a pressure of 0.01 Pa or less. The electron beam is produced by an assembly called the electron gun located in the neck of the tube. Electrons are “evaporated” from a heated filament called the cathode. They are focused into a narrow beam by a focusing electrode and are accelerated toward the fluorescent screen by the positive anode. The anode is maintained at a high positive potential relative to the cathode, of the order of 20 kV. This potential difference causes an electric field in the region between the anode and the cathode, directed toward the cathode. Electrons from the cathode are accelerated by this field. Most of them strike the anode, but some pass through a small hole to form a narrow beam which travels at a constant velocity beyond the anode to the fluorescent screen. The cathode, focusing electrode, and anode comprise the components of the electron gun. The point where the electron beam strikes the screen glows brightly (it fluoresces), and the glow persists for a few tenths of a second after the beam is no longer there. Inside the CRT, along the path of the electron beam between the anode and the screen, are two pairs of deflection plates (one pair is used to deflect the beam vertically and one pair to deflect it horizontally), as shown in Figure 6.2. If no potential difference is applied across the deflection plates, the beam is undeflected and makes a bright spot at the center of the screen. However, if a voltage is applied across the horizontal plates, the electron beam experiences a horizontal force and is deflected to the right or left, depending on the polarity of the deflection voltage. A constant deflection voltage will move the spot on the screen a fixed horizontal distance. A varying (AC) voltage, on the other hand, will deflect the beam horizontally back and forth since the polarity is continually changing. If the frequency of the AC voltage signal is high enough, the spot will trace a continuous horizontal line across the screen. Similarly, a voltage applied to the vertical deflection plates causes the spot to move vertically. In either case, the magnitude of the deflection of the spot from the center of the screen is proportional to the magnitude of the voltage applied to the deflection plates. The cathode ray oscilloscope is therefore a measurement tool that can display plots of voltage changes much like an x-y graph. Unlike a paper graph that has a beginning and an end, an oscilloscope’s plot of voltage (known as a trace) is redrawn continuously as long as signals are applied to the deflection plates. In AC applications, we usually want to display the voltage on the screen as a function of time (i.e., a graph of voltage vs. time). Internal or external electronic circuits are used to apply a linearly increasing voltage vs. time signal (called a sawtooth waveform, illustrated in Figure 6.3) to the horizontal plates. This causes the spot to sweep from left to right across the screen at a speed that is proportional to the upward slope of the sawtooth waveform, then sweep back to the left at a much faster speed (proportional to its almost vertical downward slope).

University Physics II, Exp 6: The Oscilloscope

Figure 6.3

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With no voltage on the vertical plates you would see a continuous horizontal line across the screen. But when an externally generated voltage having a sinusoidal form is applied to the vertical plates, the beam is deflected vertically as it sweeps left to right causing the beam to trace out a graph of the applied voltage vs. time as shown in Figure 6.4. Typical oscilloscopes can display voltage vs. time in events that last as short as 100 ms or as long as 10 sec. The oscilloscope is a very popular instrument and many different models exist. There are generally three distinct sets of controls on any oscilloscope. The first set controls the electron gun, adjusting the trace focus and intensity. The second set controls the internally or externally applied voltage to the horizontal plates, adjusting the electron beam’s horizontal sweep speed. The third set controls the externally applied voltage to the vertical deflection plates, adjusting vertical trace amplitude. All oscilloscopes contain these controls; however, the controls may be given different names on different models, and some models may have additional controls. In this experiment you will concentrate only on the basic controls provided on the Scope display in the Data Studio program.

Figure 6.4

Data Studio Scope Display Emulating an oscilloscope display in Data Studio is quite simple. The pages that follow walk you through the use of the Scope display in the Data Studio program. Measurements Using the Oscilloscope Perhaps the simplest measurement you can make with an oscilloscope is AC or DC voltage. You use the oscilloscope as a high-input-impedance voltmeter simply by calibrating the volts per scale division on the vertical trace, and connecting the unknown voltage to vertical (y) input. You then determine the voltage by reading the vertical deflection on the screen. Note that the oscilloscope measures instantaneous voltage, not average or rms voltage. Thus the maximum voltage Vmax is from zero to either peak, or one-half the peak-to-peak voltage. For a sinusoidal waveform, multiplying Vmax by 1 / 2 = 0.707 gives the root-mean-square (Vrms) value of the voltage. You can determine the frequency of an AC source by calibrating the horizontal sweep rate and then connecting the unknown source to the y input. The periodic sweep of the beam causes the input pattern to retrace itself and the pattern appears to stand still, as in Figure 6.5. University Physics II, Exp 6: The Oscilloscope

Figure 6.5

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By counting the number of horizontal (x) divisions required for one complete cycle of the waveform, you can easily determine the period. The frequency is the reciprocal of the period. You can also use the oscilloscope to measure the relative phase between two AC voltages having the same frequency by creating a Lissajous pattern. If you apply one sinusoidal voltage signal to the horizontal plates and the other to the vertical plates with the oscilloscope operating in the x-y mode, a Lissajous figure will appear on the screen. If you adjust the horizontal and vertical amplifiers so that the amplitudes of the two signals are the same, the equations of the two waveforms on the screen would be and

x (t ) = A sin 2πft

Equation 6.1

y(t ) = A sin(2πft + φ )

Equation 6.2

where A is the amplitude, f is the frequency, and φ is the phase difference. Using trig identities you can expand Equation 6.2 as y(t ) = A(sin 2πft cos φ + cos 2πft sin φ )

Equation 6.3

From Equation 6.1, when x(t) = 0, sin 2πft = 0 and cos 2πft = 1 ; so or

y0 = A sin φ

Equation 6.4

sin φ = y0 / A

Equation 6.5

You can read both yo and A from the screen and thus determine φ.

Procedure Selecting the Scope display 1. Plug the voltage sensor into analog channel A on the interface. Switch on the interface and the computer. Open Data Studio. 2. Open the Scope display. It should look like this: → Figure 6.6

A. Voltage Measurements at 90 Hz 1. Before turning on the Signal Generator, be sure that the amplitude is turned all the way down. Turn on the Signal Generator, select sine wave, and set the Frequency to 90.000 Hz. Measure the output of the Signal Generator with the multimeter set to measure AC voltage (remember that the multimeter measures Vrms), set the Amplitude (Vmax) to 3.000 V. Record these values in Table 6.1. 2. Connect the Voltage sensor to the Signal Generator output terminals. Activate the Scope display by clicking anywhere on it. Adjust the sweep speed (x axis variable)

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and sensitivity (y axis variable) until one complete cycle of the input sine wave appears on the screen and the pattern is almost full scale in amplitude. Record the resulting sweep speed and sensitivity settings. 3. Read the number of divisions on the x axis for one full sine-wave cycle and compute the period T for one cycle from the Scope sweep speed. Then use the period to calculate the frequency f of the signal. Finally, calculate the percent difference between your calculated frequency and the generator frequency. Record all results. 4. Read the number of vertical divisions for the peak-to-peak height of the sine wave pattern on the screen. Calculate and record Vmax in Table 6.1. Calculate and record the percent difference between your calculated Vmax and the generator Vmax.

B. Voltage Measurements at 300 Hz 1. Change the output frequency of the Function Generator to 300 Hz and repeat steps A1–4. Record your results in Table 6.2.

C. Lissajous Figures Lissajous figures are used to compare two signals using the Scope’s x-y mode to determine their phase with respect to each other, or how one signal’s frequency compares to that of the other. The external Signal Generator can supply the vertical voltage signal and Data Studio’s built in Signal Generator can provide the horizontal voltage signal. 1. Click on the On button to activate the signal generator, and set the frequency to 30 Hz. An output voltage having a sine AC waveform with an amplitude of 5.000 V should be selected. Click on the Scope window to make it active. Drag the Output Voltage (V) icon in the Data listing to the x axis of the Scope display. 2. Set the external Signal Generator to apply a 60 Hz signal to the vertical axis. Activate the Scope display by clicking anywhere on it. A trace similar to this → should appear on the display.

Figure 6.7

Note: it may be necessary to fine tune the frequency setting of the Signal Generator to obtain a stationary image. When the image appears as expected, press STOP to freeze the display. Print the pattern from Data Studio, record the input parameters on the print, and turn it in with your lab report. 3. Repeat step C2 using frequencies of 30 Hz, 90 Hz, and 180 Hz for the y input signal (external Signal Generator). Print the patterns you, label each print to indicate the input parameters, and turn them in with your lab report.

University Physics II, Exp 6: The Oscilloscope

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