CHARGING and DISCHARGING CAPACITORS

Transcription

1 Lab 4 Oscilloscopes, Electrocardiograms, Discharging Capacitors LAB 4a LAB 4b Lab 4c THE OSCILLOSCOPE ELECTROCARDIOGRAMS (ECG or EKG) CHARGING and DISCHARGING CAPACITORS EXPERIMENTAL QUESTION In this lab, you will learn about how an oscilloscope can be used to measure waveforms from an electronic function generator. You will then use the oscilloscope to look at the electrical signals produced by your body, particularly from your heartbeat, and to study how a capacitor discharges. Short sleeves and pants are convenient this week. PROCEDURE So far in lab, we have dealt only with DC circuits in which currents and voltages are constant in time. In this lab, we will use the function generator and other sources to generate periodic voltage waveforms and the oscilloscope to display such waveforms. thcan generate three very handy functions: sine waves, square waves, and triangle waves. The frequency of such waveforms is the number of complete cycles that the waveform goes through per second: frequencies are expressed in Hz, where 1 Hz = 1 cycle per second. If the time required for a complete cycle of the wave is T, then the frequency is 1/T, since the wave completes exactly one cycle in time T. Your function generators can produce sine waves, square waves, and triangle waves in the frequency range of 0.02 Hz 2 MHz. Drawings of the front panels of both your function generator and your oscilloscope are given at the very end of this handout, and you may find it convenient to have that page in front of you as you work through this experiment. Although there are a lot of buttons to fiddle with on both devices, you should feel free to experiment with any of them. The ones you will be using most are labeled and numbered on each drawing and in the lab description. The buttons are numbered on the drawings in a roughly clockwise order starting at the upper left, and the numbers appear in square brackets in both the drawings and the text. Setting up the function generator and the oscilloscope Turn the oscilloscope on with the switch on the top of the oscilloscope box (on the left). After about 15 seconds you will get a screen asking you for the language you prefer. English is the default, and if you don t do anything the display will go to the usual oscilloscope display after a few more seconds. Push the DEFAULT SETUP [7] button which produces generically useful settings. You should have a rectangular field with a heavy black horizontal line in the middle of the display. That horizontal line means that you re giving the oscilloscope a zerovoltage input, Then push the button labeled CH 1 MENU [4], and toggle the probe to 1X by repeatedly pushing the fourth function button [14d]. You will find three buttons [3] in the upper right-hand corner of the function generator with little cartoons of the waveform produced when a given button is pushed in. Push the button with the sine wave, turn on the function generator [1], and set the frequency [7] to ~500 Hz. You may need to change the range or decade setting, which is determined by the row of buttons [2] just to the left of the waveform buttons. Use a BNC cable to connecting the OUTPUT terminal [5] of your function generator to the input of channel 1 of the oscilloscope [13]. You

2 should see part of a sine wave, and a series of numbers along the bottom edge of the oscillscope screen. The number immediately after the label CH1 tells you the voltage corresponding to one large vertical division on the screen, and the number in the middle of the display gives the length of time corresponding to one large horizontal division. Without adjusting anything on the function generator, adjust the vertical scale of the oscilloscope [12] so that you can observe the entire signal. Then observe what happens tot the display as you djust the horizontal sweep, or sec/div knob [10] of the scope. Notice what happens to the display and the numbers across the bottom of the screen. Does the number of cycles of sine waves displayed increases or decreases as you change the horiontal sweep from 500 µs/div to 1 ms/div? Now experiment with the frequency adjustment knobs of the function generator [7]. Display a few cycles of a 4.7 khz sine wave on the oscilloscope. Making measurements. The lower right corner of the display of the oscilloscope should give a measurement of the frequency of the signal. The oscilloscope will also let you make measurements between two points on the screen yourself. If you were looking at a complex wave, for example, you might want to measure the time between two small features on the screen. To make such measurements, first push the CURSOR button [5] near the top of the instrument panel. The menu at the right of the display now gives you two functions, Type (currently set to Off ) and Source (currently set to CH 1 ). Push the first function button [14a] (opposite the label Type ), which will change it from Off to Voltage. Push it a second time to get Time, which is the measurement you re about to make. You should now see two dotted vertical lines on the display and some new items on the menu. You will be especially interested in the third menu item, Delta, which is the time interval between the two vertical lines. Also notice that the green indicator lights underneath the two position knobs are lit up. These lights indicate that now you use the POSITION knobs [3] and [6] to control the locations of the vertical lines (the cursors), and you ll be using both CH 1 and CH 2. Adjust the POSITION knobs and use the cursors to measure the period of your sine wave. How can you perform your measurement to reduce the uncertainty in the period? Record the period, together with its uncertainty, in your notebook. Then calculate the frequency of the sine wave, together with its uncertainty. Now you can push the first function button [14b] again and measure the peak-to-peak voltage of your sine wave with the horizontal cursors. When you are done with your measurement, you just need to press the CH 1 MENU button [4] to return to the main menu. Storing waveforms. Once you have your oscilloscope set to give a good display of some waveform from the keyboard, push the SAVE/RECALL button [2]. You will get the usual menu on the right-hand side of the display, and the first menu item is Action, with Save All right underneath it in reverse video. Push the first function button [14a] to select Save Waveform. Now you get some more menu options underneath. The next option, Save To, should be changed to File with the second function button [14b]. The next choice, Source, is the channel connected to your microphone, and it will probably be CH1. (You ve probably figured out that you would change it to Ch2 if you pushed the third function button [14c].) The last choice gives a file name which will be something like TEK0000.CSV. When you push the fifth button, you will see that menu item replaced with a clock face. The file is written when the clock face disappears and a new file name that is greater by 1 than the previous file name appears.

3 The Electrocardiogram Set Up Many of you have seen EKG or ECG curves in hospitals, in movies, or on TV. A most memorable movie title about the EKGs was a film about zombies a few years back entitled Flatliners. As you probably know our bodies are very complicated systems that send electrical signals all around the brain, to muscles, and to neurons. These electrical signals are active when we are living and can be used to study the health of the human body. The original experiments on electric potentials were first observed in 1771 when Luigi Galvani discovered that a dissected frog s leg muscle twitches in response to certain metals. This led to the development of the first batteries (also known as Galvanic Cells). One of the most important muscles in your body is your heart. It has a regular beat that is controlled by electrical impulses. In a healthy individual this heart rate or pulse is well controlled. You may know someone who wears a pacemaker, which is a device to help provide this control when the patients body does not seem to be able to do it naturally. The pacemaker is just a small electrical signal to make sure the heartbeats. Because your body is largely made of solutions of ions in water, it is a modest electrical conductor. Signals from inside your body can be observed even through your skin. Because the signals are small, and there can be large amounts of electrical noise, we don t normally notice them at all. However, with a quiet differential amplifier, and some noise filters, we can observe these signals on an oscilloscope, just like the signals in the speed of light apparatus. The differential amplifier measures the difference in the electrical potential between two different electrodes. We have made the electrodes out of copper handles, so that they will be easy to use, and comfortable to hold. There are two outputs of the amplifier box. One is plotted directly on the oscilloscope. The other has a separate gain stage, and can be used to drive a small audio speaker so that you can hear the heart beat. Your lab instructors will help you adjust the gains on the amplifiers. Too much gain causes useless feedback oscillations, which you have all heard when someone places a microphone to close to a speaker playing the amplified sound. You should explore the following questions (along with any of your own) as you have your turn with the ECG setup. Be sure to make some quantitative measures using the cursors, similar to those described in the section on the speed of light. Make sure everyone has some time being monitored. Be sure to keep a log of your observations in your lab book! Use the digital storage feature of the scope to save and then print (from the computer) a few of the waveforms that you found most useful and tape these into you lab book. 1. What happens if you put one electrode in each hand? 2. Does the pattern depend upon how relaxed your hand muscles are or how your arms are positioned? 3. What happens if you switch hands? 4. What happens if you have both electrodes in one hand? 5. What about if you use the inside of your knee to hold the electrode(s)? How about under your arm? Try lots of combinations. Which ones work best? Does it depend upon the person? 6. Try taking the measurement while lying down. Is this different?

4 7. Using the quietest combination, what is the shape of your pulse? What is its period? 8. Take at least 6 measurements of consecutive pairs of pulse waveforms using the best conditions, recording their period and frequency. How much do they vary? Calculate the average and a standard deviation. Now try taking a single measurement of ten waveforms and calculate an average period. 9. How does it compare to the other members of your group? 10. How does your ECG depend upon your recent activity or stimulus? Jump, jog, run, or do some other aerobic exercise for 5 minutes. Repeat step 8 and compare. Is the change from the rest condition statistically significant? Explain. You might want to look at what motions of the heart correspond to the ECG you have recorded. A website that shows this is: For even more on ECGs view: A normal ECG is taken with 12 electrodes. Why? (image taken from another nice site.)

5 Charging and Discharging of a Capacitor Your goal in this part of the lab is to determine the capacitance of a capacitor (on the order of 0.1 µf) by studying the discharge of the capacitor with the oscilloscope. Set the function generator to produce a square wave. Adjust the amplitude [4] and the offset adjustment buttons (to the right of the duty button [6]) such that the waveform displayed is about 2V during half the cycle and zero for the other half. Set up a circuit with a capacitor and a resistor in series. When choosing a value for the resistor, keep the following in mind: The function generator has an internal resistance of 50 Ω, which will be in series with the resistor in your circuit. Pick a resistor that is large enough such that the internal resistance of the function generator is negligible (i.e., small enough for the accuracy you are shooting for, which is probably a few percent.) When the square wave voltage is applied to this RC-circuit, the capacitor will be charged during the first half of the cycle when the voltage is high, and discharged when the voltage is zero. The current that is flowing through the resistor onto the plates of the capacitor during the charging part of the cycle is limited by the resistance R of the resistor, i.e. the time needed to charge (or discharge) the capacitor depends both on R and the capacitance C of the capacitor. In fact, in chapter E5.6 of your textbook it is shown that the voltage across a discharging capacitor decreases exponentially in time, with a time constant equal to RC. Measure the voltage across the capacitor as a function of time by displaying it on the oscilloscope simultaneously with the function generator signal. The oscilloscope has two channels, so you can display two different signals at the same time. However, the grounds of the two input are internally connected, so you have to pay attention which side of the capacitor is positive and which is negative. By analyzing the graph of voltage across the capacitor Vc vs time which is displayed on the oscilloscope screen, determine the capacitance of the capacitor. You should do so by using a single data point of the Vc vs t graph and by fitting the complete set of data. You can then make a linearized plot in LinReg (which will give you the fitting parameters with uncertainties).

6 POWER [1] RANGE [2] FUNCTION [3] PWR 1M 100K 10K 1K khz HZ FUNCTION DUTY OFFSET ADJ TTL CMOS AMPL COARSE [7a] FREQUENCY FINE [7b] VCF IN TTL/CMOS OUTPUT FREQUENCY [7] DUTY [6] OUTPUT [5] AMPLITUDE [4] Tektronix TDS 1002 oscilloscope front panel SAVE/RECALL [2] POSITION (CH 1) [3] CURSOR [5] DEFAULT SETUP [7] CH 1 MENU [4] POSITION (CH 2) [6] AUTOSET [8] Tektronix TDS 1002 HORIZ. POSITION [9] Screen [1] VOLTS/DIVVOLTS/DIV SEC/DIV CH 1 CH 2 EXT TRIG function buttons [14a -14e] VOLTS/DIV adjust [12] SEC/DIV adjust [10] CH 1 INPUT [13] CH 2 INPUT [11]