The Digital Oscilloscope and the Breadboard

Transcription

1 The Digital Oscilloscope and the Breadboard Will Johns, and Med Webster Aug. 26,2003, Revised by Julia Velkovska, September 6, Oscilloscope - General Introduction An oscilloscope is a very powerful instrument that allows you to measure almost all aspects of an electrical signal. You have used an oscilloscope in the introductory physics labs (hopefully!) and should already be familiar with some of the basics. The scopes you have used previously have probably been analog scopes; a stream of electrons is produced at the rear of the tube, deflected horizontally and vertically by the voltages applied to plates the stream passes between, and the stream of electrons produces light when it hits the phosphor on the front face of the tube. By applying a voltage which is proportional to time to produce the horizontal deflection and the voltage one wants to study (signal voltage) to make the vertical deflection, this device neatly graphs the signal to be studied vs. time. Unfortunately the phosphorescence, which shows where the beam hit the face of the tube, fades in a fraction of a second, and unless the signal repeats itself, it is hard to see what happened. The same fast electronics and cheap memory chips which make computers possible permit a different approach to solving the basic problem: What does my signal look like? The digital solution is simply to measure the signal as it varies, store the measurements in a computer memory, and plot the measurements just as you have plotted measurements in a spread sheet or some other display program. How often does the scope make a measurement of the input signal? It depends upon how rapidly the signal varies. The horizontal scale factor (sweep speed) needed to see the structure of the signal also depends upon how fast the signal varies. The scope you will use chooses the measurement spacing according to the horizontal scale factor (which you choose) so that there are 250 points 1 plotted for every cm on the time axis. The display is now just like a computer display; it stays 2 until it is replaced by another signal. For events that occur only every few seconds, like cosmic rays, this ability to hold a trace so that we can examine it is one of the significant advantages of a digital scope. Of course having the digitized values in a computer also gives us the ability to do several sophisticated analyses with the data. For 225W, 226W you will usually use the digital scopes (TDS 210 s) and this lab will help you explore some more capabilities that you should know how to use. 1 That sounds like a lot, but there can be a misrepresentation of signals which have a frequency that is a multiple of the measurement frequency. You are encouraged to ask the instructor or consult either the scope manual or a text on digital signal processing if you want more details on this problem of aliasing. 2 Actually the time until the signal fades is set by the persist setting to be discussed later. 1

2 2 Apparatus Textronix TDS 210 Digital Scope multimeter powersupply with low voltage AC floating output oscillator pulse counter, Beckman UC10 (shared with Electrical Oscillations) breadboard, resistors, capacitors neon bulb EMCO G20 DC-DC converter 3 Introduction to the Digital Oscilloscope The first thing you need to do is to check out your scope and probe. The first part of this discussion will make sense only if your probe has an attenuator and a setscrew for tuning the probe. If neither probe with your scope has these features, complain to the instructor. Hook up your scope for calibration with an internal signal as shown in Figure 1. Turn it on and press the Autoset button (C). You should see a square wave signal with a frequency of about 1000 Hz and there should be about 5 volts from the very top to the very bottom. Note that the probe is connected at channel 2. The additional line across the bottom is channel 1 and it is just constant since nothing is connected to it. Questions: (Questions are to be identified as here and answered in your lab notebook.) Q1.1 What is the period of a 1000 Hz signal? Q1.2 How does that relate to the 250 µs written at the bottom of the scope screen? Q1.3 How does the Ch mv relate to the 5 Volts suggested above? Q1.4 Is there a problem here? Here is what I got (Figure 1) after diddling a little with the knobs. I ll describe what the letters on the figure refer to below. A: This is the actual waveform. It s supposed to be a square wave with about 5 volts of peak to peak voltage that repeats at a frequency of 1 khz. Right now the waveform has a little extra feature that is the pointy bit near the letter A. Our first job is to try and remove that. For now, let s see what else we can learn. B: Ah, this is how you hook up the scope to the probe compensator. The ground (alligator clip usually) goes on the bottom hook near the broken arrow, and the probe tip goes on the top hook. I think the output is driven by the wall voltage, so the frequency out to be pretty good, but I wouldn t be shocked if the peak to peak voltage was different by 5% since that sort of variation of the line voltage is typical. C: This is the Magic button. The autoset feature. Most modern digital scopes will have one. You can press it and the scope will try to set the controls so that you are close to seeing what you want. Usually this gives you a good starting point, and you can get a much better image by rotating knobs G and E. D: Measure. This scope lets you do a lot with periodic signals. This button will pop up a menu left of I and J are that will allow you make measurements with the scope of the frequency, period, peak to peak voltage, Mean (True RMS Voltage), Cyclic RMS (basically Peak to Peak Voltage times 1/ 2. The buttons that control the menu items are to the right of I and J. 2

3 D C J A I H G E K B F Figure 1: View of the front face of the TDS 210 after the probe has been hooked up to the probe calibrator. E: This is the time base. It sets up the time between each major division on the scope. The effect is to stretch or squeeze the signal horizontally (X is time). F: This is where I chose to plug in the scope probe. It is channel 2. G: This knob controls the vertical scale for channel 2 in Volts per major division. The effect is to stretch or squeeze the signal Vertically (Y is Voltage). H: Pressing this button gives you access to the menu that controls the characteristics of channel 2. The menu pops up to the left of I and J. I: The probe button. This lets you tell the scope the attenuation of the channel. The probe we have connected right now attenuates the signal by a factor of ten. We need to adjust this to 10 so that the reading at K is 2 V. (ie your answer to the question in the previous section was off by a factor of 10!) Note that this number is only used by the computer to get the right numbers to print on the screen; changing it just changes the numbers printed on the screen and they will be wrong unless this number matches the probe. Some probes have a switch that lets you choose the probe attenuation and a few scopes have an additional contact around the probe connection so that the probe attenuation is picked up automatically by the scope. 3

4 Figure 2: Compensating the scope probe. Boy that signal s gonna look great. J: This sets up the how the channel is coupled. Basically, you can put a capacitor between the signal source and the input by choosing AC. This is useful for looking at higher frequencies that sit on top of a DC signal: You can use a high gain to see small signals without having everything go off the top or bottom of the screen. However, you can get into trouble sometimes when you are looking at frequency dependence at low frequencies (below 100 Hz for most scopes) and forget that you have chosen AC. K: Tells us the setting for the knob at G divided by the attenuation of the probe. To the right of this is the time/div setting. It is 250 µs in these figures. You probably are accustomed to seeing these scale factors in a ring around the knobs which control them on analog scopes. So lets get rid of the non-square part of the trace by turning the little screw that is in the handle of the scope. Most probes have this little screw. In Figure 2, there is a picture of the operation. In Figure 3 we have the fruit of our labors. Now, I ve pressed measure and set up a few things. See if you can too. The results are shown in Figure 4. The only trick I ve added is to press the trigger button, choose channel 2 as a source from the menu, choose normal as the mode, and turn the knob above the trigger button until trig d appears at the top of the screen. (You also may notice that the waveform changes a little if we get the trigger level correct with the knob.) Repeat the set up as shown in Figure 4 and verify the four measurements shown by using the divisions on the scope and your knowledge of the Probe Comp signal. You should be good to go on making some measurements now if the scope has checked out. 4

5 4 Triggering Why is the picture on the scope stable in all the above figures? How does the scope know to start each sweep so that it lies exactly on the preceding sweep instead of coming at random? The key is that little arrow on the right margin of the screen and 1 cm below the center in the figures. It indicates the setting of the trigger; the traces are on top of one another because each sweep is triggered when the input voltage crosses the level shown by that little arrow. Let us informally call this crossing 3 of the arrow level a trigger event. The rightmost of the four upper knobs adjusts the trigger level and is called a discriminator setting. Turn the knob until the trigger arrow moves above or below the square wave. What happens to the display? The answer depends upon some other settings. First push the display button (third from left in second row from top) and adjust persist to a couple of seconds by cycling the button to the right of persist. Note that the arrow at the top of the display is on the center line. The trigger places the trigger point underneath this arrow. Both the arrow and the time of the trigger can be shifted across the screen by the knob above the sweep speed knob. Push the button underneath the trigger discriminator to bring up the trigger display/menu at the right of the screen. Find the trigger mode setting and answer the question about what happens when the trigger discriminator is moved above or below the signal for modes of Q2.1 normal, Q2.2 single sweep, and Q2.3 auto. There is also a video trigger which we will not need in this lab. 3 Some scopes provide the option of using either the value or time derivative (slope) of the input signal to define the trigger event. Figure 3: The compensated signal. Nice. 5

6 Figure 4: View of the front face of the TDS 210 after the probe has been compensated and the measure option has been configured for channel 2. We have been looking at a square wave 4, so the triggering doesn t depend upon where the discriminator is positioned as long as it is within the wave; in the next session we will observe its effect when the signal is a sine wave and we will examine this point. Before you switch to the sine wave input, switch from rising to falling trigger and see how the trigger point is changed. The signal shown in the figures shows five points at which the signal crosses the level of the trigger discriminator. How do we know which is the right one? A small arrow along the top of the display shows the time of the trigger. The auto setup used to obtain the original settings has placed this in the middle of the screen. Change the horizontal position knob to see how both the arrow and the display move together. Note that one of these crossings remains under the trigger time arrow when the number of visible crossings is changed by changing the knob E, the sec/div knob. Q2.4 Is this still true when the trigger time is not at the center? Q2.5 See if you can find the beginning and end of the 4 No wave is ever perfectly square. You might want to turn the sweep speed way up (to a few microseconds per cm) so you can see the slope of the rising edge of the square wave. On a sweep speed where you can see the slope, you can see how the trigger level affects the trigger position in the wave form 6

7 data recording for the display by moving the horizontal position to the right and then to the left. Q2.6 Does this depend on the sweep speed setting? The ease with which we can see what happened before the trigger is a powerful advantage of a digital scope; to accomplish the same thing with an analog scope would require sending the trigger signal directly to the trigger input while delaying the display signal by inserting hundreds of feet of transmission cable in the line for the display signal. Q2.7 Does the point on the wave under the time trigger mark correspond to the trigger threshold mark? What changes when the trigger mode is switched from plus to minus? Note that there are several sources listed in the trigger source menu. If we had a signal from a different part of the same circuit sent to channel 1, both would be displayed and we could study the time differences between the two signals. We could do this while triggering on either signal 1 or 2, depending upon which had the feature in the wave form which gave the sharpest trigger. The external trigger facility permits us to trigger on a third signal while looking at two simultaneously. The line trigger works on the 60 Hz power supplied to the scope and is useful primarily for looking at circuit malfunctions which are related to electrical noise on the power. The square wave did not show details about how the trigger time depends upon the trigger discriminator or threshold as it is often called. Connect the oscillator to one of the channels of the oscilloscope by means of BNC connectors and a piece of coaxial cable (no probe used here). Set the wave form of the oscillator on the picture of a sine wave, the frequency at about 1 khz, and adjust the amplitude of the signal to about 2 Volts. You may want to use the auto trigger mode until you have adjusted the scope display and trigger. Move the trigger discriminator up and down and see how the signal moves across the screen. Do this for both positive and negative trigger settings. 5 Scope Calibrations - accuracy of scope measurements The principal is simply to compare the voltages and times measured with the scope with those measured with another instrument. In practice it is better (more precise) to use the measurement lines (cursors) provided in the measurement mode than to simply read the width and height in cm and convert by using the factors at the bottom of the screen because the observer can judge the agreement of a line with the part of the wave more precisely than he can read it directly. The readout then shows the time (or frequency) or voltage between the pair of cursor lines. Select the measurement menu and the use of these lines is probably obvious. If not, talk to the instructor. Time measurements are frequently important, so the scope is built with a precision (ie very accurate - precision is commonly used as an adjective in this sense, but accurate would be more correct) crystal oscillator and the circuits are calibrated every time the scope is turned on. Consequently we expect the time measurements to be limited primarily by our ability to position the cursors on the signal, by our precision. Use a BNC tee and another piece of coax to connect the frequency counter to the scope and oscillator. Increase the amplitude of the signal if necessary to make the frequency counter work. Set the 7

8 frequency counter for the longest counting time. On the scope use the measure mode to set up vertical cursors and adjust them to cover as many complete periods as are visible on the screen. Q3.1 Correct the time or frequency read from the scope for the number of periods included and compare with the reading of the frequency counter. Repeat for a lower frequency such as 100 HZ and for several higher frequencies up to the highest available on the oscillator. Remove the connection to the oscillator and connect a battery across one of the scope input channels. Measure the battery voltage with a multimeter and with the horizontal cursor lines on the scope. Q3.2 How will you trigger the scope with an input signal which is constant? Q3.3 Do the scope and multimeter readings agree? Remove the battery and connect the 6.3 V AC output of the power supply to one of the channels of the scope and to the multimeter. The outside sheath of the coax is effectively grounded in the scope. Effectively grounded means that it should never be more than a few volts from ground or the scope may be damaged. Ground means the case of the scope and that is attached to building ground through the third wire of the line cord. One side of the line AC is also grounded to the building ground. The 6.3 V AC is produced by a transformer and neither side of the secondary is grounded. (It is floating.) Therefore we can connect either side of the secondary to the almost ground side of the scope and the scope defines the ground of this circuit. Measure the voltage with the multimeter and with all three settings of the scope, peak to peak, Mean (True RMS Voltage), and Cyclic RMS. Correct the scope readings for the ratio of the readings observed in the battery measurement. Q3.4 What is the relationship of these three numbers to the multimeter reading? Explain what is meant by RMS voltage and current and why these are useful in computing the power delivered by an AC source. 6 Use of the Scope in a Circuit Application: Relaxation Oscillator + V S R C NEON BULB (r) Figure 5: Circuit of relaxation oscillator which you will implement on a bread board. 8

9 If you look at only the loop on the left in Figure 5 it is simply a power supply charging a capacitor through a resistor, so the voltage across the capacitor is simply the exponential increase V c = V S ( 1 e t/rc ). The voltage across the neon bulb is the same as the voltage across the capacitor and no current flows in the bulb as long as the voltage is less than its breakdown voltage, V b, so this is an accurate description of the circuit as long as V c < V b. But the neon bulb in the right loop comes into play when the voltage across in exceeds V b. That is, the neon bulb behaves like an open circuit unless the voltage across it exceeds its breakdown voltage. The bulb then acts like a relatively small resistance until the voltage drops below its extinction voltage, V e, when it returns to being an open circuit again. You will use the scope, with 10x attenuation probe, to observe how this circuit works. R 3 1 Neon Bulb C 4 G20 DC DC V Top View Figure 6: Layout on breadboard of relaxation oscillator and power supply. The complete circuit is shown in figure 6. The voltage V s is obtained from a battery and DC-DC converter which runs on a couple of Volts from the battery and puts out about 200 V. The manufacturer s specs are included as the last page of this writeup. We have inked in some additional labels to help; in means battery and out means to oscillator circuit. The power supply and battery on the bread board have no connection to ground but the circuit diagram shows a ground. Q4.1 Is the circuit in fact grounded before the scope is attached? How is it (approximately) grounded after the scope is attached? First use the multimeter as an Ohm meter to establish which holes in the bread board are connected beneath the surface and Q4.2 make a sketch of the connections in your log book. Schematic is sufficient, you don t have to show all the rows of holes, just enough to show that you have understood the pattern well enough to build the circuit. Before connecting the battery ask the instructor to check the circuit. Connect the battery and the bulb should start to flash if you have made good connections. Q4.3 Count the number of flashes in a few seconds in order to measure the period of the flashing. Measure V e, V b, V s, and the time between the breakdown and extinction. Using a much faster sweep and triggering on the falling edge of the signal, make a rough measurement of the slope of the falling edge as it begins to fall. Once the breakdown voltage is exceeded, the bulb acts like a relatively small resistance, r << R, until the voltage drops below its extinction voltage, V e, when it returns to being an open circuit. Since negligible current flows into the capacitor from the power supply during the very brief discharge time, the left loop can be ignored and the right loop is simply a capacitor initially charged to a voltage V b 9

10 discharging through a resistance r, so V c = V b e t/rc, where t is measured from the instant of breakdown and r is the resistance of the bulb while it is conducting. The approximation that r is constant is pretty crude. You will estimate (calculate) r from the slope of the voltage just after breakdown. For the first part of the discharge we can expand the exponential in a series and the equation simplifies to V c = V b (1 t/rc). Q4.4 Calculate C using the full exponential form of the charge up equation with the three measured voltages and the time between the breakdown and extinction. Then use that value of C and the slope of the initial breakdown voltage to make a crude calculation of r. R i V s R NEON BULB C (r) V t G 20 Figure 7: Layout on breadboard of relaxation oscillator and power supply. Whoops!! Did you see structure when you measured V s? That s supposed to be a DC power supply, so what is it doing with structure on it? Were you gullible enough to believe the above made sense? It s OK as a first approximation and to get the big picture of how the relaxation oscillator works, but you cn do better. Figure 7 is a reasonable model of what probably is wrong with the power supply. The very same reason that it is less dangerous implies a sort of defect. It is not a pure source of Emf but also has an internal resistance R i. You measured V s while you really want V t and you measured R while you really want R + R i. How can you find R i? You can measure the output voltage, V, at the same times (in the cycle) you measure V b and V e. The current through R i is always the same as the current through R. If we use subscripts m for measured terminal voltages, b for breakdown and e for extinction, R i b = V m,b V b R i e = V m,e V e R i i b = V t V m,b R i i e = V t V m,e Eliminate V t from the last pair and then the difference in the currents to obtain an equation for R i and then solve for V t. Use these results to recalculate C and you will get a value much closer to the one written on the capacitor! 10

11 Figure 8: Vendor s Information on EMCO DC to DC converter. We use G20. Taken from EMCO web page. 11