Objectives on the Time Varying Signal Analysis - Experiment 2 | EGR 214, Lab Reports of Electrical Circuit Analysis

Download Objectives on the Time Varying Signal Analysis - Experiment 2 | EGR 214 and more Lab Reports Electrical Circuit Analysis in PDF only on Docsity! EGR214 Laboratory Activities 1 School of Engineering Grand Valley State University EGR 214 – Laboratory #2 Time-Varying Signal Analysis Objectives • To practice using a function generator to create time-varying waveforms • To practice using an oscilloscope to analyze time-varying waveforms Pre-Lab Assignment 1. Read the Introduction section of the laboratory procedure. 2. Estimate the amplitude, offset, and frequency of the signals shown in Figures 6, 7, 14, and 24. Pre-Lab Deliverables These deliverables are due at the beginning of your laboratory period. Your instructor will verify these deliverables as you enter the laboratory and will use them to construct your laboratory grade. 1. Submit your estimates of amplitude, offset, and frequency as described above. Specify proper units for each estimate. Introduction Periodic Signals In previous laboratories you have been working with static, time-invariant, or DC signals (all meaning roughly the same thing). While these are useful for understanding basic circuit concepts, most of the “interesting” circuits in use today involve time-varying signals. We can roughly divide time-varying signals into two classes: periodic and aperiodic. The periodic signals, as their name implies, repeat at regular intervals. For example, the 120V 60Hz AC power signal available at your wall outlet is a periodic sinusoidal signal. The aperiodic signals do not repeat and are generally called transient signals. In this laboratory we will focus on periodic signals and leave the study of transient signals for a future lab. A periodic signal is characterized by properties such as wave shape (sinusoidal, square wave, triangle wave, etc.), frequency, amplitude, and duty cycle. When two or more periodic signals are considered, we can measure the relative phase (or delay) from one signal to another. Figure 1 shows the basic characteristics of all periodic signals: • The period (T ) is the duration of time occupied by one “cycle” of the waveform. It is measured in units of seconds. • The frequency (f) is the reciprocal of the period: f = 1 T Frequency is measured in units of Hertz (or kilohertz/kHz, megahertz/MHz, gigahertz/GHz, etc.)1 1Personal pet peeve: Hertz was a person. Thus it is most incorrect to treat the term as if it is the plural of “Hert” and to utter phrases such as “this is a 1 megahert signal”. Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 2 t v (t) offset amplitude period Figure 1: The basic characteristics of a periodic signal. t v (t) on-time off-time rise time fall time Figure 2: Characteristics of a square wave signal. • The offset is the average value of the signal. This is often also referred to as the DC bias or mean value. It is measured in volts (assuming the signal itself is measured in volts). • The amplitude is how far the signal rises above and below the average value. It is measured in volts (assuming the signal itself is measured in volts). The peak-to-peak value of the signal is twice the amplitude and, as its name implies, measures how much the signal varies from its most positive to most negative value. For square-wave, or pulse, signals we can also characterize additional parameters (see Figure 2): • the rise time and fall time measure (in seconds) how quickly the signal transitions from the lower voltage to the higher voltage, and vice versa. This parameter is sometimes characterized as a slew rate, measured in volts per second, which measures the rate of change of voltage with time during the transition. • the duty cycle is the ratio of “on time” (i.e., how long the signal is in its higher-voltage state) to total period. That is: duty cycle = on time T = on time on time + off time Function Generators A function generator is capable of generating periodic voltage waveforms with a wide range of parameters. The Tektronix AFG310 function generator at your workstation is shown in Figure 3. The main controls, illustrated in the figure, are function, frequency, amplitude and offset. The first choice of parameter is function, that is, the type of periodic waveform. The choices include sinusoidal wave, square wave, triangle wave, and ramp. You will have a chance in this lab to observe the Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 5 One Vertical Division Volts Per Vertical Division 0V Marker Figure 6: Vertical volts/division and 0V level display. To further illustrate the effect of the vertical controls (scale and position), Figure 7 shows the exact same signal displayed with a 1V/div scale, and the position knob has been used to adjust the 0V position to be 1 vertical division above the bottom. This is the exact same signal as in Figure 6, but a wiser selection of scale and position allows the signal to fill more of the display, thus giving us a better picture of the signal. Horizontal Adjustments The main display window also has 10 horizontal divisions on the graticule. The amount of time represented by one division is controlled by the Horizontal Scale Adjustment Knob, as shown in Figure 8. The current time-per-division setting is shown at the bottom-center of the display window (see Figure 9). This time-per- division setting is also known as the timebase. The horizontal scale must be adjusted to suit the frequency of the signal being analyzed. If, for example, a 10 Hz signal is being analyzed (period of 0.1s) then a 10µs/div horizontal scale setting is inaproppriate as only 100µs of the signal can be seen at one time (10 divisions at 10µs/div). A more appropriate setting would be 20ms/div to show a total of 200ms of the signal, or two full periods. The signal in Figure 9 has a period (one complete cycle) that is approximately 2.5 horizontal divisions. Noting from the display that one horizontal division represents 400µs, the signal’s period is approximately: 2.5div · 400µs div = 1000µs = 1ms Thus, the signal’s frequency can be estimated as being approximately: f = 1 T = 1 1ms = 1 0.001s = 1000 Hz The waveform display can be shifted to the left or right by using the Horizontal Position Adjustment Knob as shown in Figure 8. Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 6 Figure 7: The same signal from Figure 6 is shown with a 1V/div vertical scale and a vertical position adjustment (note the position of the 0V marker) so that the signal occupies more of the viewable area. Horizontal Scale Adjustment Knob Horizontal Position Adjustment Knob Figure 8: Horizontal adjustment/display for an oscilloscope. Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 7 One Horizontal Division Time Per Horizontal Division Figure 9: Horizontal divisions and display of time/division. Triggering Now that you have seen how to adjust the vertical scale and horizontal scale of the display, it is time to address the question of when the oscilloscope draws the input signal on the display. The oscilloscope takes “snapshots” of the input signal. It begins at the left side of the display, draws the input voltage for some amount of time 10 · timebase where “timebase” is the time/division setting (i.e., horizontal scale), and then starts over from the left side of the display. Unless the timebase and period of the signal are exactly aligned, the display will simply be a mess. This is because a different part of the signal will be drawn each time. The problem is illustrated in Figure 10. The top part of the figure shows a square-wave signal to be analyzed. The rectangles that move along the waveform show oscilloscope acquisition times. The width of each rectangle represents the width, in time, of the display window. If the oscilloscope draws a different part of the waveform each time, the oscilloscope display will be different each time, and the human eye will see a jumble of waveforms that do not convey much information. If, however, we tell the oscilloscope to always start drawing the waveform from the same starting point, as shown in Figure 11, a stable image appears. The dotted line on the waveform is known as the trigger level. When the signal crosses this trigger level, the oscilloscope starts drawing the waveform on the display. Then, the oscilloscope ignores the signal until it once again sees the signal cross the trigger level. It then begins drawing the signal again. Assuming the signal is periodic, it will draw the same part of the signal again, for the same duration, and a stable image appears. Note that the waveform of Figure 11 actually crosses the trigger level twice, once when the signal is increasing and again when it’s decreasing. The oscilloscope can be told to only trigger when the signal increases past the trigger level, known as a rising-edge trigger, or to only trigger when the signal decreases past the trigger level, known as a falling-edge trigger. Figure 11 illustrates a rising-edge trigger. Figure 12 shows the oscilloscope’s Trigger Level Adjustment knob. The slope of the trigger (i.e., rising edge or falling edge) can be selected by pressing the Trigger Menu button as shown in the figure and then pressing the Slope button along the bottom of the display. The Trigger Menu also allows you to change other trigger parameters, such as which oscilloscope channel will act as the trigger source. The current trigger parameters are shown at the bottom-right of the display window, as shown in Figure 13. Note that the Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 10 Trigger Level (Visual Marker) Trigger Level (Numeric Value) Trigger Slope (Rising/Falling) Trigger Source Channel (1 or 2) Figure 13: Display of trigger level, slope, and source channel. Figure 14: The left-side-image shows a display that is triggered properly. The right-side-image shows a trigger level that is too high, leading to an unstable image. Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 11 Trigger Marker Trigger Position in Data Record Trigger Position in Data Record Figure 15: The oscilloscope’s trigger point is shown in a variety of ways. Figure 16: The signal of Figure 15 is shown with the trigger set at 20%. Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 12 Figure 17: Trigger position can be set as an absolute delay when the Delay button is pressed and the green LED beside it is lit. spring-loaded cover that can be retracted to reveal a small hook. This hook can be used to attach to wires, alligator clips, etc. The grabber attachment can be removed and reattached through gentle pressure. Another important component of the oscilloscope probe is the ground clip (or ground shield, visible only without a grabber attachment). It is extremely important to note that: THE OSCILLOSCOPE IS AN EARTH-GROUNDED INSTRUMENT AND ALL VOLTAGE MEASUREMENTS ARE MADE RELATIVE TO EARTH GROUND. The oscilloscope ground clip is frequently connected to the ground reference of the system being measured in order to establish a common ground between the system-under-test and the oscilloscope. For high-speed or extremely noise-sensitive measurements, the closer the ground clip is to the probe tip, the better the measurement will be. Part I – First Steps 1. Remove the probe tray from the back of the oscilloscope and connect one oscilloscope probe to the CH1 (channel 1) input on the front of the oscilloscope. Leave the other probe in the tray. 2. Turn on the oscilloscope and wait for the self-test to complete. Press the Menu Off button (to the bottom-right of the display) when prompted to do so. 3. If your oscilloscope has been connected to the Ethernet network (as it should be), you will see a window displaying the “Instrument IP Address”. Record this address in your laboratory notebook. It may be different every time you power-on the oscilloscope thus you should record it each time. Then, press the Menu Off button. 4. Connect the probe tip hook (using the grabber attachment) to the “Probe Comp” metal tab on the front of the oscilloscope (see Figure 19). NOTE: There are two metal tabs here...the top one is the “Probe Comp” tab and outputs a 5V peak-to-peak 1 kHz square wave. The lower tab is an earth ground connection. 5. Press the Autoset Button (see Figure 19). You should see a display very similar to Figure 6. Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 15 Figure 21: Emulate this display for Part I Step 8. You should see a screen very similar to the one shown in Figure 22. If not, ask your instructor for help. To save the waveform display to a graphic file, right-click on the image and select “Save As...”. The image will be saved as a PNG file which can then be embedded in a document, viewed in a web browser, printed, etc. Note that the web browser display will only refresh periodically, even though the signal on the oscilloscope may change. You can refresh the web browser display by pressing the browser’s refresh button or pressing Ctrl-r. Also, if you right-click on the image and select “View Image”, it will appear in a new window, refreshed to match the current oscilloscope display. Interlude Go to the back of this laboratory and work through the Appendix. In the remainder of the laboratory you will be connecting the function generator to the oscilloscope, and there are several issues associated with this connection that are not obvious. Part III – Using Cursors The divisions on the graticule can be used to make rough estimates of differences in time (horizontal) or voltage (vertical). For more accurate measurements, you can use the two oscilloscope cursors. These are enabled by pressing the Cursor button on the front panel (see Figure 23). Once the Cursor button is pressed, a menu appears on the screen (Figure 24). Select the “H Bars” button to see horizontal cursors (to measure voltage) or the “V Bars” button to see vertical cursors (to measure time). Press the “Menu Off” button to dismiss the cursor menu. There are two cursors; the currently-active cursor is shown with a solid line, while the other cursor is shown with a dotted line. To switch between them, press the Select button. To adjust the position of the currently-active cursor, use the Cursor Adjustment knob. When the cursors are displayed, the distance between them is shown next to a delta symbol (∆) and the position of the currently-active cursor is shown next to an at-symbol (@). For example, in Figure 25, the Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 16 Figure 22: The display of the oscilloscope’s built-in web server Cursor Button Cursor Selector Knob Cursor Adjustment Knob Figure 23: Cursors are controlled with the Cursor button and Cursor Adjustment knob. Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 17 Figure 24: The cursor menu that appears when the Cursor button is pressed. two horizontal cursors are separated by 2.34V and the currently active cursor is shown with a solid line at the 0V position. The cursors show that this sawtooth signal has an amplitude of 2.34V. For vertical cursors, both times and voltages are shown. The voltage at which the cursor crosses the signal is shown with a small tick mark. For example, Figure 26 shows two vertical cursors separated by ∆ = 1.00ms. The left-most cursor (solid line) is at a time position of @ = −640µs. The left-most cursor crosses the signal at @ = −2.10V, and the difference between the voltage crossings of both cursors is ∆ = 60.0mV. Since the cursors are at approximately the same place on consecutive waveform periods, the period of the waveform is 1ms and its frequency is 1 kHz. 1. Set the function generator to create a 1 kHz sinusoid (approximately) with 2V amplitude and 0V offset. Use horizontal cursors to accurately set the signal amplitude. Use vertical cursors to accurately measure the signal period. Record the period in your laboratory notebook. Using the estimate of the period, compute the frequency and compare with the LED display of the function generator. 2. Set the function generator waveshape to a square wave (same 1 kHz frequency, 2V amplitude, 0V offset). The duty cycle is supposed to be approximately 50%. Use vertical cursors to accurately measure the signal’s on-time, period, and hence the duty cycle. Record your measurements and computations in your laboratory notebook. 3. Now set the function generator waveshape to be a pulse. Set the duty cycle on the function generator to 25%. Use vertical cursors to accurately measure the duty cycle and record this in your laboratory notebook. Part IV – Using Automatic Measurements The oscilloscope tries to be helpful and make common cursor measurements for you, including frequency, duty cycle, amplitude, etc. Many times, these automatic measurements are a time-saver, but they are no Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 20 Figure 27: Waveform #1 Figure 28: Waveform #2 Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 21 Figure 29: Waveform #3 Figure 30: Waveform #4 Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 22 Figure 31: Waveform #5 Figure 32: Waveform #6 Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 25 At The End Of The Laboratory • Clean up your workstation, return all wire, components, etc. to the PROPER locations. • Disconnect all cables and return them to their PROPER locations. • Turn off all test equipment. • Return all oscilloscope probes back to the tray and re-insert the tray into the oscilloscope. • Place the oscilloscope front-panel cover back on. • Make sure you clearly understand the laboratory deliverables and their due date. Laboratory Deliverables You are to submit a brief technical report by the beginning of the next laboratory. Your report must contain: • Your names, the date, the laboratory number, your laboratory section, etc. • Recorded values and computations for cursor measurements in Part III. • Recorded values for automatic measurements in Part IV, and comparisons with the measurements from Part III. • Function generator settings for each of the images you acquired in Part V. • Printouts of the saved images you acquired in Part V. Each group is responsible for handing in one report. Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 26 A Function Generators and Oscilloscopes A.1 Oscilloscope Probes The probe that you plug in to the oscilloscope is actually a complicated piece of circuitry, and is surprisingly expensive (so treat it gently). It is NOT just a wire enclosed in plastic. For example, the oscilloscope probe divides (or attenuates) the signal’s voltage by 10. Thus, if you were to probe a 1V signal, the oscilloscope probe would actually present a 0.1V signal at the connector on the front of the oscilloscope. However, the oscilloscope knows that the probe divides the signal by 10 (note that the BNC connector on the probe has a special spring-loaded pin – that’s how it knows), so it shows it to you as 1V on the display. This type of probe is known as a “10X probe” since its voltage must be multiplied by 10 to get the real value. Some oscilloscope probes don’t inform the oscilloscope that they are 10X probes, which means the oscilloscope thinks they are “1X probes” (no division by 10) and will display voltages that are 10 times too high. If you happen to encounter this situation, you can fix it by pressing the MENU button in the “Vertical” section of the oscilloscope and selecting the true probe attenuation factor (10X or 1X) with the bottom-right button. So why do oscilloscope probes divide the signal by 10? Here is one explanation from Wikipedia2 (and if you understand it, you probably don’t need to take EGR214): Passive scope probes contain no active electronic parts, such as transistors, so they require no external power. The most common design inserts a 9 megohm resistor in series with the probe tip. The signal is then transmitted from the probe head to the oscilloscope over a special coaxial cable that is designed to minimize capacitance and ringing. The resistor serves to minimize the loading that the cable capacitance would impose on the DUT. In series with the normal 1 megohm input impedance of the oscilloscope, the 9 megohm resistor creates a 10x voltage divider so such probes are normally known as either low cap(acitance) probes or 10X probes. Because the oscilloscope input has some parasitic capacitance in parallel with the 1 megohm resistance, the 9 megohm resistor must also be bypassed by a capacitor to prevent it from form- ing a severe RC low-pass filter with the ’scope’s parasitic capacitance. The amount of bypass capacitance must be carefully matched with the input capacitance of the oscilloscope so that the capacitors also form a 10x voltage divider. In this way, the probe provides a uniform 10x attenuation from DC (with the attenuation provided by the resistors) to very high AC frequencies (with the attenuation provided by the capacitors). A.2 Oscilloscope Probes and Function Generators Oscilloscope probes have BNC connectors that mate to both the function generator and the oscilloscope, so can you connect an oscilloscope probe to a function generator and use the probe tip as the waveform output? No. Why? Because you wouldn’t use a screwdriver to hammer a nail. An oscilloscope probe is meant for sensing signals, not “driving” signals, and the extra hidden resistors and capacitors inside the probe are going to distort your waveform. A.3 Direct Connection Can you use a BNC cable to directly connect the function generator output to an oscilloscope? Yes, but you can’t do much else other than observe the function generator’s output this way. This is a “1X” connection, and the oscilloscope should automatically sense this, but you may have to make sure. It is better to get into the habit of always using oscilloscope probes connected to oscilloscopes, and learn how to use both properly. 2http://en.wikipedia.org/wiki/Test_probe Copyright c© 2010 Padnos College of Engineering & Computing EGR214 Laboratory Activities 27 50Ω Vfg 50Ω Vload + - Function Generator Figure 37: The AFG310 function generator has a 50Ω output resistance and assumes it is driving into a 50Ω load resistance. 50Ω Vfg Function Generator Oscilloscope 1MΩ Vload+ - Figure 38: The oscilloscope presents a very high resistance load to the function generator. A.4 Why is it Two Times Too Big? Try this: set your function generator to output a sine wave, 1 kHz frequency, 2V amplitude, 1V offset. Now measure the waveform’s amplitude and offset on your oscilloscope. Why does your signal have a 4V amplitude and 2V offset??? The function generator has a 50Ω output resistance and assumes it is driving into a 50Ω load resistance, as illustrated in Figure 37. Why it has this output resistance, why it makes this assumption about the load resistance, and what’s so special about the number 50Ω are all good questions but they will have to wait. First, we have to understand what this means for our measurements. The 50Ω output resistance of the function generator and the assumed 50Ω load resistance form a voltage divider such that (referring to Figure 37): Vload = 50 50 + 50 · Vfg = 1 2 Vfg So if the function generator sets its internal voltage to Vfg = 1V, we will only measure Vload = 0.5V. Supposing we want the voltage at the load to be Vload = 1V, then the function generator sets its internal voltage to Vfg = 2V. The function generator is trying to be helpful – we set the desired load voltage to 1V using the front-panel keys, and the function generator automatically compensates for the division-by-2 and sets its internal voltage to be twice this number. Now, when we use the oscilloscope to make measurements of the function generator’s output, there is no 50Ω load resistance. A good model for the function generator and oscilloscope circuit is shown in Figure 38. In fact, the oscilloscope’s resistance is very high (1 megaohm in the figure), so that using the voltage divider principle: Copyright c© 2010 Padnos College of Engineering & Computing