ME 365 EXPERIMENT 1 FAMILIARIZATION WITH COMMONLY USED INSTRUMENTATION

Objectives: ME 365 EXPERIMENT 1 FAMILIARIZATION WITH COMMONLY USED INSTRUMENTATION The primary goal of this laboratory is to study the operation and limitations of several commonly used pieces of instrumentation: an oscilloscope, function generator, and digital multimeter. These devices will be used to study the behavior of a second order system. The system will be the series combination of a resistor, a capacitor and an inductor (RLC circuit). After completing this lab, you should be able to: Explain how loading occurs and how it affects measurements. Convert peak voltages to RMS voltages. Understand why the oscilloscope has AC/DC coupling and when it should be used. Use the lissajous figure to compare the phase between two signals. General Information: The Oscilloscope: Oscilloscopes are versatile instruments used to display constant or time varying voltages. The Agilent Technologies DSO1012A Digital Storage Oscilloscope used in the ME365 laboratory is a two channel unit with a maximum sensitivity of 2 mv/division and a useful frequency range from 0 Hz to 100 MHz. To use the oscilloscope, turn on the unit by pressing the power button on the lower left corner of the display. The front panel of the DSO1012A contains a series of knobs and buttons. Knobs are used most often to make adjustments. Buttons are used for run controls and to change other oscilloscope settings via menus. Figure 1 shows a picture of the front panel controls for the oscilloscope. The definitions for the specific keys and knobs are as follows: Measure Controls: Waveform Controls: Menu Controls: Vertical Controls: Cursors and Measure front panel keys. Acquire and Display front panel keys. Save/Recall and Utility front panel keys. Vertical position knobs, vertical scale knobs, channel (1, 2), Math, and Ref front panel keys. 1

Horizontal Controls: Trigger Controls: Run Controls: Setup Controls: Softkeys: Entry Knob: Position knob, Menu/zoom front panel key, and scale knob. Trigger Level knob, Menu, and Force front panel keys. Run/Stop and Single front panel keys. Auto-Scale and Default Setup front panel keys. Five gray buttons from top to bottom which select the adjacent menu items in the currently displayed menu. For the adjustment defined controls. Figure 1: Front Panel Controls When one of the oscilloscope front panel buttons turns on a menu, you can use the five menu buttons to select items from the menu. The Menu On/Off button turns on or off the menu of the last accessed menu. The 5½ Digit Multimeter 2

The Agilent U3606a 5½ Digit Multimeter is a versatile tool for measuring constant and time varying signals. It also adds the ability to measure frequency, pulse width and capacitance. In the same chassis, a 30 watt programmable DC power supply has been added as well making the instrument even more versatile. This DC power supply can supply up to 30 volts DC at 1 amp or up to 8 Volts DC at 3 Amps. It also can be used to generate up to a 4.8Khz square wave and ramp signals. To use the instrument, turn on the unit by pressing the power button on the lower left corner of the display. The Agilent instrument contains a series of buttons that control all of its functions. The front panel consists of two different sets of buttons, one set for the multimeter and one set for the DC power supply/generator. Figure 2 shows a picture of the front panel display and the instruments various controls. Figure 2: U3606a Multimeter Front Panel Controls The front panel has multiple input and output terminals. It is important to understand which terminals must be used for a specific situation. Figure 3 and Figure 4 show a picture of how to wire the front panel to measure voltage and current, respectively. Figure 3 and Figure 4 also illustrate the measurement of frequency and pulse width. Figure 3 is also used for the measurement of capacitance. Figure 5 shows how to measure resistance using the 4 wire technique. To use the more conventional 2 wire setup, the leads in Figure 3 are correct. The main advantage to the more complex 4 wire system is the fact that with a 4 wire system, the resistance of the cabling is eliminated. Thus, a more accurate measurement of resistance is measured. Lastly, Figure 6 shows how to wire the output terminals to the power supply module 3

for generating DC constant voltage, DC constant current, square wave outputs and ramp output functions. Figure 3: Wiring to Measure Voltage Figure 4: Wiring to Measure Current Figure 5: Wiring to Measure Resistance Figure 6: Wiring to Measure Frequency The Waveform Generator The Agilent 33220A 20 MHz Function / Arbitrary Waveform Generator can be used to generate sine, square, triangle, ramp, pulse, noise, arbitrary and random waveforms from 1 µhz to 20 MHz (for sine wave). The output voltages of the output signals range from 20 mv to 20 V peak to peak into an open circuit and 10 mv to 10 V peak to peak into a 50 Ω load. To use the function generator, turn on the unit by pressing the power button on the lower left corner of the display. The front panel of the 33220A contains a series of knobs and buttons. Figure 7 shows a picture of the front panel controls for the function generator. The definitions for the specific regions of knobs and buttons are as follows: 1. Graph Mode 2. On/Off Switch 3. Modulation / Sweep / Burst keys 4. State Storage Menu keys 5. Utility Help key 6. Help Menu key 4

7. Menu Operation Softkeys 8. Waveform Selection keys 9. Manual Trigger key 10. Output Enable/Disable key 11. Knob 12. Cursor keys 13. Sync Connector 14. Output Connector Figure 7: Function Generator Front Panel Controls Procedure: Measurement of Time Varying Signals: Set the function generator so that its output is a 200 Hz sine wave with an amplitude of 2 Volts peak to peak with a one volt (+) offset. Before setting up the frequency, amplitude and offset, the function generator should be set to High Z mode: a. On the function generator, press the Utility Key. b. Press the Output Setup Menu Operation Softkey. c. Press the Load/High Z Menu Operation Softkey until High Z is selected. Detailed explanation of the impedance matching will be explained later in this lab. Now you can press the Sine button. Once pressed, the Menu Operation Softkeys can be used, in conjunction with the number pad and knob to vary the frequency (Freq), amplitude (Ampl) and offset (Offset). Connect the output connector of the function generator to the channel 1 input connector of the Oscilloscope. 1. Observe the effect of changing each of the following oscilloscope controls. a. Rotate the large knob in the Horizontal Controls region. b. Rotate the top knob in the Vertical Controls region. c. Rotate the bottom knob in the Vertical Controls region. 5

d. Press the Auto-Scale button. Q1) How does each knob affect the viewing of the periodic signal? 2. The most common error in using an oscilloscope is improper use of the AC/DC coupling switch. 3. Connect the function generator output to channels 1 and 2 using a T-connector on the scope. 4. Set the function generator to a 200 Hz sine wave, 2 Volts peak to peak with zero offset. 5. Set the scope up as described initially. 6. Set the coupling switch to DC on channel 1 as follows: a. Press the Channel 1 button. A menu should appear on the screen. b. Under the Coupling Menu Defined Button, press the button until it reads DC. 7. Set the coupling switch to AC on channel 2 as follows: a. Press the Channel 2 button. A menu should appear on the screen. b. Under the Coupling Menu Defined Button, press the button until it reads AC. 8. Adjust the bottom knob in the Vertical Controls region to impose the channel 2 trace onto the channel 1 trace. 9. Lower the frequency on the function generator and observe the effect. DO NOT press the Auto-Scale button periodically to accurately see the effect because Auto-Scale defaults to AC-Coupling. Q2) At what frequency is a difference in the two signals observed? 10. Continue to lower the frequency. Q3) Two differences in the traces should be evident. What are they? 6

11. Set the function generator to a 200 Hz sine wave with an AC amplitude of 50mV and a DC offset of 4.5 Volts. If it is desired to observe only the AC part of the waveform so that it fills the screen, which channel (as they are presently set up) is the best? Q4) Which channel is best and why? 12. Often it is necessary to observe the voltage difference across a component in a circuit. To do this, channels 1 and 2 may be used together. a. Set the offset on the function generator to zero. b. Press the Auto-Scale button. c. Set the coupling on both channels to DC. d. Look at channel 1 by itself. e. Look at channel 2 alone. f. Look at channel 1 + channel 2 by doing the following: i. Press the Math button in the Vertical Controls region. ii. Press the Operate Menu Defined Button until 1+2 is displayed. g. How does the amplitude of 1+2 compare with the individual amplitudes? h. Look at channel 1 - channel 2 by doing the following: The Digital Multimeter (DMM): i. Press the Math button in the Vertical Controls region. ii. Press the Operate Menu Defined Button until 1-2 is displayed. iii. Is the result as expected? The digital multimeter can be used to measure DC voltage and current, AC voltage and current (true root mean square values), and resistance. Use of this unit is straightforward. The Measurement Function keys control what measurement is taken. Make sure the unit is set to a 4 1/2 digit reading. This is done by pressing the Shift button followed by pressing the 4 1/2 Digit button. 1. Set the output of the function generator to a 1000 Hz sine wave with a 1 Volt peak to peak amplitude and zero offset. Measure the DC offset using the DMM by pressing the b button. Refer to the beginning of this lab to make sure the proper input terminals are being used. 2. Set the DMM to AC, by pressing the button. Now switch the output to a square wave and read the output voltage. 7

Q5) Compare the actual reading with its theoretical value. Is it within the manufacturer s specifications given in the DMM documentation? Note: The documentation can be found at http://cp.literature.agilent.com/litweb/pdf/u3606-90013.pdf 3. Return the function generator to a sine wave and slowly decrease the frequency. Q6) At what frequency does the error in the RMS voltage become larger than 1%? What is the source of this error? Resistance measurements can be made by applying a known current through the unknown resistance and measuring the resulting voltage. When the Ω button is pressed, a known current is applied to the unknown resistance automatically by the meter. This results in a voltage drop which can be measured by the DMM. This is shown in the circuit diagram in Figure 1. Voltage Drop DMM I = 1.0 ma Figure 8: Current Measurement using DMM 4. Connect and measure the 0.82 Ω resistor provided by connecting it to the DMM. Refer to the beginning of this lab to review the proper way to connect the DMM using a 2 wire setup. Q7) What errors are introduced because of the way the measurement of the resistance is made? 5. Verify the resistance values of the two 10MΩ resistors with the DMM before connecting them on the patchboard as shown below in Figure 9. 8

C B A 6 V 10 M 10 M Figure 9: Circuit Diagram to Demonstrate Loading 6. Connect the circuit and measure the voltages between A and C, A and B, and B and C. Also, measure the voltage of the battery. Q8) Explain your results. 7. Reset the reset the load of the function generator to 50Ω: a. On the function generator, press the Utility Key. b. Press the Output Setup Menu Operation Softkey. c. Press the Load/High Z Menu Operation Softkey until Load is selected. d. With the number pad, input the value of 50Ω. This is the default setting of the function generator. Now, setup the function generator to output a 1 Volt peak to peak sine wave with a frequency of 1000 Hz. 8. Run the output of the function generator into the oscilloscope and into the circuit below. Function Generator Resistor Figure 10: Circuit Diagram to Demonstrate Loading of Function Generator 9. Vary the resistors and note the peak to peak voltage being read by the oscilloscope. This is done by looking in the Measure Controls region of the oscilloscope and pressing the Measure button. A menu will appear on the screen. Press the Voltage Menu Defined Button. Select Vpp. Resistance 5 MΩ 5 kω 500 Ω 120 Ω Peak to Peak Voltage The problem that is occurring has to do with loading and the function generator. The internal processing of the function generator has to know the load in the circuit in order to supply the accurate output voltage. As demonstrated, if the impedances (load or resistance) are not 9

matched, an erroneous output voltage will be supplied. There are two ways to safeguard against this error. The first is to manually adjust the function generator supplied voltage until the desired output voltage is reached, or to match the impedance of the circuit to the impedance in the function generator. 2. With the circuit wired to the 120 Ω resistor, adjust the peak to peak voltage of the function generator until the oscilloscope reads 1 Volt peak to peak. Q9) What voltage is needed at the function generator to overcome this issue? 3. Match the impedance of the function generator to that of the circuit. a. On the function generator, press the Utility Key. b. Press the Output Setup Menu Operation Softkey. c. Press the Load/High Z Menu Operation Softkey until Load is selected. d. With the number pad, input the value of your resister (120Ω). e. Press the Done Menu Operation Softkey. f. Reset the function generator voltage to 1 Volt peak to peak. Q10) What voltage is the oscilloscope reading? Have you fixed the problem? 4. Reset the function generator to the High Z setting. Triggering: To provide a more stable trace, modern oscilloscopes have a function called the trigger. When using the Trigger Controls, the oscilloscope will pause each time the sweep reaches the extreme right side of the screen. The scope then waits for a specified event before drawing the next trace. The trigger event is usually the input waveform reaching a user-specified threshold voltage. The effect is to resynchronize the time base to the input signal, preventing horizontal drift of the trace. In this way, triggering allows the display of periodic signals such as sine waves and square waves. Trigger circuits also allow the display of non-periodic signals such as single pulses or pulses that don't recur at a fixed rate. 1. Set the function generator so that its output is a 750 Hz sine wave with amplitude of 1.75 Volts peak to peak with zero offset. 10

2. Connect the output connector of the function generator to the channel 1 input connector of the Oscilloscope. 3. Press the Menu Button, a menu will appear on the screen. Press the Sweep Menu Defined Button, until it reads Normal. 4. Set the trigger level to 1 Volt. On the oscilloscope, look at the Trigger Controls region. Twist the Level knob until is reads +0.5Volt. 5. The signal should be as expected. Now, change the trigger level to +2 Volts. Q11) What happened to the signal? Can you explain your results? 6. Return the trigger level to its default setting by pressing the 50% button in the Trigger Controls region. 7. View on the oscilloscope the value of the RMS voltage. This is done by looking in the Measure Controls region of the oscilloscope and pressing the Measure button. A menu will appear on the screen. Press the Voltage Menu Defined Button. Press the Voltage 1/3 Menu Defined Button until Voltage 2/3 appears, and then Select Vrms. 8. Record the RMS Voltage for the sine wave. Now, switch the output of the function generator to a square wave. Q12) What are the RMS Voltages for the sine wave and the square wave? Why are they different? Study of a Second Order System: In this part of the laboratory we will begin to examine the behavior of a second order system; specifically an RLC circuit. Second order systems have a natural frequency, or in other words, exhibit resonance. As a result, the amplitude and phase of the output signals change as the function of the change in the input frequency. Set up the circuit shown below in Figure 11, using the filter patch board, inductor, and a 1 µf capacitor. While no resistor has been added to the circuit, the resistance of the circuit is not zero due to the intrinsic resistance of the inductor and connecting cables. 11

Inductor Function Generator V in L C Capacitor V out Figure 11: RLC Circuit to Study Second Order Systems Set the function generator to produce a 500 Hz sine wave with a 1 Volt peak-to-peak amplitude and connect it to the input of the circuit as well as Channel 1 of the oscilloscope. Connect the circuit output to Channel 2. A Lissajous figure may be used to compare the magnitude and phase of the two signals simultaneously. Set the scope to produce a Lissajous figure comparing the circuit input and output. To view a Lissajous plot press the Main/Delayed button in the Horizontal Controls region of the oscilloscope. Using the Menu Defined Buttons, press the Time Base button until the default Y-T (Channel 1 or 2 versus time) reads X-Y (Channel 1 versus Channel 2). Vary the frequency of the function generator from 5 Hz to 2000 Hz and observe how the Lissajous figure changes. Switch the scope so that two normal time traces (Y-T mode in the Main/Delayed menu) are obtained and again vary the frequency. Can you see the change in phase between the input and output? Also note that the amplitude of the input changes because the input impedance of the RLC circuit is frequency dependent. Q13) At what frequency is the input amplitude a minimum? It can be shown that when the excitation frequency equals the natural frequency of the circuit, the phase angle of the output is 90 relative to the input. Use the Lissajous figure to identify the frequency at which the phase change is equal to 90. Q14) How does this compare to the result in Q13? 12

APPENDIX A Use of a Lissajous Figures for Comparing the Phase of Two Signals As we will discover later in the course, it is often necessary to determine the phase relationship between two signals. Lissajous figures provide an easy and convenient means of doing this with an oscilloscope. Consider the two signals shown in the figure below. They have the same frequency, but differ in amplitude and phase. Note that the peaks in signal B occur later in time than the peaks associated with signal A. Thus, we say that signal B lags behind signal A in phase. If signals A and B drive the electron beam deflection in the x and y directions on an oscilloscope, then at any instant, the position of the beam can be represented as the tip of a vector with x and y coordinates V A and V B. Three interesting, "special", cases occur when the phase lag is 0, 90, and 180 respectively. These are illustrated in the following figure. 1. 0 (Signals are in phase) V B Trace on the screen is a straight line with a positive slope since V A/ V B is a positive constant at any time. V A 2. 90 V B The beam will trace out an ellipse whose major and minor axes lie along the x-and y-axes of the display screen since VA VA sin t and VB VB sin( t / 2) VB cos t 0 0 0 V A 13

3. 180 V B Here V / V sin( t ) sin t V / V. B B0 A A0 A straight line with a negative slope. V A Lissajous figures can also be used to determine when two signals have an integral frequency ratio. Some examples are shown below [1]. [1] Beckwith, Buck, and Marangoni, Mechanical Measurements, Third Edition, Addison-Wesley, 1982. 14