Lab2_Quantifying_Electrical_Energy_Handout

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Dec 6, 2023

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Department of Mechanical Engineering MECH.3020 University of Massachusetts Lowell Laboratory 2 MECH. 3020 P a g e 1 | 6 MECH.3020 Laboratory 2 Quantifying Electrical Energy Introduction Measurement engineering is defined as the proper selection and use of instrumentation systems for the purpose of experimentation, condition monitoring, and process control. One of the main components of an instrumentation system is the transducer. The transducer is an analog device, which is used to convert a change in a mechanical or thermal quantity to an electric signal that can be quantified. The purpose of this experiment is to explore methods used to quantify electrical energy. Alternating Current (AC) and Direct Current (DC) signals will be generated with a function generator and a ±20 volt DC power supply, respectively. A digital multimeter and digital oscilloscope will be used to quantify various signals. The 3dB down point of the multimeter will be determined, indicating that measurement systems have a limited accuracy range depending on the frequency of the signal. The use of analog filters will also be explored as a tool for limiting the effects of signals outside the range of interest. Pre-Lab Assignment Pre-Lab assignments are to be done in your lab notebook following normal lab notebook documentation procedures. The Pre-Labs are not to be handed in but will be checked in the lab to assure that they have been completed. 1. Read chapter 1 and 3 - Wheeler and Ganji textbook 2 nd edition 2. From textbook - Problem 3.1 - An amplifier produces an output of 5 V when the input is 5 μV. What are the gain G and the decibel gain G dB ? 3. From textbook - Problem 3.2 - An amplifier has a gain of 60 dB. If the input voltage is 3mV, what is the output voltage? 4. OPTIONAL – From textbook - Problem 3.13 - The output of a dc generator that produces a maximum voltage of 90 V is to be attenuated to 10 V for input to a filter. Specify values of the resistors in an attenuation network such that the loading error of the voltage at the output terminals of the generator is 0.1%. The output impedance of the generator is 10 Ω and the filter has an input impedance of 100 Ω. 5. A multimeter measures an 8.0 volt 100 Hz sine wave. Determine the peak-peak voltage, peak voltage, and period.

Department of Mechanical Engineering MECH.3020 University of Massachusetts Lowell Laboratory 2 MECH. 3020 P a g e 2 | 6 Assignment 1: Initialize the oscilloscope Tektronix TBS1032B The initialization of the oscilloscope is required to set the instrument to a point from which all measurements can be referenced. The following procedure should be used when the oscilloscope is used to quantify signals generated from transducers. Procedure 1. Turn the oscilloscope on. The power button is located on the top left side of the oscilloscope. 2. A previous configuration may be loaded. Load its default setup by pressing the “Default Setup” button. The message “Default setup recalled” will appear in the message bar. This bar is located at the bottom of the display. 3. The oscilloscope automatically applies to all signals an amplification factor of 10. This factor has to be changed to 1. Within the Vertical System Control area, push the yellow button “1” to bring the CH 1 setup menu up. Press the “Probe 10X Voltage” button. Then, press the “Attenuation 10X” button and by using the “Multipurpose” knob, change the attenuation fact or to “1X”. 4. Set the Vertical Scale to 5Volts/DIV 5. Set the Horizontal Scale to 5ms. The oscilloscope is now set to quantify electric signals. This initialization process should be employed whenever the oscilloscope is used to quantify the output from a transducer. Assignment 2: Quantifying Sinusoidal Waveforms A digital multimeter can be used to measure current, resistance, and the voltage of a signal. When an AC signal is recorded, the multimeter displays the root mean square (V rms ) value which can be used to obtain the peak (V p ), and peak-peak (V pp ) values of the wave. The oscilloscope is capable of measuring voltage only. However, unlike the multimeter, the oscilloscope displays the signal on a TFT-display allowing the period (T) and frequency (f) of the signal to be calculated. Procedure 1. Figure 1 shows the proper equipment configuration. The output of the function generator will be the input to the oscilloscope and multimeter. Connect the function generator to the oscilloscope’s CH. 1 . Function Generator Multimeter Oscilloscope CH. 1 Figure 1. Block diagram for Assignment 2

Department of Mechanical Engineering MECH.3020 University of Massachusetts Lowell Laboratory 2 MECH. 3020 P a g e 3 | 6 2. Turn the function generator on. Set the function generator to output a 100 Hz sinewave at a maximum amplitude. IMPORTANT: Whenever you generate a new signal, use the multimeter and oscilloscope to check the magnitude and frequency of your waveform. Note that the multimeter outputs RMS voltage for an AC signal. 3. Set the oscilloscope channel 1 COUPLING to AC . Press the yellow button ‘1’. Go to ‘Coupling DC’ menu and use the ‘Multipurpose’ knob to select ‘AC’. Adjust the Vertical and Horizontal Scale knobs to have at least one complete cycle. 4. Observe the signal with the digital multimeter and oscilloscope. Record the V pp , V p , V rms , and period of the signal. 5. Adjust the amplitude on the function generator to output a 5.0 V rms , 100 Hz. sinewave. Record the V pp , V p , V rms , and period. 6. Set the function generator output frequency to 10,000 Hz. Record the V pp , V p , V rms , and period. Assignment 3: Two Channel Analysis In Assignment 2, the digital multimeter was used to quantify the amplitude of an AC signal. In order to quantify a DC signal, the multimeter AC/DC switch must be set to DC. The oscilloscope is capable of measuring two signals simultaneously. Each signal can be comprised of an AC and DC component. If only the AC component of the signal is to be monitored, the oscilloscope should be set to AC coupling. If both the AC and DC components of the signal are desired, the oscilloscope should be set to DC coupling. The objective of this assignment is to introduce two channel analysis using the oscilloscope and examine the effects of AC/DC coupling. Procedure IMPORTANT: Whenever you generate a new signal, use the multimeter and oscilloscope to check the magnitude and frequency of your waveform. You may need to disconnect your cables from the oscilloscope in order to use the multimeter. 1. Figure 2 shows the proper equipment configuration. Adjust the cabling according to the new block diagram given below. The output from the function generator should remain connected to CH. 1 of the oscilloscope. At this time, connect the output from the power supply to CH. 2 of the oscilloscope. 2. Turn on CH. 2 by pressing the blue button ‘2’ if this is off . This will allow channels 1 and 2 to be viewed simultaneously.

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Department of Mechanical Engineering MECH.3020 University of Massachusetts Lowell Laboratory 2 MECH. 3020 P a g e 4 | 6 DC Power Supply Multimeter Function Generator CH. 1 CH. 2 Oscilloscope Figure 2. Block diagram for Assignment 3 3. Set the output of the function generator to 5 V rms at 1000 Hz. 4. Adjust the Vertical Scale of CH. 2 to 5 Volts/DIV . 5. Set the oscilloscope channel 2 COUPLING to DC . Press the blue button ‘2’. Go to ‘Coupling DC’ menu and use the ‘Multipurpose’ knob to select ‘DC’ if it was not selected before. 6. Adjust the output voltage from the power supply to 10 Volts. 7. Record the V pp , V p , V rms and periods associated with channels 1 and 2. 8. Set the oscilloscope channel 2 COUPLING to AC . Where did your DC signal go? Change the coupling back to DC .

Department of Mechanical Engineering MECH.3020 University of Massachusetts Lowell Laboratory 2 MECH. 3020 P a g e 5 | 6 Assignment 4: Digital Multimeter Upper Usable Frequency Range The multimeter can be used to measure the RMS voltage of an AC signal, but it has an upper usable frequency called the 3dB down point. The 3 dB down point is defined as the frequency at which the measured voltage (V o ) drops to 1/2 0.5 of the actual input voltage (V i ). The 3 dB down point will be determined by generating a sinusoidal wave at a constant amplitude with the function generator. The amplitude of the signal will be recorded with the multimeter and oscilloscope at various frequencies. The 3dB down point can then be determined by plotting the ratio of the measured voltage (V o ) to the input voltage (V i ) in dB versus log frequency. The frequency at which the ratio drops by 3 dB is the 3dB down point (also called the cutoff frequency). in out 10 10 dB V V log 20 G log 20 G = = Procedure 1. Equipment configuration will be identical to Assignment 2 (refer to Figure 1). 2. Set the output from the function generator to 5 volts peak at 100 Hz. Make sure the AC coupling for CH. 1 has been selected. 3. Vary the output frequency from 100 Hz. to approximately 1 MHz in 10 to 15 steps. At each frequency setting, record the voltage on the oscilloscope (V i ) and on the digital multimeter (V o ). 4. Plot the dB value versus frequency (logarithmic scale for x-axis). Determine where the multimeter begins to become inaccurate. Increase the resolution of the measurement as needed. Assignment 5: Analog Filter Effects on Signals of Various Frequencies An analog filter can be used to limit the effects of signals outside the range of interest by limiting the amplitude of these unwanted signals. Different filters have different pass, transition, and stop-band characteristics. The characteristics of the 4-pole Butterworth filter will be explored. Procedure 1. Equipment configuration will be the same as in Assignment 4 except that the filter must be wired in series between the function generator and multimeter. 2. Turn on the filter and make sure “channel” is set to 1. Type in 2000 and press “freq.” The screen under “cutoff frequency” should read 2.000 and the “freq” and “kilo” buttons should be lit. (Note: 2 kHz was set as the cutoff frequency for the filter because it is known from assignment #4 that the 3 dB down point of the multimeter is much higher than 2 kHz. This will limit the effects of the roll-off in the measurements caused by the multimeter.)

Department of Mechanical Engineering MECH.3020 University of Massachusetts Lowell Laboratory 2 MECH. 3020 P a g e 6 | 6 3. Vary the output frequency from 100 Hz. to approximately 5 kHz. in 10 to 15 steps (should still be a 5 volt peak sinusoid). At each frequency setting, record the voltage on the oscilloscope (V i ) and on the digital multimeter (V o ). 4. Plot the dB value versus frequency (logarithmic scale for x-axis). Increase the resolution of the measurement as needed. This plot is representative of the characteristics of the filter used. Post-Lab Analysis NOTE: Be brief, concise and to the point in all responses. Provide clear, concise answers to questions. Lengthy responses that ramble will not be graded and may lose additional points. Q1. Tabulate the quantities measured in Assignments 2 and 3. Compare the quantities measured by both the oscilloscope and multimeter. (15 pt.) Q2. What is the primary difference between the oscilloscope and digital multimeter? (10 pt.) Q3. Explain the difference between AC and DC coupling. (10 pt.) Q4. What purpose does the function generator serve? (10 pt.) Q5. What is the 3 dB down point of the Fluke multimeter based on the measurements? (15 pt.) Q6. Make a proper engineering plot of the V o /V i in dB vs. frequency from Assignment 4. Use logarithmic scale for x-axis. (15 pt.) Q7. Make a proper engineering plot the V o /V i in dB vs. frequency from Assignment 5. Use logarithmic scale for x-axis. (15 pt.) Q8. Two sinusoidal signals are known to exist within a given signal, a 5 V rms 100 Hz signal and a 2 V rms 3 kHz signal, but only the 100 Hz signal is of interest. If the analog filter from Assignment 5 is used with the same 2 kHz cutoff frequency, what will be the amplitude of both portions of the signal in voltage after filtering? (Hint: Use the plot from Question 7) Are the effects of the 3 kHz signal ever completely removed? (10 pt.)

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