RC Circuit Filter Experiment: Estimating Capacitance & Analyzing Filters, Lab Reports of Mechanical Engineering

Download RC Circuit Filter Experiment: Estimating Capacitance & Analyzing Filters and more Lab Reports Mechanical Engineering in PDF only on Docsity! EXPERIMENT 3A. Filters and LRC Circuits Having prepared for the experiment (including reviewing Experiment 3, preparing LabView Homework, looking up this week’s web page files and attending lecture) you should be able to answer the following questions. 1 (1) How do I estimate C (capacitance) in a RC circuit with an ohmmeter and an oscilloscope. (R is resistance) 2 (2) Sketch a low pass filter and a high pass filter (show measurement points). 3 (3) A vibration transducer measures a sinusoidal signal with a frequency up to 100Hz. Superimposed on this signal is 10KHz noise. What kind of filter do you want to use? 4 (4) What is the equation for the resonance of a series L, C, R circuit? (L is inductance) 5 (5) What is the time constant of a 1 micro-farad capacitor discharging through a 1 mega-ohm resistor? 6 (6) How does the impedance of a capacitor depend on the applied frequency and the value of the capacitor? Objectives 1) To investigate the response of a first order RC circuit (first order because there is only RC pair, second order would have two pairs) to step and sine wave inputs, and to determine the value of an unknown capacitance, C*, from this response. 2) To investigate the use of RC circuits in filtering signals (both high pass and low pass). 3) To investigate the response of a LC circuit. 1 Procedure I. Finding the value of the capacitor. Filtering with Hardware (i.e. capacitors, resistors, it is also possible to filter using software) A capacitor, C*, of unknown capacitance will be provided, and you have to determine its value. 1. Using the resistor color code, determine the value of the resistor you have been given. Record this value and compare it to the measured value you get from the DMM. Motivational question 1a: Compare the resistance value measured with the DMM and from the color code. Is the resistor within tolerance? 1b: Normally would you want to measure resistance while the resistor is in a proto-board (or breadboard)? Explain why or why not in 1-2 sentences. Be sure you know how to use a proto-board (specifically, the one on ELVIS) to measure two resistances in series and in parallel. 2. Use ELVIS to set up the first order RC circuit shown below in Figure 1. (Hopefully you paid attention in class so you know how to decipher the diagram below.) Fig. 1 Experimental setup for an RC circuit 2 Figure 3. RC Circuit: Low-Pass Filter Frequency Response D. Multiply your f-3dB value by 0.1, 0.2, 0.4, 0.6, 0.8, 1, 2, 4, 6, 8, and 10. These are the frequencies at which you are going to take measurements. Do the next steps carefully. If you make a mistake you will have to start over again. Press the single-arrow run button. Enter the first frequency you are going to measure into the Signal Generator. Type this frequency into the “Enter Frequency” box on the vi in Hertz. Check the oscilloscope display to make sure the desired frequency is being generated. Press the “Take Measurement” button. The vi will collect the Vp-p of the output waveform and store it in an array. Repeat for each remaining frequencies (e.g. type in new frequency on both vi and Signal Generator, check Oscilloscope, press Take Measurement, repeat for next frequency). E. When all the data has been collected, press the “Plot it” button. A graph of the data will be displayed (which should be similar to that of Figure 3). Print the window by selecting the “Print Window” or “Print Screen” option under the “File” catalog. Or Right click on the Graph or Chart – select “Export Simplified Image” – Save AS EMF or BMP file – Browse to save on your memory Stick Note: EMF is better as you can “Ungroup” and manipulate it in PowerPoint. Notice that the x-axis is f/f-3dB and the y-axis is 20 log [Vout/Vin ] in decibels. DO NOT PRESS THE “DONE” BUTTON! DO NOT STORE YOUR DATA ON THE HARD DRIVE! Motivational question #4: Using the “Print Window” or “Print Screen” command, print out or save in MS Word / Paint, the pop up graph 5 (from frequency response. vi) showing frequency response of low pass filter circuit. Label axis, make comments about the graph. Remember graphs should be self-explanatory for your report readers. III. Finding the -3dB of the high pass filter. 5. Change positions of the resistor and the capacitor on ELVIS (so now output voltage is across the resistor) to make a high pass filter. Go back to step 4 and repeat. (Find the -3dB frequency; run vi, make plot of frequency response). Motivational question #5a : “Why can’t I, instead of switching the resistor and capacitor, just measure output across the resistor?” Hint, if you don’t know try and see what happens. #5b Print out pop up graph (from frequency response. vi) showing frequency response of high pass filter. Label axis, make comments about graph (voltage across R) particularly in reference to the frequency response with the previous plot (voltage across C); #5c Compare theoretical and experimental (what you found in lab) -3dB frequency for low pass filter. IV. Finding the resonance frequency of a LC circuit through the “Ringing”. 6. Determine the resonance frequency of a series LC circuit. Set up low pass filter arrangement (measuring output voltage across capacitor) but now replace resistor with inductor (inductor is around 4.o mHenries). A. Choose an appropriate input square wave , typically 100Hz at 1V Pk-to-pk, and oscilloscope display setting so the output signal best shows “ringing”. Expand the “ringing” by using your Horizontal Time/Div knob, and then use the Cursor time feature of the Oscilloscope to measure the “ringing” frequency (t1, t2). Motivational question #6: Make a copy, through BenchLink or IntuiLink Data Capture, of the Oscilloscope screen showing square 6 wave “ringing” response and through judicious use of the cursor function, what the “ringing” frequency is. Again make appropriate notes (as usual) on graph. V. Finding resonance frequency of a LC circuit through the pk-to-pk voltage of the output signal. B. Input sinusoidal frequencies. Display input and output (across capacitor) voltages on Oscilloscope. Using a 1-volt peak-to-peak input signal, sweep through frequencies to find where resonance occurs. Make a BenchLink or IntuiLink data Capture plot which best displays input and output voltage, and the frequency at resonance. Make sure both input and output scales for voltage are the same. Motivational question #7: Make a copy, through BenchLink, of the Oscillscope screen showing input and output sinusoidal signals at the resonant frequency. Use time function on Oscilloscope to indicate resonant frequency. At resonance the output voltage will be higher than the input voltage. Have we created energy? If not, where did the extra energy come from? C. Open the Frequency Response.vi program. As before, enter the peak-to- peak voltage of the input waveform in the space labeled “Vin”, but now use the resonant frequency instead of –3dB frequency; therefore input previously determined resonant frequency where it asks for F-3dB . D. Again, multiply resonant frequency by 0.1, 0.2, 0.4, 0.6, 0.8, 1, 2, 4, 6, 8, and 10. Use these frequencies as your input frequencies. Remember to input frequencies into the vi in Hz. Motivational question #8: Using the “Print Window” or “Print Screen” command or Right click on the Graph or Chart – select “Export Simplified Image” – Save AS EMF or BMP file – Browse to save on your memory Stick Note: EMF is better as you can “Ungroup” and manipulate it in PowerPoint, save in MS Word or PowerPoint, the pop up graph (from frequency response. vi) showing frequency response of LC resonant 7