Lab 7 Resonant Circuits and Filters-1

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ECE 2200/2210 Lab 7: Resonant Circuits & Filters Possible Points: 126 Lab Equipment List:  Resistors (390Ω, 1kΩ, and 2kΩ)  Capacitor (0.1 μF (104) & 0.001 uF (marked 102))  Inductor (2 to 4 mH. 3.3 mH (marked 332) should work)  Function generator  Oscilloscope  Function generator  LCR meter Partnering:  Everyone must create their own lab report (fill out this document).  Groups are allowed to be maximum of 2 except in a class of odd numbers; in that case one group will be allowed to be 3. A group may use the same measurement equipment.  Discussions are encouraged, and you are also encouraged to answer each other’s questions!  Seek out the TA if you get stuck or need help. Lab Procedures: Welcome to Lab 7! In this lab we will construct two RLC circuits to observe their frequency response, specifically their resonant frequency response. Also, we’ll work with filters and plot their frequency response curves. Part 1: Series RLC Circuit Measurements (35pts) Fig. 1 1 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

ECE 2200/2210 1. This circuit has a resonant frequency due to the two energy storage circuit elements (capacitor and inductor). Compute the expected resonant frequency ( f o in Hz or kHz) of your capacitor and inductor combination (2pts) : f o = 1 2 π √ LC <28.9kHz > 2. At the resonant frequency, the inductor voltage is equal and opposite to the capacitor voltage (the inductor voltage is 180 degrees out of phase with the capacitor voltage). As a result, the capacitor and inductor together act like a _short___ circuit, and the total voltage across the capacitor + inductor is: _0___ volts. If needed, check your lecture notes from class. (3pts) 3. Now construct the circuit shown in Fig. 1. Use the function generator for the voltage source. 4. Set up the oscilloscope probe to measure the capacitor voltage (place the probe between the inductor and the capacitor). 5. Set up the function generator to output at the expected resonant frequency, and vary the frequency while looking at the capacitor voltage on the oscilloscope. Find the actual resonant frequency, which will be the frequency where you observe the largest peak-to- peak voltage. a) Record the actual resonant frequency shown on the function generator. b)Take a picture or two showing your work (circuit on breadboard, oscilloscope/function generator set up). (10pts) <a. resonance frequency : 27.2KHz> <b. attach your picture/s below > 2 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

ECE 2200/2210 6. How does your calculated resonant frequency compare to the actual resonance frequency of the circuit? (2pts) <the calculated resonance frequency is bit higher than the actual frequency > 7. What is the capacitor voltage at the observed resonant frequency? (2pts) <800mV > 8. Now move your probe to measure the voltage coming out of the function generator (place the probe between the generator and the resistor). You should notice that the voltage coming out of the function generator is about 4.5 times smaller than the capacitor voltage you just observed. 9. What is occurring in the circuit that allows the voltage across the capacitor to be this high? Let’s investigate this through a series of steps: a. Calculate the current flowing through the circuit at resonance when the inductor and capacitor together look like a short circuit, i.e. Calculate I peak = V source peak R 1 . (3pts) <0.23mA> 3 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

ECE 2200/2210 b. Use the current from (a) to calculate the magnitude of the voltage across only the inductor at resonance, i.e. Calculate | V L, peak ( ω o ) | = | I peak Z L | . Remember: Z L ( ω )= jωL and ω o = 1 √ LC . (3pts) <1.26jV> c. Use the current from (a) to calculate the magnitude of the voltage across only the capacitor, i.e. Calculate | V C ,peak ( ω o ) | = | I peak Z C | . Remember: Z C ( ω ) = 1 jωC . Also remember that at resonance the inductor and capacitor voltage are 180 degrees out of phase with each other (so their voltages should be equal and opposite). (3pts) <-1.26jV > d. Describe your results and how this leads to the high value for the measured capacitor voltage. (2pts) <The resistor has a low voltage drop across it and the inductor and capacitor compensate for the rest and have equal and opposite values which makes sense.> 10. To see the full frequency response (gain / transfer function) of the circuit, we should record the peak-to-peak voltages at a variety of frequencies. The gain is obtained by dividing the output voltage by the input voltage (v out /v in ). Make a sketch of the frequency response, take values at f o 2 , f o 4 , f o 8 , 2 f o , 4 f o , and 8 f o . Feel free to do this by hand or use any software you like(MATLAB, Microsoft excel, etc.). You should get a plot similar to that shown in Fig. 2 below. (5pts) 4 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

ECE 2200/2210 Fig. 2 Frequency response of an RLC circuit. <add a photo of your plot below> 5 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

ECE 2200/2210 Part 2: Series RLC Circuit Simulations (9pts) 1. Let’s obtain the complete frequency response of the circuit shown in Fig. 1. Open the LTSpice file Lab7_RLC_Resonance.asc. You will notice that the simulation command for this circuit is AC. If you open up the dialog for this, you will see that we are asking for a plot from 10 kHz to 1 MHz. “Decade” here means that the x-axis of the plot will be log base 10, i.e. one decade represents one multiple of 10 (such as the difference between 10 kHz and 100 kHz). 2. Run the simulation and obtain the voltage across the capacitor. You will notice that two plots are generated. On the left, the magnitude is shown in dB (decibels), which is a logarithmic scale. On the right, the phase is displayed in degrees, measuring how far off the wave is from the input wave. 3. We won’t be using the phase plot, so you can get rid of it by right clicking the right axis and clicking the “don't plot phase” button. 4. Let’s confirm that the Spice simulation is yielding the same results as your measurement. Change the magnitude plot from dB to gain(v out /v in ) by right clicking on the left axis and selecting a linear representation. The plot is now in terms of gain, and should look remarkably similar to what you generated above. Compare your plots. Does the simulated plot agree with what was measured? (3pts) <yes it does ! > 5. Now generate voltage gain plots for the voltage across the inductor (make sure to drag your cursor over the inductor rather than just clicking above it). What is different about this plot? What does it tell us about the frequency response of inductors vs. capacitors? (2pts) <the peak voltage for both the inductor and capacitor is at the resonance frequency we calculated which is 28.9KHz> 6. Look at the plots of the current through the circuit and comment on how this circuit obeys Kirchhoff's Current Law. (2pts) <the circuit obeys current in = current out> 7. Look at the plots of the voltage over the resistor and from above the inductor to ground (over both components). With what we know about the behavior of the capacitor and inductor, how does this circuit obey Kirchhoff's Voltage Law at any given moment? (2pts) <the voltage gained = to the voltage dropped > 6 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

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