Lab_2

docx

School

Virginia Tech *

*We aren’t endorsed by this school

Course

2024

Subject

Electrical Engineering

Date

Dec 6, 2023

Type

docx

Pages

8

Report

Uploaded by BailiffFire12246

ECE 2024 Lab 2: RLC filter design and analysis NOTE: Your name is required! By putting your name on this worksheet, you certify that what is presented is entirely your own work. The Virginia Tech Honor Code will be strictly enforced. You are allowed to discuss steps and procedures with other classmates, but you are not allowed to discuss specific answers. If you get stuck, do not wait for help! Jump on Piazza to get answers to your questions, and learn more in a less-frustrating way while you are at it. Frustration is counterproductive, and we are here to help. The purpose of this lab is to learn about impedance analyzers, AC frequency sweeps, and how to use your knowledge of circuits to design an RLC filter. Plenty of directions are given and you must read them carefully to save yourself time. Follow the steps in order, and have fun with your first circuits lab! There are four parts to this lab: A. Design calculations B. Simulate the circuit C. Using the AD2 impedance analyzer D. Build and test the circuit Page 1 of 7 Name:
Required Materials: Your breadboard Your AD2 oscilloscope with the USB cable, and your laptop 10mH inductor Film or ceramic capacitor(s) as needed Resistors as needed General tips to help you succeed: a. There are no expected “exact” answers. i. We don’t expect everyone to have lab-grade precision in these experiments. Remember, the components you use have tolerances and are not perfect. If you get a reading that you think is wrong, please talk to the GTA, ULAs, or your professor. b. Record the most stable reading you see on your digital multimeter (DMM): c. Carefully wire up your breadboard circuit. Ensuring it is correct as you go will save you a lot of time and frustration. d. If you need help, post a question on Piazza or see a TA, ULA, or your professor at office hours. Office hours are posted on the Canvas homepage. e. Remember how to connect your power supply to a circuit and how to measure current through a resistor. Observe the following diagram. For measuring current, you need to BREAK the circuit in order to measure in series (series elements have the same current). Page 2 of 7
A. Design calculations See the circuit shown below for a band-pass filter (BPF). This is a parallel resonant RLC circuit. Refer to section 6-7 in your text book for parallel resonance. We want to design the center frequency f o of the BPF to be around 5kHz. Also, we want to observe the change of its gain when the input frequency changes. Finally, we want to use an AD2 impedance analyzer to measure its impedance. 1. We want to limit the peak current of the AD2 to around 10 or 11 mA, so as to not create a strain on the unit for all frequencies, or our laptop’s USB supply/battery. What resistor R1 value do you choose from your part kit to ensure this with a 5 V source? Show your calculation. _________ Ohms 2. From the diagram above, derive the circuit transfer function H ( ω ) = V o V i to be in the form of N ( ) D ( ) = H ( ) . The transfer function should look like ( ) N 0 ( ) 2 D 0 + ( ) D 1 + D 2 . N 0 ,D 0 , D 1 and D 2 are coefficients to be found. Show your derivation. (Hint: Let Z 1 = R 1 and Z 2 = L 1 ¿ C 1 . Use Z 2 = [ 1 jωL + jωC ] 1 to start. H ( ω ) = V o V i = N ( ) D ( ) = Z 2 Z 1 + Z 2 . ) 3. Convert H ( ) found in step 2 to its polar form. That is to find | H ( ω ) | and H ( ω ) . Show your derivation. 4. Obtain a 1mH inductor from your kit and use your DMM to measure the resistance across the inductor from your kit. Record its resistance. This is the winding resistance inside your inductor as R2 shown below. Calculate the inductor Q s (Quality factor) at 5kHz and record it below. Q s :_______ Page 3 of 7
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
5. If Q s is greater than 10, the resonant frequency will not change much if we still use X L = X C to find the resonant frequency. Find the capacitor value C from the resonant frequency f o (5kHz). C:________ Farads 6. From step 2, we can find the Q of the circuit from D ( ) . D ( ) = ( ) 2 + ( ) ( ω o Q ) + ω o 2 . Use this expression and substitute component values to calculate the qualify factor Q of the circuit. Alternately, we can calculate Q by converting R1 to a resistor connected in parallel with the inductor and the capacitor, and use R ω o L or ω o RC to calculate the Q of the circuit. Compare both calculations. Show your calculations and results below. Calculate the bandwidth (BW) of the filter with ( f o Q ) . Refer to section 6-7 in your text book for bandwidth discussion. Show your calculation. Q (calculated from transfer function): ___ Q (calculated from R ω o L or ω o RC ): ___ Show your calculations. BW :________ Hertz Page 4 of 7
7. Calculate the impedance of the circuit at resonance. To precisely calculate the impedance, the winding resistor should be converted to a resistor in parallel. That is to convert the series L1 and R2 in the diagram above to a parallel L2 and a R3 shown below. (Formula: L p = L s [ 1 + 1 Q 2 ] , R p = R s [ Q 2 + 1 ] ) See figure 1 in this reference or (7-79) in this reference . Since the L s becomes L p , their resonant frequency will change slightly, calculate the new resonant frequency based on L p . Maximum impedance: _______Ω at (frequency)______Hz New resonant frequency based on L p ______Hz Show your calculations. B. Simulate the circuit in LTspice 8. Model your circuit as the diagram shown in step 4 with LTspice. Do a small-signal analysis (an AC Analysis) with its input set at 1 0 0 and measure the output with the following settings. Select “Type of sweep” in Decade. Enter “Number of points per decade” to 1000, Enter “Start frequency” to 500 and “Stop frequency” to 50k. Screenshot your circuit and simulation result below. This plot is the frequency response of the circuit. 9. On the same plot, attach a cursor to be placed at the peak voltage of the frequency response and use “Label Curs. Pos.” under “Notes & Annotations” in the pull-down menu of the “Plot Settings” to place a label for the present cursor position. Move the cursor to the left side of the peak and find a Mag where it’s 3dB lower than the peak then place another cursor label. Do the same thing by moving the cursor to the right side of the peak then place the 3 rd cursor label. Write their measurement below. Screenshot your simulation with cursor labeled below. Peak ( f o ¿ : _______dB at (frequency) _______ Hertz Page 5 of 7
Corner freq , < f o ( f L ¿ : _______dB at (frequency) _______ Hertz Corner freq , > f o ( f H ¿ : _______dB at (frequency) _______ Hertz 10.Compare the frequency at peak in step 9 to the desired f o ( 5 kHz ) frequency. Also compare to the new resonant frequency calculated in step 7. Are they the same? Is the simulated result closer to the desired f o or closer to the new resonant frequency? Comment on your observation. Also, find the bandwidth from step 9 and compare it to the BW as found in step 6. (Note. The winding resistance calculated was neglected in step 6.) Comment on if neglecting the winding resistance is appropriate. Show your calculation. 11.Continue from the simulation in step 8. Change the voltage source to an AC input with 1V, 3000Hz and do a transient analysis . (Set the input to “SINE”, and “Amplitude” set to 1, “Frequency” set to 3k and “Ncycles” set to 5 then set simulate to 1ms.) Use cursors to measure two maximum values between input and output. Find their angle difference between input and output with the formula ( θ = Δt T × 360 o ¿ , and calculate the amplitude gain in dB . Screenshot your measurement by labeling the cursor positions and paste it below. Show your calculation. Gain at 3kHz: _______dB Phase angle at 3kHz: ________ degrees Show your calculations. 12.Compare your measurement in step 11 and calculation to the | H ( ω ) | and H ( ω ) found in step 3 by letting ω = 2 π × 3000 and substituting the actual component values to step 3. Comment on your comparison and explain why if they are different. 20log | H ( ω ) | from step 3 at ω=6000π : ________ dB H ( ω ) from step 3 at ω=6000π : ________ degrees Show your calculations. 13.View the circuit as a one-port network and find its impedance by sweeping an ac small signal from 1k to 50kHz. The method is to go back to step 8 and plot the source voltage. Then, right click on the title of the plot of the source voltage and enter an expression to divide the source voltage by the circuit current to obtain impedance. The circuit current Page 6 of 7
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
can use the same current through the series resistor R1 which is I(R1). Compare the maximum impedance to the impedance found in step 7 to see if they are the same. Comment on your result. Also, record the impedance at 2kHz for later use, including its phase angle. Maximum impedance: _______Ω at (frequency)______Hz Impedance: _______Ω at 2kHz 14. Measure the current I c 1 through C1 at resonance by right clicking on the vertical scale on the left of the plot and change it to “linear” representation. Also, measure the circuit current through R1 at a frequency that is ( 1 5 ) of the resonant frequency. Check to see if I c 1 is Q times larger than I R 1 . Refer to page 21 in this reference . Comment on your measurement and paste your measurement below. C. Build and test your circuit with AD2 15.Build the circuit as shown in step 4 on your breadboard. The R2 in step 4 is the winding resistance inherent to the 1mH inductor. Combine two or three capacitors to make the actual capacitor value closer to the desired value. Use your DMM to verify the capacitor value. Take a picture with your DMM to show your verification and paste it below. Set up the network analyzer in your AD2 by connecting Wavegen (yellow) and Scope ch1 (Orange) to the input and connecting Scope ch2 (Blue) to the output. Connect ground (Black), ch1 negative (Orange/White) and ch2 negative (Blue/White) together. Sweep a sinusoidal voltage 1V from 500Hz to 50kHz and record its frequency response. Find the maximum output in dB and record the center frequency f o . Screenshot your measurement below. Compare it to the peak voltage in simulation found in step 9. Are they the same? If not, how much difference? Why? Comment on your measurement. Peak voltage: _______V, At f o :________ Hertz 16.Continue from step 15. Measure the output at 3kHz and its phase angle. Record their values below. Change the AD2 setup to generate a 3kHz, 1V sinusoidal signal with Wavegen and measure it with the Scope ch1 and ch2 in time domain. Find the phase angle between peaks or between zero-crossings by using formula ( θ = Δt T × 360 o ¿ . Calculate the output gain in dB. Record your measurement below. Screenshot your measurement. Compare it to step 12 and comment on your result. From frequency response: Voltage gain: ______dB at 3kHz Phase angle: ________ degrees Page 7 of 7
From time-domain output: Voltage gain: ____ at 3kHz, or ________dB Phase angle: ________ degrees Comment on your result. 17.Use the AD2 as an impedance analyzer to measure the impedance of the BPF from 1KHz to 50kHz. See the “help” in the “Waveform” program to learn how to use the impedance analyzer. Obtain a 1kΩ resistor from your kit and place it on the left side of the R1. (R1, L1 and C1 in the first diagram of the lab are the DUT below). DUT means Device Under Test. The “Resistor” below in the diagram is the abovementioned 1kΩ. Connect the Wavegen (yellow) and Scope ch1 (Orange) to the left side of the 1kΩ and Scope ch2 (Blue) to the right side of the 1kΩ resistor. Connect ground (Black), ch1 negative (Orange/White) and ch2 negative (Blue/White) together. Run the analyzer and find the impedance at 2kHz including its phase angle. Also, find the maximum impedance. At what frequency the maximum impedance occurs? Is it the resonant frequency f o ? Is the measured resonant frequency closer to the new resonant frequency found in step 7? What is the phase angle at resonant frequency? Compare to the simulation in step 13 and step 7. Screenshot your measurement and comment on your result. Impedance: ______Ω at 2kHz Phase angle: ________ degrees maximum impedance:_________ Ω At frequency________ Hertz Phase angle at resonant frequency___ degrees Comment on your observation. Screenshot your measurement 18. Take a picture of you circuit and AD2 connection. Paste it below. Page 8 of 7