Lab_2

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Virginia Tech *

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2024

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Electrical Engineering

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Dec 6, 2023

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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 ( jω ) D ( jω ) = H ( jω ) . The transfer function should look like ( jω ) N 0 ( jω ) 2 D 0 + ( jω ) 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 ( jω ) D ( jω ) = Z 2 Z 1 + Z 2 . ) 3. Convert H ( jω ) 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

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