ECE 205 Miami University Lab 6 Thevenin Equivalent Circuits Lab Report

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ECE 205

Miami University

ECE

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Thevenin Equivalent Circuits

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Thevenin_Instructions_1circuit_TC.pdf

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A lab report created using the template below. You must download the template, open it, rename as in previous labs, and complete the report using the template. Do not create your own MS Word document.
Thevenin_Report_1circuit_TC.docx

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Thevenin Equivalent Circuits Introduction According to Thevenin's theorem, any linear two-terminal circuit is equivalent to a voltage source in series with a resistor. This is illustrated in Figure 1. Thevenin's theorem allows a very complicated circuit to be replaced by a simple Thevenin equivalent circuit, and this makes it a very powerful tool. When a load is connected to terminals a-b, the Thevenin equivalent circuit will produce the same current, 𝐼𝐼, and voltage, 𝑉𝑉𝑎𝑎𝑎𝑎 , as the original circuit. Therefore, once 𝑉𝑉Th and 𝑅𝑅Th have been determined, it is easy to determine the current and voltage responses of a linear circuit when connected to various loads. In class, you learned how to find 𝑉𝑉Th and 𝑅𝑅Th using circuit analysis techniques. In this lab, you will learn how to measure 𝑉𝑉Th and 𝑅𝑅Th . RTh I a a ó Linear circuit I VTh b b Figure 1: A linear circuit and its Thevenin's equivalent. Required Lab Work In this lab, you will build a circuit and take measurements to determine the Thevenin equivalent of a given circuit, including multiple methods for measuring the Thevenin resistance. Suggestion: Before the lab time, use the methods introduced in lecture to calculate the Thevenin voltage and resistance. Then, during lab, you can check your results, identify errors, and make any necessary corrections. Important Reminder (if doing lab in-person): Always keep the power supply off when building or modifying circuits. When the circuit construction is complete, watch the overload lights on the power supply as you turn it on. If any are lit, turn the power supply off immediately, and correct the circuit before turning it back on. 1. Build the circuit shown below. Use 𝑅𝑅1 ≈ 750Ω, 𝑅𝑅2 ≈ 750Ω, 𝑅𝑅3 ≈ 1kΩ, and 𝑅𝑅4 ≈ 2kΩ. The goal is to find the Thevenin equivalent circuit at terminals a-b. R2 R1 a 5V R3 b R4 2. Find the Thevenin voltage, 𝑉𝑉Th, by using a digital multimeter (DMM) to measure the open-circuit voltage at terminals a-b. 3. Find 𝑅𝑅Th using three different methods as described below. Important: Each method is independent of the other, so after completing one method, go back to the original circuit above before starting the next method. i. ii. iii. Turn off the voltage source (in this context, “turn off” means disconnect the power supply and replace it by a wire), and use the DMM to measure 𝑅𝑅Th . Connect a potentiometer between terminals a-b. Adjust the resistance until the 𝑉𝑉 voltage across it is 2Th . At this point, the value of the potentiometer is equal to 𝑅𝑅Th . (Can you explain why?) Disconnect the potentiometer and use a DMM to measure its resistance. Use the DMM to measure the short circuit current, 𝐼𝐼N , from node a to node b. 𝐼𝐼N 𝑉𝑉 is also called the Norton current. Compute 𝑅𝑅Th using the formula 𝑅𝑅Th = 𝐼𝐼Th . N (Note: Ammeters have very low resistance. For this lab, you can assume the ammeter has zero resistance and thus functions as a short circuit.) 4. Restore the circuit back to its original form in the circuit diagram above. Consider connecting a load resistor with value 𝑅𝑅L ≈ 2kΩ. Use the measured Thevenin equivalent circuit values determined in steps 2 and 3 (use 𝑅𝑅Th from method i) to predict the voltage drop across 𝑅𝑅L when connected between terminals a-b. Next, connect the load resistor between terminals a-b, and measure the voltage across it. Does it agree with your prediction? If not, check your work and make any necessary corrections. ECE 205 Lab Report Thevenin Equivalent Circuits Your name: Click or tap here to enter text. Resistor values 𝑅1 = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. 𝑅2 = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. 𝑅3 = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. 𝑅4 = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. Thevenin Voltage Measured value of Thevenin voltage: 𝑉Th = 𝑉𝑎𝑏 = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. Screen capture of circuit showing the measurement of the Thevenin voltage. See Canvas for screen capture and circuit wiring requirements. Thevenin Resistance (Method 1) Measured value of Thevenin Resistance: 𝑅Th1 = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. Screen capture of circuit showing the measurement of the Thevenin resistance. See Canvas for screen capture and circuit wiring requirements. Thevenin Resistance (Method 2) Measured value of Thevenin resistance: 𝑅Th2 = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. Screen capture of circuit showing the measurement of the voltage across the variable resistance. See Canvas for screen capture and circuit wiring requirements. 1 ECE 205 Lab Report Thevenin Equivalent Circuits Thevenin Resistance (Method 3) Measured value of Norton current: 𝐼N = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. Thevenin resistance (calculated from measured 𝑉Th and 𝐼N ): 𝑅Th2 = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. Screen capture of circuit showing the measurement of the Norton current. See Canvas for screen capture and circuit wiring requirements. Load Resistor Measured value of load resistor: 𝑅L = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. Predicted value of voltage drop across load resistor based on measured Thevenin voltage and resistance (method 1). Hint: Use voltage division. 𝑉L = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. Measured value of voltage drop across load resistor: 𝑉L = 𝐂𝐥𝐢𝐜𝐤 𝐨𝐫 𝐭𝐚𝐩 𝐡𝐞𝐫𝐞 𝐭𝐨 𝐞𝐧𝐭𝐞𝐫 𝐭𝐞𝐱𝐭. Screen capture of circuit showing the measurement of the voltage across the load resistor. See Canvas for screen capture and circuit wiring requirements. 2 Download Start Free Trial from https://www.ni.com/en- us/shop/electronic-test-instrumentation/application-software-for- electronic-test-and-instrumentation-category/what-is- multisim/multisim-education.html Thevenin Equivalent Circuits Lab Instructions Thevenin Instructions 1circuit TC.pdf ! Deliverables A lab report created using the template below. You must download the template, open it, rename as in previous labs, and complete the report using the template. Do not create your own MS Word document. Thevenin Report 1circuit TC.docx or
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ECE 205 Lab Report
Thevenin Equivalent Circuits

Your name: Click or tap here to enter text.

Resistor values
𝑅1 = 𝟕𝟓𝟎 𝐨𝐡𝐦
𝑅2 = 𝟕𝟓𝟎 𝒐𝒉𝒎
𝑅3 = 𝟏 𝐤𝐨𝐡𝐦
𝑅4 = 2 kohm

Thevenin Voltage
Measured value of Thevenin voltage: 𝑉Th = 𝑉𝑎𝑏 = 𝟕𝟕𝟗. 𝟐𝟐 𝐦𝐕
Screen capture of circu...

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