EE242 Report 1 (1)

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California Polytechnic State University, San Luis Obispo *

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242

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Electrical Engineering

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Apr 3, 2024

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Professor: David McDonald EE 242 Section 05 12:10 pm- 3:00 pm Experiment # 1 Phasor Diagram and Power Measurements Group 8 Written By: Kush Patel, Jesus Galindo

Purpose: The purpose of this lab is to measure voltage in a series circuit where individual components can not be specifically measured, as current is being used as the reference in the circuit. This is useful when measuring the individual voltages within a circuit load. Using the Geogebra software, a phasor diagram can be constructed with the measured voltages, capacitance, and inductance to find the voltage of the individual components of the circuit load. These values can then be used to find the load resistance, load inductance, and reactive power of the circuit. Equipment: 1 Agilent 33120A Function Generator 1 Agilent 34401A Multimeter 1 Inductor Decade Box (8H) 2 Resistor Decade Box) 1 Capacitor Decade Box 1 BNC-Banana 2 Banana-Banana 1 Bag of short leads GeoGebra https://www.geogebra.org/download

Figure 1: Series RLC as a Circuit Part 1: Steps: 1. Assemble the circuit of Figure 5 without the capacitor (R-L circuit only). - Built: Jesus Galindo - Verified: Kush Patel - Worked the first time: Yes 2. Set the function generator for HIGH IMPEDANCE (Shift, Enter Enter) ˃˃˃˅˅˃ and set V S to a 1000 Hz. sinusoidal source. 3. Using digital voltmeter across the 25 k resistor, set the rms of V S to yield a convenient value of V R (such as 2.0 Vrms). 4. At your chosen value of V R , measure and record the values of V S and V A . - V R = 2.001 V - V S = 6.578 V - V A = 5.044 V

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5. Construct an accurate full-page phasor diagram (Figure 2). Figure 2: Series RL Phasor Diagram Calculations: Φ = 33.94° Θ = 46.73° V L = 3.67 V V RL + 20K = 3.46 V |I| = |V R | / R = 2.001 / 25000 = 0.08 mA V 20K = 0.08 * 10^-3 * 20000 = 1.6 V V RL = V RL + 20K - V 20K = 3.46 V - 1.6 V = 1.86 V R L = |V RL | / |I| = 1.86 / (0.08 * 10^-3) = 23250 Ω X L = |V L | / |I| = 3.67 /( 0.08 * 10^-3) = 45875 Ω L = X L / 2πf = 45875 / 2π(1000) = 7.301 H Q L (quality factor) = X L / R L = 45875 / 23250 = 1.973 Pf = cos(Φ) = cos(33.94°) = 0.830 P 25kΩ = V R ^ 2 / R = (2.001^2) / 25000 = .16 mW

P 20kΩ = V 20K ^ 2 / R = (1.6^2) / 20000 = .128 mW Q(reactive power) = V L ^ 2 / X L = 3.67 ^ 2 / 45875 = .294 mW S S ( complex ) = VI cosΦ + j VI sinΦ = (6.578)(0.08 * 10^-3) cos(33.94) + j (6.578)(0.08 * 10^-3) sin(33.94) => S s ( complex ) = 4.366 * 10^-4 + j 2.938 * 10^-4 VAR S C (complex) = (.16+.128) * 10^-3 + j 2.938* 10^-3 S C (complex) = 2.88 * 10 ^ -4 + j 2.938 * 10 ^ -4 VAR Take Away Message: After conducting the first part of the experiment it can be seen that phasor diagrams are a very reliable way to measure individual voltages in the circuit load, as the calculated values were very similar to the measured values. Part 2: Series RLC Circuit: Steps: 1. Connect the circuit shown in figure 5 with the capacitor included. With V S set to obtain the same value of V R as in part 1, measure V S , V R , V A , and V C . - Built: Kush Patel - Verified: Jesus Galindo - Worked first time: Yes - V S = 5.448 V - V R = 2.005 V - V A = 4.877 V - V C = 1.229 V 2. Construct an accurate full-page phasor diagram (Figure 3).

Figure 3: Series RLC Phasor Diagram Calculations: Φ = 31.39° Θ = 57.46° V L = 4.11 V V RL + 20K = 2.62 V |I| = |V R | / R = 2.005 / 25000 = 0.08 mA V 20K = 0.08 * 10^-3 * 20000 = 1.6 V V RL = V RL + 20K - V 20K = 2.62 V - 1.6 V = 1.02 V R L = |V RL | / |I| = 1.02 / (0.08 * 10^-3) = 12750 Ω X L = |V L | / |I| = 4.11 /( 0.08 * 10^-3) = 51375 Ω (measured) L = 7.83 H, X L = L2πf = 7.83* 2π * (1000) = 49197 Ω, R = 19.9K Ω (measured) Q(quality factor) = X L / R = 49197 / 19900 = 2.47 (calculated) L = X L / 2πf = 51375 / 2π(1000) = 8.176 H

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(calculated) Q L = X L / R L = 51375 / 12750 = 4.029 R L percent error: |(12750 - 19900) / 19900| * 100 = 35.9% X L percent error: |(51375 - 49197) / 49197| * 100 = 4.4% Pf = cos(Φ) = cos(31.39°) = 0.854 P 25kΩ = V R ^ 2 / R = (2.005^2) / 25000 = .161 mW P 20kΩ = V 20K ^ 2 / R = (1.6^2) / 20000 = .128 mW Q(reactive power) = V L ^ 2 / X L = 4.11 ^ 2 / 51375 = .329 mW S S ( complex ) = VI cosΦ + j VI sinΦ = (5.448)(0.08 * 10^-3) cos(31.39) + j (5.448)(0.08 * 10^-3) sin(31.39) => S s ( complex ) = 3.721 * 10^-4 + j 2.270 * 10^-4 VAR S C (complex) = (.161 + .128) * 10 ^ -3 + j .329 * 10 ^ -3 => S C (complex) = 2.89 * 10 ^ -4 + j 3.29 * 10 ^ -4 VAR Take Away Message: After conducting the second part of this lab, the data shows how using phasor diagrams to calculate voltages in a series RLC circuit is very reliable as the calculated values were very close to the values measured in the original circuit.

Write in 3rd person. (Avoid “I”, “We”, etc.). Envision customer reading it. Each Section/Procedure: List; “Build: (Initials) and Verified (Initials)”. Swap roles for each section/procedure. The report should be self-contained and should not refer to diagrams or other data in other documents. Don’t refer to the lab manual or other documents. The reader does not have access to these documents The report should flow, covering each circuit or technical topic in order as you likely did the experiment. Include data and calculations with circuit. DO NOT organize the report by Schematics Section, Calculations Section, and Data Section. See how a text book is organized. Use Engineering Notation vs Scientific Notation. (Powers of 3). Example, mA, uA etc. Use the same numbering scheme as in the lab manual. Everything except for text requires a Name, Number and Description. Example: Figure 1.1, Test setup for measuring propagation delay of a CMOS inverter. List Table X.X, Graph X.X, Figure X.X etc. Make questions visible Graphs need axis labels and units. All waveforms need to be labeled on the graph. Don’t let the reader guess or assume. (ex. Vin?, Vout? Axis labels/units?) ANNOTATE all important parts of a waveform. Non-annotated waveforms have no value. Show sample calculations whenever calculations done.

Comment on data that you know or believe is suspect. Be SPECIFIC with example when describing sources of “error” or differences. Make your lab partners read and agree with the report content. The TEST: Could a student or customer just like you perform the experiment and obtain the same data and draw the same conclusions using only your report. Best practice is not to cut and paste schematics from the lab manual. Use YOUR schematics with instruments labeled on the schematic. LTspice works well for this. Scope data captures need to be with all the scope settings, not processed. Align grounds with major grid lines Set /per division to 1, 2, 5, etc on O-Scope. Not “Fine” with 1.263 volts per division Data MUST be yours. Include a “Take Away Message” for each section. 1-2 sentences. What does the data tell you? What would you want the customer to know?

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