LAB 4

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CUNY New York City College of Technology *

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1222

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Electrical Engineering

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Dec 6, 2023

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Course No: EET 1222 Name: XINHONG CHEN , TANZIE RAMEN Section No: HE10 TABLE OF CONTENTS Experiment No: 4 Title:Phase Measurements Date experiment completed…………………………….03/10/2023 Date due……………………………………………..03/16/2023 Date Handed in…………………………………. Squad No…………… List Members: ………………………………………………………… …………………………………………………………. …………………………………………………………. …………………………………………………………. Students Only Faculty Only Returned For corrections…………………………….. Correction Due…………………………………………….. Corrections Handed in…………………………………. Comments Grade…………………Approved by……………………. NEW YORK CITY COLLEGE OF TECHNOLOGY OF THE CITY UNIVERSITY OF NEW YORK REPORT FOLDER 1

Section Title Page No. 1. Objective 3 2. Introduction/Brief Theory 4 3. Equipment 5 4. Result 6 5. Analysis 11 6. Conclusion 12 7. Reference 2

Objective 1. Use the dual trace(two vertical channels) to determine the phase angle between two sinusoidal waveforms. 2. Use Lissajous patterns to determine the phase angle between two sinusoidal waveforms. 3

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Introduction/Brief Theory In this laboratory, we will experiment with the phase relationship between two voltage sources using the oscilloscope in two different approaches. The first method is the two-track method of phase measurement, in which we obtain the waveform period by calculating the horizontal axis's division. Then we need to calculate the phase shift division between the two waveforms. Eventually, we can derive their Phase angle by the following equation. : θ = ( ¿ .for θ ) ( ¿ .for T ) ∗ 360 ° The second method is the Lissajous-Pattern phase measurement, which requires the oscilloscope to be set to X-Y mode to obtain the waveform pattern. The following figure shows examples of these patterns. However, to calculate the Phase angle, we need to calculate the division of the y m ∧ y o . Then we can calculate the phase angle by the following equation: θ = sin − 1 y o y m ∨ θ = 180 °− ( sin − 1 y o y m ) . 4

Equipment 1. Resistors 1KΩ , 470Ω. 2. Capacitor 0.47 µF 3. Dual Channel Oscilloscope 4. Audio Oscillator 5. Digital Multimeter(DMM) 5

Result RUN I A) Dual Trace Method of Phase Measurement ( 1KΩ Resistor) F=200Hz V=4V Peak to peak Figure 1A): Complete circuit of RUN IA)- 1KΩ Resistor -Number of the horizontal divisions in period equals 2.45 divisions. -Number of the horizontal divisions representing the phase shift equals 0.4 division. -Phase shift θ in degrees: 0.4 2.45 ∗ 360 ° ≅ 58.78 ° . -Angle θ to radians: 58.78 180 ≅ 0.327 radians . 6

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RUN I B) Dual Trace Method of Phase Measurement (470 Ω Resistor) F=200Hz V=4V Peak to peak Figure 1B): Complete circuit of RUN IB)- 470Ω Resistor -The number of the horizontal divisions in period equals 5 divisions. -The number of the horizontal divisions representing the phase shift equals 1 divisions. -Phase shift θ in degrees: 1 5 ∗ 360 ° = 72 ° . -Angle θ to radians: 72 180 = 0.4 radians . 7

RUN II A) Lissajous-Pattern Phase Measurement (1K Ω Resistor) F=200Hz V=4V Peak to peak Figure 2A): Complete circuit of RUN IIA)- 1KΩ Resistor -The number of divisions between the two y-intercepts( y o ¿ equals 3 divisions. -The number of the divisions between the peak-to-peak values of the Lissajous pattern( y m ¿ equals 4 divisions. - Angle θ = sin − 1 ( 3.6 4 ) ≅ 64.16 ° . -Angle θ to radians: 64.16 180 ≅ 0.356 radians . 8

RUN II B) Lissajous-Pattern Phase Measurement (470 Ω Resistor) F=200Hz V=4V Peak to peak Figure 2B): Complete circuit of RUN IIB)- 470Ω Resistor -The number of divisions between the two y-intercepts( y o ¿ equals 5 divisions. -The number of the divisions between the peak-to-peak values of the Lissajous pattern( y m ¿ equals 5 divisions. - Angle θ = sin − 1 ( 5 5 )= 90 ° . -Angle θ to radians: 90 180 = 0.5 radians . 9

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Question 1: Theoretical Value of 1KΩ Resistor: θ = tan − 1 ( X C R )= tan − 1 ( 1 ( 2 π )( 200 )( 0.47 ∗ 10 − 6 ) 1000 ) ≅ 59.43 ° Theoretical Value of 470Ω Resistor: θ = tan − 1 ( X C R )= tan − 1 ( 1 ( 2 π )( 200 )( 0.47 ∗ 10 − 6 ) 470 ) ≅ 74.49 ° Question 2: % difference of 1KΩ Resistor: ¿ 59.43 − 58.78 59.43 ∨ ∗ 100% ≅ 1.093 . % difference of 470Ω Resistor: ¿ 74.49 − 72 72 ∨ ∗ 100% ≅ 3.343 . Question 3: % difference of 1KΩ Resistor: ¿ 59.43 − 64.16 59.43 ∨ ∗ 100% ≅ 7.959 . % difference of 470Ω Resistor: ¿ 74.49 − 90 90 ∨ ∗ 100% ≅ 17.23 . Question 4: Compare the results of questions 2 and 3. The Dual Trace Method yields better results. Question 5: The frequency of both signals being observed must be the same when making phase measurements because when the two signals have the same frequency, it can help us to measure the phase difference more accurately. In other words, they are repeating in the same waveform repeatedly at the same rate, and the relative timing between these two signals will be the same from cycle to cycle. 10

Question 6: F = 1000 HZ ,T = 1 1000 = 0.001 s ∧ 57.6 360 ∗ 0.001 = 0.16 ms , therefore the time delay between the two waveform is 0.16ms Analysis In RUN I A), we apply Dual Trace Method to measure the phase difference between the voltage source and 1KΩ Resistor. During this experiment, we set the Frequency to 200Hz and Voltage to 4V Peak-to-peak. Finally we got the result of Phase shift θ in degrees: 0.4 2.45 ∗ 360 ° ≅ 58.78 ° and angle θ to radians: 64.16 180 ≅ 0.356 radians . ( see details on page 6) In RUN I B), we apply Dual Trace Method to measure the phase difference between the voltage source and 470Ω Resistor. During this experiment, we set the Frequency to 200Hz and Voltage to 4V Peak-to-peak. Finally we got the result of Phase shift θ in degrees: 1 5 ∗ 360 ° = 72 ° and angle θ to radians: 72 180 = 0.4 radians .( see details on page 7) In RUN II A), we apply Lissajous-Pattern Method to measure the phase difference between the voltage source and 1KΩ Resistor. During this experiment, we set the Frequency to 200Hz and Voltage to 4V Peak- to-peak. Finally we got the result of angle θ = sin − 1 ( 3.6 4 ) ≅ 64.16 ° and angle θ to radians: 64.16 180 ≅ 0.356 radians . ( see details on page 8) In RUN II B), we apply Lissajous-Pattern Method to measure the phase difference between the voltage source and 470Ω Resistor. During this experiment, we set the Frequency to 200Hz and Voltage to 4V Peak- to-peak. Finally we got the result of angle θ = sin − 1 ( 5 5 )= 90 ° . and angle θ to radians: 90 180 = 0.5 radians . ( see details on page 9) 11

Conclusion In this experiment, we learned how to use dual trace and Lissajous patterns to determine the phase angle between two sinusoidal waveforms. Also, we confirmed and compared the theoretical value with the experimental value. Overall this experiment was relatively successful. Reference 1.EXPERIMENT“PHASE MEASUREMENTS” LAB#4MANUAL, DEPARTMENT OF ELECTRICAL AND TELECOMMUNICATIONS ENGINEERING TECHNOLOGY, NEW YORK CITY COLLEGE OF TECHNOLOGY, SPRING 2023. 12

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