AC Measurements: Understanding Amplitude and Phase in Circuits
School
New Jersey Institute Of Technology**We aren't endorsed by this school
Course
ECE 291
Subject
Electrical Engineering
Date
Dec 10, 2024
Pages
12
Uploaded by CaptainHyena2060
ECE 291 Electrical Engineering Lab5Laboratory ReportExperiment No:5Experiment Name: AC MEASUREMENTS; AMPLITUDE AND PHASESTUDENT TEAM No 5On my honor,I pledge that I havenot violated the provisions of theNJITStudent HonorCodeNameSignature…………………………..Experiment performed on date 2/19/2018 Report submitted on date 2/26/2018 Returned for corrections on date Grade Returned after corrections on date Grade
Introduction:The main objective of this laboratory assignment was to observe and understand the reactance of various electrical components within an electric circuit. Another objective was to measure the amplitude of various signals in the circuit as well as the phase difference between two different signals within circuit. All of these objectives will help provide a more robust understanding of AC circuits and AC measurements which will be of great use in future lab assignments. ProcedureCircuit schematic for part 1R110kΩC19.313nFL143.1mHV20.707Vrms 1kHz 0° Circuit schematic for part 2 & 3R110kΩC19.313nFL143.1mH24V20.707Vrms 1kHz 0° 500
Circuit schematic for part 2 R110kΩC19.313nFL143.1mHV20.707Vrms 5kHz 0° The circuit above was constructed on a breadboard. One 9.313 nano-Farad, two 21 milli-Henry inductors (connected in series), and one 10 kilo-Ohm were used from the IEEE components kit. The waveform generator at the work bench was used as the AC voltage. For the first part of the lab, the digital multimeter at the work bench was used take voltage measurements. For parts 2 & 3, the digital oscilloscope at the work bench was used to conduct measurements. The digital oscilloscope was also used to ground the circuit a node 0. Without this ground, the oscilloscope wouldn’t be able take proper measurements. The phase difference cannot be measured directly using the digital oscilloscope. Rather, the period of one signal and the phase shift between the two signals had to be measured from the oscilloscope and mathematically manipulated in order to obtain the phase difference angle. Equipment used: BreadboardResistorsCapacitors Inductors Wave generatorDigital multimeterDigital oscilloscope Leads
Circuit diagramCircuit set-ups for part 1R110kΩC19.313nFL143.1mHV20.707Vrms 1kHz 0° XMM1R110kΩC19.313nFL143.1mHV20.707Vrms 1kHz 0° XMM1
R110kΩC19.313nFL143.1mHV20.707Vrms 1kHz 0° XMM1R110kΩC19.313nFL143.1mHV20.707Vrms 1kHz 0° XMM1
Circuit set-ups for part 2And R110kΩC19.313nFL143.1mHV20.707Vrms 1kHz 0° XSC1ABExt Trig++__+_R110kΩC19.313nFL143.1mHV20.707Vrms 5kHz 0° XSC1ABExt Trig++__+_
Circuit set up for part 3R110kΩC19.313nFL143.1mHV20.707Vrms 5kHz 0° XSC1ABExt Trig++__+_1 - Using a digital multimeter, measure the voltage across all components including the AC voltage source. Record each voltage, which should all be in their RMS values, and check to see ifthe voltages across each component agree with Kirchhoff’s voltage law. 2 – Using two channels of the digital oscilloscope, measure and compare the voltages across the source and the voltage across the resistor. Using the subsequent sine waves created on the oscilloscope, find the amplitude of the both voltages as well as the phase difference between bothvoltages. Increase the frequency on the voltage source to 5 kilo-Hertz and repeat. 3 – Measure the voltage across the inductor and resistor using channel A of the oscilloscope and then measure the voltage across just the resistor using channel B of the oscilloscope. Using a feature of the oscilloscope, graph the output of channel A minus channel B (voltage across the inductor), as well as the output of channel 2 alone. Comparing the graphs of the two outputs on the oscilloscope, calculate the phase difference between the voltage across the inductor and the voltage across the resistor.
Experimental DataMeasured values of components: R = 9.963kΩ ; L1= 21.4 mH L2= 21.6 mH L =43.1mH; C = 9.313nF1.)Wave parameters: VS= 0.707 (RMS) ; f = 1000HzVS=0.706 V (RMS) =0.998V(amplitude)VC=0.603V(RMS) =0.853V(amplitude)VL=11.08mV (RMS) =0.0157V(amplitude)VR=0.352V(RMS) =0.498V(amplitude)2.) Wave parameters: VS =0.707V (RMS) ; f = 1000 HzVR=0.353V(RMS) =0.499V(amplitude)VS=0.732V(RMS) =1.035V(amplitude)ϕVS - ϕVR = 59.4°T(period of VR) = 1msτ (phase shift) = 0.165ms
Oscilloscope reading for 1kHz waveWave parameters: VS=0.707V(RMS) ; f = 5000HzVS=0.727V(RMS) =1.028V(amplitude)VR=0.673V(RMS) =0.95V(amplitude)ϕVS-ϕVR =16.2°T = 200μsτ = 9μs
Oscilloscope reading for 5kHz wave3.)Wave parameters: VS= 0.707V(RMS) ; f = 1000HzϕL – ϕR = 0°
Oscilloscope reading for part 3Computation and Results1.)KVL check: (FAILS CHECK)2.)
3.) DiscussionsIn part one of this experiment, the measured voltages across all components do not abide by a traditional DC KVL. This In part two of this experiment, it appears that the voltage amplitude of the resistor increased with an increase in the frequency. Along with an increase in voltage amplitude, the phase difference between the voltage source and the resistor voltage also decreased from 59.4° to 16.2°. In part 3 of this experiment, a phase difference of 0° was obtainedbetween the inductor voltage and resistor voltage. This does not agree with theory. In theory, a phase difference of 90° is to be expected. ConclusionsThe failure of the verification of a traditional KVL for DC circuits in this experiment does not necessarily mean that KVL is invalid for AC circuits. It simply means that a more sophisticated version of Kirchhoff’s laws must implemented. Ones were both the amplitude and the phase angle of each signal. As for part two, it makes sense that the voltages across the resistor and the source, as well as their phase difference, change because the reactance of both the inductor and capacitor vary with respect to frequency. An error may have also occurred in part 3 of this experiment since the experimental results are very far from theoretical predications.Perhaps the oscilloscope was on the wrong setting when taking measurements. Other than that, the lab went well and produced results that agree with theory.