Circuit Analysis Lab reports #3, Lab Reports of Electrical Circuit Analysis

Download Circuit Analysis Lab reports #3 and more Lab Reports Electrical Circuit Analysis in PDF only on Docsity! poy ‘ IT, bid _ PIEAS > ATT EE-226 Circuit Analysis-I] Lab#3 Report Spring 2021 Experiment: Study of the Transient Response of an RLC Circuit Workstation no. : 13 Section: BSEE 19-23 Muhammad Uzair Arshad Mudassar Manzoor Instructor: Dr. Ghulam Mustafa Lab Engineer: Eng. Bilal Ahmed Group members: Department of Electrical Engineering Pakistan Institute of Engineering & Applied Sciences v Lab 3:Study of the transient response of an RLC circuit. Table of Contents 3.1 Lab no.3 : Study of the Transient Response of an RLC Circuit. 3.2 Abstract. 3.3 Introduction: 3.3.1 Objective: 3.3.2 Background: 3.4 Equipment: 3.5 Procedure: 3.6 Results: 3.6.1 Overdamped response of RL circuit, with R = 1.2KQ: 3.6.2 Underdamped response with R = 470: 3.7 Discussion: 3.8 Conclusion: 3.9 Appendix: Pre-Lab#3: Study of the transient response of an. 3.9.1 Theoretical Results: CODCSCURRWWWWWWWD 1. For R= 1.2KQ: © 2. For R= 47Q: 3.9.2 Simulation Results: 1. For R= 1.2KQ: 2. For R= 47Q: Figure 3.1: Schematic diagram of series RLC circutt. eeo 12 Figure 3.2: Plot of Vc with R = 1.2KQ, Vc(1ms) = 3V. Table 3.1: Series RLC Circuit Response with R1=1.2kQ. Figure 3.3: Plot of voltage across capacitor with R = 479, Vc(0.5ms) = 6.6V. Table 2: Series RLC Circuit Response with R1=47 Figure 4: Observation table from lab experiment, with R = 47ohm. Figure 5: Observation table from lab experiment, with R = 1.2Kohm Figure 3.6:Input(green) and Output(red) voltages, R = 1.2K. Figure 3.7: Measurement Results Figure 3.8:Input(green) and Output(red) voltages Figure 3.9: Measurement Results % Deviation | % Deviation of of . Value from Value from Value from Simulation | Experiment Quantity Theory Simulation Experiment xP from Theory | from Theory 10909 a x x x x @o 4204 x x x x Type of Overdamped Overdamped Overdamped response x x sip -20950, -867.85 x x x x 5 -5 48 0 4 veo") 5 5 5.2 0 4 vd) 1th A -10.362 B/D x x x x 1 pl nl 0.362 AB/D, x x x x -1.732 -1.741 -2.4 0.57 25 u(0.5ms) 0.626 0.620 0.240 0.37 58 u-(ims) 3.15 3.15 2.8 0 11.11 ud{2ms) Table 3.1: Series RLC Circuit Response with R1=1.2kQ 3.6.2 Underdamped response with R = 470: Figure 3.3: Plot of voltage across capacitor with R = 470, Vc(0.5ms) = 6.6V 6 Lab 3:Study of the transient response of an RLC circuit. % Deviation | % Deviation of of Value from Value from Value from Simulation | Experiment Quantity i i ri Theory* Simulation Experiment from Theory | from Theory 500 a x x x x 4612.65 @o x x x x Type of Underdamped Underdamped Underdamped response x x -500+4585i 512 S00bAS BSH x x x x + 5 -5 -5.12 0 2.34 ve(o") 5 5 48 0 4 vd) Ala! “10 (B/D x x x x ABD! -1.09 /BYD, x x x x 9.5 9.46 6.96 0.64 26.4 u(0.5ms) 6.24 6.47 6.16 3.7 48 u-(ims) 8.46 8.45 4.56 0.77 46 ud{2ms) Table 2: Series RLC Circuit Response with R1=47 *Calculations are done in appendix. Table 3.2: Series RLC Circuit Response with R1=472. % Deviation | % Deviation Quantity Value from Value from Value from of of Theory Simulation Experiment Simulation Experiment from Theory | from Theory Fe Soo x x sc x w ; J yy Elona x Xx x xX Typeof |), ) 9 \ A response Kain p é ii nd awn f2| Ndon dewng x x $12 -Sod+#4s ag ; x x x x 1¢(O* NE is >) eo . eae 2 = 5 Ni OA 2 34 veto) | €\/ a U.g a vy ) E 1 wee A,/B,/D, - q O x x x xX A,/B,/D, | 7, 94 x x x x v-(0-5ms) FAN Gath le Lia o © Lu I se zany v-(1ms) 6r14V Ri vy tie 4 ale be 4 py F muy | 4 v,(2ms) BYE OVI AR Wecey | Oo | Yh Instructor’s Signature: ..........:se:ssssesesssnnge sega gees ie Figure 4: Observation table from lab experiment, with R = 470ohm oA 10 Lab 3:Study of the transient response of an RLC circuit. dv,(0*) at = 8A, + s2A', 0 = — 862.467A', — 24669.447A', --———-— (4) Solving eq(3)and eq.(4) simultaneously gives: A, = — 10.362 Ay = 0.362 Hence eq.(2) becomes: v(t) = 5 — 103626862467 4. 0, 3626~24669-447t Now, v.(0) = —5V v,(0.5m) = — 1.732V v,(1m) = 0.626V v.(2m) = 3.154V 2. For R = 47Q: R=470,C=14,L =47m Now, initial condition is: ve(0+) = —5 The characteristic equation is: s? + 2as + Wo? = 0 -------- (1) Now, first calculating neper’s frequency: = 2 _ f spore & = OE = Txa7m = 00rad/sec Now, Resonant frequency is: 1 1 Oo” Vie Jamxin From the above calculations we can see that the response of the circuit is underdampedi.e. 42 > a’. Hence the voltage solution will; v(t) = Vet Bye“ csc wat + Be sinwgt —-----— (2) where Wg = /@.2-—a* = /(4612.656)* — (500)? = 4585.476 rad/sec The roots of the eq.(1) are = 4612.656rad/sec S12 =— a+ wai =— 500 + 4585.476i Sy = — 500 + 4585.476i Sz = — 500 — 4585.476i Roots are real and not equal hence the response is underdamped. In order to calculate B1 and B2 we use initial conditions: Att=0+: ve(0+) = Vet Bye) csc (wg X 0) + Be sin (wa X 0) -5554+.B, By = —10 Now; dv,(0* am = —aB, + wgBo 0 = —500(— 10) + 4585.476B, By = —1.09 Hence eq.(2) becomes: v(t) = 5— 10e5! csc (4585.476t) — 1.09e-5 sin (4585.476t) Now, v,(0) = —5V v.(0.5m) = 9.509V v,(1m) = 6.424V ll v.(2m) = 8.460V 3.9.2 Simulation Results: 1. For R = 1.2KQ: Circuit: EA R1 IN 2 OUT V1=-5 V2=5 TD =2u TR=1u TF =1u PW = 25m PER = 50m Results: Date/Time run: 08/25/21 05:14:26 Temperature: 27.0 (A) Lab 3.dat (active) 5.5V 4.00 2.0 ov -2.07 -4.07 “5.50 Os 20ms 40ms é0ms e0ms 100ms = v(IN ® W(OUT) Time Figure 3.6:Input(green) and Output(red) voltages, R = 1.2K Measurement Value PYatX(v(OUT) a) -6 PystX{V{OUT) 0 Sm) a yatk(v{OUT).im) EE PraXX(VLOUT) 2m) pyattrstx(VOUT}) Figure 3.7: Measurement Results 2 Lab 3:Study of the transient response of an RLC circuit. 2. For R = 47Q: Circuit: IN tein _A OUT \ C1 du V1=-5 V2=5 TD =2u TR= tu TF=1u PW=25m PER = 50m Results: (A) Lab 3.dat (active) isv : : -10¥ -15¥ os 20m3 40m3 coms soms 100ms o v(IN) * -¥(OUT) Time Figure 3.8:Input(green) and Output(red) voltages