EE 442. Lab Experiment No. 6. Step Response of a Series RLC Circuit

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1 EE 44 Laboratory Experiment 6 EE 44 Lab Experiment No. 6 0/0/007 1

2 I. INTRODUCTION EE 44 Laboratory Experiment 6 The purpose of this experiment is to measure the response of a series RLC circuit to a step change in driving voltage and to observe the effect that changes in one parameter, R, have upon the response. The experiment also introduces the student to technique of using this response to determine the values of unknown circuit parameters. II PRELAB EXERCISE The circuit shown in Figure 1 is a schematic diagram of the circuit that will be used in the laboratory to study the step response of a RLC circuit. Position Connect oscilloscope here S1 L R 5 mh 6 Vdc Vs Position 1 R_bleed 10k C 0.1 uf Figure 1 Series RLC Circuit 0 Consider that the switch S1 has been in position 1 for a long period of time and then, at a time designated as t = 0, the switch is thrown from position 1 to position. 1. Show that Vc(t) satisfies: d V dt ( t) + R dvc L dt Vc ( t) + LC c = Vs LC.. Let 1 LC ω o R L = and = ξω o and obtain values for ξ and ωo assuming L = 5mH, C = 0.1uF, and R = 100Ω. Determine the nature of damping. At what value of R is the circuit critically damped (with values for L and C unchanged)?

3 V c EE 44 Laboratory Experiment 6 3. Define cos θ = -ξ and ωn = ωo sin θ. The capacitor voltage is given by: ω n t sin( ω θ ) tan θ n t ( t ) = V 1 + e s sin θ the plot of which is shown in Figure : π tan θ V c ( t1 ) = V s [1 + e ] 3π tan θ V c ( t ) V [1 + e ] 3 = s V s t 1 = π ω n t 3 = 3π ω n Figure Plot of an Underdamped Response Calculate t1, t3, Vc(t1), and Vc(t3) for L = 5mH, C = 0.1uF, and R = 100Ω. 4. Assuming that t1, Vc(t1), Vs, and C are known, describe how to compute L and R. III. LABORATORY EXPERIMENT (Part 1) For the experimental portion of this laboratory you will build the circuit of Figure 3. This set-up will allow you to measure the step response. The 3

4 EE 44 Laboratory Experiment 6 10K Ω resistor is just a bleed resistor and has no effect on your circuit. This resistor discharges the capacitor when the switch is in position You will need to make the following settings on the oscilloscope. a. In the Trigger section of the front panel, press the Mode/Coupling button. This action will display the trigger menu on the screen. b. Look the second tap from the bottom, the Sweep tap. Press the button next to the sweep tab to change the sweep mode from Auto to Normal. (If you had a trace on the screen, it will disappear.) c. Rotate the knob marked Level (in the Trigger section). On the screen, you will see a line with a tab marked T and a label in the bottom left corner of the screen marked TRIG LVL: with a voltage reading. Adjust this level to about 50 mv. The oscilloscope is now set up to do a single sweep. Position Connect oscilloscope here S1 L R 5 mh 6 Vdc Vs Position 1 R_bleed 10k C 0.1 uf Figure 3 Circuit for measuring series RLC step response 0. Set R to be a 100 Ω resistor. 3. Hook up the scope as shown in Figure Move S1 into position 1, energize the DC supply, and set it to 6 V. 5. On the scope front panel in the run control section, push the Single button. (The scope will sweep the measurement as soon as the measured voltage rises above the 50 mv trigger level setting that you 4

5 made in step C. EE 44 Laboratory Experiment 6 6. Move S1 to position and note the trace on the screen. To take a new measurement, you need to press the Single button again. (Hint you will need to experiment with the Volts/Division and the Time base controls on the scope to get a good picture.) Plot your results in the accompanying graph paper, and note down the following values: Vc(t1) = t1 = Vc( t3) = t3 = 7. Repeat this experiment with 1000 Ω, and 4000 Ω resistor values for R. Plot these two waveforms on the same graph, and identify (on the graph) the overdamped, underdamped, and criticallydamped cases. Graph paper for plotting waveforms in questions 6 and 7. 5

6 EE 44 Laboratory Experiment 6 IV. LABORATORY EXPERIMENT (Part ) For the second part of this laboratory experiment, switch from the green 5 mh inductor to the black unknown inductor. Experiment with R values until you get a nice underdamped response. Once you have a nice waveform, plot it and use it to determine the value of the inductor and resistor (by first determining the values of ωn, θ, ξ, ωo). Check the value of the unknown inductor and resistor with the LCR meter in the corner of the room. (Ask your TA for help.) Note down the following values: ωn = θ = ξ = ωo = L(calculated)= R(calculated)= L(measured)= R(measured)= Graph paper for plotting waveform in Part. 6

Electric Circuit Fall 2017 Lab10. LABORATORY 10 RLC Circuits. Guide. Figure 1: Voltage and current in an AC circuit.

Electric Circuit Fall 2017 Lab10. LABORATORY 10 RLC Circuits. Guide. Figure 1: Voltage and current in an AC circuit. LABORATORY 10 RLC Circuits Guide Introduction RLC circuit When an AC signal is input to a RLC circuit, voltage across each element varies as a function of time. The voltage will oscillate with a frequency