Experiment4

# Experiment4 - Department of Electrical Computer Engineering...

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- Department of Electrical & Computer Engineering Course ECSE-291 EXPERIMENT 4 Transient Response Of RLC Ciruits 2003-2004 -1- Objective: To study the step response of first-order and second-order RLC circuits, and to introduce some related methods of measurement. Preparation: 1. Sketch the unit-step response of each circuit shown in Figs. 1 and 2. Indicate the values at t=0, at one time constant, and in the steady state. 2. (a) Show that the transient of a first-order circuit will decay to less than 0.7% of its initial value in a time equal to 5 time constants. (b) The step response of a linear circuit can be conveniently displayed on an oscilloscope by exciting the circuit with a square wave whose frequency is low enough for the transient to decay to a negligible value in half of the period. If the transient is considered negligible after 5 time constants, what should be the frequency of the square wave for displaying the step response of each circuit shown in Figs. 1 and 2? 3. Calculate the un-damped natural frequency ω o , the damping coefficient α , and the final value of the unit step response for the circuit shown in Fig. 3 with R d = 0. Find the values of R d for which the circuit is (i) critically damped, and (ii) overdamped. Plot the critically damped step response, and sketch two other responses to illustrate the underdamped and overdamped cases in the same graph.

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- Department of Electrical & Computer Engineering Course ECSE-291 EXPERIMENT 4 Transient Response Of RLC Ciruits 2003-2004 -2- Apparatus: 1 Oscilloscope 2 Function Generators 1 DC Power Supply Laser Printer / Switch Experiment: Answer ALL questions during the laboratory period, but those marked with an asterisk (*) may be answered later when writing the report. Please SKETCH when asked to sketch, do not print on the printer unless asked to do so. 1. First-Order RC Circuits: (a) By using an appropriate square wave as input, measure the time constants of the circuit shown in Fig. 1. Note: The period of the square wave must be long enough for the transient to become negligible in half of the period (>5 TC). The time constant can be found by measuring the time required for a step response to change by 63.2% of the difference between the final resting value and the initial value. In order
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## This note was uploaded on 12/22/2010 for the course ECSE ECSE 291 taught by Professor Khazaka during the Winter '03 term at McGill.

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Experiment4 - Department of Electrical Computer Engineering...

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