Prove that the expression for the damping ratioĪnd the undamped resonant frequency for the circuit of Figure 1 is equal (Basic Engineering Circuit Analysis, by D. Review the sections on RLC circuit in textbook It will be checked for completion at the beginning of your lab section.***ġ. Pre-Lab Reading and Questions ***Please do your entire pre-lab, individually, in your lab notebook, starting on a new page. Figure 3: Underdamped response to a unit input (5) Figure 3 shows an underdamped response to a unit input (4) Figure 2 shows an overdamped response to a unit inputįigure 2: Critically and overdamped responseĬase 3: Underdamped response: two complex The case of a critically damped response toĪ unit input step function is shown in Figure 2. The total response consists of the sum of the complementaryĪnd the particular solution. S 2 + (R/L)×s + 1/(LC) = 0 (2) Depending on the value of the damping ratio one has (1) in which is the damping ratio and is the undamped resonant frequency.įor the example of the series RLC circuit one has theįollowing characteristic equation for the current i L(t) or v C(t), This solution depends on the roots of the characteristic equation, Let's focus on the complementary solution. Response), and a x p(t) is the particular solution (also called theįorced response). (solution of the homogeneous differential equation and also called the natural X(t) = x n(t) + x p(t), in which x n(t) is the complementary solution Figure 1: Series RLC circuitīy using KVL, one gets a second-order differentialĮquation. The discussion is also applicable to other RLC circuits such as a Let's take a series RLC circuit as shown in Figureġ. RLC circuits have a much richer and interesting response RLC circuits is more complex than that of the RC circuits we have seen in Such as filters in communications systems, ignition systems in automobiles,Īnd defibrillator circuits in biomedical applications.
RLC circuits are widely used in a variety of applications
You will study and measure the overdamped, critically damped, and underdamped circuit responses. To build RLC circuits and to observe the transient ESE205 - Lab 10: RLC Step Response UNIVERSITY of PENNSYLVANIA DEPARTMENT of ELECTRICAL ENGINEERING ESE UndergraduateĮlectrical Circuits and Systems I Laboratory Step response of RLC Circuits
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