Lab08_Transients - TRANSIENTS AND RC TIME CONSTANTS The...

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TRANSIENTS AND RC TIME CONSTANTS The capacitor has a wide range of applications in electronic circuits, some of which are energy storage, dc blocking, filtering, and timing. Thus, it is important for engineering students to understand capacitor operation. This experiment is designed to familiarize the student with the simple transient response of two-element RC circuits, and the various methods for measuring and displaying these responses. Theory RC Transients In normal operation, a capacitor charges part of the time and discharges at other times. These terms are described below in two parts: first, capacitor charging, and then discharging. Consider the circuit shown in Fig. 9.1. For t < 0, switch S 2 is closed and S 1 is open. At t = 0 , switch S 1 is closed and S 2 is opened. If we assume that the circuit was in a dc steady state before the switching occurred, there was no energy stored on the capacitor and therefore v o (0) = 0. Fig. 9.1 Series RC circuit Applying KCL at the upper capacitor node (for t > 0) yields , 0 R V v t v C s o o or , RC V RC v t v s o o The solution is
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) 1 ( ) ( RC t s o e V t v , 0 t (9.1) This is the equations describing the capacitor voltage while charging. A graph of the capacitor voltage is shown in Fig. 9.2. The voltage begins at zero, rises rapidly, and approaches V s as t . For all practical purposes, v o (t) = V s when t = 5( RC ). In Eq. (9.1), RC is the time constant of the circuit. The quantity symbol for the time constant is . Thus, for this RC circuit, = RC . Fig. 9.2 Increasing exponential for the charging case Now consider the discharging process. Suppose that the capacitor voltage has reached V s ( t >> ). Then, at t = t 1 , switch S 1 is suddenly opened and S 2 closed. KCL applied at the upper capacitor node (for t > t 1 ) yields 0 RC v t v o o the solution to which is RC t t s o e V t v ) ( 1 ) ( , 1 t t (9.2) Equation (9.2) describes the capacitor voltage while discharging. A graph of Eq. (9.2) for (
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Lab08_Transients - TRANSIENTS AND RC TIME CONSTANTS The...

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