lab6_u11_RC_Transient

# lab6_u11_RC_Transient - University of Florida Department of...

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University of Florida EEL 3111 — Summer 2011 Drs. E. M. Schwartz & R. Srivastava Department of Electrical & Computer Engineering Ode Ojowu, TA Page 1/8 Revision 1 30-Jun-11 Lab 6: RC Transient Circuits OBJECTIVES Understand RC transient circuits. Determine the time constant of a circuit through simulation, experiment, and analytically. Understand the differentiating and integrating RC circuits and how the performance is affected by frequency and the time constant. MATERIALS Your lab parts. Printouts (required) of the below documents: o Pre-lab analyses o Answers to pre-lab questions o Multisim screenshots e-mailed to course e-mail Graph paper. INTRODUCTION A Simple RC Circuit 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. Case 1: Capacitor is Charging In normal operation, a capacitor charges part of the time and discharges at other times. Consider first the charging process. In the circuit of Fig. 1, for t < 0, both of the switches are open and no energy is stored on the capacitor. We say that the initial conditions are zero, or v o (0) = 0. At time t = 0, switch S1 closes and the capacitor begins charging. In deriving the circuit equation for this circuit, we will use the current/voltage relationship for a capacitor: ± ²³´ µ ¶ ·¸ ± ²³´ ·³ That is, current through the capacitor is proportional to the time derivative of the voltage across the Figure 1 – Series RC circuit. i c

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University of Florida EEL 3111 — Summer 2011 Drs. E. M. Schwartz & R. Srivastava Department of Electrical & Computer Engineering Ode Ojowu, TA Page 2/8 Revision 1 30-Jun-11 Lab 6: RC Transient Circuits capacitor. The coefficient C , is the capacitance measured in farads. Applying KCL at the upper capacitor node (for t > 0) yields ± ²³´ µ · ²³´ ¸ ¹ º » ¼ ½ ¾ ¿¶ · ²³´ ¿³ µ · ²³´ ¸ ¹ º » ¼ ½ ¿¶ · ²³´ ¿³ µ · ²³´ »¾ ¼ ¹ º »¾ Note that the capacitor voltage v c , is the same as the output voltage v o . The solution of this linear, constant-coefficient differential equation is · ²³´ ¼ ¹ º ÀÁ ¸ Â Ã Ä ÅÆ ÇÈÈÈÈÈÈÈÈÈÈÈÈÈÉÊËÈ³ Ì ½ An important quantity for an RC circuit is known as the time constant , τ=RC , so the above equation can be written as · ²³´ ¼ ¹ º ÀÁ ¸ Â Ã Ä ÇÈÈÈÈÈÈÈÈÈÈÈÈÈÉÊËÈ³ Ì ½ Figure 2 – Plot of capacitor output voltage with time for the charging case.
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lab6_u11_RC_Transient - University of Florida Department of...

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