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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
30Jun11
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
Prelab analyses
o
Answers to prelab questions
o
Multisim screenshots emailed to course email
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
twoelement 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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View Full DocumentUniversity 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
30Jun11
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,
constantcoefficient 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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