ch7-response of first-order rl and rc circuits
TRANSCRIPT
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ECE 2132 CIRCUIT
ANALYSIS
Dr Hasmah Mansor
E2-2-13.1
mailto:[email protected]:[email protected] -
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CONTENTS
7.1 The Natural Response of an RLCircuit7.2 The Natural Response of an RCCircuit
7.3 The Step Response of RLand RCCircuits
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7.1 The Natural Response of
an RLCircuit
RLcircuit RCCircuit
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7.1 The Natural Response of
an RLCircuit
A first-order circuitmay be reduced to a
Thvenin (or Norton) equivalent connected toeither a single equivalent inductor or
capacitor.
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7.1 The Natural Response
of an RLCircuit
An inductor connected toa Thvenin equivalent
An inductor connected to
a Norton equivalent
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7.1 The Natural Response
of an RCCircuit
An capacitor connected to
a Norton equivalent
An capacitor connected toa Thvenin equivalent
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7.1 The Natural Response
of an RLCircuit
The natural response is the currents and
voltages that exist when stored energy is
released to a circuit that contains noindependent sources.
Natural response of an RLcircuit
0,)()(
0
teitit
L
R
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7.1 The Natural Response
of an RLCircuit
The time constant of an RLcircuitequals the
equivalent inductance divided by the Thvenin
resistance as viewed from the terminals of theequivalent inductor.
R
L
Time constant for RLcircuit
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Value of for tequalto integral multiples of
7.1 The Natural Response
of an RLCircuit
t
e
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A graphic interpretation of the
time constant of the RLcircuit
7.1 The Natural Response
of an RLCircuit
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7.2 The Natural Response
of an RCCircuit
AnRCcircuit
After
Switching
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7.2 The Natural Response
of an RCCircuit
Initial capacitor voltage
0)0()0()0( vvvvv g
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The time constant of an RCcircuitequals
the equivalent capacitance times the
Thvenin resistance as viewed from the terminalsof the equivalent capacitor.
7.2 The Natural Response
of an RCCircuit
RC
Time constant for RCcircuit
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The natural response of an RC circuit
7.2 The Natural Response
of an RCCircuit
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7.2 The Natural Response
of an RCCircuit
Calculating the natural response of an RC
circuitcan be summarized as follows:
1. Find the initial voltage, V0, across thecapacitor.
2. Find the time constant of the circuit, = RC.
3. Use,v(t) = V0e-t/, t 0 togeneratev(t)fromV0
and.
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Example 7.1The switch has been closed for a long time before it is opened at t=0. Find
a) iL(t) for t 0,
b) i0(t) for t 0+
,
c) v0(t) for t 0,
d) The percentage of the total energy stored in the 2H inductor that is
dissipated in the 10 resistor
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Problem 7.4
The switch in the circuit has been closed for a long time before opening at t = 0.a) Find i1(0-) and i2(0-).
b) Find i1(0+) and i2(0+).
c) Find i1(t) for t 0.
d) Find i2(t) for t 0+
e) Explain why i2(0-
) i2(0+
)
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Example 7.3
The switch in the circuit shown has been in positionxfor a long time. At t=0,the switch moves instantaneously to position y. Find
a) vc(t) for t 0,
b) v0(t) for t 0+,
c) i0(t) for t 0+,
d) The total energy dissipated in the 60 kresistor.
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Problem 7.23The switch in the circuit has been in position a for a long time and v2= 0 V. At t = 0,
the switch is thrown to position b. Calculate
a) i, v1and v2for t 0+.
b) The energy stored in the capacitor at t = 0.
c) The energy trapped in the circuit and the total energy dissipated in the 5 k
resistor if the switch remains in position b indefinitely.
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7.3 The Step Response of
RLand RCCircuits
Step response of RLcircuit
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The step response of the RLcircuit whenI0= 0.
7.3 The Step Response of
RLand RCCircuits
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Inductor voltage versus time
7.3 The Step Response of
RLand RCCircuits
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A circuit used to illustrate the stepresponse of a first-order RCcircuit
7.3 The Step Response of
RLand RCCircuits
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Step response of an RCcircuit
7.3 The Step Response of
RLand RCCircuits
0,)( 0
teRIVRIv RCt
sSc
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Example 7.6
The switch in the circuit shown has been in position 1 for a long time. At t = 0,
the switch moves to position 2. Find
a) v0(t) for t 0 and
b) i0(t) for t 0+.
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Problem 7.83The voltage signal source in the circuit is generating the signal shown in (b).
There is no stored energy at t = 0.
a) Derive the expression for v0(t) that apply in the intervals t < 0; 0 t 4ms;
4ms t 8ms; and 8ms t infinity.
b) Sketch v0and vson the same axes.
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Example 7.12The uncharged capacitor in the circuit is initially switched to terminal a. At t=0,
the switch is moved to position b, where it remains for 15 ms. After 15 ms
delay, the switch is moved to position c where it remains indefinitely.
a) Derive the expression for v(t).
b) Plot v(t) versus t.
c) When will the voltage on the capacitor equal to 200 V?
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END OF CHAPTER 7