Download Chapter 8 The Complete Response of RL and RC Circuits

Chapter 8: The Complete Response of RL and RC Circuits
Chapter 8
The Complete Response of
RL and RC Circuits
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.0-1
A plan for analyzing firstorder circuits. (a) First,
separate the energy
storage elements from
the rest of the circuit. (b)
Next, replace the circuit
connected to a capacitor
by its Thévenin
equivalent circuit, or
replace the circuit
connected to an inductor
by its Norton equivalent
circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.0-2
(a) A circuit and
(b) its complete
response.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.1-1
(a) A printer connected to a laptop
computer. (b) Two circuits connected by a
cable and (c) an equivalent circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.1-2
Voltages that occur during a transition
from a logic 0 to a logic 1.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.2-1
Common forms of electrical signals
shown on the screen of an oscilloscope.
Courtesy of Panasonic Industrial Co.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.2-2
(a) An analog
signal and the
corresponding
sampled signal.
(b) A digital signal
obtained by
encoding the
sampled signal.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.2-3
(a) A signal is sent from the transmitter to the
receiver using a cable. (b) The cable is modeled as
a first-order circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.3-1
(a) A first-order circuit containing a capacitor. (b) After
the switch closes, the circuit connected to the capacitor
is replaced by its Thévenin equivalent circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.3-2
(a) A first-order circuit containing an inductor. (b) After
the switch closes, the circuit connected to the inductor
is replaced by its Norton equivalent circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.3-3
A graphical technique for measuring the
time constant of a first-order circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.3-4
(a) A first-order circuit and (b) an equivalent circuit that
is valid after the switch opens. (c) A plot of the complete
response, v(t), given in Eq. 8.3-8.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.3-5
(a) A first-order circuit and (b) an equivalent circuit that
is valid after the switch closes. (c) A plot of the complete
response, i(t), given by Eq.8-3-9.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.3-6
(a) A first-order circuit. The equivalent circuit for
(b) t  0 and (c) t  0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.3-7
(a) A first-order circuit. The equivalent circuit for
(b) t  0 and (c) t  0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.3-8
(a) A first-order circuit, (b) the circuit after the
switch opens, and (c) the equivalent circuit after
the switch opens.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.3-1
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.3-2
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.3-3
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.3-4
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.3-5
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.3-6
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.4-1
(a) A circuit with sequential switching. (b) The equivalent
circuit before t  0. (c) The equivalent circuit for 0  t 
l ms. (d) The equivalent circuit after t  1 ms.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.4-2
Current waveform for t  0. The exponential has
a different time constant for 0  t  t1 and for t  t1
where t1  1 ms.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.4-3
A comparator.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.4-4
A comparator is used to compare the capacitor
voltage, vc (t), to a threshold voltage, VT.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.4-5
The initial capacitor voltage is vc(0)  1.667 volts, and
the comparator output is to switch from VL  0 to VH  5
volts at time t1  1 ms.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.4-6
A comparator is used to compare the resistor
voltage, vR(t), to a threshold voltage, VT.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.4-1
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.4-2
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.5-1
(a) A first-order circuit containing a dependent source. (b) The
circuit used to calculate the initial condition. (c) The circuit
used to calculate Voc. (d) The circuit used to calculate RTH.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.5-2
(a) A first order circuit containing a dependent source.
(b) The circuit used to calculate the Thévenin resistance
of the part of the circuit connected to the capacitor.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.6-1
Application of a constant-voltage source at t  t0
using two switches both acting at t  t0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.6-2
Unit step forcing function. u(t  t0).
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.6-3
Single-switch equivalent circuit for the step
voltage source.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.6-4
Symbol for the step voltage source of
magnitude V0 applied at t  t0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.6-5
(a) Rectangular voltage pulse. (b) Two-step
voltage waveforms that yield the voltage
pulse.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.6-6
Two-step voltage sources that yield a rectangular
voltage pulse, v(t) with a magnitude of V0 and a duration
of (t1  t0) where t0  t1.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.6-7
Pulse source connected to an RL circuit. The pulse is
generated by the combination of two-step voltage
sources each with units in volts.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.6-8
Response of the RL circuit shown in
Figure 8.6-7.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.6-1
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.6-2
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.6-3
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.7-1
(a) A circuit with a nonconstant source, (b) the appropriate
equivalent circuit after the switch opens; and (c) the
appropriate equivalent circuit before the switch opens.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.7-2
(a) A circuit with a nonconstant source. (b) The
equivalent circuit for t  0.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.7-1
(a) The NASA space station design shows the longer
habitable modules that would house an orbiting scientific
laboratory. (b) The circuit for energy storage for the
laboratories. Photograph courtesy of the National
Aeronautics and Space Administration.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.7-2
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure E 8.7-3
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.8-1
(a) A first-order circuit
with a sinusoidal input
and (b) a plot of its
complete response
produced using
MATLAB.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.9-1
(a) An RC circuit. (b) The circuit redrawn for Pspice.
(c) The Pspice input file.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.9-2
Complete responses, v(t), of the RC circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.10-1
(a) A transient
response and
(b) the corresponding
circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.10-2
Circuits used to calculate the (a) initial voltage,
(b) final voltage, and (c) time constant.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.10-3
Interpretation of the transient response.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.10-4
(a) A transient
response and
(b) the corresponding
circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.10-5
Circuits used to calculate (a) the steady-state voltage when
the switch is open, (b) the steady-state voltage when the
switch is closed, (c) the time constant when the switch is
open, and (d) the time constant when the switch is closed.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.10-6
Interpretation of the transient response.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.11-1
(a) A printer connected to a laptop computer. (b)
Two circuits connected by a cable and (c) an
equivalent circuit.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed
Chapter 8: The Complete Response of RL and RC Circuits
Figure 8.11-2
Voltages that occur during a transition from a
logic 0 to a logic 1.
©2001, John Wiley & Sons, Inc.
Introduction To Electric Circuits, 5th Ed