Illustration of sinusoidal waveforms: (a) A sin ωt, (b) A cos ωt, (c) A
sin(ωt + φ ), and (d ) the relation between sin and cos: A sin ωt = A cos(ωt – 90°), A cos
ωt = A sin(ωt + 90°).
Figure 6.1
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.2
A general periodic function: x(t) = x(t ± nT ).
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.3
Representing (a) a
periodic function
(a square wave) as
(b) the sum of
sinusoidal
components.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.4
Representing a
periodic source
waveform as the sum
of its sinusoidal
components so that
superposition can be
used to determine
the response to that
periodic waveform.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.5
An example of a circuit that is driven by a sinusoidal source.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.6
Representation of a complex number as a vector in two-dimensional space.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.7
Illustration of (a) the sum and (b) the difference of two complex numbers
as the addition and subtraction of vectors.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.8
Representation of a complex exponential source as the connection of two
sources (series for a voltage source and parallel for a current source) using Euler’s identity.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.9
The key to the phasor method: in order to determine the response to either
a sine or a cosine source, replace the source with the complex exponential source and use
superposition.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.10
Solution of the circuit of Fig. 6.5 by replacing the original source with
the complex exponential source and using Euler’s identity and superposition.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.4
Exercise Problem 6.4.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.11
The phasor impedances for (a) the resistor, (b) the inductor, and (c) the capacitor.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.12
Illustration of converting (a) the time-domain circuit to (b) its phasor, or
frequency-domain, equivalent.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.13
Example 6.4.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.6
Exercise Problem 6.6.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.14
Example 6.5.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.7
Exercise Problem 6.7.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.15
Example 6.6.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.8
Exercise Problem 6.8.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.16
Example 6.7.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.9
Exercise Problem 6.9.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.17
Example 6.8.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.10
Exercise Problem 6.10.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.18
Example 6.9.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.11
Exercise Problem 6.11.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.19
Example 6.10.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.12
Exercise Problem 6.12.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.20
Example 6.11.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.21
Example 6.12.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.14
Exercise Problem 6.14.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.15
Exercise Problem 6.15.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.22
Illustration of average
power delivered to an
element: (a) the timedomain relation for
the element, (b) plot
of the instantaneous
power, and (c) the
average power
delivered to an
element in terms of its
phasor voltage and
phasor current.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.23
Example 6.13.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.24
Illustration of the power relations for a resistor.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.25
Illustration of the power relations for an inductor.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.26
Illustration of the power relations for a capacitor.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.27
Example 6.14.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.17
Exercise Problem 6.17.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.28
Illustration of the concept of power factor.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.29
Example 6.15.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.30
Illustration of a power transmission line connecting a source to a load.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.31
Illustration of the
typical source-load
configuration for
determining
maximum power
transfer.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.32
Illustration of the
principle of
superposition of
average power
for sinusoidal
sources of
different
frequencies.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.33
Example 6.18.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.20
Exercise Problem 6.20.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.34
Example 6.19.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.21
Exercise Problem 6.21.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.35
Application of a current source having a periodic waveform to a resistor.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.36
Example 6.20.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.22
Exercise Problem 6.22.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.37
Use of rms voltages and currents in phasor circuits.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.38
Example 6.21.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.39
Interpreting a phasor
quantity in the time
domain as the
projection of the
rotating phasor on the
real axis (for a cosine)
or on the imaginary
axis (for a sine).
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.40
An example
illustrating the
visualization of
phasor voltages and
currents in a phasor
diagram: (a) the
time-domain circuit,
(b) the phasor circuit,
and (c) the phasor
diagram.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.23
Exercise Problem 6.23.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.41
Element impedances for computing transfer functions where p = jω.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.42
Viewing a linear system or electric circuit in block diagram form:
(a) time domain, and (b) frequency domain.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.43
Example 6.22.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.24
Exercise Problem 6.24.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.44
Example 6.23.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.25
Exercise Problem 6.25.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.45
Illustration of series resonance: (a) the series LC circuit, (b) the phasor
equivalent, and (c) a plot of the magnitude of the series impedance versus radian frequency
showing that the impedance is zero at ω0 = 1/√ LC, where the series combination acts like
a short circuit.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.46
Illustration of parallel resonance: (a) the parallel LC circuit, (b) the
phasor equivalent, and (c) a plot of the magnitude of the parallel admittance versus radian
frequency showing that the admittance is zero at ω0 = 1/√ LC where the parallel
combination acts like an open circuit.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.47
Illustration of the magnitude of the transfer function for (a) a lowpass
filter, (b) a highpass filter, (c) a bandpass filter, and (d ) a bandreject filter.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.48
Circuit implementation of
(a) a lowpass filter, (b) a
highpass filter, (c) a bandpass
filter, and (d ) a bandreject
filter.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.49
An op-amp (active) bandpass filter.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure E6.30
Exercise Problem 6.30.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.50
Representation of a
three-phase power
source: (a) the circuit
model, (b) the phasor
diagram, and (c) physical
construction of a
three-phase generator.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.51
Two common load
connections: (a) the
wye-connected load,
and (b) the deltaconnected load.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.52
Example 6.27.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.53
Example 6.28.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.54
PSPICE plots of the
frequency response of the
bandpass filter of Fig. 6.53:
(a) magnitude (in decibels),
(b) magnitude (absolute),
and (c) phase (degrees).
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.55
Example 6.29.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.56
Example 6.30.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.57
MATLAB plots of the frequency response of the bandpass filter of Fig.
6.53: (a) magnitude (in decibels), and (b) phase (degrees).
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.58
AM radio transmission.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.59
Design of a filter for AM radio transmissions: Example 6.31.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure 6.60
Illustration of the
phenomenon of crosstalk
between wire-connected
circuits: (a) the physical
configuration of two pairs
of closely spaced wires,
(b) magnetic field coupling,
(c) electric field coupling,
(d) a lumped-circuit model
of the interaction between
the two circuits, and (e)
typical element values
along with the PSPICE
node labeling.
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.3-1
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.3-2
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.3-3
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.3-4
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.3-5
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.3-6
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.3-7
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.3-8
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-9
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-10
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-11
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-12
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-13
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-14
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-15
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-16
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-17
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-18
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-19
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-20
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-21
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-22
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.4-23
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.5-1
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.5-2
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.5-3
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.5-4
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.5-5
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.5-6
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.5-7
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.5-8
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.5-9
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.5-10
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-1 (a–d)
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-2
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-3
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-4
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-5
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-6
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-7
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-8
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-9
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-10
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-11
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-12
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-13
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-14
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-15
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-16
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-17
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-18
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-19
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-20
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-21
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.6-22
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.8-5
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.8-6
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.8-7
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.8-8
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.8-9
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.9-1
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.9-2
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.9-3
Fundamentals of Electric Circuit Analysis, by Clayton Paul
Figure P6.9-4
Fundamentals of Electric Circuit Analysis, by Clayton Paul