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electronics fundamentals
circuits, devices, and applications
THOMAS L. FLOYD
DAVID M. BUCHLA
chapter 10
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Sinusoidal response of RC circuits
When both resistance and capacitance are in a series
circuit, the phase angle between the applied voltage and
total current is between 0 and 90, depending on the
values of resistance and reactance.
VR
VC
V R leads VS
V C lags V S
R
C
VS
I
I leads V S
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Impedance of series RC circuits
In a series RC circuit, the total impedance is the phasor
sum of R and XC.
R is plotted along the positive x-axis.
XC is plotted along the negative y-axis.
 XC 

 R 
  tan 1 
R
R


Z is the diagonal
XC
XC
Z
Z
It is convenient to reposition the
phasors into the impedance triangle.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Impedance of series RC circuits
Sketch the impedance triangle and show the
values for R = 1.2 kW and XC = 960 W.
Z
1.2 kW 
2
+  0.96 kW 
 1.33 kW
  tan 1
0.96 kW
1.2 kW
 39
Electronics Fundamentals 8th edition
Floyd/Buchla
2
R = 1.2 kW

39o
Z = 1.33 kW
XC =
960 W
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Analysis of series RC circuits
Ohm’s law is applied to series RC circuits using Z,
V, and I.
V  IZ
V
I
Z
V
Z
I
Because I is the same everywhere in a series circuit,
you can obtain the voltages across different
components by multiplying the impedance of that
component by the current as shown in the following
example.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Analysis of series RC circuits
Assume the current in the previous example is 10 mArms.
Sketch the voltage phasor diagram. The impedance
triangle from the previous example is shown for reference.
The voltage phasor diagram can be found from Ohm’s
law. Multiply each impedance phasor by 10 mA.
R = 1.2 kW

39o
Z = 1.33 kW
Electronics Fundamentals 8th edition
Floyd/Buchla
x 10 mA
=
XC =
960 W
VR = 12 V

39o
VS = 13.3 V
VC =
9.6 V
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Variation of phase angle with frequency
Phasor diagrams that have reactance phasors can only
be drawn for a single frequency because X is a
function of frequency.
R
As frequency changes,
Increasing f



the impedance triangle
Z
X
f
for an RC circuit changes
Z
as illustrated here
because XC decreases
f
X
Z
with increasing f. This
determines the frequency
f
X
response of RC circuits.
3
2
1
3
C3
3
C2
2
C1
1
2
1
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Applications
For a given frequency, a series RC circuit can be used to
produce a phase lag by a specific amount between an
input voltage and an output by taking the output across
the capacitor. This circuit is also a basic low-pass filter, a
circuit that passes low frequencies and rejects all others.
V
R

Vin
C
Vout
VR
f
(phase lag)
Vout
Electronics Fundamentals 8th edition
Floyd/Buchla
Vout
f
Vin
Vin
(phase lag)
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Applications
Reversing the components in the previous circuit produces
a circuit that is a basic lead network. This circuit is also a
basic high-pass filter, a circuit that passes high frequencies
and rejects all others. This filter passes high frequencies
down to a frequency called the cutoff frequency.
C
V
Vout

Vin
(phase lead)
Vin
R
Vout
Vout
VC
Electronics Fundamentals 8th edition
Floyd/Buchla
Vin

(phase lead)
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Applications
An application showing how the phase-shift network is
useful is the phase-shift oscillator, which uses a
combination of RC networks to produce the required 180o
phase shift for the oscillator.
Amplifier
Rf
Phase-shift network
C
C
C
R
Electronics Fundamentals 8th edition
Floyd/Buchla
R
R
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Frequency Response of RC Circuits
When a signal is applied to an RC circuit, and the output is taken
across the capacitor as shown, the circuit acts as a low-pass filter.
As the frequency increases, the output amplitude decreases.
Vin
10 V dc
Vout
10
10VVrms
rms
10 V rms
0
10 V dc
100
100W
W
W
100
20
kHz
ƒƒƒ == 110
kHz
kHz
V 8.46
rms V rms
10 V dc 1.57
0.79V
rms
0
11 mm
mFF
F
Vout (V)
9.98
Plotting the response:
8.46
1.57
0.79
9
8
7
6
5
4
3
2
1
0.1
Electronics Fundamentals 8th edition
Floyd/Buchla
1
10 20
100
f (kHz)
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Frequency Response of RC Circuits
Reversing the components, and taking the output across the resistor as
shown, the circuit acts as a high-pass filter.
As the frequency increases, the output amplitude also increases.
Vin
10 V dc
Vout
10V
V rms
rms
10
10 V rms
0
10 V dc
m
F
11mm
mF
F
1
F
ƒ
=
100
Hz
ƒ
=
1
kHz
ƒ = 10 kHz
9.87V rms
5.32 V rms
0.63 V rms
100 W
W
100
100
100 W
0 V dc
Vout (V)
9.87
Plotting the response:
5.32
0.63
Electronics Fundamentals 8th edition
Floyd/Buchla
10
9
8
7
6
5
4
3
2
1
0
0.01
0.1
1
10
f (kHz)
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Selected Key Terms
Impedance The total opposition to sinusoidal current
expressed in ohms.
Phase angle The phase difference between source voltage
and total current in a reactive circuit.
Bandwidth The range of frequencies passed from input to
the output of a circuit.
RC Lag Circuit A phase shift circuit where the output voltage
lags the input voltage by its phase angle. The
output voltage decreases as the input
frequency increases.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Selected Key Terms
RC Lead A phase shift circuit where the output voltage
Circuit leads the input voltage by its phase angle. The
output voltage increases as the input
frequency increases.
Frequency In electric circuits, the variation of the output
response voltage (or current) over a specified range of
frequencies.
Cutoff The frequency at which the output voltage of
frequency a filter is 70.7% of the maximum output
voltage.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Quiz
1. If you know what the impedance phasor diagram looks
like in a series RC circuit, you can find the voltage phasor
diagram by
a. multiplying each phasor by the current.
b. multiplying each phasor by the source voltage.
c. dividing each phasor by the source voltage.
d. dividing each phasor by the current.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Quiz
2. A series RC circuit is driven with a sine wave. If the
output voltage is taken across the resistor, the output
will
a. be in phase with the input.
b. lead the input voltage.
c. lag the input voltage.
d. none of the above.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Quiz
3. A series RC circuit is driven with a sine wave. If you
measure 7.07 V across the capacitor and 7.07 V across the
resistor, the voltage across both components is
a. 0 V
b. 5 V
c. 10 V
d. 14.1 V
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Quiz
4. If you increase the frequency in a series RC circuit,
a. the total impedance will increase.
b. the reactance will not change.
c. the phase angle will decrease.
d. none of the above.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Quiz
5. If you decrease the frequency in a series RC circuit,
a. the total impedance will increase.
b. the reactance will not change.
c. the phase angle will decrease.
d. none of the above.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Quiz
6. In an RC Lead Circuit, increasing the input frequency
a. increases the output voltage.
b. decreases the output voltage.
c. increases the phase angle.
d. none of the above.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Quiz
7. In an RC Lag Circuit, increasing the input frequency
a. increases the output voltage.
b. decreases the output voltage.
c. increases the phase angle.
d. none of the above.
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Quiz
8. The cutoff frequency of an RC circuit can be expressed
as a condition when:
a. its resistance is equal to the reactance
b. fc = 1/(2RC)
c. its output voltage is 70.7% of its maximum value
d. all of the above
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Quiz
9. The range of frequencies passed from input to the
output of a circuit is called the
a. bandwidth
b. cutoff frequencies
c. rejecting frequencies
d. limiting frequencies
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Quiz
10. When power is calculated from voltage and current for an
ac circuit, the voltage and current should be expressed as
a. average values
b. rms values
c. peak values
d. peak-to-peak values
Electronics Fundamentals 8th edition
Floyd/Buchla
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.
Chapter 10
Quiz
Answers:
Electronics Fundamentals 8th edition
Floyd/Buchla
1. a
6. a
2. b
7. b
3. c
8. d
4. c
9. a
5. a
10. b
© 2010 Pearson Education, Upper Saddle
River, NJ 07458. All Rights Reserved.