Transcript Chapter 19

Basic Electronics
Ninth Edition
Grob
Schultz
©2002 The McGraw-Hill Companies
Basic Electronics
Ninth Edition
CHAPTER
19
Capacitive Circuits
©2003 The McGraw-Hill Companies
Topics Covered in Chapter 19
 XC and R in Series
 Sine-Wave VC Lags IC by 90o
 RC Phase-Shifter Circuit
 XC and R in Parallel
Topics Covered in Chapter 19
(continued)
 Sine-Wave IC Leads VC by 90o
 RF and AF Coupling Capacitors
 Capacitive Voltage Dividers
 The General Case of Capacitive
Current IC
RC Voltage and Current
Series Circuit
• The sine-wave ac voltage across a
capacitor lags the capacitor’s charge and
discharge currents by 90°.
• The sine-wave ac voltage across a resistor
is always in phase with its current.
• The total sine-wave ac voltage for a series
RC circuit always lags the total current by
an angle between 0° and 90°.
Waveforms and Phasors for a Series RC Circuit
q = 0
VR
I
I
q = - 90
I
VC
Note: since current is constant in a series circuit, the
current waveforms and current phasors are shown in the
reference positions.
Source Voltage and Current Phasors
XC < R
q < 0
I
VS
VS
I
Note: the source voltage
lags the current by an
amount proportional to
the ratio of capacitive
reactance to resistance.
XC = R
q = - 45
I
VS
XC > R
q < - 45
VS
I
Phasors for Series
RC Circuits
VR
q
VC
VT
q
R
ZT
XC
Voltage Phasors
Impedance Phasor
VT =
ZT =
VC2  VR2
X 2C  R 2
The Impedance of a Series RC Circuit
I=2A
R
R = 30 W
VS = 100
XC = 40 W
XC
Z
Z = R 2  XC 2 = 302  402 = 50 W
V
S = 100 =
=
I
2A
Z 50
The impedance is the total opposition to current flow.
It’s the phasor sum of resistance and reactance in a series circuit
The Tangent Function
opposite
Tanq = adjacent
opposite
q = Tan adjacent
-1
opposite
Tanq =
adjacent
opposite
q = Tan
adjacent
-1
adjacent
q
opposite
negative
angle
positive
angle
q
adjacent
opposite
The Phase Angle of a Series RC Circuit
I=2A
q
30 W
R = 30 W
VS = 100
XC = 40 W
q = Tan -1
-53°
I
XC
R
= Tan -1 -
40 W
40
= -53
30
VS lags I by 53°
VC
VS
50 W
KVL in a Series RC Circuit
I=2A
60 V
R = 30 W
VS = 100
XC = 40 W
80 V
VR = IR = 2 x 30 = 60 V
VC = IXC = 2 x 40 = 80 V
2
2
=

VS
60 80 = 100V
100 V
RC Voltage and Current
Parallel Circuit
• The sine-wave ac charge and discharge
currents for a capacitor lead the capacitor
voltage by 90°.
• The sine-wave ac voltage across a resistor is
always in phase with its current.
• The total sine-wave ac current for a parallel
RC circuit always leads the applied voltage
by an angle between 0° and 90°.
Current Phasors for Parallel
RC Circuits
IC
IT
q
IR
Current Phasors
I T = I 2R  I 2C
Currents in a Parallel RC Circuit
IT = 5 A
IC
VS = 120
R = 30 W
IT
XC = 40 W
IR
VS
120
=
=
= 4A
IR
R
30
IC =
VS
XC
=
120
= 3A
40
2
2
IT = I R  I C = 4 2  3 2 = 5 A
Phase Angle in a Parallel RC Circuit
IT = 5 A
3A
VS = 120
R = 30 W
5A
XC = 40 W
q
IC
4A
3
q = Tan
= Tan
= 37
IR
4
-1
-1
The total current leads the source voltage by 37°.
Impedance in a Parallel RC Circuit
IT = 5 A
3A
VS = 120
R = 30 W
5A
XC = 40 W
4A
Z EQ
VS
120
=
=
= 24W
IT
5
Summary of R, XC and Z
• Resistance (R) in Ohms, W
Voltage in phase with current.
• Capacitive Reactance (XC) in Ohms, W
Voltage lags current by 90°.
Summary of R, XC and Z
(continued)
• Series circuit impedance (ZT) in
Ohms, W
 Voltage lags current.
 Becomes more resistive with
increasing f.
 Becomes more capacitive with
decreasing f.
Summary of R, XC and Z
(continued)
• Parallel circuit impedance (ZEQ) in
Ohms, W
 Voltage lags current.
 Becomes more capacitive with
increasing f.
 Becomes more resistive with
decreasing f.
Summary of Formulas
• Series RC
XC =
1
2p fC
XC =
2
2
VT = VR  VC
2
ZT = R  X C
Tanq = -
XC
R
• Parallel RC
2
1
2p fC
2
2
=

IT
IR
IC
Z EQ =
VS
Tan q =
IC
IT
I
R