Transcript Chapter 27

Basic Electronics
Ninth Edition
Grob
Schultz
©2002 The McGraw-Hill Companies
Basic Electronics
Ninth Edition
CHAPTER
27
Filters
©2003 The McGraw-Hill Companies
Topics Covered in Chapter 27
 Examples of Filtering
 Direct Current Combined with
Alternating Current
 Transformer Coupling
 Capacitive Coupling
 Bypass Capacitors
 Filter Circuits
Topics Covered in Chapter 27
(continued)




Low-Pass Filters
High-Pass Filters
Analyzing Filter Circuits
Decibels and Frequency Response
Curves
 Resonant Filters
 Interference Filters
Low-Pass Filters
• Low-pass filters pass dc and the lower
frequencies, but block higher
frequencies.
• For a practical low-pass filter:
The resistor or inductor is in series
with the load.
The associated capacitor is shunted
across the line.
High-Pass Filters
• High-pass filters block dc and lower
frequencies and pass higher
frequencies.
• For a practical high-pass filter:
The capacitor is in series with the
load.
The associated resistor or inductor is
shunted across the line.
Pulsating DC
• Pulsating direct current or voltage
consists of:
An average dc value
An ac component that goes above
and below the average dc value.
• Filters can be used to separate the dc
and ac components.
RC Bypass and RC Coupling
Circuits
• An RC bypass circuit is effectively a
low-pass filter (often used to reject
noise).
• RC bypass circuits pass dc (0 Hz).
• An RC coupling circuit is effectively
a high-pass filter.
• RC coupling blocks dc (0 Hz).
RC coupling blocks
the DC component.
B
A
4 VP-P
1 kHz
5V
10 mF
1 kW
+7
Volts
+5
A
AC+DC
B
AC
5V
+3
+2
0
0V
-2
0
1
2
Time in ms
3
Cutoff Frequency
At the cutoff frequency (fc):
• The output voltage is reduced to
70.7% of maximum output voltage.
• XL or XC is equal to R.
• fc = 1/(2pRC) for RC filters.
• fc = R/(2pL) for RL filters.
• The phase angle is 45°.
Frequency Response of an RC Low-Pass Filter
0
10 V
7
f
1 kW
1 mF
-30
vOUT
4
-60
1
-90
0
0.2
1
2pRC
0.4
0.6
Frequency in kHz
0.8
1
Phase angle in degrees
vOUT in Volts
10
Frequency Response of an RC High-Pass Filter
90
10 V
7
f
1 mF
1 kW
vOUT
60
4
30
1
0
0
0.2
1
2pRC
0.4
0.6
Frequency in kHz
0.8
1
Phase angle in degrees
vOUT in Volts
10
Log-Log Graph (4 cycle by 2 cycle)
10
1 octave
1 decade
1 decade
1
1 octave
0.1
1
1 decade
10
2
30
100
500
1k
10 k
The dB Unit of Measurement
• The decibel (dB) unit of measure is often
used to compare output to input.
• The formula for the dB power ratio is:
NdB = 10 log(Pout/Pin)
• The formula for the dB voltage ratio is:
NdB = 20 log(Vout/Vin)
The Half-Power Point
• The cutoff frequency of a filter is where the
output power drops to half of maximum
output (-3 dB).
fc = 10 log(Pout/Pin) = 10 log(0.5) = -3 dB
• Power varies as the square of the voltage. P
= V2/R
• Doubling the logarithm of a quantity is the
same as squaring the quantity.
fc = 20 log(Vout/Vin) = 20 log (0.707) = -3 dB
Bandpass/Bandstop Filters
Low-pass and high-pass filters can be
combined to pass or block a certain band of
frequencies.
• A bandpass filter passes only a selected
band of frequencies.
• A bandstop filter passes all frequencies
except those in a selected band.
RC Bandpass Filter (1.3 dB passband loss)
0.47 mF
1 kW
f
10 kW
4.7 nF
100 kW
0.47 nF
vOUT
0
vOUT in dB
cutoff
3 dB
-10
BW = 2.2 kHz
-20
10
100
1k
Frequency in Hz
10 k
Resonant filters work well at radio frequencies.
4W
20 V
1 mH
f
1 nF
fr =
1
2p LC
=
1
2p 1x10 x1x10
-6
-9
= 5.03MHz
5
Current in A
4
3
2
1
0
1
2
3
4
5
6
7
Frequency in MHz
8
9
10
RC Bandstop (notch) Filter
f
1
fN =
4pR1C1
2R1
2R1
30 kW
10 nF
30 kW
2C1
5 nF
5 nF
C1
R1
vOUT
500 kW
C1
15 kW
1
= 1.06kHz
fN =
12.6 x 15kx 5n
RC Bandstop (notch) Filter
0
-20
vOUT in dB
LP
-40
HP
-60
-80
0.1
1
Frequency in kHz
10