ee303sp09 l05 filters
TRANSCRIPT
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EE303 Lesson 5:
Filters
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90.7
WSDL
Ocean City
90.3
WHID
Salisbury
Frequency
(MHz)
Receiver tuned to 90.9 MHz
90.5
WKHS
Worton
91.3
WMLU
Farmville
90.9
WETA
Washington
91.1
WHFC
Bel Air
91.5
WBJC
Baltimore
Tuning a radio
Consider tuning FM radio station.
What allows your radio to isolate one station
from all of the adjacent stations?
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Filters
A filter is a frequency-selective circuit.
Filters are designed to pass some frequencies
and reject others.
Frequency
(MHz)
Receiver tuned to 90.9 MHz
90.9
WETA
Washington
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Basic kinds of filters
There are four basic kinds of filters:
Low-pass filter. Passes frequencies below a criticalfrequency called the cutoff frequency and attenuates
those above. High-pass filter. Passes frequencies above critical
frequency but rejects those below.
Bandpass filter. Passes only frequencies in anarrow range between upper and low cutoff.
Bandstop filter. Rejects or stops frequencies in anarrow range but passes others.
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Basic kinds of filters
Bandpass filter response
f(Hz)fco
passband stopband
f(Hz)fco
passbandstopband
f(Hz)fc
passband
f1
f2
passbandstopband
f(Hz)fc
passband
f1
f2
stopband stopband
Low-pass filter response High-pass filter response
Bandstop filter response
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Filters construction
There are numerous ways to construct filters.
Passive filters a composed of only passive
components (resistors, capacitors, inductors)
and do not provide amplification. Active filters typically employ RC networks and
amplifiers with feedback and offer a number ofadvantages.
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Filter circuits
Filter circuits depend on the fact that theimpedance of capacitors and inductors is afunction of frequency.
Some common bandpass filter circuits
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Calculate the impedance of a resistor, a capacitor and aninductor at the following frequencies.
Example Problem 1
100 Hz
ZC
ZL
R
10,000 Hz1000 Hzf
2C
jZf C
2L Z j f L
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Calculate the impedance of a resistor, a capacitor and aninductor at the following frequencies.
Example Problem 1
-j1000
j10
100
100 Hz
-j10 -j100 ZC
j1000 j100 ZL
100 100 R
10,000 Hz1000 Hzf
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RC low-pass filter
What is the ratio of the output voltage (Vo) to theinput voltage (Vs)?
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RC low-pass filter
What is the ratio of the output voltage (Vo) to theinput voltage (Vs)?
2
1
1
1 1
1
1
Co s
C
o
s
o
s
j C
j RC R
j C
RC
ZV V
R Z
V
V
V
V
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RC low-pass filter
A low-pass filter passes frequencies below acritical frequency called the cutoff frequency andattenuates those above.
f(Hz)fco
RClow-pass filter response
actual filter output
passband stopband
ideal filter output
cutoff frequency
o
s
V
V
0 dB
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Cutoff frequency
The cutoff frequency is frequency at which theoutput amplitude is 70.7% of the input.
f(Hz)fco
RClow-pass filter response
actual filter output
passband stopband
ideal filter output
cutoff frequency
2
co
co
1 1
21
which implies
[rad/sec]
or [Hz]2
o
s RC
RC
fRC
V
V
o
s
V
V
0 dB
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What is the cutoff frequency of a single-section RC low-
pass filter with R = 8.2 k and C = 0.0033 F?
Example Problem 2
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RL low-pass filter
A low-pass filter can also be implemented with aresistor and inductor, the cutoff frequency isgiven
f(Hz)fco
RL low-pass filter response
actual filter output
passband stopband
ideal filter output
cutoff frequency
o
s
V
V
0 dB
co [Hz]2
RfL
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Filters
Notice the placement of the elements in RC andRL low-pass filters.
What would result if the position of the elementswere switched in each circuit?
RL low-pass filterRClow-pass filter
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High-pass filter
Switching elements results in a high-pass filter.
f(Hz)fco
high-pass filter response
actual
passbandstopband
ideal
cutoff frequency
o
s
V
V
0 dB
co co
1or [Hz]
2 2
Rf f
RC L
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What resistor value R will produce a cutoff frequency of
3.4 kHz with a 0.047F capacitor? Is this a high-pass orlow-pass filter?
Example Problem 3
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Improving filter response
One method of creating a more selective filter isto cascade filter stages.
The attenuation of this two-stage filter is 40dB/decade instead of 20 dB/decade.
Two stage RCfilter
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LCFilters
At higher frequencies (> 100-kHz), it is morecommon to find LC filters made with inductorsand capacitors.
The response curves of the major families offilters are shown below.
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Bandpass filter
A bandpass filter passes frequencies below acritical frequency called the cutoff frequency andattenuates those above.
f(Hz)fc
LCbandpass filter response
actual filter output
passband
ideal filter output
center frequency
o
s
V
V
0 dB
f1 f2
upper cutofflower cutoff
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Cascading bandpass filter
Improved selectivity with steeper skirts on thecurve can be obtained by cascading severalbandpass sections.
How cascading filter sections narrow the bandwidth and improve selectivity.
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Active filters
Active filters incorporate RCnetworks andamplifiers with feedback to produce low-pass,high-pass, bandpass and bandstop responses.
Active bandpass and notch filters.