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ANALOG FILTERS
ELEC 202 Circuit Analysis II
Definition
A frequency-selective device or circuit
designed to pass signals with desired
frequencies and reject or attenuate
signals with unwanted frequencies
Limit the frequency spectrum of a signal
to some specified band of frequencies
Applications in communications and
control systems
Types of Filters
– passes low frequencies and
stop high frequencies
Highpass – passes high frequencies and
rejects low frequencies
Bandpass – passes frequencies within a
certain band and blocks
frequencies outside the band
Bandstop – passes frequencies outside a
certain band and blocks
frequencies within the band
Lowpass
Lowpass Filter
Highpass Filter
Bandpass Filter
Bandstop Filter
Passive vs. Active Filters
A passive filter consists of only passive
elements (e.g., R, L, and C).
An active filter consists of active elements
(e.g., transistors and op amps) in addition
to passive elements.
Cutoff Frequency
The frequency at which the frequency
response drops in magnitude to 70.71%
(or 3dB) of its maximum value.
Or, the frequency at which the output
power of the filter is half of the maximum
input power half-power frequency
Also called corner frequency or roll-off
frequency
Obtained by setting the magnitude of
H ( j ) to 1 / 2
Lowpass Filter
Designed to pass only frequencies from dc up to
the cutoff frequency.
H ( j )
H() 0
1
1 jRC
M ( j c ) H ( j c )
1
1 c2R 2C 2
1
2
c
1
RC
Highpass Filter
Designed to pass all frequencies above its cutoff
frequency.
H() 1
jRC
H ( j )
1 jRC
M ( j c ) H ( j c )
c RC
1 c2R 2C 2
1
2
c
1
RC
Example
What type of passive filter does the following
circuit represent? Also, calculate its cutoff
frequency.
R 2k , L 2H , C 2F
Example
For the circuit shown, identify the type of
filter it represent by obtaining Vo ( j ) /Vi ( j )
and calculate its corner frequency.
R1 R2 100 , L 2mH
Bandpass Filter
Designed to pass all frequencies within a certain
Band of frequencies.
H ( j )
H(1) 0
R
R j (L 1 / C )
H() 0
o center frequency
1 , 2 half - power frequencie s
1 - 2 3 - dB passband bandwidth
Bandpass Filter
H ( j )
R
R j (L 1 / C )
M ( jo ) H ( jo )
M ( j ) H ( j )
R
1
R 2 o L
o C
R
1
R 2 L
C
2
R
1
R
1
2L
2
L
LC
2
2
1
o
1
LC
1
2
2
R
1
R
2
2L
LC
2L
Bandstop Filter
Designed to stop all frequencies within a certain
band of frequencies.
j (L 1 / C )
H ( j )
R j (L 1 / C )
H(1) 1
H() 1
o rejection frequency
1 , 2 half - power frequencie s
1 - 2 3 - dB rejection bandwidth
Bandstop Filter
j (L 1 / C )
H ( j )
R j (L 1 / C )
M ( jo ) H ( jo )
M ( j ) H ( j )
R
1
R 2 o L
o C
R
1
R 2 L
C
2
R
1
R
1
2L
2
L
LC
2
2
1
o
1
LC
1
2
2
R
1
R
2
2L
LC
2L
Narrowband vs. Wideband
Rule of thumb:
If the 3-dB bandwidth of a bandpass filter
is more than twice the center frequency,
the filter is said to be wideband.
Examples of narrowband filters:
Resonator, Comb filters, notch filters,
inverse comb filters