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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  jRC
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
jRC
H ( j ) 
1  jRC
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  2F
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 ( jo )  H ( jo ) 
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 ( jo )  H ( jo ) 
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

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