Transcript Filter quality “Q” - Agricultural engineering

Filter quality “Q” and Filter types
2/19/2004
BAE 5413
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“Q” - Quality factor
• Consider a band pass filter
G(s) 
Q
As
2
 1  2 2
  s 
s 1
c
 c 
As
 2 2
 s  2s  1
1
2
G( s) 
As
 s 
2 2
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
Q

s 1
As
 1

 2 f
2
 2
1
 s 
s 1
2 f Q

BAE 5413
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“Q” Examples
• Q=1,
G( s) 
As
2
 1  2
1

 s 
s 1
2 1000
 2 1000
Gain dB
0
-50
-100 -1
10
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BAE 5413
0
1
2
10
10
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Frequency3 of(rad/sec
“Q” Examples
• Q=10, G( s) 
As
2
 1  2
1

 s 
s 1
2 10000
 2 1000
Gain dB
0
-50
-100
-1
10
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BAE 5413
0
1
2
10
10
Frequency (rad/sec)
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Filter types
• Butterworth - Ripple-free passband and a smooth stop band.
Butterworth has least distortion due to almost linear phase.
• Chebyshev - Predetermined passband ripple and requires
smaller order than a Butterworth filter for a desired response.
Superior for applications where passband includes only one
frequency of interest
• Elliptical - Equiripple pass- and stop-band, Predetermined
amount of passband ripple along with ripple in the stop band.
Elliptic filters require smallest order for a desired magnitude
response
• Bessel -constant propagation delay across the input frequency
spectrum
• Gaussian -the most gradual pass band roll-off and the lowest
group delay. Low distortion across the spectrum.
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BAE 5413
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