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SALLEN-KEY LOW-PASS FILTER DESIGN PROGRAM
By Bruce Trump and R. Mark Stitt (602) 746-7445
Although low-pass filters are vital in modern electronics,
their design and verification can be tedious and time
consuming. The Burr-Brown FilterPro鈩?program makes
it easy to design unity-gain low-pass active filters. The
program supports the most commonly used all-pole fil-
ters: Butterworth, Chebyshev, and Bessel.
Butterworth鈥攎aximally
flat magnitude. This filter has
the flattest possible pass-band magnitude response. At-
tenuation is 鈥?dB at the design cutoff frequency. Attenu-
ation above the cutoff frequency is a moderately steep
鈥?0dB/decade/pole. The pulse response of the Butterworth
filter has moderate overshoot and ringing.
Chebyshev鈥攅qual
ripple magnitude. (Sometimes trans-
lated Tschebyscheff or Tchevysheff). This filter response
has steeper attenuation above the cutoff frequency than
Butterworth. This advantage comes at the penalty of
amplitude variation (ripple) in the pass-band. Unlike
Butterworth and Bessel responses, which have 3dB at-
tenuation at the cutoff frequency, Chebyshev cutoff fre-
quency is defined as the frequency at which the response
falls below the ripple band. For even-order filters, all
ripple is above the 0dB DC response, so cutoff is at 0dB鈥?/div>
see Figure 1a. For odd-order filters, all ripple is below the
0dB DC response, so cutoff is at 鈥?ripple) dB鈥攕ee Figure
1b. For a given number of poles, a steeper cutoff can be
achieved by allowing more pass-band ripple. The
Chebyshev has even more ringing in its pulse response
than the Butterworth.
FilterPro鈩? Burr-Brown Corp.
Bessel鈥攎aximally
flat delay, (also called Thomson).
Due to its linear phase response, this filter has excellent
pulse response (minimal overshoot and ringing). For a
given number of poles, its magnitude response is not as
flat, nor is its attenuation beyond the 鈥?dB cutoff fre-
quency as steep as the Butterworth. It takes a higher-order
Bessel filter to give a magnitude response similar to a
given Butterworth filter, but the pulse response fidelity of
the Bessel filter may make the added complexity worth-
while.
SUMMARY
Butterworth
Advantages鈥擬aximally
flat magnitude response in the
pass-band.
Disadvantages鈥擮vershoot
and ringing in step response.
Chebyshev
Advantages鈥擝etter
attenuation beyond the pass-band than
Butterworth.
Disadvantages鈥擱ipple
in pass-band. Even more ringing
in step response than Butterworth.
Bessel
Advantages鈥擡xcellent
step response.
Disadvantages鈥擡ven
poorer attenuation beyond the pass-
band than Butterworth.
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FILTER RESPONSE vs FREQUENCY
+10
0
+10
0
FILTER RESPONSE vs FREQUENCY
Ripple
鈥?0
鈥?0
鈥?0
鈥?0
鈥?0
f
C
/100
4-Pole Chebyshev
3dB Ripple
鈥?0
鈥?0
鈥?0
鈥?0
鈥?0
f
C
/100
5-Pole Chebyshev
3dB Ripple
Ripple
f
C
/10
f
C
10f
C
f
C
/10
f
C
10f
C
Normalized Frequency
Normalized Frequency
FIGURE 1a. Response vs Frequency of Even-Order
(4-pole), 3dB-Ripple Chebyshev Filter
Showing Cutoff at 0dB.
漏
FIGURE 1b. Response vs Frequency of Odd-Order
(5-pole), 3dB-Ripple Chebyshev Filter
Showing Cutoff at 鈥?dB.
Printed in U.S.A. August, 1991
1990 Burr-Brown Corporation
AB-017C
1
Application Bulletin Number 17
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Filter Response (dB)
Filter Response (dB)
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