廬
APPLICATION BULLETIN
Mailing Address: PO Box 11400 鈥?Tucson, AZ 85734 鈥?Street Address: 6730 S. Tucson Blvd. 鈥?Tucson, AZ 85706
Tel: (602) 746-1111 鈥?Twx: 910-952-111 鈥?Telex: 066-6491 鈥?FAX (602) 889-1510 鈥?Immediate Product Info: (800) 548-6132
MFB 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 con-
suming. The Burr-Brown FilterPro鈩?program, FILTER2,
makes it easy to design low-pass active filters. The program
is intended to aid in the design of low-pass filters imple-
mented with the Multiple Feedback (MFB) topology. Be-
cause there are instances where the Sallen-Key filter topol-
ogy is a better choice, the program also supports Sallen-Key
low-pass filter design.
An ideal low-pass filter would completely eliminate signals
above the cutoff frequency, and perfectly pass signals below
cutoff (in the pass-band). In real filters, various trade-offs
are made in an attempt to approximate the ideal. Some filter
types are optimized for gain flatness in the pass-band, some
trade-off gain variation (ripple) in the pass-band for steeper
roll-off, still others trade-off both flatness and rate of roll-off
in favor of pulse-response fidelity. FILTER2 supports the
three most commonly used all-pole filter types: Butterworth,
Chebyshev, and Bessel.
Butterworth
(maximally flat magnitude). This filter has the
flattest possible pass-band magnitude response. Attenuation
is 鈥?dB at the design cutoff frequency. Attenuation above
the cutoff frequency is a moderately steep 鈥?0dB/decade/
pole. The pulse response of the Butterworth filter has mod-
erate overshoot and ringing.
FILTER RESPONSE vs FREQUENCY
+10
0
Chebyshev
(equal ripple magnitude). (Also transliterated
Tschebychev, Tschebyscheff or Tchevysheff.) This filter
type has steeper attenuation above the cutoff frequency than
Butterworth. This advantage comes at the penalty of ampli-
tude variation (ripple) in the pass-band. Unlike Butterworth
and Bessel responses, which have 3dB attenuation at the
cutoff frequency, Chebyshev cutoff frequency is defined as
the frequency at which the response falls below the ripple
band. For even-order filters, all ripple is above the 0dB-gain
DC response, so cutoff is at 0dB鈥攕ee Figure 1A. For odd-
order filters, all ripple is below the 0dB-gain 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 allow-
ing more pass-band ripple. The Chebyshev has even more
ringing in its pulse response than the Butterworth.
Bessel
(maximally flat time 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 frequency as steep as
the Butterworth. It takes a higher-order Bessel filter to give
a magnitude response which approaches that of a given
Butterworth filter, but the pulse response fidelity of the
Bessel filter may make the added complexity worthwhile.
FILTER RESPONSE vs FREQUENCY
+10
0
Ripple
Filter Response (dB)
Filter Response (dB)
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 Show-
ing Cutoff at 0dB.
FIGURE 1B. Response vs Frequency of Odd-Order (5-
pole), 3dB Ripple Chebyshev Filter Showing
Cutoff at 鈥?dB.
漏
1991 Burr-Brown Corporation
AB-034B
Printed in U.S.A. July, 1993
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