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AD8031BNZ 开发手册 - ADI（亚德诺）
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ADI（亚德诺）
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运算放大器
封装:
DIP-8
描述:
ANALOG DEVICES AD8031BNZ 运算放大器, 单路, 80 MHz, 1个放大器, 30 V/µs, 2.7V 至 12V, DIP, 8 引脚
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–2–
AN-649
–3–
AN-649
BESSEL FILTER
Butterworth lters have fairly good amplitude and transient
behavior. The Chebyshev lters improve on the amplitude
response at the expense of transient behavior. The Bessel
lter is optimized to obtain better transient response due
to a linear phase (i.e., constant delay) in the pass band.
This means that there will be relatively poor frequency
response (less amplitude discrimination).
The frequency response, group delay, impulse response,
and step response for the Bessel lter are shown in
Figure 7.
The pole locations and corresponding
o
and
terms are tabulated in Table VIII.
LINEAR PHASE WITH EQUIRIPPLE ERROR
The linear phase lter offers linear phase response in the
pass band, over a wider range than the Bessel, and superior
attenuation far from cutoff. This is accomplished by letting
the phase response have ripples, similar to the amplitude
ripples of the Chebyshev. As the ripple is increased, the
region of constant delay extends further into the stop band.
This will also cause the group delay to develop ripples,
since it is the derivative of the phase response. The step
response will show slightly more overshoot than the Bessel
and the impulse response will show a bit more ringing.
The frequency response, group delay, impulse response,
and step response for equiripple lters with error of 0.05°
and 0.5° are shown in Figures 8 and 9, respectively. The pole
locations and corresponding
o
and terms are tabulated
in Tables IX and X.
GUASSIAN-TO-6 dB AND GUASSIAN-TO-12 dB FILTER
Gaussian-to-6 dB and Gaussian-to-12 dB lters are a com-
promise between a Chebyshev lter and a Gaussian lter,
which is similar to a Bessel lter. A transitional lter has
nearly linear phase shift and smooth, monotonic roll-off
in the pass band. Above the pass band and especially at
higher values of n, there is a break point beyond which
the attenuation increases dramatically compared to that
of the Bessel.
The Gaussian-to-6 dB lter has better transient response in
the pass band than does the Butterworth lter. Beyond the
breakpoint, which occurs at
o
= 1.5, the roll-off is similar
to that of the Butterworth lter.
The Gaussian-to-12 dB lter’s transient response in the pass
band is much better than that of the Butterworth lter. Beyond
the 12 dB breakpoint, which occurs at
o
= 2, the attenuation
is less than that of the Butterworth lter.
The frequency response, group delay, impulse response,
and step response for Gaussian-to-6 dB and Gaussian-
to-12 dB lters are shown in Figures 10 and 11, respectively.
The pole locations and corresponding
o
and terms are
tabulated in Tables XI and XII.
USING THE PROTOTYPE RESPONSE CURVES
The response curves and design tables for several of the
low-pass prototypes of the all-pole responses discussed
previously are now cataloged. All of the curves are normal-
ized to a –3 dB cutoff frequency of 1 Hz. This allows direct
comparison of the various responses. In all cases, the
amplitude response for the 2- through 10-pole cases for
the frequency range of 0.1 Hz to 10 Hz will be shown. Then,
a detail of the 0.1 Hz to 2 Hz pass band will be shown.
The group delay from 0.1 Hz to 10 Hz, the impulse response,
and the step response from 0 seconds to 5 seconds will
also be shown.
Curves must be denormalized if they are to be used to
determine the response of real life lters. In the case of
the amplitude responses, this is accomplished by simply
multiplying the frequency axis by the desired cutoff fre-
quency, F
C
. To denormalize the group delay curves, divide
the delay axis by 2 F
C
and multiply the frequency axis by
F
C
. Denormalize the step response by dividing the time axis
by 2 F
C
. Denormalize the impulse response by dividing
the time axis by 2 F
C
and multiplying the amplitude axis
by 2 F
C
.
For a high-pass lter, simply invert the frequency axis
for the amplitude response. In transforming a low-pass
lter into a high-pass lter, the transient behavior is not
preserved. Zverev provides a computational method for
calculating these responses.
In transforming a low-pass into a narrow-band band-
pass, the 0 Hz axis is moved to the center frequency, F
0
.
It stands to reason that the response of the band-pass
case around the center frequency would then match the
low-pass response around 0 Hz. The frequency response
curve of a low-pass lter actually mirrors itself around
0 Hz, although we generally do not concern ourselves
with negative frequency.
To denormalize the group delay curve for a band-pass
filter, divide the delay axis by BW, where BW is the
3 dB bandwidth in Hz. Then, multiply the frequency axis
by BW/2. In general, the delay of the band-pass lter at F
0
will be twice the delay of the low-pass prototype with the
same bandwidth at 0 Hz. This is due to the fact that the
low-pass to band-pass transformation results in a lter
with order 2n, even though it is typically referred to as
having the same order as the low-pass lter we derive it
from. This approximation holds for narrow-band lters.
As the bandwidth of the lter is increased, some distortion
of the curve occurs. The delay becomes less symmetrical,
peaking below F
0
.
The envelope of the response of a band-pass lter
resembles the step response of the low-pass prototype.
More exactly, it is almost identical to the step response of
a low-pass lter with half the bandwidth. To determine the
REV. 0
REV. 0
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