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參數(shù)資料
| 型號(hào)： | MF4 |
| 廠商： | National Semiconductor Corporation |
| 英文描述： | MF4 4th Order Switched Capacitor Butterworth Lowpass Filter |
| 中文描述： | MF4四階巴特沃斯低通開關(guān)電容濾波器 |
| 文件頁(yè)數(shù)： | 8/14頁(yè) |
| 文件大小： | 481K |
| 代理商： | MF4 |
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1.0 MF4 Application Hints
(Continued)
If the MF were set up for a cutoff frequency of 10 kHz the in-
put impedance would be:
In this example with a source impedance of 10K the overall
gain, if the MF4 had an ideal gain of 1 or 0 dB, would be:
Since the maximum overall gain error for the MF4 is
±
0.15 dB with R
≤
2 k
the actual gain error for this case
would be +0.06 dB to 0.24 dB.
1.4 CUTOFF FREQUENCY RANGE
The filter’s cutoff frequency (f
) has a lower limit due to leak-
age currents through the internal switches draining the
charge stored on the capacitors. At lower clock frequencies
these leakage currents can cause millivolts of error, for ex-
ample:
The propagation delay in the logic and the settling time re-
quired to acquire a new voltage level on the capacitors limit
the filter’s accuracy at high clock frequencies. The amplitude
characteristic on
±
5V supplies will typically stay flat until f
exceeds 750 kHz and then peak at about 0.5 dB at the cor-
ner frequency with a 1 MHz clock.As supply voltage drops to
±
2.5V, a shift in the f
/f
ratio occurs which will become
noticeable when the clock frequency exceeds 250 kHz. The
response of the MF4 is still a good approximation of the ideal
Butterworth low-pass characteristic shown in Figures 6, 7
2.0 Designing With The MF4
Given any low-pass filter specification, two equations will
come in handy in trying to determine whether the MF4 will do
the job. The first equation determines the order of the
low-pass filter required to meet a given response specifica-
tion:
(3)
where n is the order of the filter, A
is the minimum stop-
band attenuation (in dB) desired at frequency f
, and A
is
the passband ripple or attenuation (in dB) at cutoff frequency
f
. If the result of this equation is greater than 4, more than a
single MF4 is required.
The attenuation at any frequency can be found by the follow-
ing equation:
Attn (f) = 10 log [1 + (10
0.1A
max
1) (f/f
b
)
2n
] dB
where n = 4 for the MF4.
(4)
2.1 A LOW-PASS DESIGN EXAMPLE
Suppose the amplitude response specification in Figure 8 is
given. Can the MF4 be used The order of the Butterworth
approximation will have to be determined using Equation (1)
Since n can only take on integer values, n = 4. Therefore the
MF4 can be used. In general, if n is 4 or less a single MF4
stage can be utilized.
Likewise, the attenuation at f
can be found using Equation
(4) with the above values and n = 4:
Attn (2 kHz) = 10 log [1 + 10
0.1
1) (2 kHz/1 kHz)
8
] =
18.28 dB
This result also meets the design specification given in Fig-
ure 8 again verifying that a single MF4 section will be ad-
equate.
Since the MF4’s cutoff frequency (f
), which corresponds to
a gain attenuation of 3.01 dB, was not specified in this ex-
ample, it needs to be calculated. Solving Equation (4) where
f = f
c
as follows:
where f
= f
/50. To implement this example for the
MF4-50 the clock frequency will have to be set to f
=
50(1.184 kHz) = 59.2 kHz, or for the MF4-100, f
CLK
= 100
(1.184 kHz) = 118.4 kHz.
2.2 CASCADING MF4s
When a steeper stopband attenuation rate is required, two
MF4s can be cascaded (Figure 9) yielding an 8th order slope
of 48 dB per octave. Because the MF4 is a Butterworth filter
and therefore has no ripple in its passband when MF4s are
cascaded, the resulting filter also has no ripple in its pass-
band. Likewise the DC and passband gains will remain at
1V/V. The resulting response is shown in Figure 10 Figure
11
In determining whether the cascaded MF4s will yield a filter
that will meet a particular amplitude response specification,
as above, Equations (5), (6) can be used, shown below.
(5)
(6)
where n = 4 (the order of each filter).
Equation (5) will determine whether the order of the filter is
adequate (n
≤
4) while Equation (6)can determine the actual
stopband attenuation and cutoff frequency (f
) necessary to
obtain the desired frequency response. The design proce-
dure would be identical to the one shown in section 2.0.
www.national.com
8
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