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參數資料
| 型號： | LMF40 |
| 文件頁數： | 10/16頁 |
| 文件大?。?/td> | 321K |
| 代理商： | LMF40 |
2.0 Designing with the LMF40
(Continued)
Likewise, the attenuation at f
s
can be found using (3) with
the above values and n
e
4:
Attn (2 kHz)
e
10 log
[
1
a
10
0.1
b
1) (2 kHz/1 kHz)
8
]
e
18.28 dB
This result also meets the design specification given in Fig-
ure 6 again verifying that a single LMF40 section will be
adequate.
f
c
e
f
b
Since the LMF40’s cutoff frequency (f
c
), which corresponds
to a gain attenuation of
b
3.01 dB, was not specified in this
example, it needs to be calculated. Solving equation (3)
where f
e
f
c
as follows:
10
0.1(3.01 dB)
b
1
(10
0.1Amax
b
1)
1/(2n)
e
1 kHz
D
10
0.301
b
1
10
0.1
b
1
1/8
e
1.184 kHz
where f
c
e
f
CLK
/50 or f
CLK
/100. To implement this exam-
ple for the LMF40-50 the clock frequency will have to be set
to f
CLK
e
50(1.184 kHz)
e
59.2 kHz, or for the LMF40-100,
f
CLK
e
100 (1.184 kHz)
e
118.4 kHz.
2.2 CASCADING LMF40s
When a steeper stopband attenuation rate is required, two
LMF40s can be cascaded (Figure 7) yielding an 8th order
slope of 48 dB per octave. Because the LMF40 is a Butter-
worth filter and therefore has no ripple in its passband,
when LMF40s are cascaded the resulting filter also has no
ripple in its passband. Likewise the DC and passband gains
will remain at 1V/V. The resulting response is shown inFig-
ure 8a.
In determining whether the cascaded LMF40s will yield a
filter that will meet a particular amplitude response specifi-
cation, as above, equations (4) and (5) can be used, shown
below.
n
e
log
[
(10,
0.05Amin
b
1)/(10
0.05Amax
b
1)
]
2 log(f
s
/f
b
)
Attn (f)
e
10 log
[
1
a
(10
0.05Amax
b
1) (f/f
b
)
2
]
dB
where n
e
4 (the order of each filter).
(4)
(5)
Equation (4) will determine whether the order of the filter is
adequate (n
s
4) while equation (5) can determine the actu-
al stopband attenuation and cutoff frequency (f
c
) necessary
to obtain the desired frequency response. The design pro-
cedure would be identical to the one shown in Section 2.0.
2.3 CHANGING CLOCK FREQUENCY
INSTANTANEOUSLY
The LMF40 responds well to an instantaneous change in
clock frequency. If the control signal in Figure 9 is low the
LMF40-50 has a 100 kHz clock making f
c
e
2 kHz; when
this signal goes high the clock frequency changes to 50 kHz
yielding f
c
e
1 kHz. AsFigure 9 illustrates, the output signal
changes quickly and smoothly in response to a sudden
change in clock frequency.
The step response of the LMF40 in Figure 10 is dependent
on f
c
. The LMF40 responds as a classical fourth-order But-
terworth low-pass filter.
2.4 ALIASING CONSIDERATIONS
Aliasing effects have to be considered when input signal
frequencies exceed half the sampling rate. For the LMF40
this equals half the clock frequency (f
CLK
). When the input
signal contains a component at a frequency higher than half
the clock frequency f
CLK
/2, as in Figure 11a, that compo-
nent will be ‘‘reflected’’ about f
CLK
/2 into the frequency
range below f
CLK
/2, as in Figure 11b. If this component is
within the passband of the filter and of large enough ampli-
tude it can cause problems. Therefore, if frequency compo-
nents in the input signal exceed f
/2 they must be attenu-
ated before being applied to the LMF40 input. The neces-
sary amount of attenuation will vary depending on system
requirements. In critical applications the signal components
above f
CLK
/2 will have to be attenuated at least to the fil-
ter’s residual noise level.
TL/H/10557–7
f
e
1
RC In
D#
V
CC
b
V
t
b
V
CC
b
V
t
a
J#
V
t
a
V
t
b
J(
f
j
1
1.37 RC
(V
CC
e
10V)
FIGURE 1. Schmitt Trigger R/C Oscillator
10
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