Datasheet
C =
R
1
Z
o
Q
R
2
=
Q
2
R
1
Q =
R
1
C
1
+ R
2
C
1
- R
1
C
2
R
1
R
2
C
1
C
2
Q =
R
1
C
1
+ R
2
C
1
+ (1 - K
2
) * R
1
C
2
R
1
R
2
C
1
C
2
1
R
1
R
2
C
1
C
2
Z
o
=
K
2
QZ
o
jZ
Z
o
2
(jZ)
2
+ 1
+
G(jZ) = K
1
*
H(s) =
s
2
+ s *
R
1
R
2
C
1
C
2
1
1
R
1
C
2
+
R
2
C
2
+
+
K
1
* K
2
(1 - K
2
)
R
2
C
1
1
R
1
R
2
C
1
C
2
1
LMP8601, LMP8601-Q1
SNOSAR2E –SEPTEMBER 2008–REVISED MARCH 2013
www.ti.com
ADDITIONAL SECOND ORDER LOW PASS FILTER
The LMP8601/LMP8601Q has a third order Butterworth low-pass characteristic with a typical bandwidth of 60
kHz integrated in the preamplifier stage of the part. The bandwidth of the output buffer can be reduced by adding
a capacitor on the A1 pin to create a first order low pass filter with a time constant determined by the 100 kΩ
internal resistor and the external filter capacitor.
It is also possible to create an additional second order Sallen-Key low pass filter by adding external components
R
2
, C
1
and C
2
. Together with the internal 100 kΩ resistor R
1
as illustrated in Figure 34, this circuit creates a
second order low-pass filter characteristic.
When the corner frequency of the additional filter is much lower than 60 kHz, the transfer function of the
described amplifier van be written as:
(1)
Where K
1
equals the gain of the preamplifier and K
2
that of the buffer amplifier.
Equation 1 can be written in the normalized frequency response for a 2
nd
order low pass filter:
(2)
The cutoff frequency ω
o
in rad/sec (divide by 2π to get the cut-off frequency in Hz) is given by:
(3)
and the quality factor of the filter is given by:
(4)
With K
2
= 2x, Equation 4 transforms results in:
(5)
With this filter gain K2= 2x, the design procedure can be very simple if the two capacitors are chosen to be
equal, C
1
=C
2
=C. In this case, given the predetermined value of R1 = 100kΩ( the internal resistor), the quality
factor is set solely by the value of the resistor R
2
.
R
2
can be calculated based on the desired value of Q as the first step of the design procedure with Equation 6:
(6)
For instance, the value of Q can be set to 0.5√2 to create a Butterworth response, to 1/√3 to create a Bessel
response, or a 0.5 to create a critically damped response. Once the value of R
2
has been found, the second and
last step of the design procedure is to calculate the required value of C to give the desired low-pass cut-off
frequency using:
(7)
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