LMP8601MASLASHNOPB datasheet(14/29 Pages) TI1

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C =

R1Zo

R2 =

Q =

R1C1 + R2C1 - R1C2

R1R2C1C2

Q =

R1C1 + R2C1 + (1 - K2) * R1C2

R1R2C1C2

Zo =

QZo

(jZ)

+ 1

G(jZ) = K1 *

H(s) =

+ s *

R1R2C1C2

R1C2

R2C2

K1 * K2

(1 - K2)

R2C1

R1R2C1C2

LMP8601, LMP8601-Q1

SNOSAR2E – SEPTEMBER 2008 – REVISED MARCH 2013

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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 k

Ω

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

R2, C1 and C2. Together with the internal 100 kΩ resistor R1 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 K1 equals the gain of the preamplifier and K2 that of the buffer amplifier.

Equation 1 can be written in the normalized frequency response for a 2nd order low pass filter:

(2)

The cutoff frequency

ωo 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 K2 = 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, C1=C2=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 R2.

R2 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 R2 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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