The LMP86x1-Q1 have a third-order Butterworth lowpass characteristic with a typical bandwidth of 60kHz integrated in the preamplifier stage. 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 100kΩ internal resistor and the external filter capacitor.

Creating an additional second-order is also possible, Sallen-Key, low-pass filter by adding external components R₂, C₁ and C₂. Together with the internal 100kΩ resistor R₁ as illustrated in Figure 6-1, this circuit creates a second-order, low-pass filter characteristic.

When the corner frequency of the additional filter is much lower than 60kHz, the transfer function of the described amplifier can be written as:

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 second-order lowpass filter:

The cutoff frequency ω_o in rad/sec (divide by 2π to get the cut-off frequency in Hz) is given by:

and the quality factor of the filter is given by:

With K₂ = 2x, Equation 4 transforms results in:

For any filter gain K > 1x, the design procedure can be very simple if the two capacitors are chosen to in a certain ratio.

Inserting this in Equation 4 for Q results in:

Which results in:

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 the following equation:

For the gain of 2 for the LMP8601-Q1, the result is:

For the gain of 5 for the LMP8602-Q1, the result is:

For the gain of 10 for the LMP8603-Q1, the result is:

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. After 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:

For the gain = 2, the result is:

The gain = 5 results in:

The gain = 10 gives:

For C₂ the value is calculated with:

For a gain = 2:

Or for a gain = 5:

And for a gain = 10:

Note that the frequency response achieved using this procedure is only accurate if the cut-off frequency of the second-order filter is much smaller than the intrinsic 60kHz, low-pass filter. In other words, select the frequency response of the LMP8601-Q1 circuit so that the internal poles do not affect the external second-order filter.