# Filtering with the LMF100

In general, the second order bandpass response is given by:

where *H*_{OBP} is the gain of the filter at the center frequency *f*_{0}, *Q* is the quality factor of the complex pole pair, and ω_{0} is the center frequency in rad/sec.

ω

_{0}= 2π

*f*

_{0}

For each mode described in the datasheet this simplifies down to a couple of governing equations relating external resistances to the properties of the bandpass filter. If the chip is wired for Mode 1 operation, then the important equations are:

From these equations you can determine the frequency of the incoming clock signal needed for a desired center frequency, and the values of resistors needed to set a desired center freqency gain and bandwidth (or alternately, Q). If the chip is wired as two cascaded, Mode 1, second order, bandpass filters, as shown in below, and each filter is constructed with the same external resistors, the fourth order filter response is:

The primary advantage to using the LMF100 with the PIC or a waveform generator like the AD9833 is that it allows the filter to be tuned directly by the PIC, by varying the input clock frequency. Beware when doing this, however, because by changing the center frequency of the filter you will also change your bandwidth in order to keep the constant Q value that is set by the external resistors.