Analog Signal Processing

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Passive Butterworth Filter Cookbook

This book should allow anyone with basic electronics skills to quickly design a passive Butterworth filter. All possible low pass and high pass filters up to tenth order, and all possible band pass and band stop filters up to eighth order are covered.

Available in: PDF ($12.95) or Paperback ($24.95)

Low Pass Butterworth Filters

The program alpbw.c will calculate the component values for a low pass butterworth filter. The program is run on the command line with parameters as follows:

Usage: alpbw n t f
  n = filter order
  t = termination
      0 = same source and load resistance
      1 = either source or load resistance
  f = 3db cutoff frequency

The program outputs the component values for the LC ladder network that implements the filter. The termination resistances are assumed to equal 1. For a termination resistance equal to R multiply inductance values by R and divide capacitance values by R. The component values are assigned to the inductors and capacitors as shown in the following examples.

For an odd order filter with source resistance and infinite load resistance the first element must always be a shunt capacitor as shown in the following figure for a third order filter. The first output is the value of C₁. The second output is the value of L. The third output is the value of C₂. The same pattern applies to higher odd order filters with the same termination.

For an odd order filter with zero source resistance and finite load resistance the first element must be a series inductor as shown in the following figure. The component values are assigned in opposite order to the above example. The first output is the value of L₂. The second output is the value of C. The third output is the value of L₁. The same pattern applies to higher odd order filters with the same termination.

For equal source and load resistance there are two possible configurations for an odd order filter as shown in the following figures. In both cases the outputs specify the component values from left to right in shunt-series order or series-shunt order depending on the configuration.

For an even order filter with unequal source and load termination the first element will always be a series inductor as shown in the following two figures. In the first case (source resistance) the component values are assigned in series-shunt order from left to right. In the second case (load resistance) component values are assigned in shunt-series order from right to left.

For equal source and load resistance there are two possible configurations for an even order filter as shown in the following figures. In both cases the outputs specify the component values from left to right in shunt-series order or series-shunt order depending on the configuration.

These low pass filters can be transformed into high pass, band pass, and band stop filters using the transformations discussed in our book.