Odd Order Butterworth High Pass Filter with Passive Components Applet.

Cuthbert Nyack
The basic filter structure for passive filters is the normalized low pass filter from which other types can be derived by various transformations.
On this page a high pass filter is derived from a low pass structure. The image below shows a fifth order dual low pass filter and its high pass equivalent. The normalized high pass component values are the inverse of the low pass equivalents. ie C1 = 1/L1 etc. The dual low pass structure is chosen as the starting point because the resulting high pass has more capacitors than inductors.
Component values for odd order passive high pass Butterworth filters can be derived from the applet below. Fn = 1 to 4 shows filters with order 3, 5, 7 and 9. Fn = 5 to 8 shows only numerical values.
Normalized high pass values are shown at the top in green and denormalized values are shown in yellow in the bottom. The sensitivity of the transfer function to variation in component values can be seen by changing scrollbars 11 to 30.

Image below shows a 9th order high pass Butterworth Filter. Denormalized values shown in yellow are for a filter with RS = 100W, RL = 100W, a 3dB frequency of 1KHz and an impedance scaling factor of 100.0.
Image below shows how the transfer function of the filter is affected when the Capacitor C1 is 10% larger than its correct value.

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COPYRIGHT 2011 Cuthbert Nyack.