# Odd Order Butterworth Low Pass Filter with Passive Components Applet.

Cuthbert Nyack
Analytic expressions are available for calculating component values for odd and even Butterworth and odd Chebyshev filters with equal terminations. Odd order Butterworth and Chebyshev filters are symmetric and the impedance of each half can be scaled independently to derive component values for unequal terminations.
The circuits for third and ninth order filters and their duals are shown below.
For all cases at low frequencies, the impedance of the inductors is small and that of the capacitors is large, so the output Vo ~ VS (RL/(RL + RS)). At high frequencies the output goes to zero. Capacitors are connected as shunt elements and inductors as series elements. The third order filter would be described as RS, C1, L2, C3, RL and its dual by RS, L1, C2, L3, RL. The applet below can be used to calculate component values for low pass odd order Butterworth filters with RS = 1 and variable RL.

Other applets on the following pages can be used calculate component values for HP, BP and BS Butterworth and Chebyshev filters.

The function of the applet is controlled by Fn which is set scrollbar 0.
Fn = 1 to 4 shows filters with order 3, 5, 7 and 9. Fn = 5 to 8 shows dual circuit filters with orders 3, 5, 7 and 9.
Fn = 9 to 16 show only the values without the plots.
Normalized component values are shown in green and denormalized values in yellow.
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 Butterworth Filter. Denormalized values shown in yellow are for a filter with RS = 100W, RL = 150W, a 3dB frequency of 4KHz and an impedance scaling factor of 100.0. All resistances are in ohms, all inductances in henries and all capacitances in farads. Image below shows how the transfer function of the filter is affected when the Inductor L8 is 5% larger than its correct value. The magnitude and phase of the error is shown in pink and cyan. 