Elliptic High Pass Filter with the State Variable Biquad -Applet.

Cuthbert Nyack
The circuit for a second order filter and its transfer function with 2 poles and 2 zeros is shown below. C7-R7 can be added to the output of the circuit to produce a third order section. With R1 = R4, the zeros are on the imaginary axis and by choice of components, the zeros can be at lower frequencies than the poles. This makes the circuit suitabe for a high pass filter. This circuit is expensive in opamps but a current diffrerence opamp can be used to replace the integrator and inverter, reducing the number of opamps by 1.
Applet below can be used to determine denormalized component values for Elliptic filters with orders 2 to 9 and for different values of r and q. Filter order is set by scrollbar 0. n, r, q, R, C and F3dB must be set to get correct denormalized values.

Image below shows component values for a 7th order Elliptic low pass filter implemented as 2 second order and 1 third order section.
r = 25 and q = 29°.
R is set to 100KW, C = 0.01 mF and the 3dB frequency is 3kHz.
The normalized transition BW is ~0.516rad/s, the minimum stop band attenuation is > 100dB and the pass band ripple is 0.28dB.

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