LTSPICE Active filter simulation example
fn=4kHz, Q=10, Fliege type Band-Elimination-Filter




The transfer function of the band eliminate filter circuit shown above is,
T(s) =  \frac{V_\mathrm{o}}{V_\mathrm{i}}
= \frac{s^2 + s  \displaystyle\frac{1}{C_2}\left(  \displaystyle\frac{1}{R_6} -   \displaystyle\frac{R_2}{R_1 R_5} \right) +  \frac{R_2}{C_1 C_2 R_1 R_3 R_4} }
{s^2 + s   \displaystyle\frac{1}{C_2 R_5}  +  \displaystyle\frac{R_2}{C_1 C_2 R_1 R_3 R_4}}
To make the natural frequency ωn simple, we set
C1 = C2 = C0, R1 = R2 = R3 = R4 = R0
To make the second-order transfer function a band-eliminate-filter, i.e. to eliminate the second term in the denominator, we set
R5 = R6 = RQ
Then with Q that is the quality factor, we have
1 / ω0 = C0 R0

ω0 / Q = C0 RQ
So Q will be
Q = RQ / R0
See Also
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