Question 9.7: Determine the center frequency, Q, and BW for the band-pass ...
Determine the center frequency, Q, and BW for the band-pass output of the statevariable filter in Figure 9–22.
For each integrator,
f_c=\frac{1}{2 \pi R_4 C_1}=\frac{1}{2 \pi R_7 C_2}=\frac{1}{2 \pi(1.0 ~\mathrm{k} \Omega)(0.022~ \mu \mathrm{F})}=7.23 ~\mathrm{kHz}
The center frequency is approximately equal to the critical frequencies of
the integrators.
f_0=f_c=7.23~ \mathrm{kHz}
Q=\frac{1}{3}\left(\frac{R_5}{R_6}+1\right)=\frac{1}{3}\left(\frac{100~ \mathrm{k} \Omega}{1.0~ \mathrm{k} \Omega}+1\right)=33.7
B W=\frac{f_0}{Q}=\frac{7.23~ \mathrm{kHz}}{33.7}=\mathbf{2 1 5}~ \mathrm{Hz}
PRACTICE EXERCISE
Determine f_0, Q, and BW for the filter in Figure 9–22 if R_4=R_6=R_7=330 ~\Omega with all other component values the same as shown on the schematic.