Question 19.2: Refer to Fig. 19.10. Assume R=100kΩ and C=1nF . Specify the...
Refer to Fig. 19.10. Assume R=100 \mathrm{k} \Omega and C=1 \mathrm{nF} . Specify the external resistors R_G, R_F, R_Q to obtain a bandpass filter having center frequency f_c=10 \mathrm{kHz} , bandwidth W=500 \mathrm{~Hz} , and maximum passband gain K_{B P}=100 . Construct a plot of gain versus frequency as a check on the design.
From (19.50) we find
\begin{aligned} R_F &=\frac{1}{2 \pi \sqrt{10} f_c C}, Q=\frac{f_c}{W}, \\\\ R_G &=Q \frac{\sqrt{10} R}{K_{B P}}, \\\\ R_Q &=\frac{10 \sqrt{10} R_G R}{\left(10 R+11 R_G\right) Q-\sqrt{10} R_G} . \end{aligned} (19.50)
R_F=5.033 \mathrm{k} \Omega, Q=20, R_G=63.246 \mathrm{k} \Omega , R_Q=5.932 \mathrm{k} \Omega . Figure 19.11 shows graphs of gain versus frequency, normalized to the maximum gain, given by \left|H_{v B P}\left(j 2 \pi f_c\right)\right|=K_{B P}=100 . Thus
A_v=20 \log \left|\frac{H_{v B P}(j 2 \pi f)}{K_{B P}}\right| \mathrm{dB} .
In Fig. 19.11(a), 100 \mathrm{~Hz} \leq f \leq 1 \mathrm{MHz} on a logarithmic scale. In Fig. 19.11(b), 9.75 \mathrm{kHz} \leq f \leq 10.25 \mathrm{kHz} on a linear scale, to show that the half-power (-3 \mathrm{~dB}) bandwidth is as specified.
