Refer to Fig. 19.10. Assume R=100kΩ and C=1nF . Specify the external resistors RG,RF,RQ to obtain a bandpass filter having center frequency fc=10kHz , bandwidth W=500 Hz , and maximum passband gain KBP=100 . Construct a plot of gain versus frequency as a check on the design.

Question

Refer to Fig. 19.10. Assume [latex] R=100 \mathrm{k} \Omega[/latex] and [latex] C=1 \mathrm{nF}[/latex] . Specify the external resistors [latex] R_G, R_F, R_Q[/latex] to obtain a bandpass filter having center frequency [latex] f_c=10 \mathrm{kHz}[/latex] , bandwidth [latex] W=500 \mathrm{~Hz} [/latex] , and maximum passband gain [latex] K_{B P}=100[/latex] . Construct a plot of gain versus frequency as a check on the design.

Accepted Answer

From (19.50) we find

[latex] \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 ight) Q-\sqrt{10} R_G} . \end{aligned}[/latex] (19.50)

[latex] R_F=5.033 \mathrm{k} \Omega, Q=20, R_G=63.246 \mathrm{k} \Omega[/latex] , [latex] R_Q=5.932 \mathrm{k} \Omega[/latex] . Figure 19.11 shows graphs of gain versus frequency, normalized to the maximum gain, given by [latex] \left|H_{v B P}\left(j 2 \pi f_c ight) ight|=K_{B P}=100[/latex] . Thus

[latex] A_v=20 \log \left|\frac{H_{v B P}(j 2 \pi f)}{K_{B P}} ight| \mathrm{dB} . [/latex]

In Fig. 19.11(a), [latex] 100 \mathrm{~Hz} \leq f \leq 1 \mathrm{MHz}[/latex] on a logarithmic scale. In Fig. 19.11(b), [latex] 9.75 \mathrm{kHz} \leq f \leq 10.25 \mathrm{kHz}[/latex] on a linear scale, to show that the half-power [latex] (-3 \mathrm{~dB})[/latex] bandwidth is as specified.

Question 19.2: Refer to Fig. 19.10. Assume R=100kΩ and C=1nF . Specify the...

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