Chapter Questions
List the four types of filters.
What type of filter has a constant output voltage from dc up to the cutoff frequency?
What is a filter called that passes a band of frequencies while attenuating all frequencies outside the band?
In Fig. 11-2(a), if $R=100 \mathrm{k} \Omega$ and $C=0.02 \mu \mathrm{F}$, what is the cutoff frequency?
The low-pass filter of Fig. 11-2(a) is to be designed for a cutoff frequency of $4.5 \mathrm{kHz}$. If $C=0.005 \mu \mathrm{F}$, calculate $R$.
Calculate the cutoff frequency for each value of $C$ in Fig. P11-6.
What are the two characteristics of a Butterworth filter?
Design a $-40-\mathrm{dB} /$ decade low-pass filter at a cutoff frequency of $10 \mathrm{krad} / \mathrm{s}$. Let $C_1=$ $0.02 \mu \mathrm{F}$.
In Fig. 11-4(a), if $R_1=R_2=10 \mathrm{k} \Omega, C_1=0.01 \mu \mathrm{F}$, and $C_2=0.002 \mu \mathrm{F}$, calculate the cutoff frequency $f_c$.
Calculate (a) $R_3$, (b) $R_1$, and (c) $R_2$ in Fig. $11-5$ (a) for a cutoff frequency of $10 \mathrm{krad} / \mathrm{s}$. Let $C_3=0.005 \mu \mathrm{F}$.
If $R_1=R_2=R_3=20 \mathrm{k} \Omega, C_1=0.002 \mu \mathrm{F}, C_2=0.008 \mu \mathrm{F}$, and $C_3=0.004 \mu \mathrm{F}$ in Fig. 11$5(\mathrm{a})$, determine the cutoff frequency $\omega_c$.
In Fig. 11-5(a), $C_1=0.01 \mu \mathrm{F}, C_2=0.04 \mu \mathrm{F}$, and $C_3=0.02 \mu \mathrm{F}$. Calculate $R$ for a cutoff frequency of $1 \mathrm{kHz}$.
Calculate $R$ in Fig. 11-7(a) if $C=0.04 \mu \mathrm{F}$ and $f_c=500 \mathrm{~Hz}$.
In Fig. 11-7(a) calculate (a) $\omega_c$ and (b) $f_c$ if $R=10 \mathrm{k} \Omega$ and $C=0.01 \mu \mathrm{F}$.
Design a 40-dB/decade high-pass filter for $\omega_c=5 \mathrm{krad} / \mathrm{s} . C_1=C_2=0.02 \mu \mathrm{F}$.
Calculate (a) $R_1$ and (b) $R_2$ in Fig. 11-8(a) for a cutoff frequency of $40 \mathrm{krad} / \mathrm{s} . C_1=C_2=$ $250 \mathrm{pF}$.
For Fig. 11-9(a), let $C_1=C_2=C_3=0.05 \mu \mathrm{F}$. Determine (a) $R_3$, (b) $R_1$, and (c) $R_2$ for a cutoff frequency of $500 \mathrm{~Hz}$.
The circuit of Fig. 11-9(a) is designed with the values $C_1=C_2=C_3=400 \mathrm{pF}, R_1=$ $100 \mathrm{k} \Omega, R_2=25 \mathrm{k} \Omega$, and $R_3=50 \mathrm{k} \Omega$. Calculate the cutoff frequency $f_c$.
Find the (a) bandwidth, (b) resonant frequency, and (c) quality factor of a bandpass filter with lower and upper cutoff frequencies of 55 and $65 \mathrm{~Hz}$.
A bandpass filter has a resonant frequency of $1000 \mathrm{~Hz}$ and a bandwidth of $2500 \mathrm{~Hz}$. Find the lower and upper cutoff frequencies.
Use the capacitor and resistor values of the high-pass filter in Fig. 11-11 to prove $f_c=$ $3000 \mathrm{~Hz}$.
Use the capacitor and resistor values of the high-pass filter in Fig. 11-11 to prove that $f_c=300 \mathrm{~Hz}$.
Find $Q$ for the bandpass filter of Fig. 11-11.
Design a narrow bandpass filter using one op amp. The resonant frequency is $128 \mathrm{~Hz}$ and $Q=1.5$. Select $C=0.1 \mu \mathrm{F}$ in Fig. 10-12.
(a) How would you convert the bandpass filter of Problem 11-24 into a notch filter with the same resonant frequency and $Q$ ? (b) Calculate $f_l$ and $f_h$ for the notch filter.