Analog and Digital Filters
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c. Transform the circuit into a PBF, where the pass-band region is between 2000
and 4000 Hz.
d. Repeat part (c) for the case of a BSF.
P.6.12 The circuit diagram shown in Figure 6.89 is called a notch fi lter tuned at 2 rad/s.
a. Verify the preceding statement by obtaining plots of H(w) = V o (w)/V i (w).
b. Modify the circuit to a notch fi lter tuned at 10 rad/s.
P.6.13 Determine the lowest order of the analog transfer function of an LPF with the following specs: −2 dB at 2000 Hz, a minimum attenuation of 30 dB at 7000 Hz, for the
following fi lters types:
a. Butterworth
b. Chebyshev (types 1 and 2)
c. Elliptic
d. Bessel
P.6.14 Obtain the transfer function coeffi cients and the frequency response plots of a 10thorder maximally fl at analog LPF with a 3 dB cutoff angular frequency at 1 rad/s.
P.6.15 State and discuss the order of the analog fi lter obtained as a result of the LP-to-LP
fi lter transformation. Illustrate your conclusion with a 9th-order LP Butterworth
normalized fi lter with a cutoff frequency of w c = 0.35 rad/s that is transformed to
an equivalent LPF with w c = 3 rad/s.
P.6.16 State and discuss the order of the analog fi lter obtained as a result of the LP-to-HP
fi lter transformation. Illustrate your conclusion with a 9th-order LP Butterworth
normalized fi lter with a cutoff frequency w c = 0.4 rad/s that is transformed to an
equivalent HPF with w c = 4 rad/s.
P.6.17 State and discuss the order of the analog fi lter obtained as a result of the LP-to-BP
fi lter transformation. Illustrate your conclusion with a 10th-order low-pass
Butterworth normalized fi lter with a cutoff frequency w c = 0.45 rad/s that is
transformed to an equivalent BPF with w c = 10 rad/s and BW of 2 rad/s.
P.6.18 Repeat problem P.6.17 for the case of a BPF with a stop-band range given by 9 rad/s <
w < 11 rad/s.
FIGURE 6.88
Circuit diagrams of P.6.11.
RL = 1 Ω
L
C
V i (w )
V o (w)
FIGURE 6.87
Circuit diagrams of P.6.9.
L
C
R
V i (s)
V o (s)
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663
c. Transform the circuit into a PBF, where the pass-band region is between 2000
and 4000 Hz.
d. Repeat part (c) for the case of a BSF.
P.6.12 The circuit diagram shown in Figure 6.89 is called a notch fi lter tuned at 2 rad/s.
a. Verify the preceding statement by obtaining plots of H(w) = V o (w)/V i (w).
b. Modify the circuit to a notch fi lter tuned at 10 rad/s.
P.6.13 Determine the lowest order of the analog transfer function of an LPF with the following specs: −2 dB at 2000 Hz, a minimum attenuation of 30 dB at 7000 Hz, for the
following fi lters types:
a. Butterworth
b. Chebyshev (types 1 and 2)
c. Elliptic
d. Bessel
P.6.14 Obtain the transfer function coeffi cients and the frequency response plots of a 10thorder maximally fl at analog LPF with a 3 dB cutoff angular frequency at 1 rad/s.
P.6.15 State and discuss the order of the analog fi lter obtained as a result of the LP-to-LP
fi lter transformation. Illustrate your conclusion with a 9th-order LP Butterworth
normalized fi lter with a cutoff frequency of w c = 0.35 rad/s that is transformed to
an equivalent LPF with w c = 3 rad/s.
P.6.16 State and discuss the order of the analog fi lter obtained as a result of the LP-to-HP
fi lter transformation. Illustrate your conclusion with a 9th-order LP Butterworth
normalized fi lter with a cutoff frequency w c = 0.4 rad/s that is transformed to an
equivalent HPF with w c = 4 rad/s.
P.6.17 State and discuss the order of the analog fi lter obtained as a result of the LP-to-BP
fi lter transformation. Illustrate your conclusion with a 10th-order low-pass
Butterworth normalized fi lter with a cutoff frequency w c = 0.45 rad/s that is
transformed to an equivalent BPF with w c = 10 rad/s and BW of 2 rad/s.
P.6.18 Repeat problem P.6.17 for the case of a BPF with a stop-band range given by 9 rad/s <
w < 11 rad/s.
FIGURE 6.88
Circuit diagrams of P.6.11.
RL = 1 Ω
L
C
V i (w )
V o (w)
FIGURE 6.87
Circuit diagrams of P.6.9.
L
C
R
V i (s)
V o (s)
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