PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Analog and Digital Filters 661

P.6.2 Given the following fi lter’s transfer functions:

a. Hjw jw

jw a

()
 a



for  0

b. Hjw jw w

jw b jw w

() b

()

()

()





2 02

2 02 for ^0 notch filter

Evaluate by hand:

a. The fi lter type

b. The gain at H(w = 0 ) and H(w = ∞)

c. The cutoff frequency wc

d. The gain at |H(w = wc)| and phase at H(w = wc)

e. The fi lter’s BW

P.6.3 Obtain the magnitude and phase plots for the transfer functions of P.6.1 for the fol-

lowing cases: a = 2, 6, and 10, and discuss the effect of a.

P.6.4 Obtain the magnitude and phase plots of the transfer functions of P.6.2 for the fol-

lowing cases:

a. a = 2, b = 2

b. a = 2, b = 5, and wo = 15

P.6.5 Verify that the circuit shown in Figure 6.85 is of a normalized LPF, where all the

corresponding element values are in ohms, henries, and farads.

P.6.6 Transform the LPF of P.6.5 (Figure 6.85) into an LPF with a cutoff frequency at

5 kHz, and a load impedance of R = 600 Ω connected at its output terminals.

P.6.7 Transform the LPF of Figure 6.85 into a normalized HPF (wc = 1 and a load imped-

ance of R = 1 Ω).

P.6.8 Analyze the circuits shown in Figure 6.86 and

a. Verify the given expressions of H(w) = Vo(w)/Vi(w).

b. Obtain analytical expressions of the magnitudes [H(w)] and phases of H(w).

c. Let the values of the electrical elements be R 1 = 1 Ω, R 2 = 2 Ω, R 3 = 3 Ω, C 1 = 1 F,

and C 2 = 2 F.

Then create the script fi le plots that returns the plots of magnitude [H(w)] versus w

and phase [H(w)] versus w.

d. For each circuit evaluate or determine the following:

i. The BW

ii. The type of fi lter

FIGURE 6.85

Circuit diagram of P.6.5.

R = 1

Ro = 1

C1 = 1 C2 = 1

L = 2

Vi(w) Vo(w)