PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Analog and Digital Filters 599

Then, H(s) = 4 s

(^2) + 6 s

6 s^2 + 9 s
is synthesized into the network shown in Figure 6.24.
R.6.145 The synthesis process for digital fi lters is simpler compared to the analog case.
Once the transfer function H(z) is known, the difference equation can be obtained
and an implementation can be realized (see Chapter 5 for details).

6.4 Examples

Example 6.1

Given the fi rst-order analog LPF shown in the circuit diagram of Figure 6.25, evaluate

by hand the following:

a. The transfer function H(w) = Vo(w)/ Vi(w)

b. Obtain expressions for H(w) and ∠ H(w)

Create the script fi le LP_fi lter_analysis that returns the following plots:

c. H(f) versus f and ∠H(f) versus f using the MATLAB function freqs

d. H(f)dB versus f and ∠H(f) versus f using a semilog scale and the MATLAB function

freqs

e. Bode plots of H(w) and ∠H(w) over the range − (^5) (1/(R C)) ≤ w ≤ (^5) (1/(R C))
f. Bode plots of H(w) and ∠H(w) with no argument (w)
FIGURE 6.23
Synthesis of Zb.
Zb R^2 = 1/2 C^1 = 4/3
FIGURE 6.24
Synthesis of H(s) = 4 s
(^2) + 6 s
____ 6 s (^2) + 9 s of R.6.144.
L 1 = 1/3 C 1
= 4/3
R 1 = 1/2 R^2 = 1/2
Vi(s) 1 Vo(s)