PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Analog and Digital Filters 571

Observe that the effect of the inductor in an LPF can be replaced by a capacitor.

R.6.47 Examples of normalized passive fi rst-order HPFs are illustrated in Figure 6.7.

Observe again that the effect of the inductor in the HPF can be replaced by employ-

ing a capacitor.

R.6.48 The preceding simple prototype fi lter types (LP and HP) are typically implemented

as segments (eliminating the resistors), and are referred to as T and π sections, dis-

cussed in R.6.49.

R.6.49 Typical T and π LPF prototype segments, also referred to as sections or blocks, are

illustrated in Figure 6.8.

An all-pole prototype LPF can be realized by connecting T sections as illustrated

in Figure 6.9. The order of the fi lter is then given by the total number of indepen-

dent capacitors and inductors. For the network shown in Figure 6.9, the order n of

the LPF is given by n = 2 m.

R.6.50 Typical HP T and π sections are illustrated in Figure 6.10, and are obtained by

replacing the inductors by capacitors and capacitors by inductors of the LP sections

shown in Figure 6.8.

FIGURE 6.7

Normalized passive fi rst-order HPF.

R = 1 Ω

C = 1 F R = 1 Ω

Vi(s) Vo(s) Vi(s) L = 1 H Vo(s)

H(s) = Vo(s)

Vi(s)

= s

s+1

The transfer function of either network is given by

FIGURE 6.8

T and π LPF prototype segments.

L/2 L/2 L

C C C

FIGURE 6.9

All-pole prototype LPF.

L 1 L 2 Lm − 1 Lm

C 1 C 2 Cm − 1 Cm R

FIGURE 6.10

T and π HPF prototype segments.

C C

L L C L