PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

572 Practical MATLAB® Applications for Engineers

FIGURE 6.11
Typical active fi lter structures and its respective transfer functions.

R 1

R 1

R 2

R 2

R 1

R 1

R 2

R 2

C 2

C 1

C 1

C 2

C 2

C 1

1

2

3

Vi

Vi

Vi

Vi

Vo

Vo

Vo

Vo

1

2

3

a 1 =

Hlp(s)=

Hhp(s) =

1

2

3

1

2

3

Hbr(s) =

Hbp(s) =

A=

(R (^1) C1) (R (^2) C2)
(^1) a 2 =^1
1
,
A s + a 2
R (^1) *C 2
1
R 2
R 1 s + a 1
s
s + a 1
C 2 s + a 2
C 1
(s + a1)(s + a2)
A
R.6.51 Let us turn our attention to the most common active fi lter structures. Confi gura-
tions as well as the respective transfer functions are indicated in Figure 6.11.
R.6.52 The loading effects associated with passive fi lters are overcome by using OA. Many
complex fi lt e r r e a l i z at io n s c a n t h e n b e i mple me nt e d by c o n n e c t i n g pr o t o t y p e s r e s u lt-
ing into products or sum structures of simple (fi rst- or second-order) fi lter types.
R.6.53 Figure 6.12 illustrates a second-order BRF employing simple fi rst-order fi lters
(LP and HP, with w 2 > w 1 ). Observe that by changing the summation by a product
(by cascading an LP with an HP, with w 1 > w 2 ), a BPF may be implemented.