ACTIVE_FILTERS_Theory_and_Design

Introduction 5
A
Ideal Filter
A max
A o
f o f 2
A max
dB
A min
Pass-band
A min
Passband
f 1
Band
Reject
Transition
Region
Passband
f
FIGURE 1.5 Band-reject frequency response.
The selectivity factor Q is the ratio of the center frequency of a band-pass
filter to bandwidth, i.e.,
f
Q = =
BW f
0 0
f
− f
2 1
(1.7)
4. Band-reject filters reject frequencies within a specified band and pass
components outside this band (Figure 1.5).
1.3 THE MATHEMATICS OF ELEMENTARY FILTERS
The transfer functions consist of a numerator divided by a denominator, each of
which is a function of s, so they have the form:
Ns ()
Hs () =
Ds ()
(1.8)
The numerator and denominator can always be written as polynomials in s. To be
completely general, a transfer function for an nth-order network can be written as
Kb0
Hs ()=
sn
+ b sn−
1
+ b sn−2
+ bs+
b
n−1
n−2
1 0
(1.9)