158 Chapter
7
2
0
a
0
a
1
S
)
(S
H
Figure 7-24. Frequency response of a real lowpass filter
We may distinguish between highpass, lowpass, bandpass and bandstop
filters. Depending on the type of polynomial used in the transition function
H(s), different types of filters are available such as Chebyshev, Butterworth,
elliptical, etc. The frequency responses differ in the tolerances of passband,
stopband and the slope of the transition. Other categories of filters are
possible, for example analog or digital, finite or infinite impulse response
(FIR and IIR). A general block diagram is shown in Figure 7-25.
Figure 7-25. Block diagram of an RF filter model
In this section we only consider Butterworth type filters, which are
known to have a maximally flat frequency response. For a lowpass filter this
is expressed in the Laplace domain as
0
2
( )
,
(1
)
i
i
i
a
H S
a S b S
with
1,...,
2
g
s
i
S
f
,
where S is the complex variable normalized on the frequency f
g
.
Through transformation of the variables a highpass description can be
obtained from this lowpass transfer function.
Summary :
For a lowpass filter this is expressed in the Laplace domain as 0 2 ( ) , (1 ) i i i a H S a S b S with 1,..., 2 g s i S f , where S is the complex variable normalized on the frequency f g .
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filters,frequency,lowpass,figure,response,filter,function,transition,block,725,butterworth,diagram,type