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Characteristics of Prototype Analog Filters 401
FIGURE 8.12
Realization of the coupled form oscillator
8.3.1 BUTTERWORTH LOWPASS FILTERS
This filter is characterized by the property that its magnitude response is
flat in both passband and stopband. The magnitude-squared response of
an Nth-order lowpass filter is given by
|H a (jΩ)| 2 1
= ( ) 2N
(8.45)
Ω
1+
Ω c
where N is the order of the filter and Ω c is the cutoff frequency in rad/sec.
The plot of the magnitude-squared response is as follow.
From this plot, we can observe the following properties:
• at Ω=0,|H a (j0)| 2 =1for all N.
• at Ω=Ω c , |H a (jΩ c )| 2 = 1 2
for all N, which implies a 3 dB attenuation
at Ω c .
• |H a (jΩ)| 2 is a monotonically decreasing function of Ω.
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