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Band-Pass Filter Design
After α has been determined, all quantities of the partial filters can be calculated using the
following equations:
The mid frequency of filter 1 is:
f m1
f m
(16–14)
the mid frequency of filter 2 is:
f m2
f m·
(16–15)
with f m being the mid frequency of the overall forth-order band-pass filter.
The individual pole quality, Q i , is the same for both filters:
Q i
Q· 1 2 b 1
·a 1
(16–16)
with Q being the quality factor of the overall filter.
The individual gain (A mi ) at the partial mid frequencies, f m1 and f m2 , is the same for both
filters:
A mi
Q i
Q ·
A
m
B1
(16–17)
with A m being the gain at mid frequency, f m , of the overall filter.
Example 16–6. Fourth-Order Butterworth Band-Pass Filter
The task is to design a fourth-order Butterworth band-pass with the following parameters:
mid frequency, f m = 10 kHz
bandwidth, B = 1000 Hz
and gain, A m = 1
From Table 16–2 the following values are obtained:
a1 = 1.4142
b1 = 1
α = 1.036
16-34