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Lesson 38 – Filters III (Variant of Section 124) (Variant of CLO 122)
This is the last of two lessons on filter analysis and design.
The first focused on firstorder LP and HP.
The second
focuses on BP and BR.
In discussing BP and BR filters start by using ideal models – students seem to
grasp easily the concept when presented that way. Again reintroduce our block
diagram and point out that in an ideal system
H(j
ϖ
)
, the filter’s gain,
can be
only either “1” or “0”. If the signal falls in the pass band it comes out the output
unscathed (
H(j
)
= 1).
If, however it falls in the stop band it does not exit at all
(

H(j
)
= 0). If we look at the
ideal filters, we see that the LPF
will pass all signals up to
LP
and the HPF will pass signals greater than
HP
.
Since the two
filters are connected in cascade, only those signals that are
between
HP
and
LP
will pass through both filters.
Hence, we
have a BPF with a
Bandwidth, B, of
HP
–
LP
.
Once they appreciate how an ideal
filter works draw in “real” filter curves so they can see what
performance to expect.
Next, show how they can design a BRF.
There are two differences
between BPF and BRF.
The first is that in a BRF the two filters
are connected in parallel rather in cascade – and therefore
requiring a summer. The other difference is that the LP filter’s
cutoff
LP
is the desired low frequency cutoff of the filter.
In a
BPF the
LP
is the cutoff of the HP filter.
Similarly, that the HP
filter’s cutoff
HP
is the desired high frequency cutoff of the filter.
In a BPF the
HP
is the cutoff of the LP filter.
Devote a good amount of time to actually
designing a BPF.
Since there will be a HPF and
LPF designed, this exercise will review the
earlier lesson as well as this one.
Once a student
understands how to design a BPF designing a
BRF is not difficult. In their BPF design efforts
the
students will need to find the transfer function
for
their particular design.
Then they can partition the solution into two or three stages.
They can design it as Filter 1
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This note was uploaded on 10/12/2010 for the course MAE 140 taught by Professor Mauriciodeoliveria during the Spring '08 term at UCSD.
 Spring '08
 MAURICIODEOLIVERIA

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