�
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Lecture S14
Muddiest Points
General
Comments
We wrapped
up
the last Signals
and
Signals lectures by
talking
about
transfer functions, which
describe the ratio
of
the output amplitude to
the input
amplitude, for sinusoidal inputs. We saw
that
we can compute the transfer
function
from
the statespace description, or by
using
impedance methods.
Of
course,
the two
approaches give the same results.
We applied these results
to
a
bandpass filter, and
showed
how a
bandpass filter can
selectively
filter out
all
frequencies
except for
those in
a
narrow band
of frequencies.
And,
of course,
we had
doughnuts.
Responses
to MuddiestPartoftheLecture
Cards
(41
cards)
1.
If the transfer
function
is
G
(
s
) =
C
(
sI
−
A
)
−
1
B
+
D
(38)
and
(
sI
−
A
)
−
1
is
a matrix, how
is
it
that
G
(
s
)
is
just
a
scalar
function?
(2
students)
If
A
is
n
×
n
,
B
is
n
×
1,
C
is 1
×
n
, then
the product
C
(
sI
−
A
)
−
1
B
is a
scalar.
2.
How
did you find
�
�
v
1
� �
y
(
t
) =
1
0
+ 0
u
(
t
)
?
(39)
i
2
(3)
Because the output terminals connect
to
the same nodes as the capacitor,
y
(
t
) =
v
1
(40)
This is
the same as
�
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 Fall '05
 MarkDrela
 Input/output, Electrical impedance

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