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Elements of Linear Circuit Theory
•
Passive circuits
⇒
no external energy supply
•
Active circuits
⇒
needs to be "powered up" to work, e.g. opamps
•
Laplace Transforms : if
f
(
t
), then
( )
0
()
st
f
tf
t
e
∞
−
ℑ=
∫
d
t
and
f
tF
=
s
ℑ
, where
s
is complex,
si
σ
ω
=
+
Inverse Transform :
1
Fs
ft
•
Impedance Z
≡
(applied voltage)/(forcing current)
•
Some basic components
Resistor
Capacitor
Inductor
R
i
C
i
L
i
et
R it
=⋅
1
C
itd
t
=
∫
di
dt
L
=
Es
R Is
1
Cs
Is
=
⋅
LsIs
= ⋅⋅
Z
R
=
1
Zs
Cs
=
Z
sL
s
=
⋅
•
in series:
Z
1
Z
2
E
out
E
in
Total Impedance = Z
1
(s) + Z
2
(s)
•
in parallel:
Z
1
Z
2
E
out
E
in
Total Impedance =
1
12
11
Z(s)=
+
Z( )
Z(s)
s
1
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R
i(t)
C
e
(t)
out
e
(t)
in
0
1
()
1
( )
[first order O.D.E]
t
RC
RC
in
out
out
out
in
out
t
out
in
et R
i
i
d
t
C
de
et
i
d
t
i
t C
Cd
de
C
e
dt
ee e
ed
τ
ττ
−
=⋅+
=⇒ =
=+
=
∫
∫
∫
t
Simpler to use Laplace Transforms
1
1
1
1
in
out
out
in
Es I
sR
Cs
s
Cs
Es
R
C
s
R
C
=⋅
=
+
2
•
Impedance Matching
Thevenin's Theorem.:
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This note was uploaded on 07/20/2009 for the course AME 341AL taught by Professor Pottebaum during the Fall '07 term at USC.
 Fall '07
 Pottebaum

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