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Lecture 18
Series RLC
Some intuition
Step responses
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View Full Document Series RLC circuit
• K VL gives us a 2
nd
order
differential equation
– Can reformulate in a general
form
– Just like before, but with
different alpha (same
ω
o
)
• Note:
α
looks like 1/(2
τ
)
– For parallel,
α
=1/(2RC)
– like
τ
for RC circuit
– For series,
α
=R/(2L)
– like
τ
for LR circuit
LC
L
R
I
dt
dI
dt
I
d
LC
I
dt
dI
L
R
dt
I
d
IR
dt
C
I
dt
dI
L
t
1
,
2
2
0
0
0
2
0
2
2
2
2
0
=
=
+
+
=
+
+
=
+
+
=
∫
ϖ
α
+
V
R


V
L
+
L
C
R
V
C
+

Intuition, part 1: sketching solns
• Over damped: 2
exponentials
– Can say fast one
decays to slow one.
– 2
nd
order: only two
curvatures (only one
inflection point)
• Under damped:
– Period is 2
π
/
ω
d
– Envelope decays as
exp(
α
t)
1.5
1
0.5
0
0.5
1
1.5
2
2.5
0
1
2
3
4
5
tau1
tau2
tot
1.5
1
0.5
0
0.5
1
1.5
0
1
2
3
4
5
Period, T= 2
π
/
ω
d
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View Full Document Intuition, part 2: cheesy water
analogies
Resistor
constricted pipe
Capacitor
tank
Inductor
propeller with flywheel
RLC
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This note was uploaded on 11/21/2011 for the course ECE 2100 taught by Professor Kelley/seyler during the Spring '05 term at Cornell University (Engineering School).
 Spring '05
 KELLEY/SEYLER

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