6.002
CIRCUITS
AND
ELECTRONICS
Sinusoidal Steady State
6.002 Fall 2000 Lecture
16
1
Review

We now understand the why of:
5V
C
R
L
v
Today, look at response of networks
to sinusoidal drive.
Sinusoids important because signals can be
represented as a sum of sinusoids. Response to
sinusoids of various frequencies -- aka frequency
response -- tells us a lot about the system
6.002 Fall 2000 Lecture
16
2
Motivation
For motivation, consider our old friend,
the amplifier:
S
V
v

3
Sinusoidal Response of RC Network
Example:
+
–
R
i
C
+
v
I
v
C
–
v
I
(
t
)
= V
i
cos
ω
t
for
t ≥
0 (
V
i
real)

–
R
Our Approach
i
C
+
v
I
v
C
–
Determine v
C
(t)
I
nd
u
l
g
e
m
e
!

Effort
l
e
c
t
u

s
hi
T
t
x
e
N
6.002 Fall 2000 Lecture
16
5
Let’s use the usual approach…
1
Set up DE.
2
Find
v
p
.
3
Find
v
H
.
4
v
C
=
v
P
+