Review
We now understand the why of:
For motivation, consider our old friend,Motivation
)real (i V Sinusoidal Response of RC Network
t
m e !Our Approach
Let’s use the usual approach…
Set up DE.
1
Usual approach…
1Set up DE
2
t
V dt
RC i ωcos =t
ωφcos +t ωcos
Let’s get sneaky!
Try solution st
p PS e
V v =Nice IS PS PS
v v dt dv RC =+(S : sneaky :-))
st
i e V =Find particular solution to another input…
Fact 1:Finding the response to
t j i e V ω
V i cos ωt .
RC ωφ?=so,
[][]
t
j p PS e
V Re Re ω==complex
Recall,
RC
t H Ae
v ?=Find v H 3
Find total solution
4H
C v v +RC
t Ae
V ?+)
RC (1
ω??
We are usually interested only in the particular solution for sinusoids, i.e. after transients have died.
RC
1
ω??Steps ,were a waste of 34
Visualizing the process of finding the ]
i
p
V V j H =
)(ωtransfer function
2
2
2
11C
R V V i
p ω+=
ω
Magnitude Plot
RC
tan 1
ωφ?=?Phase Plot