6.002x circuits and electronics · 15 superposition with initial conditions and sources . 16...
TRANSCRIPT
4
We will also understand how to model drug delivery
If the input duration is much shorter than system time constant, then shape or duration of input does not matter, only total amount of drug delivered. Model input as a short pulse à Impulse
10
Let’s Stare at Current Pulse
Becomes “impulse” as Lim T à 0 Denoted by Impulse is an important signal type
)(tδ
11
As the pulse gets narrower à impulse
Becomes “impulse” as Lim T à 0 Denoted by Impulse is an important signal type
)(tδ
)(ti
0 tT
TQI =
)(tQδ)(tvC
t0 T
)(tiR )(tvCC
−
+
T2 T3 T1 T2 T3 T1
3TQ
12
Response to impulse – limit case
)(ti R )(tvCC−
+
0)0( =−Cv
)(ti
t0 T
QCharge Q
t: 0 – T
)(tvC
t0
t > T
Lim T à 0
14
Current and voltage impulses
R )(tvCC−
+
0)0( =−Cv)(ti
t0
Q
)(tvC
t0
CQ
RCt
eCQ −
)()( tQti δ=
Current impulse delivers charge
Voltage impulse delivers flux linkage Λ
Q
17
Back to:
Problem:
ideal
slow! observed
pin 2 pin 1
chip
LC
v
So the engineers decided to speed it up…
made RL small made RON small
RL RON
19
Slower may be better
pin 2 pin 1
chip
LC
v:
v
… 6.002x expert saw the solution
Slow the edges down!
We now have the tools to understand why