1 Impulses, Steps and Ramps 6.002x CIRCUITS AND ELECTRONICS
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1
Impulses, Steps and Ramps
6.002x CIRCUITS AND ELECTRONICS
2
Slower may be better
In our previous sequence…
3
6.002x expert saw the solution!
In our previous sequence…
We will see why here…
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
5
First, let’s understand a step input
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Rising step response of RC circuit
Sec. 10.1.1 of A&L
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Falling step response of RC circuit
)(ti R )(tvCC−
+
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Pulse input: Rising step followed by falling step (much later)!
)(ti R )(tvCC−
+
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Short pulse input: Rising step followed by falling step (shortly thereafter)!
)(ti R )(tvCC−
+
10
Let’s Stare at Current Pulse
Becomes “impulse” as Lim T à 0 Denoted by Impulse is an important signal type
)(tδ
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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
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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
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Response to impulse
)(ti R )(tvCC−
+
0)0( =−Cv
)(ti
t0
Q
)(tvC
t0
remember drug delivery
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
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Superposition with initial conditions and sources
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Impulses, steps and ramps
For linear systems (remember, no sources and initial conditions)
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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
Slower may be better
Problem: pin 2 pin 1
chip
LC
v
VIL
v:
expected
observed
… but, disaster!
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
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Why? Consider … 1 Case
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Why? Consider … 2 Case
1R
0Rpin1
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Why? Consider … Model:
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Why? Consider … 2 Case
1R
0Rpin1
PCcrosstalk!
Model: +!
–!v
R
PC
+!–!
2R
pin2
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3 Case
… 6.002x expert saw the solution PC
1R
0R2R
+!–!
slower transitions! Demo
25
Why? Consider … Model: +!
–!Rv
R C+!–!
+!–! Cv
Iv
Iv
t
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