6002 L1 Oei12 Gaps Annotated
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Transcript of 6002 L1 Oei12 Gaps Annotated
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6.002xCIRCUITS ANDELECTRONICS
Introduction and
Lumped Circuit Abstrac
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6.002x is Exciting!
Whatsbehind this?
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and this
Chip photo of Intels 22nm multicore processor codenamed Iv
PhotographcourtesyofIntelCorp
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nPrerequisitesnAP level course on electricity and magnetism; e.g., MITs 8.02 (chMIT OpenCourseware)
nIt is also useful to have a basic knowledge of solving simple diffenTextbook Agarwal and Lang (A&L)
Underlined readings (in course-at-a-glance handout) are very imporas they stress intuition
nWeekly homeworks and labs must be completed by the deadline indicaassignmentnAssessments
ADMINISTRIVIA
Homeworks 15%Labs 15%1 Midterm 30%Final exam 40%
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What is engineering?
What is 6.002x about?
Purposeful use of science
Gainful employment of Maxwells equat
From electrons to digital gates and op
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Simpleamplif
ierabstraction
Instructionsetabstraction
Pentium,
MIPS
Filters
Operational
amplifierabst
r.
-+"
Digitalabstraction
Programminglanguages
J
C
M
l b
P h
Combination
allogic
f
Lumpedcircuitabstraction
6.002x
Natureasobs
ervedinexperim
ents
Physicslawsorabstractions
lM
axwells
lO
hms
V=RI
abstract
ionfor
tablesof
data
Clockeddigi
talabstraction
Analog
subsystems
Modulators,
oscillators
+
R
C
L
M
S
V
6.0
04,
6.8
46
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Consider
V
Suppose we wish to answer this question:
What is the current through the bulb?
The Bigfrom p
to E
Lumped Element Abstraction
Reading: Skim through Chapter 1 o
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Apply Maxwells
Faradays
Continuity
Others
t
BE
=
tJ
=
0
E
=
lll
tdlE
B
=
t
qdSJ
=
0
qdSE =
lll
We could do it the Hard Way
Integral fDifferential form
V
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Instead, there is an Easy WayFirst, let us build some insight:
Analogy
I ask you: What is the acceleration?
You quickly ask me: What is the mass?
I tell you:
You respond:
Done!!!
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Instead, there is an Easy Way
In doing so, you ignoredl the objects shapel its temperaturel its colorl point of force applicationl
Point-mass discretization
F
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The Easy WayConsider the filament of the light bulb.
We do not care aboutl how current flows inside the filamentl its temperature, shape, orientation, etc.
A
B
We can replace the bulb with adiscrete resistor
for the purpose of calculating the current.
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The Easy Way
Replace the bulb with adiscrete resistor
for the purpose of calculating the current.
A
B
Th E W
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The Easy Way
R represents the only property of interest!
Like with point-mass:
replace objects with their mass m to find a =
In EECS, we dothe easy way
A
B
A
B
R
I
+
V
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R
VI =
V-I Relationship
R represents the only property of interest!
andR
VI =
relates element VandIR
called element v-i relationship
A
B
R
I
+
V
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R is a lumped element abstraction for th
L d El
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Lumped circuit element
described by itsvi
relaPower consumed by elem
Lumped Elements
+
-
Voltage source
+""Viv
i
v
+
-
Resistor
i
v
i
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Lumped element exampleswhose behavior is completelycaptured by their VI relation
Demoonly for thesorts of
questions weas EEs wouldlike to ask!
Exploding resistor democant predict that!
Pickle democant predict light, smell
Demo
N t f t th h
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Not so fast, though A
B
Although we will take the easy way using lumped afor the rest of this course, we must make sure (at
the first time) that our abstraction is reasonable.
are defined for the element
V IIn this case, ensuring that
It b d fi d
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A
B
I
+
I must be defined.
V
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I
I into = I out of
True only when in the filament!0=
tq
Imust be defined. True when
BAII = only if 0=
t
q
Were engineers! So lets make it true!
So, are w
I
AS
BS
I
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V
defined whenABV 0=
t
B
outside elementsdlEVABAB
=
seeA&L
AppendixA.1
Must also bedefined.
So lets assume this too!
So
Also, signal speeds of interest should be way lower than spe
A
B
I
+
V
W l t th EECS Pl
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Welcome to the EECS PlaygroThe world
The EECS playgroundOur self imposed constraints in this playground
0=
t
B Outside
0=
t
q Inside elements
Bulb, wire, battery
Whergoodthings
happe
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Connecting using ideal wires lumped elementsthat obey LMD to form an assembly results
the lumped circuit abstraction
Lumped Matter Discipline (LMD)
0=
t
B outside
0=
t
qinside elementsbulb, wire, battery
Or self imposed constraints:
More inChapter 1
of A & L
So what does LMD buy us?
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Replace the differential equations with simple algelumped circuit abstraction (LCA).
What can we say about voltages in a loop under the lumped ma
+""
1R
2R
3R
a
b
c
V
So, what does LMD buy us?
For example:
Reading: Chapter 2.1 2.2.2 of A&L
What can we say about voltages in a loop un
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What can we say about voltages in a loop un
Kirchhoffs Voltage Law (KVL):
The sum of the voltages in a loop is 0.
Remembertrue everyour EECS
+""1
R
2R
a
b
c
V
Wh b ?
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What can we say about currents?
+""V
What can we say about currents?
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What can we say about currents?ca
I
Kirchhoffs Current Law (KCL):The sum of the currents into a node is 0.
simply conservation of charge
KVL d KCL S
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KVL:
KCL:
KVL and KCL Summary
Summary L d M tt Di i li LMD
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Remember, our EECS playground
0=
t
B
0=
t
q
Outside eleme
Inside element
Allows us to create the lumped circuit ab
wires resistors
Summary Lumped Matter Discipline LMD:Constraints we impose on ourselves toanalysis
Also, signals speeds of interest should lower than speed of light
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Lumped circuit element+
-
v
i
power consumed by element =vi
Summary
Summary
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KVL:
loop
KCL:
node
0=j j
0=j ji
ReviewSummary
Maxwells equations simplify to algebraic KVLKCL under LMD.
This is amazi