6.002x
CIRCUITS AND
ELECTRONICS
Introduction and Lumped Circuit Abstraction
1 6.002x is Exciting!
What’s
behind this?
2 …and this
Chip photo of Intel’s 22nm multicore processor codenamed Ivy Bridge
Photograph courtesy of Intel Corp. 3 ADMINISTRIVIA
n  Prerequisites
n  AP level course on electricity and magnetism; e.g., MIT’s 8.02 (check it out on
MIT OpenCourseware)
n  It is also useful to have a basic knowledge of solving simple differential equations
n  Textbook Agarwal and Lang (A&L)
Underlined readings (in course-at-a-glance handout) are very important
as they stress intuition
n  Weekly homeworks and labs must be completed by the deadline indicated on the
assignment
n  Assessments
Homeworks 15%
Labs 15%
1 Midterm 30%
Final exam 40%
4 What is engineering?
Purposeful use of science
What is 6.002x about?
Gainful employment of Maxwell’s equations
From electrons to digital gates and op-amps
5 6.002x
6 V C
L
f
S
Java, C++, Matlab, Python
Programming languages
6.00
Mice, toasters, sonar, stereos, angry birds,
space shuttle, iPAD
6.455 6.172,6.173
Software systems Operatin
6.033
6.061 systems, Browsers
Modulators,
oscillators,
RF amps,
power supplies
Instruction set abstraction
Analog subsystems Pentium, MIPS 6.004, 6.846 Clocked digital abstraction
Combinational logic
+"
Filters
Digital abstraction
M
Operational
amplifier abstr.
Simple amplifier abstraction
R
+ –"
Lumped circuit abstraction
Physics laws or “abstractions”
l Maxwell’s
abstraction for
l Ohm’s
tables of data
V=RI
Nature as observed in experiments
Lumped Element Abstraction
Consider
The Big Jump
from physics
to EECS
V
Suppose we wish to answer this question:
What is the current through the bulb?
Reading: Skim through Chapter 1 of A&L
7 We could do it the Hard Way…
Apply Maxwell’s
Differential form
Faraday’s
Continuity
Others
∂B
∇× E = −
∂t
∂ρ
∇⋅ J = −
∂t
ρ
∇⋅ E =
ε0
l
l
l
I? V
Integral form
∂φ B
∫ E ⋅ dl = − ∂t
∂q
∫ J ⋅ dS = − ∂t
q
∫ E ⋅ dS =
ε0
l
l
l
8 Instead, there is an Easy Way…
First, 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 ! ! !
9 Instead, there is an Easy Way…
a?
F
In doing so, you ignored
l the object’s shape
l its temperature
l its color
l  point of force application
l  …
Point-mass discretization
10 The Easy Way…
Consider the filament of the light bulb.
A
B
We do not care about
l how current flows inside the filament
l its temperature, shape, orientation, etc.
We can replace the bulb with a
discrete resistor
for the purpose of calculating the current.
11 The Easy Way…
A
Replace the bulb with a
B
discrete resistor
for the purpose of calculating the current.
12 The Easy Way…
A
+
V
–
A
B
I
R
V
I=
R
B
In EECS, we do things
the easy way…
R represents the only property of interest!
Like with point-mass:
F
replace objects with their mass m to find a =
m
13 V-I Relationship
A
I
+
V
–
R
and
I=
V
R
B
R represents the only property of interest!
R relates element V and I
I=
V
R
called element v-i relationship
14 R is a lumped element abstraction for the bulb.
15 Lumped Elements
Lumped circuit element
described by its vi relation
Power consumed by element = vi
Resistor + i
v
-­‐ Voltage source i
+ v
i
v +"
–"V
-­‐ i
v
16 Demo
only for the
sorts of
questions we
as EEs would
like to ask!
Demo
Lumped element examples
whose behavior is completely
captured by their V–I relationship.
Exploding resistor demo
can’t predict that!
Pickle demo
can’t predict light, smell
17 Not so fast, though …
A
B
Bulb
filament
Although we will take the easy way using lumped abstractions
for the rest of this course, we must make sure (at least for
the first time) that our abstraction is reasonable.
In this case, ensuring that V
I
are defined for the element
18 I
must be defined.
A
+
I
V
B
–
black box
19 I
must be defined. True when
IA
I out of S B
∂q
True only when
= 0 in the filament!
∂t
I into S A
SA
=
I A = IB
∂q
=0
only if
∂t
IB
SB
So, are we stuck?
We’re engineers! So, let’s make it true!
20 Must also be defined.
V
A
+
I
V
∂φ B
B
=0
∂t
outside elements
VAB defined when
So
VAB = ∫AB E ⋅ dl
–
.1
A
x
e
i
se
end
p
p
A
So let’s assume this too!
A&L
Also, signal speeds of interest should be way lower than speed of light
21 Welcome to the EECS Playground
The world
The EECS playground
Our self imposed constraints in this playground
∂φ B
=0
∂t
∂q
=0
∂t
Outside
Inside elements
Bulb, wire, battery
Where
good
things
happen
22 Lumped Matter Discipline (LMD)
Or self imposed constraints:
More in
Chapter 1
of A & L
∂φ B
= 0 outside
∂t
∂q
= 0 inside elements
∂t
bulb, wire, battery
Connecting using ideal wires lumped elements
that obey LMD to form an assembly results in
the lumped circuit abstraction
23 So, what does LMD buy us?
Replace the differential equations with simple algebra using
lumped circuit abstraction (LCA).
a
For example: V+"
–"
b
R1
R3
R2
R4
d
R5
c
What can we say about voltages in a loop under the lumped matter discipline?
Reading: Chapter 2.1 – 2.2.2 of A&L
24 What can we say about voltages in a loop under LMD?
a
V+"
–"
b
R1
R4
R3
d
R2
R5
c
Kirchhoff’s Voltage Law (KVL):
The sum of the voltages in a loop is 0.
Remember, this is not
true everywhere, only in
our EECS playground
25 What can we say about currents?
a
V+"
–"
b
R1
R4
R3
d
R2
R5
c
26 What can we say about currents?
I ca
S
a
I da
I ba
Kirchhoff’s Current Law (KCL):
The sum of the currents into a node is 0.
simply conservation of charge
27 KVL and KCL Summary
KVL:
KCL:
28 Summary
Lumped Matter Discipline LMD:
Constraints we impose on ourselves to simplify our
analysis
∂φ B
=0
∂t
∂q
=0
∂t
Outside elements
Inside elements
wires
resistors
sources
Also, signals speeds of interest should be way
lower than speed of light
Allows us to create the lumped circuit abstraction
Remember, our EECS playground
29 Summary
i
+ v
Lumped circuit element
-­‐ power consumed by element = vi
30 Summary
Review
Maxwell’s equations simplify to algebraic KVL and
KCL under LMD.
KVL:
∑ jν j = 0
loop
This is amazing!
KCL:
∑jij = 0
node
31