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te as: Anant Agarwal and Jeffrey Lang, course material

6.002 CIRCUITS ANDELECTRONICS

Introduction and Lumped Circuit Abstraction

http:/electrical.globalautomation.info

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e as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MITpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY

Lecturer: Prof. Anant Agarwal Textbook: Agarwal and Lang (A&L)

Readings are important!

Handout no. 3 Web site

http://electrical.globalautomation.info

Assignments

Homework exercisesLabsQuizzesFinal exam

ADMINISTRIVIA

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Two homework assignments canbe missed (except HW11).

Collaboration policyHomework

You may collaborate withothers, but do your ownwrite-up.

LabYou may work in a team oftwo, but do you own write-up.

Info handout

Reading for today Chapter 1 of the book

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What is engineering?

What is 6.002 about?

Purposeful use of science

Gainful employment ofMaxwells equations

From electrons to digital gatesand op-amps

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Simple amplifier abstraction

Instruction set abstractionPentium, MIPS 6.004

Software systems 6.033Operating systems, Browsers

Filters

Operationalamplifier abstractionabstraction

-

+

Digital abstraction

Programming languages

Java, C++, Matlab 6.001

Combinational logicf

Lumped circuit abstraction

R V C L M +

6.

00

2

Nature as observed in experiments

0.40.30.20.1I

12963V

Physics laws or abstractions Maxwells

OhmsV = R I

abstraction for

tables of data

Clocked digital abstraction

Analog systemcomponents:Modulators,

oscillators,RF amps,power supplies 6.061

Mice, toasters, sonar, stereos, doom, space shuttle6.1706.455

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Consider

Suppose we wish to answer this question:

What is the current through the bulb?

V

I

?

The Big Jumpfrom physics

to EECS

Lumped Circuit Abstraction

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We could do it the Hard Way

Apply Maxwells

Differential form Integral form

Faradays

Continuity

Others

t

BE

=

tJ

=

0

E

=

tdlE B

=

t

qdSJ

=

0

qdSE =

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e as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MITenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY

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: m

You respond:m

Fa =

Done!!!

F

a ?

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Instead, there is an Easy Way

In doing so, you ignored the objects shape its temperature

its color point of force application

Point-mass discretization

F

a ?

First, let us build some insight:

Analogy

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The Easy Way

Consider the filament of the light bulb.

A

B

We do not care about how current flows inside the filament its temperature, shape, orientation, etc.

Then, we can replace the bulb with a

discrete resistorfor the purpose of calculating the current.

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The Easy Way

A

B

Replace the bulb with a

discrete resistorfor the purpose of calculating the current.

R represents the only property of interestLike with point-mass: replace objects

with their mass m to findm

Fa =

andR

VI =

A

B

R

I+

V

In EE, we do thingsthe easy way

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The Easy Way

R represents the only property of interest

andR

VI =

A

B

R

I+

V

In EE, we do thingsthe easy way

R

VI =

relates element v and iR

called element v-i relationship

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R is a lumped element abstraction

for the bulb.

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R is a lumped element abstractionfor the bulb.

Not so fast, though

are definedfor the element

V I

A

B

black box

AS

BS

I

+

V

Although we will take the easy wayusing lumped abstractions for the restof this course, we must make sure (atleast the first time) that ourabstraction is reasonable. In this case,ensuring that

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must be definedfor the element

V I

A

B

black box

AS

BS

I

+

V

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I

I into = I out of

in the filament!True only when 0=

t

qAS BS

BA II = only if 0=

t

q

t

qdSJdSJ

A BS S

=

AI BI

AS

dSJ

BS

dSJ

fromMax

well

must be defined. True when

So lets assume this

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V

defined whenABV 0=

t

B

outside elementsdlEVABAB

=

see

A&L

Must also be defined.

So lets assume this too

So

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Lumped circuit abstraction applies when

elements adhere to the lumped matterdiscipline.

Lumped Matter Discipline (LMD)

0=

tB

outside

0=

t

qinside elementsbulb, wire, battery

Or self imposed constraints:

More inChapter 1of A & L

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Lumped element exampleswhose behavior is completelycaptured by their VIrelationship.

Demoonly for thesorts ofquestions we

as EEs wouldlike to ask!

Exploding resistor democant predict that!

Pickle demo

cant predict light, smell

Demo

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Replace the differential equationswith simple algebra using lumped

circuit abstraction (LCA).

For example

What can we say about voltages in a loopunder the lumped matter discipline?

+

1R

2R

4R

5R

3R

a

b d

c

V

So, what does this buy us?

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What can we say about voltages in a loopunder LMD?

+

1R

2R

4R

5R

3R

a

b d

c

V

tdlE B

= under DMD

0

Kirchhoffs Voltage Law (KVL):

The sum of the voltages in a loop is 0.

=++bcabca

dlEdlEdlE 0

=+++bcabca

VVV 0

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What can we say about currents?

Consider

ScaI daI

baI

a

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What can we say about currents?

ScaI daI

baI

t

qdSJ

S

= under LMD

0

0=++badaca III

Kirchhoffs Current Law (KCL):

The sum of the currents into a node is 0.

simply conservation of charge

a

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KVL:0

loop

KCL:

node

=j j

0=j ji

KVL and KCL Summary

Documents

F9C98EFA-0495-4A52-AC9F-D36A65140630_001