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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!

"=#$

"""

tdlE

B

!

!"=#

%

t

q

dSJ !

!

"=

#

0!

qdSE ="

"""

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 ignored" the objects shape" its temperature" its color"

point of force application

"

Point-mass discretization

F


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The Easy WayConsider the filament of the light bulb.

We do not care about" how current flows inside the filament"

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


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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


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Lumped circuit element

described by itsvi

relaPower consumed by elem

Lumped Elements

?

@

Voltage source

+

V

i

v

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 f h 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

I


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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

BA II = 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 whenAB

V 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


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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

Wh t c n e s b ut v lt es in l p 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

+

1R

2R

a

b

c

V


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What can we say about currents?

+

V

Wh t c n e s b ut 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


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KVL:

KCL:

KVL and KCL Summary

S


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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

S mm


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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

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