Handouts 6002 L3 Oei12 Gaps Annotated

8/11/2019 Handouts 6002 L3 Oei12 Gaps Annotated

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Superposition,Thvenin and Norton

Reading: Chapter 3 of A&L

6.002 CIRCUITS AND ELECTRONICS


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ReviewCircuit Analysis Methods

! Circuit composition rules! Node method the workhorse of 6.002

KCL at nodes using V s referenced from groundKVL implicit in pattern

! KVL: KCL: VI


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! Introduction to linear circuits! Properties of linearity! The superposition tool for your toolkit! The Thvenin method! The Norton method

Overview

Lets start by introducing linearity


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ConsiderLinearity

Write node equations

1 R

2 R

+

!

e

V I


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LinearityWrite node equations --

Rearrange --

021

=!+!

I R

e

R

V e

linear in I V e ,,

1 R

2 R

+ V


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1 R

2 R

+ V

Linearity0

21

=!+!

I

R

e

R

V e

I R

V e

R R+=!

#$&

+

121

11


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Linearity HomogeneitySuperposition!


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Linearity HomogeneitySuperpositionHomogeneity

...

!

...


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Linearity HomogeneitySuperpositionSuperposition

!

......

.

..


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Specific superposition example:


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Method 4: Superposition method

1. Find the responses of the circuit to eachsource acting alone2. Sum the individual respones


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i

+

+

-

v

i

short

+

-

v

i

!

+

-

v

Each source acting alone means this

i

open

+

-

v


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Back to the example1

R

2 R

+

!

e

V I

Use superposition method


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+ V

Back to the exampleUse superposition method

V actingalone V

0= I 2

R+

1 R


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Back to the exampleUse superposition method

+ V

I actingalone 0=V

I

1 R

2 R !

I e

V R R

Re

V

21

2

+=

Voil

By superposition, sum the two partial voltages


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outpsup

saltwater

Low freqsinusoid+

High freqtriangular wave

+

Y h h d


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Consider Yet another method

resistors

!

mV

n I

A r b i t r a r y n e t w o r k N

+

-v !

i

i

By superposition

ne t


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Ri I V vn

nnm

mm

++= !! " # resistors

!

mV

n I


Independent of externalexcitation and behaves like avoltage.

TH v

alsoindepeof exteexcitembehavea resistLet s c

Let

s call it

yne tRiIV !! "#


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resistors

!

mV

n I

A r b i t r a r y n e t w o r k N Ri I V v n

nnm

mm

++= !! " #

In other words, as far as the external world is concerned (for the purpo

i-v relation), arbitrary network N is indistinguishable from:

yne t


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i RvvTH TH

+=

i+

TH

R

TH v !

+

-

v

Thveninequivalentnetwork

N

resistors

!

mV

n I


TH R

TH v

Resistance of network seen from port( s, s set to 0)mV n I

Open circuit voltage seen at terminal pa

h d h h i h d


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Method 4: The Thvenin Method

E

!

+ +

i

+

-v

N

+

TH R

TH v

+

-

v

i

EThveninequivalent

1. Replac

with its Th

equivalent2. Then so

external ne

E l Fi d i


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Example: Find i 1 1

R

V +

1i

Step 1: Replace N withThvenin equivalent

Network N

2 R I !

1 R

V +

1i

Network E

Network E

Step 1: Replace with Thvenin equivalent


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:TH V

:TH

R

2 R

Step 1: Replace with Thvenin equivalent

open circuit voltage of network N

turn off all independent sources and measure resistan

Step 2: Solve with external network E 1 Ri


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1 R

V +

1i

TH R

TH V +

Step 2: Solve with external network E

Network E

1

V +

1i

E

Graphically iR


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Graphically, i Rvv TH TH +=i

v

+

Method 5: The Norton Method


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Method 5: The Norton Method

!

+

+

i

+

-v

Norton equivalen

N TH R R = N I !

TH R

Resistance of network seen from port

( s, s set to 0)mV n I

Short circuit current seen at port

mV

n I

N I


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+

TH R

TH v

+

v

i

Norton equivalen

N TH R R = N I !

Thevenin equivalent

S


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SummaryDiscretize matter by agreeing to

observe the lumped matter discipline

S


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Circuit analysis methods

KVL, KCL, I VCombination rulesNode methodSuperpositionThveninNorton

Summary

Next Nonlinear networks

Handouts 6002 L3 Oei12 Gaps Annotated

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