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Special Techniques

Superposition Theorem

Source Transformation

Thevenins Theorem

Nortons Theorem

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Linear elements vs. linear circuits

Linear element: passive element that has a

linear voltage-current relationship, i.e.

v(t)=R*i(t)

Linear dependent source: source whose outputis proportional only to the first power, i.e.,

v1 = 0.6i1-14v2 Linear circuit: composed of independent

sources, linear dependent sources, and linearelements

2

Superposition Theorem

One of the properties of linearity

Definition:

voltage across or current thru anyresistor or source may be calculated byadding all the individual voltage or currents

caused by the separate independentsource acting alone

3

Implementation

Other independentvoltage sources givezero voltage, then actlike short circuits.

Other independentcurrent sources givezero current, then actlike open circuits.

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Example

I1 = 1A

I2 = 2A

I total = 1+2 = 3A

5

Example

I1 = 1A

I2 = 0A

I total = 1+0 = 1A

6

Example

Find voltage Vx

7

V

VxV

333.9

42)7/12(6

)7/12(42

)4||3(6

)4||3()42(

=

+

=+

=

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V

Vx V

333.3

1042

210

4)3||6(

)3||6()10(

=

+

=+

=

9

V

VxVxVx VV

6333.3333.9

)10()42(

==

+=

10

Example 1

use superposition to find ix

11

Example 1 (cont.)

= 0.2 A'xi

= 0.8 A''xi

= 1.0 Axi

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Special Techniques

Superposition Theorem

Source Transformation

Thevenins Theorem

Nortons Theorem

13

Practical voltage source

LssL iRvv =

s

sLsc

soc

R

vi

vv

=

=

14

Practical current source

p

LsL

R

vii =

sLsc

spLoc

ii

iRv

=

=

15

Equivalent practical sources

THNTH

NTH

RIV

RR

=

=

Head of current = +

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Equivalent practical sources (cont.)

The two practical sources are equivalent

only with respect to what transpires at theload terminals; they are not equivalentinternally!

Note: goal is to have either all current sources or all

voltage sources in the circuitmaking nodal/meshanalysis easier

17

Special Techniques

Superposition Theorem

Source Transformation

Thevenins Theorem

Nortons Theorem

18

Thevenins Theorem

Equivalent circuit

19

Thevenins Equivalent Circuit

Composed of VTH andRTHconnected in series

VTH = Voc (open-circuit voltage)

RTH= equivalent R (total R) in the circuit

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A statement of Thevenins Theorem

Disconnect a load network from the circuit

by substituting an open circuit, and findVoc across the load, which is equivalent toVTH.

Open load and evaluate RTH by zeroingout every independent source (opencurrent source, short voltage source).

21

Example

Find Thevenins equivalent circuit and thecurrent passing thruRL given RL = 1

22

0V

10V

0V 0V

6V 6V

VVTH 61032

3=

+=

Find VTH

23

Short voltage source

RTH

=

++

+=

++=

2.13

232

3210

23||210TH

R

Find RTH

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Thevenins equivalent circuit

The current thru RL = 1is A423.012.13

6=

+

25

Example

Find Thevenins equivalent circuit

26

Find VTH

0V

5V

0V 0V

3V 3V

VVTH

331 ==

27

Open circuitcurrent source

RTH

=

++=

15

2310THR

Find RTH

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Thevenins equivalent circuit

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Example: Bridge circuit

Find Thevenins equivalent circuit

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Find VTH

0V

10V

8V 2V

VTH = 8-2 = 6V

31

Find RTH

RTH

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KKK

KKKKRTH

4.28.06.1

1||48||2

=+=

+=

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Thevenins equivalent circuit

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