Dc Circuit Anays Is

8/10/2019 Dc Circuit Anays Is

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TECHNIQUES OF DC CIRCUIT ANALYSIS:

Superposition Principle

Thevenins Theorem

Nortons Theorem

Source Transformation

Maximum Power Transfer


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Applies only for LINEARCIRCUIT

Circuit containing linear

elements, linear dependent and

independent sources

A LINEARrelationship

between voltage and

current

What do we mean by a linear relationship?


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What do we mean by a linear relationship?

When the relationship fulfilled 2 properties:

Homogeneity (scaling)

Additivity

f(x) = y f(kx) = ky = kf(x)

f(x) = y f(x1+ x2) = f(x1) + f(x2) = y1+ y2


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Superposition Principle: The voltage across an element ( or thecurrent through an element) of a linear circuit containing more than

one independent source, is the algebraic sum the voltage acrossthat element (or the current through that element) due to each

independent source acting alone.

All other independent sources are KILLED

voltage sources are shorted

current sources are opened

Dependent sources CANNOT be killed !


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may involve MORE work

cannot be applied to power calculation find ior v

first (using superposition) before calculating power !

most suitably used when involved with sources of different

properties or types, e.g. different frequencies, mixture ofDC and AC, etc.


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Thevenins Theorem: A linear two-terminal circuit can bereplaced by an equivalent circuit consisting of a voltage source in

series with a resistor

Linear two-

terminal

circuit

Load

+

V

+

V LoadVTh

RTh VTh= ?

RTh= ?

In 1883, M.L. Thevenin proposed a theorem .

I

I


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To determine VTh

Linear two-

terminal

circuit Load

VTh

RTh

Load

=


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To determine VTh

Linear two-terminal

circuit Load

VTh

RTh

open circuit voltage = Voc

+

= VTh

Load


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To determine VTh

Linear two-terminal

circuit

VTh

RTh


+

= VTh


+

Load


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To determine VTh

Linear two-terminal

circuit

VTh

RTh


+

= VTh


+

VTh= Voc= Open circuit voltage

= VTh (Since the circuit is equivalent)


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To determine RTh

Case 1 Network with NO dependent sources

Kill all the independent sources

Find the equivalent R looking between the terminals

Linear

circuit

independent

sources

killed

Rin = RTh


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To determine RTh

Case 2 Network with dependent sources

Kill all the independent sources - dependent sources

stay as they are

Introduce a voltage (or current) source.

Linear

Circuit

ONLY

dependent

sources

killed

+

-vo

io

RThis calculated as:

o

o

Th

i

v

R


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Nortons Theorem: A linear two-terminal circuit can be replacedby an equivalent circuit consisting of a current source in parallel with

a resistor

43 years later, E.L. Norton proposed a similar theorem. .

IN= ?

RN= ?

Linear two-

terminal

circuit

Load

+

V

I

+

V

I

LoadIN RN


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a resistor

To determine IN

Linear

circuit

ININ

RN


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a resistor

IN= Short circuit current

To determine IN

INRN

Linear

circuitShort circuit current = IN


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a resistor

To determine IN

IN= Short circuit currentIN

RN

Linear

circuitShort circuit current = IN

IN= Isc= Short circuit current


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a resistor

To determine RN

SIMILAR METHOD AS HOW TO OBTAIN RTh

RN= RTh


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Relationship between Nortons and Thevenins equivalents

INRN

b

a

VThRTh

b

a

Since both circuits are equivalent, vocmust

be the sameTh

Thh

V

R s

o

v

NNoc RIv +

Thoc Vv +


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Source Transformation:A tool used to simplify circuit; a process ofreplacing a voltage source in series with a resistor by a current source

in parallel with a resistor or vice versa

vs

R

a

b

is R

a

b

If the circuit is equivalent at terminala-b

, their open-circuit andshort-circuit characteristics are similar

voc= vs

isc= vs/R

voc= isR

isc= is


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Source Transformation:A tool used to simplify circuit; a process ofreplacing a voltage source in series with a resistor by a current source

in parallel with a resistor or vice versa

vs

R

a

b

is R

a

b

voc= vs

isc= vs/R

voc= isR

isc= is

RivorR

vi ss

ss


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Linear circuitRL What would be the value of RLfor

power delivered to it become

MAXIMUM?


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Linear circuitRL What would be the value of RLfor

power delivered to it become

MAXIMUM?

VTh

RTh

L

2

LTh

L

Th

LR

RR

RV

P L

2

LTh

Th RRR

V


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0 10 20 30 40 50 600.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

RL

p


L

2

LTh

L

Th

LR

RR

RV

P L

2

LTh

Th RRR

V

Rl=linspace(1,60,500);

Vth=10;

Rth=12;

p=((Vth./(Rl+Rth)).^2).*Rl;

plot(Rl,p,'r');

grid;

Maximum power

RL= 12


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L

2

LTh

L

Th

LR

RR

R

VP L

2

LTh

Th RRR

V

Mathematically, we evaluate RLwhen 0dRdP

L

L

0)RR(

VR

)RR(

V2

dR

dP2

LTh

2Th

L3LTh

2Th

L

L

0

)RR(

RRR2V

dR

dP3

LTh

LThL

2

Th

L

L

ThL RR


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Using PSpice to verify Nortons and Thevenins Theorems

Find Thevenin equivalent at terminals a-b


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0

R9

2

-+

+-

E2

E

R8

2

R7

6

R6

4

I3

1Aac

TRAN =

0


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0

R9

2

-+

+-

E2

E

R8

2

R7

6

R6

4

I3

1Aac

TRAN =

0

I4

1Aac

TRAN =

1


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R8

2

6.000V

1.333V

R6

4

4.000V

R7

6

I3

1Aac

TRAN =

0

0

R9

2

-+

+-

E2

E

I4

1Aac

TRAN =

1

RTh= 6/1 = 6


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I4

1Aac

TRAN =

0

R8

2

R7

6

20.00V

R6

4

6.667V

0

-+

+-

E2

E

20.00V

I3

1Aac

TRAN =

5

R9

2

VTh= 20V

Dc Circuit Anays Is

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