Lab. Lab. 4 4 중첩정리중첩정리, , TheveninThevenin 및및 Norton Norton 정리정리
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이이 실험의실험의 목표목표이이 실험의실험의 목표목표
Superposition Theorem 이해 Superposition Theorem 이해 What is Linearity of circuit systems?
Thevenin’s Theorem 이해 Thevenin s Theorem 이해
Norton’s Theorem 이해
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Superposition TheoremSuperposition TheoremSuperposition TheoremSuperposition Theorem
The Superposition theorem is The Superposition theorem is very helpful in determining the voltage across an element or
current through a branch when the circuit contains multiple b f lt tnumber of voltage or current sources
One big advantage is that we do not have to use Cramer’s rule or complicated that we do not have to use Cramer s rule or complicated
mathematical operations but simply algebraically adding solutions obtained from analyzing the network with one source activated at a timesource activated at a time
The Superposition theorem states that “Th t th h lt l t i li “The current through, or voltage across an element in any linear
bilateral network is equal to the algebraic sum of the currents or voltages produced independently by each source”
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Superposition TheoremSuperposition TheoremSuperposition TheoremSuperposition Theorem
in other words, this theorem allows us to find a solution for a o e o ds, s eo e a o s us o d a so u o o acurrent or voltage using only one source at a time
once we have a solution for each source we can combine the results to obtain the total solutionresults to obtain the total solution
LinearityLi t h th t th t if d( ) ( ) ( ) ( ) Linear system have the property that if and , then
Consider the square-law system of
1 1( ) ( )x t y t 2 2( ) ( )x t y t
1 2 1 2( ) ( ) ( ) ( ) ( ) ( )x t x t x t y t y t y t 2( ) ( )y t x t Linear system?q y
1( )x t 1( )y t( )w t
1( )x t( )y t( )x t
( ) ( )y y
2 ( )x t 2 ( )y t 2 ( )x t( )
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( )w t ( )y twill equal when the system is linear !
Superposition TheoremSuperposition TheoremSuperposition TheoremSuperposition Theorem
Analyzing procedure: To consider the effects of each Analyzing procedure: To consider the effects of each source, the other sources have to be removed when removing a voltage source from a network schematic,
replace it with a direct connection (short-circuit) of zero ohms when removing a current source from a network schematic,
replace it by an open circuit of infinite ohmsreplace it by an open circuit of infinite ohms any internal resistance associated with the removed source(s)
must remain in the network
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Superposition TheoremSuperposition TheoremSuperposition TheoremSuperposition Theorem
Since the effect of each source will be determined S ce e e ec o eac sou ce be de e edindependently, the number of networks to be analyzed will equal the number of sources
For Superposition All dependent sources must be left intact!! For Superposition, All dependent sources must be left intact!! You can’t apply O/C and S/C on dependent sources
Superposition cannot be applied to power
1 2TI I I
2 2 2 2 21 2 1 2 1 2 1 2 1 2
delivered to the circuits are ( ) 2T
The powerP I I R I R I R I I R P P I R I R 6
Superposition TheoremSuperposition TheoremSuperposition TheoremSuperposition Theorem
Example: Find v in the circuit shown Example: Find v in the circuit shown
3A is discarded by i itopen-circuit
6V is discarded by 6V is discarded by short-circuit
Th i 10 VThe answer is v = 10 V7
Superposition TheoremSuperposition TheoremSuperposition TheoremSuperposition Theorem
Example: Find vx in the circuit shown Example: Find vx in the circuit shown
The answer is vx = 12.5 V
2A is discarded 2A is discarded by open-circuit
20 v120 v2
10V is discarded by open-circuit
Dependant source keep unchanged
4 10 V+
0.1v14
2 A0.1v24 0.1v2
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(a) (b)
Thevenin’sThevenin’s TheoremTheoremThevenin sThevenin s TheoremTheorem
It states that a linear two-terminal circuit (Fig a) can be It states that a linear two terminal circuit (Fig. a) can be replaced by an equivalent circuit (Fig. b) consisting of a voltage source VTH in series with a resistor RTH
VTH is the open-circuit voltage at the terminals RTH is the input or equivalent resistance at the terminals when
the independent sources are turned off Voltage sources are replaced by short circuits Voltage sources are replaced by short circuits Current sources are replaced by open circuits
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Thevenin’sThevenin’s TheoremTheorem
Example:
Thevenin sThevenin s TheoremTheorem
Example:
Rth=8Ω
Vth=20V
RthVth
Rth
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Thevenin’sThevenin’s TheoremTheorem
Example:
Thevenin sThevenin s TheoremTheorem
Example: Measuring ETH :
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Thevenin’sThevenin’s TheoremTheorem
Example:
Thevenin sThevenin s TheoremTheorem
Example: Measuring RTH :
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Norton’s TheoremNorton’s Theorem
It states that a linear two-terminal circuit can be
Norton s TheoremNorton s Theorem
It states that a linear two terminal circuit can be replaced by an equivalent circuit of a current source IN in parallel with a resistor RN
IN is the short circuit current through the terminals R is the input or equivalent resistance at the terminals when RN is the input or equivalent resistance at the terminals when
the independent sources are turned off Voltage sources are replaced by short circuits Current sources are replaced by open circuits
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Norton’s TheoremNorton’s Theorem
Experimental Procedure
Norton s TheoremNorton s Theorem
Experimental Procedure IN :
Norton current can be determined by placing an ammeter across the output terminals of the network
RN : Since R = R the experimental procedures described for Since RN = RTH , the experimental procedures described for
the Thevenin equivalent circuit can be applied here also
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Norton’s TheoremNorton’s Theorem
Example: Be solved by Norton’s theorem
Norton s TheoremNorton s Theorem
Example: Be solved by Norton s theorem
(a) Original circuit. (b) Short circuit across terminals A and B.
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Norton’s TheoremNorton’s Theorem
The Norton Equivalent Circuit
Norton s TheoremNorton s Theorem
e o o qu a e C cu Replace R2 with a short and determine IN Determine RN = RTH The current source provides 12 A total flow, regardless of
what is connected across it When shorted all of the current will flow in the short When shorted, all of the current will flow in the short
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(c) The short-circuit current IN is 36/3 = 12 A. (d) Open terminals A and B but short-circuit V to find RAB is 2 Ω, the same as RTH
Norton’s TheoremNorton’s TheoremNorton s TheoremNorton s Theorem
212 6 A4
NL N
N L
RI IR R
(e) Norton equivalent circuit. (f) RL reconnected to terminals A and B to find that IL is 6A.
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L
Source TransformationsSource Transformations
The Norton equivalent circuit can be obtained directly
Source TransformationsSource Transformations
The Norton equivalent circuit can be obtained directly from the Thevenin equivalent circuit using a simple source conversion
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