TECHNIQUES OF DC CIRCUIT ANALYSIS:

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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 LINEAR CIRCUIT

What do we mean by a linear relationship?
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When the relationship fulfilled 2 properties

• Homogeneity (scaling)

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

• Additivity

f(x) y ? f(x1 x2) f(x1) f(x2) y1
y2
What do we mean by a linear relationship?
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Superposition Principle The voltage across an
element ( or the current through an element) of a
linear circuit containing more than one
independent source, is the algebraic sum the
voltage across that element (or the current
through that element) due to each independent
source acting alone.
All other independent sources are KILLED
Dependent sources CANNOT be killed !
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Superposition Principle The voltage across an
element ( or the current through an element) of a
linear circuit containing more than one
independent source, is the algebraic sum the
voltage across that element (or the current
through that element) due to each independent
source acting alone.
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Superposition Principle The voltage across an
element ( or the current through an element) of a
linear circuit containing more than one
independent source, is the algebraic sum the
voltage across that element (or the current
through that element) due to each independent
source acting alone.

• may involve MORE work

• cannot be applied to power calculation find i
  or v first (using superposition) before
  calculating power !

• most suitably used when involved with sources of
  different properties or types, e.g. different
  frequencies, mixture of DC and AC, etc.

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Thevenins Theorem A linear two-terminal circuit
can be replaced by an equivalent circuit
consisting of a voltage source in series with a
resistor
In 1883, M.L. Thevenin proposed a theorem .
VTh ?
RTh ?
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Thevenins Theorem A linear two-terminal circuit
can be replaced by an equivalent circuit
consisting of a voltage source in series with a
resistor
To determine VTh
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Thevenins Theorem A linear two-terminal circuit
can be replaced by an equivalent circuit
consisting of a voltage source in series with a
resistor
To determine VTh
RTh
VTh
VTh
Linear two-terminal circuit
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Thevenins Theorem A linear two-terminal circuit
can be replaced by an equivalent circuit
consisting of a voltage source in series with a
resistor
To determine VTh
RTh
VTh
VTh
Linear two-terminal circuit
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Thevenins Theorem A linear two-terminal circuit
can be replaced by an equivalent circuit
consisting of a voltage source in series with a
resistor
To determine VTh
VTh Voc Open circuit voltage
VTh (Since the circuit is equivalent)
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Thevenins Theorem A linear two-terminal circuit
can be replaced by an equivalent circuit
consisting of a voltage source in series with a
resistor
To determine RTh
Case 1
Network with NO dependent sources

• Kill all the independent sources

• Find the equivalent R looking between the
  terminals

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Thevenins Theorem A linear two-terminal circuit
can be replaced by an equivalent circuit
consisting of a voltage source in series with a
resistor
To determine RTh
Case 2
Network with dependent sources

• Kill all the independent sources - dependent
  sources stay as they are

RTh is calculated as

• Introduce a voltage (or current) source.

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Nortons Theorem A linear two-terminal circuit
can be replaced by 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 ?
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Nortons Theorem A linear two-terminal circuit
can be replaced by an equivalent circuit
consisting of a current source in parallel with a
resistor
To determine IN
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Nortons Theorem A linear two-terminal circuit
can be replaced by an equivalent circuit
consisting of a current source in parallel with a
resistor
To determine IN
IN
RN
IN
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Nortons Theorem A linear two-terminal circuit
can be replaced by an equivalent circuit
consisting of a current source in parallel with a
resistor
To determine IN
IN Isc Short circuit current
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Nortons Theorem A linear two-terminal circuit
can be replaced by an equivalent circuit
consisting of a current source in parallel with a
resistor
To determine RN
SIMILAR METHOD AS HOW TO OBTAIN RTh
RN RTh
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Relationship between Nortons and Thevenins
equivalents
OR
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Relationship between Nortons and Thevenins
equivalents
Since both circuits are equivalent, voc must be
the same
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Source Transformation A tool used to simplify
circuit a process of replacing a voltage source
in series with a resistor by a current source in
parallel with a resistor or vice versa
If the circuit is equivalent at terminal a-b,
their open-circuit and short-circuit
characteristics are similar
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Source Transformation A tool used to simplify
circuit a process of replacing a voltage source
in series with a resistor by a current source in
parallel with a resistor or vice versa
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Maximum Power Transfer
What would be the value of RL for power delivered
to it become MAXIMUM?
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Maximum Power Transfer
What would be the value of RL for power delivered
to it become MAXIMUM?
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Maximum Power Transfer
Rllinspace(1,60,500) Vth10 Rth12 p((Vth./(R
lRth)).2).Rl plot(Rl,p,'r') grid
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Maximum Power Transfer
Mathematically, we evaluate RL when
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Using PSpice to verify Nortons and Thevenins
Theorems
Find Thevenin equivalent at terminals a-b
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Using PSpice to verify Nortons and Thevenins
Theorems
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Using PSpice to verify Nortons and Thevenins
Theorems
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Using PSpice to verify Nortons and Thevenins
Theorems
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Using PSpice to verify Nortons and Thevenins
Theorems
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Using PSpice to verify Nortons and Thevenins
Theorems
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Using PSpice to verify Nortons and Thevenins
Theorems