Chapter 08
Methods of Analysis
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Source:
Circuit Analysis: Theory and Practice Delmar Cengage Learning
Outline

Source Conversion

Mesh Analysis

Nodal Analysis

Delta-Wye (-Y) Conversion

Bridge Networks
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Source Conversions
If internal resistance of a source is considered:
 Voltage source may be converted to current source
 Calculate current from E/RS , RS does not change,
and place current source and resistor in parallel
 Current source may be converted to voltage source
 E = I RS and place voltage source in series with
resistor
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Current and Voltage Sources Exchange

A load connected to a voltage source or its
equivalent current


Although sources are equivalent


Should have same voltage and current for either
source
Currents and voltages within sources may differ
Sources are only equivalent external to
terminals
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Mesh Analysis
Step0: Arbitrarily assign a clockwise current
to each interior closed loop (Mesh)
Step1: Indicate voltage polarities across
all resistors
Step2: Write KVL equations
Step3: Solve resulting simultaneous
equations

Branch currents determined by:

Algebraically combining loop currents common to
branch
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Example1: Mesh Analysis


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Assign loop currents and voltage polarities
Using KVL: 6 - 2I1 - 2I1 + 2I2 - 4 = 0
4 - 2I2 + 2I1 - 4I2 + 2 = 0
Simplify and solve equations
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Nodal Analysis
Step0: Assign a reference node within circuit
and indicate node as ground


Convert voltage sources to current sources
Arbitrarily assign a current direction to each branch
where there is no current source
Step1: Assign voltages V1, V2, etc. to
remaining nodes
Step2: Apply KCL to all nodes except
reference node

Rewrite each current in terms of voltage
Step3: Solve resulting equations for voltages
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Example0: Nodal Analysis
Assign voltage at node, then using KVL
(V1-6)/2 + (V1-4)/2 + (V1-(-2))/4= 0

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Delta-Wye (-Y) Conversion

Resistors connected to a point of Y


Obtained by finding product of resistors connected to same
point in Delta
Divided by sum of all Delta resistors
R1=(RC*RB) / (RA+RB+RC)
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Wye-Delta Conversions

A Delta resistor is found:
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Taking sum of all two-product combinations of Y
resistor values
Divided by resistance of Y directly opposite
resistor being calculated
RA=(R1R2+R2R3+R1R3) /R1
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Bridge Networks
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Three same equivalent bridge networks
Balanced bridge:
R1R4 = R2R3 and IR5=0
Unbalanced bridge:
R1R4  R2R3 and IR50
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Example: Bridge Networks
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Balanced bridge:
3*24 = 6*12
R1R4 = R2R3 and IR5=0
R5 can be replaced with
an open circuit or
a short circuit.
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Kernel abilities
1. Can use Mesh Analysis for solving the unknown
voltage and current of a circuit.
2. Can use Nodal Analysis for solving the unknown
voltage and current of a circuit.
3. Can use Delta-Wye (-Y) Conversion for solving the
unknown voltage and current of a circuit.
4. Can recognize a Bridge circuit whether is balance or
unbalance and solve the unknown voltage and
current.
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