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NETWORK THEOREMS MODULE
Superposition
• Superposition Theorem – the response of a
circuit to more than one source can be
determined by analyzing the circuit’s
response to each source (alone) and then
combining the results
Insert Figure 7.2
Superposition
Insert Figure 7.3
Superposition
• Analyze Separately, then Combine Results
Use superposition to find the current ix.
Current source is zero – open circuit as I = 0 and solve iXv
Voltage source is zero – short circuit as V= 0 and solve iXv
i X  i Xv  i Xc
Use superposition to find the current ix.
The controlled voltage source is included in all cases as
it is controlled by the current ix.
Voltage and Current Sources
Insert Figure 7.7
Voltage and Current Sources
Insert Figure 7.8
Voltage and Current Sources
Insert Figure 7.9
Source Transformation
VS
Under what condition, the voltage and
current of the load is the same when
operating at the two practical sources?
For voltage source
iL
RS
+
+
_
VL
RL
_
For current source
i S RP
VL 
RL
R P  RL
iL
,
+
IS
RP
VL
_
VS
VL 
RL
R S  RL
We have,
RL
VS
iS RP

R S  RL RP  RL
VS
RP  RS , iS 
RS
Voltage and Current Sources
• Equivalent Voltage and Current Sources – for every
voltage source, there exists an equivalent current
source, and vice versa
Thevenin’s Theorem
• Thevenin’s Theorem – any resistive circuit
or network, no matter how complex, can be
represented as a voltage source in series
with a source resistance
Thevenin’s Theorem
• Thevenin Voltage (VTH) – the voltage
present at the output terminals of the
circuit when the load is removed
Insert Figure 7.18
Thevenin’s Theorem
• Thevenin Resistance (RTH) – the resistance
measured across the output terminals with
the load removed
Thévenin Equivalent
Circuits
Thévenin Equivalent
Circuits
Vt  voc
voc
Rt 
isc
Thévenin Equivalent Circuits
Finding the Thévenin
Resistance Directly
When zeroing a voltage source, it becomes
a short circuit. When zeroing a current
source, it becomes an open circuit.
We can find the Thévenin resistance by
zeroing the sources in the original
network and then computing the resistance
between the terminals.
Computation of Thévenin resistance
Equivalence of open-circuit and Thévenin voltage
A circuit and its Thévenin equivalent
Superposition
As the voltage source does not contribute any output voltage,
Only the current source has the effect.
Determine the Thévenin and Norton Equivalents of Network A in (a).
Source transformation
Find the Thévenin equivalent of the circuit shown in (a).
v
As i = -1, therefore, the controlled voltage source is -1.5V.
Use nodal analysis at node v,
v  (1.5) v
  1, v  0.6
3
2
Thus,
Rth =v/I = 0.6/1 = 0.6 ohms
Applications of Thevenin’s Theorem
• Load Voltage Ranges – Thevenin’s theorem
is most commonly used to predict the
change in load voltage that will result from
a change in load resistance
Applications of Thevenin’s Theorem
• Maximum Power Transfer
– Maximum power transfer from a circuit to a
variable load occurs when the load resistance
equals the source resistance
– For a series-parallel circuit, maximum power
occurs when RL = RTH
Applications of Thevenin’s Theorem
• Multiload Circuits
Insert Figure 7.30
Norton’s Theorem
• Norton’s Theorem – any resistive circuit or network,
no matter how complex, can be represented as a
current source in parallel with a source resistance
Norton’s Theorem
• Norton Current (IN) – the current through
the shorted load terminals
Insert Figure 7.35
Computation of Norton current
Norton’s Theorem
• Norton Resistance (RN) – the resistance
measured across the open load terminals
(measured and calculated exactly like RTH)
Norton’s Theorem
• Norton-to-Thevenin and Thevenin-to-Norton
Conversions
Insert Figure 7.39
Step-by-step Thévenin/NortonEquivalent-Circuit Analysis
1. Perform two of these:
a. Determine the open-circuit voltage Vt = voc.
b. Determine the short-circuit current In = isc.
c. Zero the sources and find the Thévenin
resistance Rt looking back into the
terminals.
2. Use the equation Vt = Rt In to compute
the remaining value.
3. The Thévenin equivalent consists of a
voltage source Vt in series with Rt .
4. The Norton equivalent consists of a
current source In in parallel with Rt .
Maximum Power Transfer
The load resistance that absorbs the
maximum power from a two-terminal
circuit is equal to the Thévenin
resistance.
Power transfer between source and load
Graphical representation of maximum
power transfer