INC 111 Basic Circuit Analysis

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INC 111 Basic Circuit Analysis

• Week 5
• Thevenins Theorem

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Special Techniques

• Superposition Theorem
• Thevenins Theorem
• Nortons Theorem
• Source Transformation

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Linearity Characteristic
If RL change its value , how will it effect the
current and voltage across it?
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I
Voc Voltage open-circuit Isc Current
short-circuit
ISC
V
VOC
For any circuit constructed from only linear
components Not just RL, all resistors have
this property.
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Thevenins Theorem
When we are interested in current and voltage
across RL, we can simplify other parts in the
circuit.
Equivalent circuit
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I
ISC
Slope 1/R
V
VOC
Voc Voltage open-circuit Isc Current
short-circuit R R equivalent
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Thevenins Equivalent Circuit
Thevenins equivalent circuit
VTH Voc (by removing RL and find the voltage
difference between 2 pins) RTH (by looking into
the opened connections that we remove RL, see how
much resistance from the connections. If we see a
voltage source, we short circuit. If we see a
current source, we open circuit.)
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Why do we needequivalent circuit?

• To analyze a circuit with several values of RL
• For circuit simplification (source
  transformation)
• To find RL that gives maximum power (maximum
  power transfer theorem)

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Procedure

• Remove RL from the circuit
• Find voltage difference of the 2 opened
  connections. Let it equal VTH.
• From step 2 find RTH by
• 3.1 short-circuit voltage sources
• 3.2 open-circuit current sources
• 3.3 Look into the 2 opened connections. Find
  equivalent resistance.

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Example
Find Thevenins equivalent circuit and find the
current that passes through RL when RL 1?
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Find VTH
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Find RTH
Short voltage source
RTH
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Thevenins equivalent circuit
If RL 1?, the current is
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Example
Find Thevenins equivalent circuit
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Find VTH
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Find RTH
Open circuit current source
RTH
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Thevenins equivalent circuit
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Example Bridge circuit
Find Thevenins equivalent circuit
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10V
Find VTH
8V
2V
0V
VTH 8-2 6V
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Find RTH
RTH
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Thevenins equivalent circuit
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Special Techniques

• Superposition Theorem
• Thevenins Theorem
• Nortons Theorem
• Source Transformation

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I
ISC
V
VOC
For any point in linear circuit
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Thevenins Equivalent Circuit
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Nortons Equivalent Circuit
In Isc from replacing RL with an electric wire
(resistance 0) and find the current Rn RTH
(by looking into the opened connections that we
remove RL, see how much resistance from the
connections. If we see a voltage source, we short
circuit. If we see a current source, we open
circuit.)
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Example
Find Nortons equivalent circuit and find the
current that passes through RL when RL 1?
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Find In
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Find Rn
Short voltage source
RTH
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Nortons equivalent circuit
If RL 1?, the current is
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Relationship BetweenThevenins and Nortons
Circuit
I
ISC
Slope - 1/Rth
V
VOC
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Nortons equivalent circuit
Thevenins equivalent circuit
Same R value
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Example
Find Nortons equivalent circuit
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Find In
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Find RTH
Open circuit current source
RTH
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Nortons equivalent circuit
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Thevenins equivalent circuit
Nortons equivalent circuit
0.2 x 15 3
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Equivalent Circuits withDependent Sources
We cannot find Rth in circuits with dependent
sources using the total resistance method.
But we can use
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Example
Find Thevenin and Nortons equivalent circuit
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Find Voc
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Solve equations I1 3.697mA I2 3.678mA
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Find Isc
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Find Isc
I1 0.632mA I2 0.421mA I3 -1.052 A Isc I3
-1.052 A
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Nortons equivalent circuit
Thevenins equivalent circuit