Source Transformation

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Source Transformation
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Equivalent Sources

• An ideal current source has the voltage necessary
  to provide its rated current.
• An ideal voltage source supplies the current
  necessary to provide its rated voltage.
• A real voltage source cannot supply arbitrarily
  large amounts of current.
• A real current source cannot have an arbitrarily
  large terminal voltage.

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A More Realistic Source Model
i(t)
The Circuit

Rs

vs(t)
v(t)
-
-
The Source
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I-V Relationship

• The I-V relationship for this source model is
• v(t) vs(t) - Rs i(t)

v(t)
i(t)
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What are the points where the I-V
characteristics intersect the axes?
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What do these intersection points represent
physically?
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Open Circuit Voltage

• If the current flowing from a source is zero,
  then it is connected to an open circuit.
• The voltage at the source terminals with i(t)
  equal to zero is called the open circuit voltage
• voc(t)

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Short Circuit Current

• If the voltage across the source terminals is
  zero, then the source is connected to a short
  circuit.
• The current that flows when v(t) is zero is
  called the short circuit current
• isc(t)

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voc(t) and isc(t)
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voc(t) and isc(t)

• Since the open circuit voltage and the short
  circuit current determine where the I-V line
  crosses both axes, they completely define the
  line.
• Any circuit that has the same I-V characteristics
  is an equivalent circuit.

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Equivalent Current Source
i(t)
The Circuit

is(t)
Rs
v(t)
-
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Voltage and Current Sources
Is
Rs
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Source Transformation

• Equivalent sources can be used to simplify the
  analysis of some circuits.
• A voltage source in series with a resistor is
  transformed into a current source in parallel
  with a resistor.
• A current source in parallel with a resistor is
  transformed into a voltage source in series with
  a resistor.

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Averaging Circuit

• How can source transformation make analysis of
  this circuit easier?

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Source Transformations
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Source Transformations

1kW
1kW
V2 /1kW
Vout
-
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A Single Node-Pair Circuit!