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Source Transformations (or source conversion) There are two types of source transformations:

I. I. +. +. R. S. +. Load. Load. R. V. V. V. _. P. I. S. P. _. _. Real Voltage Source. Real Current Source. Lecture #11 EGR 260 – Circuit Analysis. Reading Assignment: Sections 4.9 - 4.16, in Electric Circuits, 9 th Ed. by Nilsson .

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Source Transformations (or source conversion) There are two types of source transformations:

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  1. I I + + R S + Load Load R V V V _ P I S P _ _ Real Voltage Source Real Current Source Lecture #11 EGR 260 – Circuit Analysis Reading Assignment: Sections 4.9 - 4.16, in Electric Circuits, 9th Ed. by Nilsson • Source Transformations (or source conversion) • There are two types of source transformations: • Transform a real voltage source into a real current source • Transform a real current source into a real voltage source In order for the two types of sources to be equivalent, they should provide the same voltage and current to any load. This can be accomplished by equating their characteristics. In particular, the x-intercepts, y-intercepts, and slopes should be equal (actually equating any 2 of these 3 items fixes the remaining item).

  2. I IP Slope = 1/RP I V IP RP Real voltage source characteristics Real current source characteristics VS /RS Slope = 1/RS V VS Lecture #11 EGR 260 – Circuit Analysis Equating the y-intercepts yields: VS/RS = IP Equating the x-intercepts yields: VS = IPRP Equating the slopes yields: RS = RP

  3. I I Convert V - source to I - source 4 + + + 20 V V _ 5 A 4 V _ _ Convert I - source to V - source Lecture #11 EGR 260 – Circuit Analysis Source Transformations - Conversion Formulas: Simple Example:

  4. 3 2 + + 27 V 6 _ 5 V X _ Lecture #11 EGR 260 – Circuit Analysis Example: Determine VX in the circuit below using source transformations.

  5. Lecture #11 EGR 260 – Circuit Analysis Example: Determine VX in the circuit below using source transformations.

  6. Lecture #11 EGR 260 – Circuit Analysis Example: Determine VX in the circuit below.

  7. + V1 - I + R S + Load Load V2 RP V _ I S P _ Lecture #11 EGR 260 – Circuit Analysis Important notes on source transformations: 1) Transformed sources are equivalent in that they provide the same terminal voltage and terminal current (V and I) to any connected load. 2) Transformed sources are not equivalent internally. For example, the current through or the voltage across RS and RP is not the same. To assume that they are the same is a common error. Example: In the circuit below, V1 V2. 3) All sources are not transformable. Note that a voltage source MUST have a SERIES resistor to be transformable. Note that a current MUST have a PARALLEL to be transformable. 4) Dependent sources can be transformed also.

  8. Lecture #11 EGR 260 – Circuit Analysis Source Transformations - not always possible The last page stated that all sources are not transformable so source transformations cannot be used on all circuits. Example: Draw a circuit that cannot be analyzed using source transformations.

  9. Lecture #11 EGR 260 – Circuit Analysis Example: Determine VX in the circuit below. Show a correct and an incorrect approach.

  10. Lecture #11 EGR 260 – Circuit Analysis Example: Determine VX in the circuit below.

  11. Lecture #11 EGR 260 – Circuit Analysis • Superposition • The superposition theorem essentially states that independent sources act separately. In particular, the current or voltage in any part of the circuit can be calculated by determining the current or voltage due to each independent source (with all other independent sources killed) and then by adding the results algebraically. • Independent sources are killed by: • Shorting voltage sources (which is equivalent to setting the voltage to zero) • Opening current sources (which is equivalent to setting the current to zero) • Notes: • Never kill a dependent source • Superposition applies to voltage and current, but not to power

  12. Lecture #11 EGR 260 – Circuit Analysis Example: Determine the current IX using superposition.

  13. 12 5 6 + _ + 2 A 10 V _ 30 V V 6 + X _ Lecture #11 EGR 260 – Circuit Analysis Example: Determine the voltage VX using superposition.

  14. Lecture #11 EGR 260 – Circuit Analysis Example: Determine the voltage VX using superposition.

  15. Lecture #11 EGR 260 – Circuit Analysis Example: A) Determine the voltage VX using superposition.

  16. Lecture #11 EGR 260 – Circuit Analysis Example: (continued) B) Show that superposition does not apply to power. I.e., show that PT P1 + P2 for the top right 18 ohm resistor.

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