1. Lesson 7: Current Sources / Source Conversion

2. Learning Objectives
Analyze a circuit consisting of a current source, voltage source and resistors.
Convert a current source and a resister into an equivalent circuit consisting of a voltage source and a resistor.
Evaluate a circuit that contains several current sources in parallel.

3. Ideal Sources
An ideal source is an active element that provides a specified voltage or current that is completely independent of other circuit elements.
DC Voltage Source
DC current source

4. Current Sources
In general, a current source determines the direction and magnitude of the current in the branch where it is located.
Furthermore, the magnitude and the polarity of the voltage across a current source are each a function of the network to which the voltage is applied.

5. Constant Current Sources
A constant current source will maintain the same current in branch of circuit.
It doesn’t matter how components are connected external to the source.
The direction of the current source indicates direction of the current flow in branch.

6. Constant Current Sources
Series circuit
Current must be same everywhere in circuit.
Current source in a series circuit
Value of the current for that circuit.
For the circuit shown
Is = 2 mA

7. Constant Current Sources
If we wanted to find Vs, V1 and V2; we can simply apply Ohm’s Law and KVL:

8. Constant Current Sources
The voltage across the current source (VS) is dependent on how other components are connected to it.
Changing R2 from 2kΩ to 6kΩ causes the voltage across the current source to change polarity to maintain KVL.
Current source voltage polarity does NOT have to follow the current source’s arrow!

9. Practical Voltage Sources
A real or practical source supplies its rated voltage when its terminals are not connected to a load (open-circuited) but its voltage drops off as the current it supplies increases.

10. Practical Voltage Source
A real (or practical) voltage source supplies its rated voltage when its terminals are open-circuited (NOT connected to a load), but its voltage drops off as the current supplied increases.
We can model a practical voltage source using an ideal source vs in series with an internal resistance Rs.

11. Practical Current Source
A practical current source supplies its rated current when its terminals are short-circuited but its current drops off as the load resistance increases.
We can model a practical current source using an ideal current source is in parallel with an internal resistance Rs.

12. Source Conversions
Source conversion.

13. Source Transformation Voltage Source to Current Source
Replace a voltage source vs in series with a resistor R by a current source is in parallel with the SAME resistor R.
How do you calculate the new current source value?
Just apply Ohm’s Law:

14. Source Transformation Current Source to Voltage Source
Replace a current source is in parallel with a resistor R by a voltage source vs in series with the SAME resistor R.
How do you calculate the new voltage source value?
Just apply Ohm’s Law:

15. Example Problem 1
Use source transformation to determine vo.

16. Example Problem 2
Use source transformation to determine vo.

17. Current Sources – A Rule
We found that voltage sources of different terminal voltages cannot be placed in parallel because of a violation of Kirchhoff’s voltage law.
Similarly, current sources of different values cannot be placed in series due to a violation of Kirchhoff’s current law.

18. Current Sources – A Parallel Rule
However, current sources can be placed in parallel just as voltage sources can be placed in series.
In general, two or more current sources in parallel can be replaced by a single current source having a magnitude determined by the difference of the sum of the currents in one direction and the sum in the opposite direction. The new parallel internal resistance is the total resistance of the resulting parallel resistive elements.
Take care to note the polarity of the sources!

19. Example Problem 3
Use source transformation and parallel current source rule to simplify the circuit and determine vo.
- Convert the voltage source into a current source:
- Calculate the Is needed:
- Redraw the circuit with the new current source
- Redraw again to show the added current sources to get IT = 7A. 4A
- Use CDR to calculate for Io: 7A 4Ω
- Use Ohm’s Law to calculate for Vo:

20. Source Transformation
Use source transformation to determine V0
Unfortunately, ONLY one source transformation is possible!
The voltage source is in parallel with the 6Ω resistor (thus not a source resistance) and the 3A current source is in series with the 3Ω resistor (again not a source resistor).
Changing only the 9A source into a voltage source doesn’t help you solve the problem….

21. Example Problem 5 Determine I2 and V3.
- Redraw the circuit with the combined current source (6A-2A=4A).
- Now calculate RT. 4A
- Now calculate I2 using CDR.
- Finally calculate V2 using Ohm’s Law.

22. QUESTIONS?