1. Lesson 6: 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
Maintains same current in branch of circuit
Doesn’t matter how components are connected external to the source
Direction of current source indicates direction of 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
I = 2 mA

7. Constant Current Sources

8. Constant Current Sources
The voltage across the current source (VS) is dependant on how other components are connected to it.
Changing R2 from 2kΩ to 6kΩ causes the voltage across the current source to change polarity.
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
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 transformation
Replace a voltage source vs in series with a resistor R by a current source is in parallel with the SAME resistor R.

13. SOURCE CONVERSIONS
FIG. 8.6 Source conversion.

14. Source transformation
How do you calculate the new current source value?
Just apply Ohm’s Law:

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

16. Source transformation Part II
Replace a current source is in parallel with a resistor R by a voltage source vs in series with the SAME resistor R.

17. Source transformation
How do you calculate the new voltage source value?
Just apply Ohm’s Law:

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

19. CURRENT SOURCES IN PARALLEL
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.

20. Current Sources in Series

21. CURRENT SOURCES IN PARALLEL
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.

22. Parallel Current Sources
Parallel current sources simply add together, and can be simplified by a single current source.

23. Example Problem 3
Use source transformation and parallel current source rule to simplify the circuit and determine vo.

24. Example Problem 4 Use source transformation to determine V0
ONLY one source transformation is possible! And it doesn’t help you solve the problem….

25. Example Problem 5
Determine I2 and V3.