1. Ideal sources vs. realistic sources Open circuit voltage, V oc Short circuit current, I sc I - V relationship Source transformation Lecture 7. Realistic Sources & Source Transformation 1

2. 2 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.

3. 3 A More Realistic Source Model vs(t)vs(t) RsRs + - The Circuit A Realistic Source: Modeled by an ideal source in series with a resistor i(t)i(t) + - v(t)v(t)

4. 4 I-V Relationship The I-V relationship for this source model is v(t) = v s (t) - R s i(t) v(t)v(t) i(t)i(t)

5. 5 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: v oc (t)

6. 6 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: i sc (t)

7. 7 v oc (t) and i sc (t) v(t)v(t) i(t)i(t) v oc (t) i sc (t)

8. 8 v oc (t) and i sc (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.

9. 9 Equivalent Current Source is(t)is(t)RsRs The Circuit i(t)i(t) + - v(t)v(t)

10. 10 Voltage and Current Sources VsVs + - RsRs IsIs RsRs

11. 11 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.

12. 12 Example: Averaging Circuit How can source transformation make analysis of this circuit easier? + - V out 1k  V1V1 + - V2V2 + -

13. 13 Source Transformations + - V out 1k  V1V1 + - V2V2 + -

14. 14 Source Transformations + - V out 1k  V 1 /1k  1k  V 2 /1k 

15. 15 A Single Node-Pair Circuit!

16. 16 Class Examples Drill Problems P3-3 and P3-4