1. Resistor Combinations; Source Transformation Dr. Holbert February 4, 2008 EEE 202

2. Introduction • For analysis, series resistors/impedances can be replaced by an equivalent resistor/ impedance • Parallel resistors/impedances can be replaced by an equivalent resistor/ impedance • Complicated networks of resistors/ impedances can be replaced by a single equivalent resistor/impedance EEE 202

3. i(t) i(t) + + v(t) Req v(t) – – Equivalent Resistance • Req is equivalent to the resistor network on the left in the sense that they have the same i-v characteristics • The rest of the circuit cannot tell whether the resistor network or the equivalent resistor is connected to it EEE 202

4. Req Series Resistance Req = R1 + R2 + R3 R1 R2 R3 EEE 202

5. R1 R2 Req Parallel Resistance R3 EEE 202

6. 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 EEE 202

7. A More Realistic Source Model i(t) The Circuit + Rs + – vs(t) v(t) – The Source EEE 202

8. I-V Relationship The I-V relationship for this source model is v(t) = vs(t) –Rsi(t) v(t) i(t) EEE 202

9. Open Circuit Voltage • If the current flowing from a source is zero, then the source 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) EEE 202

10. 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) equals zero is called the short circuit current: isc(t) EEE 202

11. 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 v(t) voc(t) isc(t) i(t) EEE 202

12. Equivalent Current Source i(t) The Circuit + is(t) Rs v(t) – EEE 202

13. Source Transformation Rs + – Vs Is Rs EEE 202

14. 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 of the same value • A current source in parallel with a resistor is transformed into a voltage source in series with a resistor of the same value EEE 202

15. Averaging Circuit How can source transformation make analysis of this circuit easier? 1kW 1kW + + – + – V1 Vout 1kW V2 – EEE 202

16. Source Transformations 1kW 1kW + + – + – V1 Vout 1kW V2 – EEE 202

17. Source Transformations + 1kW 1kW 1kW V1 /1kW V2 /1kW Vout – Which is a single node-pair circuit that we can use current division on! EEE 202

18. Class Examples • Drill Problems P3-1, P3-2, P3-3 EEE 202