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Resistor Combinations; Source Transformation

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

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Resistor Combinations; Source Transformation

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  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

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