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Thévenin's and Norton’s Theorems

Thévenin's and Norton’s Theorems. Dr. Holbert February 6, 2008. Thevenin’s Theorem. Any circuit with sources (dependent and/or independent) and resistors can be replaced by an equivalent circuit containing a single voltage source and a single resistor

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Thévenin's and Norton’s Theorems

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  1. Thévenin's and Norton’s Theorems Dr. Holbert February 6, 2008 EEE 202

  2. Thevenin’s Theorem • Any circuit with sources (dependent and/or independent) and resistors can be replaced by an equivalent circuit containing a single voltage source and a single resistor • Thevenin’s theorem implies that we can replace arbitrarily complicated networks with simple networks for purposes of analysis EEE 202

  3. RTh + – Voc Thevenin equivalent circuit Independent Sources (Thevenin) Circuit with independent sources EEE 202

  4. Thevenin ↔ Norton • Any Thevenin equivalent circuit is in turn equivalent to a current source in parallel with a resistor [source transformation] • A current source in parallel with a resistor is called a Norton equivalent circuit • Finding a Norton equivalent circuit requires essentially the same process as finding a Thevenin equivalent circuit EEE 202

  5. Isc RTh Norton equivalent circuit Independent Sources(Norton) Circuit with one or more independent sources EEE 202

  6. No Independent Sources(Thevenin and Norton) RTh Circuit without independent sources Thevenin equivalent circuit EEE 202

  7. Ib + 2kW 1kW 50W + – Vo 100Ib – Example Thevenin Equivalent RTh + + – Voc Vo – EEE 202

  8. Basic Approach to Finding the Thevenin/Norton Equivalent • Circuits with independent sources: • Find Voc and/or Isc • Compute RTh (= Voc/Isc) • Circuits without independent sources: • Apply a test voltage (current) source • Find resulting current (voltage) • Compute RTh (= Vtest/Itest) EEE 202

  9. Thevenin/Norton Analysis 1. Pick a good breaking point in the circuit (cannot split a dependent source and its control variable) 2. Thevenin: Compute open circuit voltage, VOC Norton: Compute the short circuit current, ISC For case 3(b): both VOC=0 and ISC=0 [so skip step 2 above] EEE 202

  10. Thevenin/Norton Analysis 3. Compute the Thevenin equivalent resistance, RTh (or impedance, ZTh). Three possibilities: (a) If there are only independent sources, then short circuit all the voltage sources and open circuit the current sources (just like superposition). (b) If there are only dependent sources, then must use a test voltage or current source in order to calculate RTh (or ZTh) = Vtest/Itest (c) If there are both independent and dependent sources, then compute RTh (or ZTh) from VOC/ISC. EEE 202

  11. Thevenin/Norton Analysis 4. Thevenin: Replace circuit with VOC in series with RTh (or ZTh). Norton: Replace circuit with ISC in parallel with RTh (or ZTh). Note: for 3(b) the equivalent network is merely RTh (or ZTh), that is, no voltage (or current) source. Only steps 2 & 4 differ from Thevenin & Norton! EEE 202

  12. Class Examples • Drill Problems P3-6, P3-7, P3-8 EEE 202

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