1. Lect7EEE 2021 Thévenin's and Norton’s Theorems Dr. Holbert February 6, 2008

2. Lect7EEE 2022 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

3. Lect7EEE 2023 Independent Sources (Thevenin) Circuit with independent sources R Th V oc Thevenin equivalent circuit +–+–

4. Lect7EEE 2024 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

5. Lect7EEE 2025 Independent Sources (Norton) Circuit with one or more independent sources R Th Norton equivalent circuit I sc

6. Lect7EEE 2026 No Independent Sources (Thevenin and Norton) Circuit without independent sources R Th Thevenin equivalent circuit

7. Lect7EEE 2027 Example Thevenin Equivalent R Th V oc + – VoVo +–+– 1k  100I b + – VoVo 50  IbIb 2k  +–+–

8. Lect7EEE 2028 Basic Approach to Finding the Thevenin/Norton Equivalent Circuits with independent sources: –Find V oc and/or I sc –Compute R Th (= V oc / I sc ) Circuits without independent sources: –Apply a test voltage (current) source –Find resulting current (voltage) –Compute R Th (= V test / I test )

9. Lect7EEE 2029 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, V OC Norton: Compute the short circuit current, I SC For case 3(b): both V OC =0 and I SC =0 [so skip step 2 above]

10. Lect7EEE 20210 Thevenin/Norton Analysis 3. Compute the Thevenin equivalent resistance, R Th (or impedance, Z Th ). 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 R Th (or Z Th ) = V test /I test (c) If there are both independent and dependent sources, then compute R Th (or Z Th ) from V OC /I SC.

11. Lect7EEE 20211 Thevenin/Norton Analysis 4. Thevenin: Replace circuit with V OC in series with R Th (or Z Th ). Norton: Replace circuit with I SC in parallel with R Th (or Z Th ). Note: for 3(b) the equivalent network is merely R Th (or Z Th ), that is, no voltage (or current) source. Only steps 2 & 4 differ from Thevenin & Norton!

12. Lect7EEE 20212 Class Examples Drill Problems P3-6, P3-7, P3-8