1. Thevenin’s Theorem & Norton’s Theorem Made by: Dhara Vihol Enroll. No.:140770107249 CE-D SILVER OAK COLLEGE OF ENGINEERING AND TECHNOLOGY

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

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

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

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

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

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

8. 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. 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. 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. 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. Class Examples Drill Problems P3-6, P3-7, P3-8

13. THEVENIN & NORTON THEVENIN’S THEOREM: Example 10.1. Find V X by first finding V TH and R TH to the left of A-B. Figure 10.8: Circuit for Example 10.1. First remove everything to the right of A-B.

14. THEVENIN & NORTON THEVENIN’S THEOREM: Example 10.1. continued Figure 10.9: Circuit for finding V TH for Example 10.1. Notice that there is no current flowing in the 4  resistor (A-B) is open. Thus there can be no voltage across the resistor.

15. THEVENIN & NORTON THEVENIN’S THEOREM: Example 10.1. continued We now deactivate the sources to the left of A-B and find the resistance seen looking in these terminals. R TH Figure 10.10: Circuit for find R TH for Example 10.10. We see, R TH = 12||6 + 4 = 8 

16. THEVENIN & NORTON THEVENIN’S THEOREM: Example 10.1. continued After having found the Thevenin circuit, we connect this to the load in order to find V X. Figure 10.11: Circuit of Ex 10.1 after connecting Thevenin circuit.