1. 4.1 Superposition 4.3 Thevenin's Theorem and Norton's Theorem 4.2 Source Transformation 4.4 Maximum Power Transfer Chapter 4 Circuit Theorems 电路定理

2. 4.1 Superposition The superposition principle states that the voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across (or currents through ) that element due to each independent source acting alone. Note : 1. We consider one independent source at a time while all other independent sources are turned off （置零） ( replace voltage source by 0V or a short circuit, and current source by 0A or an open circuit). 2. Dependent sources are left intect （完整）. 叠加定理

3. Example 4.1 Calculate the voltage v in the circuit. + Solution:

4. 4.2 Source Transformation A source transformation is the process of replacing a voltage source v s in series with a resistor R by a current source i s in parallel with a resistor R, or vice versa. The two circuits are equivalent （等效） at terminals a-b 电源转换

5. i + +   i v v

6. 1. The arrow of the current source is directed toward the positive terminal of the voltage source. NOTE: 2. The source transformation is not possible for the ideal sources.

7. Transformation of controlled sources

8. Example 4.2 Use source transformation to find v 0 in the circuit.

9. 4.3 Thevenin’s Theorem and Norton’s Theorem Thevenin's theorem states that a linear two- terminal circuit can be replaced by an equivalent circuit consisting of a voltage source V Th in series with a resistor R Th,where V Th is the open-circuit voltage at the terminals and R Th is the input or equivalent resistance at the terminals when the independent sources are turned off. 戴维宁定理和诺顿定理

10. Thevenin’s equivalent circuit

11. Finding R Th when circuit has dependent sources.

12. Example 4.3 Find i in the circuit. Solution:

13. Example 4.4 Find i in the circuit. + - v1v1 ? - Solution: i1i1 For loop 1: so ① At node 1: and so Hence

14. Norton's Theorem 诺顿定理

15. Norton's theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source I N in parallel with a resistor R N,where I N is the short-circuit current through the terminals and R N is the input or equivalent resistance at the terminals when the independent sources are turned off.

16. Norton equivalent circuit. Finding Norton current I N. R N =R Th =R eq

17. 4.4 Maximum Power Transfer Maximum power is transferred to the load when the load resistance equals the Thevenin resistance as seen from the load. 最大功率传输

18. Example 4.5 Find the value of R L for maximum power transfer in the circuit. Find that maximum power. R eq Solution: i For loop : 6+2i+2i=12 i=1.5A so Then: For maximum power transfer The maximum power is

19. 部分电路图和内容参考了： 电路基础（第 3 版），清华大学出版社 电路（第 5 版），高等教育出版社 特此感谢！