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

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

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

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

i + +   i v v

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.

Transformation of controlled sources

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

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

Thevenin’s equivalent circuit

Finding R Th when circuit has dependent sources.

Example 4.3 Find i in the circuit. Solution:

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

Norton's Theorem 诺顿定理

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.

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

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

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

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！