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.

+V2vV8v

V10 vvv

Solution:

4.2 Source Transformation

A source transformation is the process of replacing a voltage source vs in series with a resistor R by a current source is 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

iRvv s Riiv s ）（

R

viorRiv ssss

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

c c

+ +

i i

v v

Riv cc

Example 4.2 Use source transformation to find v0 in the circuit.

A4.0228

2

Ai V2.384.0 ov

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 VTh in series

with a resistor RTh,where VTh is the open-circuit

voltage at the terminals and RTh 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 RTh when circuit has dependent sources.

Example 4.3 Find i in the circuit.

Solution:

A5.016

81 i

V305.01224 ocv

412//41ThR

A3i

Example 4.4 Find i in the circuit.

11 25.0 vi +

-v1?-

Solution:

i1101 11 iv

A21 iV14101210 11 iivoc

0125.012

1iv

1

12

11

v

3

25.10 i 4.2

1

0iReq

For loop 1:

so①

At node 1:

and

so

A26.44.2

14

iHence

Norton's Theorem 诺顿定理

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 IN in parallel with a

resistor RN,where IN is the short-circuit current

through the terminals and RN is the input or

equivalent resistance at the terminals when the

independent sources are turned off.

Norton equivalent circuit.

Finding Norton current IN. RN=RTh=Req

4.4 Maximum Power Transfer

ThL RR

Maximum power is transferred to the load when the load resistance equals the Thevenin resistance as seen from the load.

Th

Th

R

Vp

4

2

max

最大功率传输

Example 4.5 Find the value of RL for maximum power transfer in the circuit. Find that maximum power.

V95.126 ocv

12//2eqR

V9 ocTh vV

Req

Solution:

i

For loop : 6+2i+2i=12

i=1.5Aso

Then:

1eqTh RR 1ThL RRFor maximum power transfer

The maximum power is W25.204

9

4

22

max Th

Th

R

Vp

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！