1. Chapter 10 Magnetically Coupled Circuits and Resonance
磁耦合电路及谐振
10.1 Mutual Inductance
10.2 Resonance

2. When two loops with or without contacts between them affect each other through the magnetic field generated by one of them, they are said to be magnetically coupled.

3. Self-induced voltage自感电压
10.1 Mutual Inductance 互感
1. inductance (L) and mutual inductance (M)
Magnetic linkage 磁链 N1 N2 i1 i2 + –
v11 + –
v21 + –
v12 2 2′ + –
v22 1 1′
Self- inductance自感
Mutual inductance互感
Self-induced voltage自感电压
Mutual voltage互感电压

4. Mutual Inductance is the ability of one inductor to induce a voltage across a neighboring inductor, measured in henrys (H). N1 N2 i1 i2 + –
v12
v21
v22
v11 ● ● 2 2′ 1 1′ + – v1 + – v2
Dotted terminals 同名端

5. 1 and 2′are Dotted terminals● ● 1 1′ 2 2′
1 and 2′are Dotted terminals 2′ M L1 L2 1 2 1′

6. 2. dot convention
If a current enters the dotted terminal of one coil, the reference polarity of the mutual voltage in the second coil is positive at the dotted terminal of the second coil. 2′ M L1 L2 1 2 1′ 2′ M L1 L2 1 2 1′ i1 i1 + + - -

7. 3. Series connection Series-aiding connection 顺接 equivalent inductanceM L1 L2 i v + - v + - i
equivalent inductance M
Series-opposing connection 反接 L1 L2 i v + - v + - i
equivalent inductance

8. The phase form
The equivalent impedance
then

9. Example 10.1 Calculate the phasor currents and in the circuit.
Solution:
For loop 1: KVL gives
For loop 2: KVL gives So

10. 4. The coefficient of coupling
The coupling coefficient k is a measure of the magnetic coupling between two coils.
When k<0.5, loosely coupled 疏耦合
k>0.5, tightly coupled 紧耦合
If k=1, perfectly coupled 全耦合

11. 10.2 Resonance 谐振 1. Series Resonance 串联谐振
Resonance is a condition in an RLC circuit in which the capacitive and inductive reactance are equal in magnitude, thereby resulting in a purely resistive impedance.
1. Series Resonance 串联谐振
When

12. 2. The resonant frequency 谐振频率or
KVL gives: so

13. The quality factor 品质因数
Note
（1）The equivalent impedance is purely resistive
（2）The voltage and current are in phase
（3）The magnitude of Z is minimum and Irms is maximum
（4）The inductor voltage VL and capacitor voltage VC can be much more than the source voltage VS

14. 3. Parallel Resonance 并联谐振
Resonant occurs when or
The resonant frequency So
purely resistive

15. 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！