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Dr. Norbert Cheung's Lecture Series
诺伯特-张博士系列讲座

Level 1 Topic no:
第 1 级 议题编号:

AC network theorems 交流网络定理

Contents 目录

  1. Independent vs Dependent Sources
    独立来源与依赖来源
  2. Mesh Analysis 网格分析
  3. Node Analysis 节点分析
  4. Star Delta conversion 星三角洲改装
  5. Superposition Theorem 叠加定理
  6. Thevenin's Theorem 特维宁定理
  7. Norton's Theorem 诺顿定理
  8. Glossary 术语表

Reference: 参考资料

Introductory Circuit Analysis edition, Boylesad Olivari
电路分析入门 版,Boylesad Olivari
Basic Circuit Analysis - Schaum's Outline Series
基本电路分析 - Schaum's Outline Series
Email: 电子邮件: norbertcheung@ szu.edu.cn
Web Site: 网站: http://norbert.idv.hk
Last Updated: 最后更新
AC network theorems
交流网络定理

1. Independent vs dependent sources
1.独立来源与从属来源

The term independent specifies that the magnitude of the source is independent of the network to which it is applied and that the source displays its terminal characteristics even if completely isolated.
独立 "一词说明信号源的大小与所应用的网络无关,即使完全隔离,信号源也能显示其终端特性。

FIG. 18.1 图 18.1
Independent sources. 独立消息来源
A dependent or controlled source is one whose magnitude is determined (or controlled) by a current or voltage of the system in which it appears.
从属源或受控源是指其大小由其所在系统的电流或电压决定(或控制)的源。
(a)
(b)
FIG. 18.2 图 18.2
Controlled or dependent sources.
受控源或依赖源。
(a)
(b)
FIG. 18.3 图 18.3
Special notation for controlled or dependent sources.
受控源或从属源的特殊标记。
EXAMPLE 18.3 Convert the voltage source in Fig. 18.8(a) to a current source.
例 18.3 将图 18.8(a) 中的电压源转换为电流源。
(a)
(b)
FIG. 18.8 图 18.8
Source conversion with a voltage-controlled voltage source.
使用压控电压源进行源转换。
Solution: 解决方案

network theorems
网络定理

2. Mesh Analysis 2.网格分析

  1. Assign a distinct current in the clockwise direction to each independent closed loop of the network. It is not absolutely necessary to choose the clockwise direction for each loop current. However, it eliminates the need to have to choose a direction for each application. Any direction can be chosen for each loop current with no loss in accuracy as long as the remaining steps are followed properly.
    为网络的每个独立闭合回路分配顺时针方向的不同电流。为每个回路电流选择顺时针方向并非绝对必要。但是,这样就无需为每种应用选择一个方向。只要正确执行其余步骤,就可以为每个环路电流选择任何方向,而不会降低精度。
  2. Indicate the polarities within each loop for each impedance as determined by the assumed direction of loop current for that loop. assumed loop currents.
    指出每个环路内每个阻抗的极性,由该环路的假定环路电流方向决定。
EXAMPLE 18.5 Using the general approach to mesh analysis, find the current in Fig. 18.10.
例 18.5 使用网格分析的一般方法,求图 18.10 中的电流
FIG. 18.10 图 18.10
Example 18.5. 例 18.5.
The network is redrawn in Fig. 18.11 with subscripted impedances:
图 18.11 用下标阻抗重新绘制了该网络:
Steps 1 and 2 are as indicated in Fig. 18.11.
步骤 1 和 2 如图 18.11 所示。
FIG. 18.11 图 18.11
Assigning the mesh currents and subscripted impedances for the network in Fig. 18.10.
为图 18.10 中的网络分配网格电流和下标阻抗。

1-02-j AC network theorems
1-02-j 交流网络定理

Step 3: 步骤 3:
or
Step 4: 步骤 4:
Determinants 决定因素
so that 以便
Substituting numerical values yields
代入数值得出
FIG. 18.13 图 18.13
Applying mesh analysis to a network with a voltage-controlled voltage source.
将网格分析应用于具有电压控制电压源的网络。

EXAMPLE 18.6 Write the mesh currents for the network in Fig. 18.13 having a dependent voltage source.
例题 18.6 请写出图 18.13 中具有从属电压源的网络的网状电流。

Solution: 解决方案

Steps 1 and 2 are defined in Fig. 18.13.
步骤 1 和 2 的定义见图 18.13。
Step 3: 步骤 3:
Then substitute
然后用 代替
The result is two equations and two unknowns:
结果是两个方程和两个未知数:
EXAMPLE 18.8 Write the mesh currents for the network in Fig. 18.15 having a dependent current source.
例 18.8 写出图 18.15 中具有从属电流源的网络的网状电流。

Solution: 解决方案

Steps 1 and 2 are defined in Fig. 18.15.
步骤 1 和 2 的定义见图 18.15。
The result is two equations and two unknowns.
结果是两个方程和两个未知数。
FIG. 18.15 图 18.15
Applying mesh analysis to a network with a current-controlled current source.
将网格分析应用于具有电流控制电流源的网络。

1-02-j AC network theorems
1-02-j 交流网络定理

Assigning the mesh currents and subscripted impedances for the network in Fig. 18.10 (repeated).
为图 18.10 中的网络分配网格电流和下标阻抗(重复)。

EXAMPLE 18.9 Using the format approach to mesh analysis, repeat Example 18.5. The block impedance diagram is repeated as Fig. 18.16 for convenience
例 18.9 使用网格分析的格式方法,重复例 18.5。为方便起见,块阻抗图重复如图 18.16 所示

Solution: 解决方案

Step 1 is as indicated in Fig. 18.16.
步骤 1 如图 18.16 所示。
Steps 2 through 4 result in the following:
步骤 2 至 4 的结果如下:
which can be rewritten as
可改写为
and we have the same set of equations as in Example 18.5 resulting in the same solution of
与例 18.5 中的方程组相同,得出的解为
EXAMPLE 18.10 Using the format approach to mesh analysis, find the current in Fig. 18.17.
例 18.10 使用网格分析的格式方法,找出图 18.17 中的电流
Solution: The network is redrawn in Fig. 18.18:
解决方案:网络重绘如图 18.18 所示:
FIG. 18.17 图 18.17
Example 18.10. 例 18.10.
EXAMPLE 18.11 Write the mesh equations for the network in Fig. 18.20. Do not solve.
例 18.11 为图 18.20 中的网络写出网格方程。不要求解。
FIG. 18.20 图 18.20
Example 18.11. 例 18.11.

1-02-j AC network theorems
1-02-j 交流网络定理

Solution: The network is redrawn in Fig. 18.21. Again note the reduced complexity and increased clarity provided by the use of subscripted impedances:
解答:网络重绘如图 18.21。请再次注意,使用下标阻抗降低了复杂性,提高了清晰度:
FIG. 18.21 图 18.21
Assigning the mesh currents and subscripted impedances for the network in Fig. 18.20.
为图 18.20 中的网络分配网格电流和下标阻抗。
and
or
Example 18.12. 例 18.12.
EXAMPLE 18.12 Using the format approach, write the mesh equations for the network in Fig. 18.23.
例 18.12 使用格式法,写出图 18.23 中网络的网格方程。
Solution: The network is redrawn as shown in Fig. 18.23, where
解答:网络重绘如图 18.23 所示,其中
and
Note the symmetry about the diagonal axis; that is, note the location of , and off the diagonal.
注意关于对角线轴的对称性;也就是说,注意 的位置,以及 偏离对角线的位置。
FIG 18.23 network in Fig. 18.22.
图 18.23 图 18.22 中的网络。

1-02-j AC network theorems
1-02-j 交流网络定理

3. Node Analysis 3.节点分析

  1. Determine the number of nodes within the network.
    确定网络内的节点数量。
  2. Pick a reference node and label each remaining node with a subscripted value of voltage: , and so on.
    选取一个参考节点,然后在其余每个节点上标注下标电压值: 以此类推。
  3. Apply Kirchhoff's current law at each node except the reference. Assume that all unknown currents leave the node for each application of Kirchhoff's current law.
    在除参考点以外的每个节点上应用基尔霍夫电流定律。假设在每次应用基尔霍夫电流定律时,所有未知电流都离开节点。
  4. Solve the resulting equations for the nodal voltages.
    求解由此得出的节点电压方程。
EXAMPLE 18.13 Determine the voltage across the inductor for the network in Fig. 18.24.
例 18.13 确定图 18.24 中网络的电感两端电压。
FIG. 18.24 图 18.24
Example 18.13. 例 18.13.
Solution: 解决方案
Steps 1 and 2 are as indicated in Fig. 18.25.
步骤 1 和 2 如图 18.25 所示。
Step 3: Note Fig. 18.26 for the application of Kirchhoff's current law to node :
步骤 3:请注意图 18.26,将基尔霍夫电流定律应用于节点
FIG. 18.25 图 18.25
Assigning the nodal voltages and subscripted impedances to the network in Fig. 18.24.
为图 18.24 中的网络分配节点电压和下标阻抗。
FIG. 18.26 图 18.26
Applying Kirchhoff's current law to the node in Fig. 18.25.
对图 18.25 中的节点 应用基尔霍夫电流定律。
Rearranging terms gives 重排后得出
FIG. 18.27 图 18.27
Applying Kirchhoff's current law to the node in Fig. 18.25.
对图 18.25 中的节点 应用基尔霍夫电流定律。
Note Fig. 18.27 for the application of Kirchhoff's current law to node
将基尔霍夫电流定律应用于节点 时,请注意图 18.27。
Rearranging terms gives 重排后得出

1-02-j AC network theorems
1-02-j 交流网络定理