Basic Circuit Analysis - Schaum's Outline Series 基本电路分析 - Schaum's Outline Series
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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
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。
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。
Determine the number of nodes within the network. 确定网络内的节点数量。
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。
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。
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
EXAMPLE 18.14 Write the nodal equations for the network in Fig. 18.28 having a dependent current source. 例 18.14 写出图 18.28 中具有从属电流源的网络的节点方程。
Applying nodal analysis to a network with current-controlled current source. 对具有电流控制电流源的网络进行节点分析。
Solution: 解决方案
Steps 1 and 2 are as defined in Fig. 18.28 步骤 1 和 2 如图 18.28 所示
Step 3: At node 步骤 3：在节点 上
and
At node 在节点 上
and
resulting in two equations and two unknowns 得出两个方程和两个未知数
4. Star-delta conversion 4.星三角转换
FIG. 18.49 configuration. 图 18.49 配置。
For the impedances of the in terms of those for the , the equations are 对于 的阻抗与 的阻抗，方程为
In the study of dc networks, we found that if all of the resistors of the or Y were the same, the conversion from one to the other could be accomplished using the equation 在对直流网络的研究中，我们发现如果 或 Y 的所有电阻都相同，就可以通过公式实现从一个电阻到另一个电阻的转换
For ac networks, 用于交流网络、
5. Superposition Theorem 5.叠加定理
The sum of the powers delivered by each of two or more ac sources of the same frequency is not equal to the power delivered by all the sources. However, for a network with a dc source and an ac source the total power can be determined by the sum of the powers delivered by each source. 两个或两个以上频率相同的交流电源各自输出的功率之和并不等于所有电源输出的功率。不过，对于一个具有直流电源和交流电源的网络，总功率可以由每个电源输出的功率之和确定。
1-02-j AC network theorems 1-02-j 交流网络定理
EXAMPLE 19.1 Using the superposition theorem, find the current I through the reactance in Fig. 19.1. 例 19.1 利用叠加定理，求通过图 19.1 中 电抗 的电流 I。
FIG. 19.1 图 19.1
Example 19.1 例 19.1
FIG. 19.2 图 19.2
Assigning the subscripted impedances to the network in Fig. 19.1. 为图 19.1 中的网络分配下标阻抗。
Solution: For the redrawn circuit (Fig. 19.2), 解答：对于重新绘制的电路（图 19.2）、
Considering the effects of the voltage source (Fig. 19.3) by replacing by a short circuit, we have 考虑到电压源 的影响（图 19.3），将 替换为短路，我们得出
Determining the effect of the voltage source on the current of the network in Fig. 19.1 by replacing by a short circuit. 通过将 替换为短路，确定电压源 对图 19.1 中网络的电流 的影响。
and
(current divider rule) （当前分隔规则）
Considering the effects of the voltage source (Fig. 19.4), we have 考虑到电压源 的影响（图 19.4），我们得出
Determining the effect of the voltage source on the current I of the network in Fig. 19.1 by replacing by a short circuit. 将 替换为短路，确定电压源 对图 19.1 中网络电流 I 的影响。
and 和
The resultant current through the reactance (Fig. 19.5) is 通过 电抗 （图 19.5）的结果电流为
FIG. 19.5 图 19.5
Determining the resultant current for the network in Fig. 19.1 确定图 19.1 中网络的结果电流
1-02-j AC network theorems 1-02-j 交流网络定理
6. Thevenin's Theorem 6.特维宁定理
Any two-terminal linear ac network can be replaced with an equivalent circuit consisting of a voltage source and an impedance in series, as shown in Fig. 19.23. 如图 19.23 所示，任何两端线性交流网络都可以用由电压源和阻抗串联组成的等效电路来代替。
Since the reactances of a circuit are frequency dependent, the Thévenin circuit found for a particular network is applicable only at one frequency. 由于电路的电抗与频率有关，为特定网络找到的泰维宁电路只适用于一种频率。
The steps required to apply this method to dc circuits are repeated here with changes for sinusoidal ac circuits. As before, the only change is the replacement of the term resistance with impedance. Again, depen- 将此方法应用于直流电路所需的步骤在此重复，并对正弦交流电路进行修改。与之前一样，唯一的变化是用阻抗代替了电阻。同样，取决于
dent and independent sources are treated separately. 有争议来源和独立来源分别处理。
FIG. 19.23 图 19.23
FIG. 19.24 图 19.24
Example 19.7. 例 19.7.
EXAMPLE 19.7 Find the Thévenin equivalent circuit for the network external to resistor in Fig. 19.24 例 19.7 求图 19.24 中电阻 外部网络的泰文等效电路
Solution: 解决方案
Steps 1 and 2 (Fig. 19.25): 步骤 1 和 2（图 19.25）：
FIG. 19.25 图 19.25
Assigning the subscripted impedances to the network in Fig. 19.24. 为图 19.24 中的网络分配下标阻抗。
Step 3 (Fig. 19.26) 步骤 3（图 19.26）
FIG. 19.26 图 19.26
Determining the Thévenin impedance for the network in Fig. 19.24. 确定图 19.24 中网络的泰弗宁阻抗。
FIG. 19.27 图 19.27
Determining the open-circuit Thévenin voltage for the network in Fig. 19.24. 确定图 19.24 中网络的开路特维宁电压。
Step 4 (Fig. 19.27) 步骤 4（图 19.27）
Step 5: The Thévenin equivalent circuit is shown in Fig. 19.28. 步骤 5：Thévenin 等效电路如图 19.28 所示。
FIG. 19.28 图 19.28
The Thévenin equivalent circuit for the network in Fig. 19.24. 图 19.24 中网络的泰维宁等效电路。
1-02-j AC network theorems 1-02-j 交流网络定理
7. Norton's Theorem 7.诺顿定理
Remove that portion of the network across which the Norton equivalent circuit is to be found. 移除网络中需要找到诺顿等效电路的部分。
Mark ( , and so on) the terminals of the remaining two-terminal network. 在剩下的两端网络的两端标记（ ，以此类推）。
Calculate by first setting all voltage and current sources to zero (short circuit and open circuit, respectively) and then finding the resulting impedance between the two marked terminals. 计算 时，首先将所有电压源和电流源设置为零（分别为短路和开路），然后找出两个标记端子之间的阻抗。
Calculate by first replacing the voltage and current sources and then finding the short-circuit current between the marked terminals. 计算 时，首先替换电压源和电流源，然后找出标记端子之间的短路电流。
Draw the Norton equivalent circuit with the portion of the circuit previously removed replaced between the terminals of the Norton equivalent circuit. 绘制诺顿等效电路，在诺顿等效电路的端子之间替换之前移除的电路部分。
FIG. 19.60 图 19.60
The Norton equivalent circuit for ac networks. 交流网络的诺顿等效电路。
FIG. 19.61 图 19.61
Conversion between the Thévenin and Norton equivalent circuits. 泰维宁等效电路和诺顿等效电路之间的转换。
EXAMPLE 19.14 Determine the Norton equivalent circuit for the network external to the resistor in Fig. 19.62. 例 19.14 确定图 19.62 中 电阻器外部网络的诺顿等效电路。
FIG. 19.62 图 19.62
Example 19.14. 例 19.14.
FIG. 19.63 图 19.63
Assigning the subscripted impedances to the network in Fig. 19.62 为图 19.62 中的网络分配下标阻抗
Solution: 解决方案
Steps 1 and 2 (Fig. 19.63): 步骤 1 和 2（图 19.63）：
Step 3 (Fig. 19.64) 步骤 3（图 19.64）
1-02-j AC network theorems 1-02-j 交流网络定理
FIG. 19.64 图 19.64
Determining the Norton impedance for the network in Fig. 19.62. 确定图 19.62 中网络的诺顿阻抗。
FIG. 19.65 图 19.65
Determining for the network in Fig. 19.62. 确定图 19.62 中网络的 。
Step 5: The Norton equivalent circuit is shown in Fig. 19.66. 步骤 5：诺顿等效电路如图 19.66 所示。
FIG. 19.66 图 19.66
The Norton equivalent circuit for the network in Fig. 19.62. 图 19.62 中网络的诺顿等效电路。
1-02-j AC network theorems 1-02-j 交流网络定理
Apply Kirchhoff's voltage law around each closed loop in the clockwise direction. Again, the clockwise direction was chosen to establish uniformity and to prepare us for the format approach to follow. 沿顺时针方向在每个闭合回路周围应用基尔霍夫电压定律。同样，选择顺时针方向是为了建立均匀性，并为接下来的格式化方法做好准备。
a. If an impedance has two or more assumed currents through it, the total current through the impedance is the assumed current of the loop in which Kirchhoff's voltage law is being applied, plus the assumed currents of the other loops passing through in the same direction, minus the assumed currents passing through in the opposite direction. a.如果一个阻抗有两个或两个以上的假定电流通过，那么通过阻抗的总电流就是应用基尔霍夫电压定律的回路的假定电流，加上同方向通过的其他回路的假定电流，再减去反方向通过的假定电流。
b. The polarity of a voltage source is unaffected by the direction of the assigned loop currents. b.电压源的极性不受指定回路电流方向的影响。
Solve the resulting simultaneous linear equations for the 求解由此得到的
