Name: current sources in mesh circuit analysis
Uploaded: 2024-04-11T12:48:30.000Z
Duration: 1 min 10 s
Channel: JoVE

在含有电流源的电路中，网孔分析更为简便，因为它们所需的分析方程数量更少。
考虑一个双网孔电路，其中仅在一个网孔中存在电流源。
设定网孔电流，并在网孔分析中排除包含电流源的支路。
对剩余的网孔应用基尔霍夫电压定律，得到一个线性方程。
由于第二个网孔中的电流在大小上与源电流相等但方向相反，因此简化后的方程可用于确定第一个网孔中的电流。
现在，考虑另一个在两个网孔之间具有电流源的电路。
通过排除电流源及其串联连接的元件，可创建一个更大的超网孔。
同样，对超网应用基尔霍夫电压定律可得到一个线性方程。
此外，将基尔霍夫电流定律应用于连接有电流源支路的节点，可得到另一个将两个支路电流关联起来的线性方程。
联立方程组的解提供了网孔电流的值。

带电流源的网格分析

当电路中存在电流源（无论是独立的还是受控的）时，网格分析变得更为简单。电流源的存在减少了分析所需的方程数量。以下两个案例说明了这一点： 

电流源位于一个网格中：当电路中只有一个网格中存在电流源时，分析过程很简单。网格电流仍按常规分配，但包含电流源的网格不包含在分析中。基尔霍夫电压定律 (KVL，Kirchhoff's voltage law) 应用于剩余网格，得到一个线性方程。由于带源网格中的电流大小相等方向相反，因此可以轻松确定第一个网格中的电流。 

电流源位于两个网格之间：如果电流源位于两个网格之间，则可以通过创建超网格来简化分析。这需要排除电流源和与其串联的任何元件。将基尔霍夫电压定律应用于超网格可得到一个线性方程。此外，应用基尔霍夫电流定律 (KCL，Kirchhoff's current law) 于连接电流源分支的节点，可得到另一个连接两个分支电流的线性方程。求解这些方程可得出各网格电流的值。 

超网格的重要性质包括：

<ul style="padding-left: 35px; list-style: disc;">

	<li>超网格内的电流源对求解网状电流施加了一个必要的约束方程。</li> 

	<li>超网格没有自己的独立电流；其电流包含了来自其所包围的各个网格的电流。</li> 

	<li>可像任何其他网格一样应用KVL 和 KCL于超网格。</li>

</ul>

网孔分析在含有电流源的电路中更为简便，因为它们所需的分析方程数量较少。  
考虑一个包含两个网孔且具有电流……的电路

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

DC Circuit Analysis

直流电路分析

KEY TERMS AND CONCEPTS

关键术语与概念

Mesh Analysis with Current Sources

current sources in mesh circuit analysis

Current sources make mesh circuit analysis easier because they can reduce the number of equations needed. This applies to both independent and dependent current sources. The method depends on where the current source is placed in the circuit.

When a current source appears in only one mesh, the setup is simple. Assign mesh currents as usual, but leave out the mesh that contains the current source from the equation process. Then apply Kirchhoff's voltage law, or KVL, to the remaining mesh to get a linear equation. The current in the mesh with the source is equal in magnitude but opposite in direction, so the first mesh current is easy to find.

A different case happens when a current source lies between two meshes. Here, the circuit can be handled with a supermesh, which is formed by excluding the current source and any elements in series with it. KVL is applied around the supermesh to create a linear equation. Then Kirchhoff's current law, or KCL, is used at a node connected to the current-source branch to link the two branch currents.

The current source inside a supermesh adds a needed constraint equation for solving the mesh currents. A supermesh has no current of its own. It combines the currents from the meshes it encloses. KVL and KCL are still applied to the supermesh like they are in any other mesh.

Current Sources in Mesh Circuit Analysis

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mesh analysis with current sources

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Analyzing Circuits with Superposition

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key terms and concepts

Learn how current sources simplify mesh circuit analysis, including one-mesh cases and supermeshes, using KVL and KCL to solve for mesh currents.

Current Sources in Mesh Circuit Analysis | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Current Sources in Mesh Circuit Analysis

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