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

L’analyse du maillage est plus simple dans les circuits avec des sources de courant car ils nécessitent moins d’équations pour l’analyse.
Considérons un circuit à deux mailles avec une source de courant dans un seul maillage.
Les courants de maillage sont attribués et la branche contenant la source de courant est exclue de l’analyse du maillage.
La loi de tension de Kirchhoff est appliquée au maillage restant pour obtenir une équation linéaire.
Comme le courant dans le deuxième maillage est égal en intensité mais de direction opposée au courant source, l’équation simplifiée permet de déterminer le courant dans le premier maillage.
Considérons maintenant un autre circuit avec une source de courant entre les deux mailles.
Un supermaillage plus grand est créé en excluant la source actuelle et les éléments connectés en série avec elle.
Encore une fois, l'application de la loi de tension de Kirchhoff au supermaillage donne une équation linéaire.
De plus, la loi du courant de Kirchhoff est appliquée à un nœud où la branche avec la source de courant est connectée, ce qui donne une autre équation linéaire qui relie les deux courants de branche.
Les solutions des équations simultanées fournissent les valeurs des courants de maillage.

analyse de maillage avec sources de courant

L'analyse de maillage est simplifiée lors de l'analyse de circuits avec sources de courant, qu'elles soient indépendantes ou dépendantes. La présence de sources de courant réduit le nombre d'équations nécessaires à l'analyse. Deux cas illustrent ce phénomène : 

Source de courant dans un maillage : L'analyse est simple lorsqu'une source de courant est présente dans un seul maillage du circuit. Les courants dans les autres maillages sont déterminés comme d’habitude, en excluant le maillage avec la source de courant. La loi de Kirchhoff sur les tensions (KVL) est appliquée au maillage restant, ce qui donne une équation linéaire à résoudre. Grâce à l’égalité de l’intensité du courant dans le maillage avec la source, mais dans des directions opposées, il est aisé de calculer le courant dans le premier maillage. 

Source de courant entre deux maillages : Lorsqu'une source de courant est située entre deux maillages, l'analyse peut être simplifiée en créant un super-maillage. Cela implique d'exclure la source de courant et tous les éléments connectés en série avec elle. L'application de la KVL au super-maillage donne une équation linéaire. De plus, la loi de Kirchhoff sur les courants (KCL) est appliquée à un nœud auquel la branche avec la source de courant est connectée, ce qui fournit une autre équation linéaire reliant les courants des deux branches. La résolution de ces équations fournit les valeurs des courants du maillage. 

Les propriétés critiques d'un super-maillage incluent :

<ul style="padding-left: 35px; list-style: disc;"> 

	<li>La source de courant au sein du super-maillage impose une équation de contrainte nécessaire à la résolution des courants du maillage.</li> 

	<li>Un super-maillage ne possède pas de courant propre ; il englobe les courants des mailles individuelles qu'il englobe.</li> 

	<li>Les lois KVL et KCL s'appliquent à un super-maillage comme à tout autre maillage.</li>

</ul>

Analyse de maillage avec sources de courant

L’analyse du maillage est plus simple dans les circuits avec des sources de courant car ils nécessitent moins d’équations pour l’analyse.
Considérons un circuit à deux mailles avec un courant ...

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

DC Circuit Analysis

Analyse des circuits CC

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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

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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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