Name: supernode equations in nodal analysis
Uploaded: 2025-05-22T09:06:13.000Z
Duration: 1 min 11 s
Channel: JoVE

L’analyse nodale peut simplifier efficacement l’analyse des circuits ayant des sources de tension dépendantes ou indépendantes.
Considérons un circuit avec quatre résistances et deux sources de tension configurées de manière à ce qu’une source de tension soit connectée entre un nœud non de référence et le nœud de référence.
Ici, la tension au nœud non référent peut être écrite comme égale à la tension de la source.
L’autre source de tension est connectée entre deux nœuds non de référence. Ceux-ci forment un super-nœud ou un nœud généralisé.
Pour analyser un circuit avec un supernœud, il faut appliquer à la fois la loi de courant et la loi de tension de Kirchhoff pour déterminer les tensions des nœuds.
Tout d'abord, la loi du courant de Kirchhoff est appliquée au supernœud, en considérant les courants traversant chaque élément. L’équation obtenue peut être écrite en termes de tensions de nœud.
Ensuite, le circuit est redessiné pour appliquer la loi de tension de Kirchhoff au supernoeud.
En faisant le tour de la boucle contenant le supernode dans le sens des aiguilles d’une montre, on obtient une équation de contrainte.
Les trois équations résultantes peuvent maintenant être résolues pour déterminer les tensions des nœuds.

analyse nodale avec des sources de tension

L'analyse nodale est une méthode remarquablement efficace utilisée en génie électrique pour simplifier l'analyse de circuits complexes, y compris ceux comportant des sources de tension dépendantes ou indépendantes. Sa force réside dans son approche systématique consistant à décomposer les circuits en composants gérables, ce qui facilite la compréhension et la résolution des ingénieurs. Considérons un circuit contenant quatre résistances et deux sources de tension, comme le montre la figure 1. L'une de ces sources de tension est connectée entre un nœud non-référence et le nœud de référence. Dans cette configuration, la tension au nœud non-référence peut être écrite directement comme égale à la tension de la source. Cela simplifie le problème en réduisant le nombre d'inconnues. <img alt="Figure1" src="/files/ftp_upload/15048/15048_PT_Figure_1.svg" style="text-align: center; height: 140px;"> L'autre source de tension est connectée entre deux nœuds non-référence. Cette configuration forme ce que l’on appelle un super-nœud ou nœud généralisé. Les supernodes sont un concept unique dans l'analyse nodale, qui aide à gérer les situations dans lesquelles des sources de tension sont connectées entre des nœuds non références. L'analyse d'un circuit avec un super-nœud nécessite l'application à la fois de la loi du courant de Kirchhoff (KCL) et de la loi de la tension de Kirchhoff (KVL). Tout d’abord, KCL est appliqué au super-nœud. Cette loi stipule que la somme des courants entrant dans un nœud est égale à la somme des courants qui en sortent. En considérant les courants traversant chaque élément du super-nœud, une équation peut être obtenue et écrite en termes de tensions de nœud. Ensuite, pour appliquer KVL, le circuit est redessiné pour mettre en évidence la boucle contenant le supernode. KVL déclare que la somme des forces électromotrices dans toute boucle fermée ou maillage d'un réseau est égale à la somme des chutes de potentiel dans cette boucle. Faire le tour de cette boucle dans le sens des aiguilles d’une montre donne une équation de contrainte. Avec ces étapes, trois équations sont obtenues, qui représentent le comportement du circuit. Ces équations peuvent être résolues simultanément pour déterminer les tensions des nœuds.

Analyse nodale avec des sources de tension

L’analyse nodale peut simplifier efficacement l’analyse des circuits ayant des sources de tension dépendantes ou indépendantes.
Considérons un circuit avec quatre résistances ...

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

Nodal Analysis with Voltage Sources

supernode equations in nodal analysis

Nodal analysis uses node voltages and Kirchhoff’s laws to solve circuits with voltage sources. It is a systematic method for breaking a complex circuit into smaller parts that are easier to analyze. In this example, the circuit includes four resistors and two voltage sources.

One voltage source is connected between a non-reference node and the reference node. In that case, the non-reference node voltage can be written directly as the source voltage. This removes one unknown and makes the circuit easier to solve.

The other voltage source is connected between two non-reference nodes. That connection creates a supernode, also called a generalized node. A supernode is a special case in nodal analysis that helps when a voltage source sits between two nodes that are not the reference node.

To analyze the supernode, Kirchhoff’s Current Law (KCL) is used first. KCL says the total current entering a node equals the total current leaving it. The currents through the elements in the supernode are written in terms of the node voltages to form one equation.

Next, Kirchhoff’s Voltage Law (KVL) is applied. The circuit is redrawn to show the loop that includes the supernode, and the loop is traced in a clockwise direction. KVL states that the sum of the electromotive forces in a closed loop equals the sum of the voltage drops in that loop, which gives a second constraint equation.

These steps produce three equations for the circuit. The equations can then be solved together to find the node voltages. This approach shows how nodal analysis handles voltage sources connected to both the reference node and other nodes.

Supernode Equations in Nodal Analysis

nodal analysis

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nodal analysis with voltage sources

Nodal analysis uses node voltages and Kirchhoff’s laws to solve circuits with voltage sources. It is a systematic method for breaking a complex circuit into smaller parts that are easier to analyze. In this example, the circuit includes four resistors and two voltage sources. One voltage source is connected between a non-reference node and the reference node. In that case, the non-reference node voltage can be written directly as the source voltage. This removes one unknown and makes the...

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superposition theorem

Analyzing Circuits with Superposition

Superposition is a circuit analysis method for linear circuits with more than one independent source. It lets you find the voltage across or current through an element by adding the separate effects of each source acting alone. To use superposition, keep one independent source active and turn off the others. A voltage source is replaced by a short circuit, and a current source is replaced by an open circuit. Then calculate the output from the single active source. Repeat the process for each...

thevinin's theorem

Thevenin Circuit Equivalents

Thevenin circuit equivalents simplify linear two-terminal circuits by replacing the fixed part of a network with one equivalent source and one resistor. This method is useful when a circuit has a fixed section and a load that can change. A household electrical outlet is a familiar example, because different appliances can be plugged in or removed. Each change in load can require a new circuit analysis, so an equivalent circuit makes the work easier. Thevenin's theorem states that a linear...

norton's theorem

Norton Equivalent Circuit in DC Analysis

Norton equivalent circuit in DC analysis shows how a linear two-terminal circuit can be replaced by a simpler network. The replacement uses a current source, called I_N, in parallel with a resistor, called R_N. I_N is the short-circuit current through the terminals, and R_N is the input or equivalent resistance seen at the terminals when the independent sources are turned off. To find Norton's resistance, all independent sources in the circuit are set to zero. The resistance measured at the...

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A strain gauge and Wheatstone bridge work together to turn mechanical strain into an electrical signal. In engineering, this setup is often used to measure force or pressure. Each part of the bridge has a resistance that changes slightly when strain is applied. The main goal is to turn a very small voltage output into a larger, easier-to-read signal. A voltmeter can then measure that output more clearly. To do this, an engineer designs the strain gauge circuit and figures out how much...

key terms and concepts

Learn how nodal analysis uses supernodes, KCL, and KVL to solve circuits with voltage sources and find unknown node voltages.

Supernode Equations in Nodal 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

Supernode Equations in Nodal Analysis

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