Name: using node voltages in circuit analysis
Uploaded: 2024-04-11T12:48:30.000Z
Duration: 1 min 10 s
Channel: JoVE

L’analyse nodale est une méthode générale permettant de simplifier l’analyse de circuit en utilisant les tensions de nœud comme variables de circuit.
Considérons un circuit avec trois nœuds et trois résistances.
Pour trouver les tensions de nœud dans ce circuit, vous devez d’abord sélectionner un nœud de référence ou de référence, dont la tension est attribuée à zéro.
Les nœuds non de référence restants se voient attribuer des tensions nodales par rapport au nœud de référence.
Ensuite, l'application de la loi de courant de Kirchhoff aux nœuds non référents 1 et 2 donne la relation entre les courants de branche.
De plus, en utilisant la loi d'Ohm, les courants de branche passant par les trois résistances sont exprimés en termes de tensions de nœud.
Maintenant, les valeurs des courants de branche peuvent être substituées dans les équations obtenues en utilisant la loi du courant de Kirchhoff pour obtenir deux équations simultanées.
Pour un circuit à n nœuds, on obtient n - 1 équations indépendantes.
Si les valeurs des résistances et des courants sources sont connues, elles peuvent être substituées dans les deux équations, qui peuvent ensuite être résolues pour obtenir les tensions de nœud.

analyse nodale

L'analyse nodale est une méthode fondamentale en génie électrique utilisée pour simplifier le processus d'analyse des circuits. Cette méthode s'articule autour du concept d'utilisation des tensions de nœuds comme variables principales pour l'analyse des circuits. L'objectif est de déterminer la tension à chaque nœud d'un circuit, qui peut ensuite être utilisée pour trouver d'autres quantités intéressantes, telles que les courants traversant des composants spécifiques. Considérons, par exemple, un circuit simple composé de trois nœuds et de trois résistances, comme le montre la figure 1. La première étape de l'analyse nodale consiste à sélectionner un nœud de référence ou de référence. Ce nœud est généralement choisi en fonction de sa commodité et sa tension se voit attribuer une valeur nulle. <img alt="Figure1" src="/files/ftp_upload/15047/15047_PT_Figure_1.svg" style="text-align: center; height: 136px;"> Figure 1 Les nœuds suivants, appelés nœuds non-référence, se voient attribuer des tensions nodales par rapport à ce nœud de référence. Dans l'exemple considéré ici, il existe deux nœuds non-référence étiquetés 1 et 2, chacun avec leurs tensions de nœud respectives. Pour établir une relation entre les courants de branche, la loi du courant de Kirchhoff (KCL) est appliquée aux nœuds non-référence. KCL déclare que la somme algébrique des courants entrant dans un nœud (ou une frontière fermée) est nulle. Cette loi repose sur le principe de conservation des charges, c’est-à-dire qu’une charge ne peut être créée ou détruite. Suite à l'application de KCL, la loi d'Ohm est utilisée pour exprimer les courants de branche traversant les trois résistances en termes de tensions de nœud. La loi d'Ohm postule que le courant traversant un conducteur entre deux points est directement proportionnel à la tension aux bornes des deux points. Les courants de dérivation étant exprimés en termes de tensions de nœuds, ces valeurs sont substituées dans les équations dérivées de KCL. Cette substitution donne lieu à deux équations simultanées puisque, pour un circuit à « n » nœuds, on obtient « n-1 » équations indépendantes. Enfin, si les valeurs des résistances et des courants sources sont connues, elles peuvent être substituées dans les deux équations. La résolution de ces équations donnera les tensions aux nœuds. Ces informations sont inestimables, car elles peuvent aider à comprendre le comportement du circuit et à concevoir ou dépanner des circuits électriques. En conclusion, l’analyse nodale est un outil puissant dans l’analyse des circuits, fournissant une méthode systématique pour déterminer la distribution des tensions au sein d’un circuit, qui peut ensuite être utilisée pour calculer d’autres paramètres tels que les courants et la puissance.

Analyse nodale

L’analyse nodale est une méthode générale permettant de simplifier l’analyse de circuit en utilisant les tensions de nœud comme variables de circuit.
Considérons un circuit à trois nœuds et ...

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

using node voltages in circuit analysis

Nodal analysis uses node voltages to simplify circuit analysis. In this method, the voltage at each node becomes the main variable. Once those voltages are known, they can be used to find other values, such as the current through specific circuit parts.

The process begins by choosing a reference node, also called a datum node. This node is selected for convenience and assigned a voltage of zero. The other nodes, called non-reference nodes, are then measured relative to that point. In the example described, there are three nodes total, with two non-reference nodes labeled 1 and 2.

Next, Kirchhoff's Current Law, or KCL, is applied to the non-reference nodes. KCL states that the algebraic sum of currents entering a node is zero. This follows the idea that charge is conserved, so charge cannot be created or destroyed. After that, Ohm's Law is used to write the branch currents through the three resistors in terms of the node voltages.

Those current expressions are then substituted into the KCL equations. Because a circuit with n nodes gives n - 1 independent equations, the example produces two simultaneous equations. If the resistor values and source currents are known, they can be placed into these equations. Solving them gives the node voltages, which helps explain circuit behavior and can support circuit design or troubleshooting.

Using Node Voltages in Circuit Analysis

nodal analysis

Nodal analysis uses node voltages to simplify circuit analysis. In this method, the voltage at each node becomes the main variable. Once those voltages are known, they can be used to find other values, such as the current through specific circuit parts. The process begins by choosing a reference node, also called a datum node. This node is selected for convenience and assigned a voltage of zero. The other nodes, called non-reference nodes, are then measured relative to that point. In the...

nodal analysis with voltage sources

Supernode Equations in Nodal Analysis

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Mesh Currents for Circuit Analysis

Mesh currents give students a simpler way to analyze planar circuits. In mesh analysis, the unknowns are currents, not voltages. The method uses Kirchhoff's voltage law, or KVL, to build the equations needed to solve the circuit. A mesh is a closed loop in a circuit that does not contain any smaller loops inside it. Each independent mesh is assigned a mesh current, and this current is usually drawn in the clockwise direction. These mesh currents are used as the main circuit variables during...

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...

source transformation

Circuit Source Equivalents

Circuit source equivalents make it easier to simplify electrical circuits in circuit analysis. A source transformation replaces a voltage source in series with a resistor by a current source in parallel with a resistor, or it replaces a current source in parallel with a resistor by a voltage source in series with a resistor. The key idea is that the equivalent resistance at the circuit terminals stays the same when the original sources are turned off. When making the change, the current source...

linear circuits

Circuit Linearity and Resistor Behavior

Circuit linearity describes how a circuit responds when its input changes. A linear circuit has an output that is directly proportional to its input. This behavior follows two rules: homogeneity and additivity. Homogeneity means that if the input, or excitation, is multiplied by a constant factor, the response is multiplied by the same factor. For example, if the current is increased by a constant k, the voltage also increases by k times. Additivity means that the response to a sum of inputs...

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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Load Matching in Thevenin Circuits

Load matching in Thevenin circuits helps a source deliver the most power to a connected load. This matters in engineering fields such as telecommunications, where power delivery must be optimized. Even then, internal losses can be significant and may equal or exceed the power sent to the load. The Thevenin equivalent circuit is a useful way to study this situation. It replaces the full linear circuit with a simpler source and resistance while keeping the load in place. In this setup, the load...

design example: strain gauge bridge or wheatstone bridge

design-example-strain-gauge-bridge-or-wheatstone-bridge

Wheatstone Bridge Output for Strain Gauge Design

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 a reference node, KCL, and Ohm's Law to find node voltages and solve simple circuit equations in high school electronics.

Using Node Voltages in 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

Using Node Voltages in Circuit Analysis

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