Name: delta-wye network conversion
Uploaded: 2025-05-22T09:06:14.000Z
Duration: 1 min 16 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS+Phy.P4

HS+Phy.P4U1.8

Equivalent Resistance

Les applications pratiques, telles que la transmission électrique triphasée et les moteurs, utilisent des réseaux interconvertibles à trois terminaux en Y ou en T, et en delta ou pi.
Considérons un réseau delta composé de trois résistances. Sa transformation en réseau Y implique la superposition du réseau Y correspondant sur le réseau delta par l’ajout d’un nœud central.
Étant donné que la résistance entre chaque paire de nœuds dans le réseau delta est équivalente à la résistance entre la même paire dans le réseau Y, un ensemble de trois équations est établi. La résolution de ces équations donne les résistances du réseau Y.
Dans le réseau Y, la valeur de chaque résistance est le produit des résistances dans les deux branches delta adjacentes, divisé par la somme des trois résistances delta.
De même, un réseau Y peut être transformé en un réseau delta équivalent. Dans le réseau delta, la valeur de chaque résistance est déterminée en additionnant tous les produits possibles de résistances Y prises deux à la fois, puis en divisant par la résistance Y opposée.
Pour un réseau équilibré avec des résistances égales dans les configurations Y et delta, la formule de conversion simplifie.

réseaux delta et y

Dans l'analyse des circuits, il arrive souvent que les résistances ne soient ni en série ni en parallèle. Pour aborder de tels scénarios, des réseaux équivalents à trois terminaux comme les réseaux en étoile (Y) (Figure 1 (a)) ou en té (T) et delta (Δ) (Figure 1 (b)) ou pi (π) entrent en jeu. Ces réseaux offrent des solutions polyvalentes et sont fréquemment rencontrés dans diverses applications, notamment les systèmes électriques triphasés, les filtres électriques et les réseaux adaptés. <img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;"> L'essence de ces réseaux réside dans leur adaptabilité. Ils peuvent être utilisés individuellement ou intégrés dans des circuits plus complexes. Par exemple, lorsqu'il s'agit d'un réseau en triangle mais qu'il est plus pratique de travailler avec un réseau en étoile, un réseau en étoile peut être superposé à la configuration en triangle existante. Pour déterminer les résistances équivalentes au sein du réseau en étoile, il est crucial de s'assurer que la résistance entre chaque paire de nœuds du réseau delta est égale à la résistance entre la même paire de nœuds du réseau Y (ou T). Le processus de conversion entre ces réseaux implique des relations mathématiques liées aux résistances. La transformation est facilitée en introduisant un nœud supplémentaire « n » et en respectant la règle de conversion : dans le réseau Y, chaque résistance est le produit des résistances des deux branches Δ (delta) adjacentes, divisé par la somme des trois Δ. résistances. A l’inverse, pour convertir un réseau étoile en un réseau triangle équivalent, on peut utiliser la règle de conversion suivante : Chaque résistance du réseau est la somme de tous les produits possibles des résistances Y prises deux à la fois, divisée par la résistance Y opposée. Ces formules de conversion simplifient les réseaux équilibrés où les résistances dans les configurations Y et Δ sont égales. Cette transformation n'implique pas l'ajout ou la suppression de composants du circuit mais remplace des modèles de réseau à trois bornes mathématiquement équivalents. Il transforme efficacement un circuit, permettant d'analyser les résistances comme si elles étaient en série ou en parallèle, facilitant ainsi le calcul de la résistance équivalente si nécessaire.

Réseaux Delta et Y

Les applications pratiques, telles que la transmission électrique triphasée et les moteurs, utilisent des réseaux interconvertibles à trois terminaux en Y ou en T, et en delta ou pi.
...

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

Basics of Electric Circuits

Les bases des circuits électriques

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

delta-wye network conversion

Delta-wye network conversion helps analyze resistor circuits that are not arranged in simple series or parallel paths. These three-terminal equivalent networks use the wye (Y), also called tee (T), and the delta (Δ), also called pi (π), as practical circuit models.

These networks are useful in many circuit settings. They appear in three-phase electrical systems, electrical filters, and matching networks. They can also be used on their own or combined with more complex circuits.

A delta network can be replaced with an equivalent wye network when that makes the circuit easier to solve. The key rule is that the resistance between each pair of nodes must stay the same in both networks. To find the wye resistors, each one is the product of the two adjacent delta resistors divided by the sum of all three delta resistors.

A wye network can also be converted into an equivalent delta network. In this case, each delta resistor is found from the sum of all possible pairs of wye-resistor products, divided by the opposite wye resistor. These formulas become simpler for balanced networks, where the resistances in the Y and Δ forms are equal. The transformation does not add or remove parts from the circuit. It replaces one mathematically equivalent three-terminal pattern with another, which can make later equivalent-resistance calculations easier.

Delta-Wye Network Conversion

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kirchhoff's current law

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voltage dividers

Series Resistors and Voltage Split

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current dividers

Parallel Resistors and Current Division

Parallel resistors share the same two nodes, so each resistor has the same voltage across it. In this circuit setup, Kirchhoff's current law applies. The source current equals the sum of the currents through each branch. Ohm's law helps find the branch currents from the source voltage and the resistor values. The source current is equal to the source voltage times the sum of the reciprocals of the resistances. This makes it easier to calculate how current divides in the circuit. The current...

equivalent resistance

Delta-wye network conversion helps analyze resistor circuits that are not arranged in simple series or parallel paths. These three-terminal equivalent networks use the wye (Y), also called tee (T), and the delta (Δ), also called pi (π), as practical circuit models. These networks are useful in many circuit settings. They appear in three-phase electrical systems, electrical filters, and matching networks. They can also be used on their own or combined with more complex circuits. A delta...

design example: resistive touchscreen

Resistive Touchscreen Voltage Mapping

A resistive touchscreen uses voltage mapping to locate a finger touch on a mobile device. It is built from two metallic layers. The top layer is flexible, and the bottom layer is rigid. A narrow gap separates them, and the high resistance between the layers is an important part of the design. When a user touches the screen, the two layers meet at one point. That contact point is called the touchpoint. The touch lowers the resistance between the layers at that spot and changes the electrical...

key terms and concepts

Learn how delta and wye resistor networks are converted into equivalent forms to simplify circuit analysis when resistors are not in series or parallel.

Delta-Wye Network Conversion | 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.

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Delta-Wye Network Conversion

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