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

Aplicações práticas, como transmissão elétrica trifásica e motores, usam redes Y ou T interconversíveis de três terminais e redes delta ou pi.
Considere uma rede delta composta por três resistores. Sua transformação em uma rede Y envolve a sobreposição da rede Y correspondente à rede delta, adicionando um nó central.
Como a resistência entre cada par de nós na rede delta é equivalente à resistência entre o mesmo par na rede Y, um conjunto de três equações é estabelecido. Resolver essas equações produz as resistências para a rede Y.
Na rede Y, o valor de cada resistor é o produto das resistências nos dois ramos delta adjacentes, dividido pela soma dos três resistores delta.
Da mesma forma, uma rede Y pode ser transformada em uma rede delta equivalente. Na rede delta, o valor de cada resistor é determinado pela soma de todos os produtos possíveis de resistores Y tomados dois de cada vez e, em seguida, dividindo pelo resistor Y oposto.
Para uma rede balanceada com resistências iguais nas configurações Y e delta, a fórmula de conversão simplifica.

redes delta e y

Na análise de circuitos, muitas vezes surgem situações em que os resistores não estão em configurações em série nem em paralelo. Para lidar com tais cenários, redes equivalentes de três terminais, como as redes estrela (Y) (Figura 1 (a)) ou tee (T) e delta (Δ) (Figura 1 (b)) ou pi (π) entram em jogo. Essas redes oferecem soluções versáteis e são frequentemente encontradas em diversas aplicações, incluindo sistemas elétricos trifásicos, filtros elétricos e redes correspondentes.

<img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;" />

A essência dessas redes reside na sua adaptabilidade. Eles podem ser empregados individualmente ou integrados em circuitos mais complexos. Por exemplo, ao lidar com uma rede delta, mas achar mais conveniente trabalhar com uma rede estrela, uma rede estrela pode ser sobreposta à configuração delta existente. Para determinar as resistências equivalentes dentro da rede estrela, é crucial garantir que a resistência entre cada par de nós na rede delta seja igual à resistência entre o mesmo par de nós na rede Y (ou T).

O processo de conversão entre essas redes envolve relações matemáticas relacionadas às resistências. A transformação é facilitada pela introdução de um nó extra 'n' e pela adesão à regra de conversão: Na rede Y, cada resistor é o produto dos resistores nos dois ramos Δ (delta) adjacentes, dividido pela soma dos três Δ resistores. Por outro lado, para converter uma rede estrela em uma rede delta equivalente, pode-se usar a seguinte regra de conversão: cada resistor na rede é a soma de todos os produtos possíveis de resistores Y tomados dois a dois, dividido pelo resistor Y oposto.

Essas fórmulas de conversão são simplificadas para redes balanceadas onde as resistências nas configurações Y e Δ são iguais. Essa transformação não envolve adicionar ou remover componentes do circuito, mas substitui padrões de rede de três terminais matematicamente equivalentes. Ele efetivamente transforma um circuito, permitindo que os resistores sejam analisados ​​como se estivessem em série ou em paralelo, facilitando o cálculo da resistência equivalente se necessário.

Redes Delta e Y

Aplicações práticas, como transmissão elétrica trifásica e motores, usam redes Y ou T interconversíveis de três terminais e redes delta ou pi.
...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Basics of Electric Circuits

Fundamentos de Circuitos Elétricos

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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

charge and current

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kirchhoff's current law

Kirchhoff's Current Law at Circuit Nodes

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Voltage Balance in Closed Circuit Loops

Kirchhoff's Voltage Law explains how voltage is balanced in a closed circuit loop. It is a basic rule in electrical engineering and comes from the idea of energy conservation. Energy can change form, but it cannot be created or destroyed. KVL states that the algebraic sum of all voltages around a closed path, or loop, is zero. In other words, the total voltage supplied in a loop equals the total voltage drop across the components in that loop. A loop can be traced clockwise or anticlockwise,...

voltage dividers

Series Resistors and Voltage Split

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current dividers

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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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