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

В практических приложениях, таких как трехфазные электрические передачи и двигатели, используются взаимопереходные трехконтактные сети Y или T, а также дельта или пи.
Рассмотрим дельта-сеть, состоящую из трех резисторов. Ее преобразование в сеть Y включает в себя наложение соответствующей сети Y на дельта-сеть путем добавления центрального узла.
Поскольку сопротивление между каждой парой узлов в дельта-сети эквивалентно сопротивлению между той же парой в сети Y, устанавливается набор из трех уравнений. Решение этих уравнений дает сопротивления для Y-сети.
В сети Y значение каждого резистора является произведением сопротивлений в двух смежных дельта-ветвях, деленным на сумму трех дельта-резисторов.
Аналогичным образом, сеть Y может быть преобразована в эквивалентную дельта-сеть. В дельта-сети значение каждого резистора определяется путем суммирования всех возможных произведений Y-резисторов, взятых по два, а затем деления на противоположный Y-резистор.
Для сбалансированной сети с равными сопротивлениями как в Y-, так и в дельта-конфигурациях формула преобразования упрощается.

Сети delta и y

При анализе цепей часто возникают ситуации, когда резисторы не включены ни последовательно, ни параллельно. Для решения таких сценариев в игру вступают эквивалентные сети с тремя клеммами, такие как сети Wye (Y) (рис. 1 (а)) или тройник (T), и Delta (Δ) (рис. 1 (б)) или пи (π). Эти сети предлагают универсальные решения и часто встречаются в различных приложениях, включая трехфазные электрические системы, электрические фильтры и согласующие сети.

<img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;" />

Суть этих сетей заключается в их адаптивности. Их можно использовать индивидуально или интегрировать в более сложные схемы. Например, если вы имеете дело с дельта-сетью, но считаете, что работать с сетью Wye удобнее, сеть Wye можно наложить на существующую дельта-конфигурацию. Чтобы определить эквивалентные сопротивления в сети Wye, решающее значение имеет обеспечение того, чтобы сопротивление между каждой парой узлов в сети Delta» равнялось сопротивлению между одной и той же парой узлов в сети Wye (или T).

Процесс преобразования между этими сетями включает в себя математические соотношения, связанные с сопротивлениями. Преобразование облегчается введением дополнительного узла «n» и соблюдением правила преобразования: в сети Wye каждый резистор представляет собой произведение резисторов в двух соседних ветвях Δ (дельта), деленное на сумму трех дельта резисторов. И наоборот, чтобы преобразовать сеть Wye в эквивалентную сеть дельта, можно использовать следующее правило преобразования: каждый резистор в сети представляет собой сумму всех возможных произведений резисторов Wye, взятых по два одновременно, разделенных на противоположный резистор Wye.

Эти формулы преобразования упрощаются для сбалансированных сетей, где сопротивления в конфигурациях Wye и дельта равны. Это преобразование не предполагает добавления или удаления компонентов из схемы, а заменяет математически эквивалентные трехполюсные сетевые схемы. Оно эффективно преобразует схему, позволяя анализировать резисторы так, как если бы они были включены последовательно или параллельно, что при необходимости облегчает расчет эквивалентного сопротивления.

Сети Delta и Y

В практических приложениях, таких как трехфазные электрические передачи и двигатели, используются взаимопереходные трехконтактные сети Y или T, а также дельта или пи.
...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Basics of Electric Circuits

Основы электрических цепей

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

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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...

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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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