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

Praktyczne zastosowania, takie jak trójfazowa przekładnia elektryczna i silniki, wykorzystują wymienne trójzaciskowe sieci Y lub T oraz trójkątne lub pi.
Rozważmy sieć delta składającą się z trzech rezystorów. Jej przekształcenie w sieć Y polega na nałożeniu odpowiedniej sieci Y na sieć delta poprzez dodanie węzła centralnego.
Ponieważ rezystancja między każdą parą węzłów w sieci delta jest równoważna rezystancji między tą samą parą w sieci Y, ustalany jest zestaw trzech równań. Rozwiązanie tych równań daje rezystancje dla sieci Y.
W sieci Y wartość każdego rezystora jest iloczynem rezystancji w dwóch sąsiednich gałęziach trójkąta, podzielonym przez sumę trzech rezystorów trójkąta.
Podobnie, sieć Y może zostać przekształcona w równoważną sieć delta. W sieci delta wartość każdego rezystora jest określana przez zsumowanie wszystkich możliwych iloczynów rezystorów Y wziętych po dwa na raz, a następnie podzielenie przez przeciwny rezystor Y.
W przypadku zrównoważonej sieci o jednakowych rezystancjach zarówno w konfiguracji Y, jak i trójkąta, formuła konwersji jest uproszczona.

sieci delta i y

Podczas analizy obwodów często pojawiają się sytuacje, w których rezystory nie są skonfigurowane ani szeregowo, ani równolegle. Aby stawić czoła takim scenariuszom, w grę wchodzą sieci równoważne z trzema końcówkami, takie jak gwiazda (Y) (Figure 1 (a)) lub litera T (T) i delta, trójkąt (Δ) (Figure 1 (b)) lub sieci pi (π). Sieci te oferują wszechstronne rozwiązania i są często spotykane w różnych zastosowaniach, w tym w trójfazowych systemach elektrycznych, filtrach elektrycznych i sieciach dopasowujących.

<img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;" />

Istota tych sieci polega na ich zdolności adaptacyjnej. Można je stosować pojedynczo lub zintegrować z bardziej złożonymi obwodami. Na przykład, gdy mamy do czynienia z siecią typu delta, ale uznamy, że wygodniej jest pracować z siecią typu gwiazda, sieć typu gwiazda można nałożyć na istniejącą konfigurację typu delta. Aby określić równoważne rezystancje w sieci typu gwiazda, kluczowe znaczenie ma zapewnienie, że rezystancja pomiędzy każdą parą węzłów w sieci delta jest równa rezystancji pomiędzy tą samą parą węzłów w sieci Y (lub T).

Proces konwersji między tymi sieciami obejmuje zależności matematyczne dotyczące rezystancji. Transformacja jest ułatwiona poprzez wprowadzenie dodatkowego węzła „n” i zastosowanie odpowiedniej zasady przekształcania: w sieci gwiazdy (Y) każda rezystancja jest iloczynem rezystancji z dwóch sąsiednich gałęzi delty (Δ), podzielonym przez sumę trzech rezystancji Δ. Natomiast konwersja sieci gwiazdy na równoważną sieć delty odbywa się według zasady, w której każda rezystancja w sieci jest sumą wszystkich możliwych iloczynów rezystancji Y, branych po dwie, podzieloną przez przeciwległą rezystancję Y.

Te wzory konwersji ulegają uproszczeniu w przypadku sieci zrównoważonych, w których rezystancje w konfiguracjach Y i Δ są równe. Transformacja ta nie wymaga dodawania ani usuwania elementów z obwodu, lecz polega na matematycznym zastąpieniu jednej trójzaciskowej struktury inną, równoważną. Umożliwia to przekształcenie obwodu tak, aby rezystory mogły być analizowane jak połączenia szeregowe lub równoległe, co ułatwia obliczenie rezystancji zastępczej w razie potrzeby.

Sieci Delta i Y

Praktyczne zastosowania, takie jak trójfazowa przekładnia elektryczna i silniki, wykorzystują wymienne trójzaciskowe sieci Y lub T oraz trójkątne lub pi.
...

Education

JoVE Core

Electrical Engineering

Elektrotechnika

Unit 1

Jednostka 1

Basics of Electric Circuits

Podstawy obwodów elektrycznych

KEY TERMS AND CONCEPTS

KLUCZOWE POJĘCIA I KONCEPCJE

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

Electric Charge in Circuits

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voltage

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power and energy

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ohm's law

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kirchhoff's current law

Kirchhoff's Current Law at Circuit Nodes

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kirchhoff's voltage law

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voltage dividers

Series Resistors and Voltage Split

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current dividers

Parallel Resistors and Current Division

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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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