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

Le applicazioni pratiche, come la trasmissione elettrica trifase e i motori, utilizzano reti interconvertibili a tre terminali Y o T e reti delta o pi.
Si consideri una rete delta composta da tre resistori. La sua trasformazione in una rete Y comporta la sovrapposizione della corrispondente rete Y alla rete delta aggiungendo un nodo centrale.
Poiché la resistenza tra ogni coppia di nodi nella rete delta è equivalente alla resistenza tra la stessa coppia nella rete Y, viene stabilito un insieme di tre equazioni. Risolvendo queste equazioni si ottengono le resistenze per la rete Y.
Nella rete Y, il valore di ciascun resistore è il prodotto delle resistenze nei due rami delta adiacenti, diviso per la somma dei tre resistori delta.
Allo stesso modo, una rete Y può essere trasformata in una rete delta equivalente. Nella rete delta, il valore di ciascun resistore è determinato sommando tutti i possibili prodotti dei resistori Y presi due alla volta e poi dividendo per il resistore Y opposto.
Per una rete bilanciata con resistenze uguali in entrambe le configurazioni Y e delta, la formula di conversione semplifica.

reti delta e y

Nell'analisi dei circuiti, spesso si verificano situazioni in cui i resistori non sono né in serie né in parallelo. Per affrontare tali scenari, entrano in gioco reti equivalenti a tre terminali come le reti Wye (Y) (Figure 1 (a)) o Tee (T) e Delta (Δ) (Figure 1 (b)) o Pi (π). Queste reti offrono soluzioni versatili e si incontrano frequentemente in varie applicazioni, inclusi sistemi elettrici trifase, filtri elettrici e reti di adattamento.

<img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;">

L’essenza di queste reti risiede nella loro adattabilità. Possono essere impiegati singolarmente o integrati in circuiti più complessi. Ad esempio, quando si ha a che fare con una rete delta ma si trova più conveniente lavorare con una rete a stella, è possibile sovrapporre una rete a stella alla configurazione delta esistente. Per determinare le resistenze equivalenti all'interno della rete a stella, è fondamentale garantire che la resistenza tra ciascuna coppia di nodi nella rete delta sia uguale alla resistenza tra la stessa coppia di nodi nella rete Y (o T).

Il processo di conversione tra queste reti implica relazioni matematiche relative alle resistenze. La trasformazione è facilitata introducendo un nodo aggiuntivo 'n' e aderendo alla regola di conversione: nella rete Y, ciascun resistore è il prodotto dei resistori nei due rami Δ (delta) adiacenti, diviso per la somma dei tre Δ resistori. Al contrario, per convertire una rete a stella in una rete a triangolo equivalente, è possibile utilizzare la seguente regola di conversione: ciascun resistore nella rete è la somma di tutti i possibili prodotti dei resistori Y presi due alla volta, diviso per il resistore Y opposto.

Queste formule di conversione si semplificano per reti bilanciate in cui le resistenze nelle configurazioni Y e Δ sono uguali. Questa trasformazione non comporta l'aggiunta o la rimozione di componenti dal circuito ma sostituisce modelli di rete a tre terminali matematicamente equivalenti. Trasforma efficacemente un circuito, permettendo di analizzare i resistori come se fossero in serie o in parallelo, facilitando, se necessario, il calcolo della resistenza equivalente.

Reti Delta e Y

Le applicazioni pratiche, come la trasmissione elettrica trifase e i motori, utilizzano reti interconvertibili a tre terminali Y o T e reti delta o pi.
...

Education

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JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

Basics of Electric Circuits

Fondamenti dei circuiti elettrici

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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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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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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