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

Las aplicaciones prácticas, como la transmisión eléctrica trifásica y los motores, utilizan redes interconvertibles de tres terminales Y o T, y delta o pi.
Considere una red delta compuesta por tres resistencias. Su transformación en una red Y implica la superposición de la red Y correspondiente en la red delta mediante la adición de un nodo central.
Dado que la resistencia entre cada par de nodos en la red delta es equivalente a la resistencia entre el mismo par en la red Y, se establece un conjunto de tres ecuaciones. Resolviendo estas ecuaciones se obtienen las resistencias de la red Y.
En la red Y, el valor de cada resistencia es el producto de las resistencias en las dos ramas delta adyacentes, dividido por la suma de las tres resistencias delta.
Del mismo modo, una red Y se puede transformar en una red delta equivalente. En la red delta, el valor de cada resistencia se determina sumando todos los productos posibles de las resistencias Y tomados de dos en dos y luego dividiéndolos por la resistencia Y opuesta.
Para una red equilibrada con resistencias iguales en configuraciones Y y delta, la fórmula de conversión se simplifica.

redes delta e y

En el análisis de circuitos, a menudo surgen situaciones en las que las resistencias no están en configuraciones en serie ni en paralelo. Para abordar tales escenarios, entran en juego redes equivalentes de tres terminales como las redes estrella (Y) (Figura 1 (a)) o T (T) y delta (Δ) (Figura 1 (b)) o pi (π). Estas redes ofrecen soluciones versátiles y se encuentran con frecuencia en diversas aplicaciones, incluidos sistemas eléctricos trifásicos, filtros eléctricos y redes coincidentes. <img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;"> La esencia de estas redes radica en su adaptabilidad. Pueden emplearse individualmente o integrarse en circuitos más complejos. Por ejemplo, cuando se trata de una red en delta pero le resulta más conveniente trabajar con una red en estrella, se puede superponer una red en estrella a la configuración delta existente. Para determinar las resistencias equivalentes dentro de la red en estrella, es crucial asegurarse de que la resistencia entre cada par de nodos en la red delta sea igual a la resistencia entre el mismo par de nodos en la red Y (o T). El proceso de conversión entre estas redes implica relaciones matemáticas que se relacionan con las resistencias. La transformación se facilita introduciendo un nodo 'n' adicional y siguiendo la regla de conversión: en la red Y, cada resistencia es el producto de las resistencias en las dos ramas Δ (delta) adyacentes, dividido por la suma de las tres Δ resistencias. Por el contrario, para convertir una red en estrella en una red en delta equivalente, se puede usar la siguiente regla de conversión: cada resistencia en la red es la suma de todos los productos posibles de las resistencias Y tomadas de dos en dos, dividida por la resistencia Y opuesta. Estas fórmulas de conversión se simplifican para redes balanceadas donde las resistencias en las configuraciones Y y Δ son iguales. Esta transformación no implica agregar ni quitar componentes del circuito, sino que los sustituye por patrones de red de tres terminales matemáticamente equivalentes. Transforma efectivamente un circuito, permitiendo analizar resistencias como si estuvieran en serie o en paralelo, facilitando el cálculo de resistencia equivalente si es necesario.

Redes Delta e Y

Las aplicaciones prácticas, como la transmisión eléctrica trifásica y los motores, utilizan redes interconvertibles de tres terminales Y o T, y delta o pi.
...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Basics of Electric Circuits

Fundamentos de los circuitos eléctricos

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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

Series resistors split voltage across a circuit. In a series setup, resistors are linked one after another. The same current flows through each resistor in the chain. To analyze this behavior, Ohm's law is used to relate voltage, current, and resistance. Kirchhoff's voltage law says the voltages around a series loop add up to the source voltage. That means the current in the circuit equals the source voltage divided by the total resistance in series. The current value can then be used in Ohm's...

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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