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

Practical applications, such as three-phase electrical transmission and motors, use interconvertible three-terminal Y or T, and delta or pi networks.
Consider a delta network composed of three resistors. Its transformation into a Y network involves overlaying the corresponding Y network onto the delta network by adding a central node.
Since the resistance between each pair of nodes in the delta network is equivalent to the resistance between the same pair in the Y network, a set of three equations is established. Solving these equations yields the resistances for the Y network.
In the Y network, each resistor&#39;s value is the product of the resistances in the two adjacent delta branches, divided by the sum of the three delta resistors.
Similarly, a Y network can be transformed into an equivalent delta network. In the delta network, each resistor&#39;s value is determined by summing all possible products of Y resistors taken two at a time and then dividing by the opposite Y resistor.
For a balanced network with equal resistances in both Y and delta configurations, the conversion formula simplifies.

delta- en y-netwerken

Bij circuitanalyse doen zich vaak situaties voor waarin weerstanden zich niet in serie of parallelle configuraties bevinden. Om dergelijke scenario's aan te pakken, komen equivalente netwerken met drie terminals in beeld, zoals de wye (Y) (Figure 1 (a)) of tee (T) en delta (Δ) (Figure 1 (b)) of pi (π) netwerken. Deze netwerken bieden veelzijdige oplossingen en worden vaak aangetroffen in verschillende toepassingen, waaronder driefasige elektrische systemen, elektrische filters en bijpassende netwerken.
<img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;">
De essentie van deze netwerken ligt in hun aanpassingsvermogen. Ze kunnen afzonderlijk worden gebruikt of worden geïntegreerd in complexere circuits. Wanneer u bijvoorbeeld te maken heeft met een delta-netwerk, maar u het handiger vindt om met een wye-netwerk te werken, kan een wye-netwerk over de bestaande delta-configuratie worden heen gelegd. Om de equivalente weerstanden binnen het Y-netwerk te bepalen, is het van cruciaal belang ervoor te zorgen dat de weerstand tussen elk paar knooppunten in het deltanetwerk gelijk is aan de weerstand tussen hetzelfde paar knooppunten in het Y- (of T-) netwerk.
Het conversieproces tussen deze netwerken omvat wiskundige relaties die betrekking hebben op de weerstanden. De transformatie wordt vergemakkelijkt door een extra knooppunt 'n' te introduceren en zich aan de conversieregel te houden: in het Y-netwerk is elke weerstand het product van de weerstanden in de twee aangrenzende Δ (delta) takken, gedeeld door de som van de drie Δ weerstanden. Omgekeerd, om een Y-netwerk om te zetten in een gelijkwaardig deltanetwerk, kan men de volgende conversieregel gebruiken: Elke weerstand in het netwerk is de som van alle mogelijke producten van Y-weerstanden, twee tegelijk genomen, gedeeld door de tegenovergestelde Y-weerstand.
Deze conversieformules vereenvoudigen voor gebalanceerde netwerken waarbij de weerstanden in zowel Y- als Δ-configuraties gelijk zijn. Deze transformatie omvat niet het toevoegen of verwijderen van componenten uit het circuit, maar vervangt wiskundig equivalente netwerkpatronen met drie terminals. Het transformeert effectief een circuit, waardoor weerstanden kunnen worden geanalyseerd alsof ze in serie of parallel staan, waardoor indien nodig de berekening van equivalente weerstand wordt vergemakkelijkt.

Delta- en Y-netwerken

In circuit analysis, situations often arise where resistors are neither in series nor parallel configurations. To tackle such scenarios, three-terminal ...

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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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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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