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

Praktische Anwendungen, wie z. B. Drehstromgetriebe und Motoren, verwenden interkonvertierbare Y- oder T-Netze mit drei Anschlüssen sowie Delta- oder Pi-Netzwerke.
Stellen Sie sich ein Delta-Netzwerk vor, das aus drei Widerständen besteht. Bei der Umwandlung in ein Y-Netzwerk wird das entsprechende Y-Netz durch Hinzufügen eines zentralen Knotens auf das Delta-Netz aufgelegt.
Da der Widerstand zwischen den einzelnen Knotenpaaren im Delta-Netzwerk dem Widerstand zwischen demselben Paar im Y-Netzwerk entspricht, wird ein Satz von drei Gleichungen aufgestellt. Das Lösen dieser Gleichungen ergibt die Widerstände für das Y-Netzwerk.
Im Y-Netzwerk ist der Wert jedes Widerstands das Produkt aus den Widerständen in den beiden benachbarten Delta-Zweigen, dividiert durch die Summe der drei Delta-Widerstände.
Auf ähnliche Weise kann ein Y-Netzwerk in ein äquivalentes Delta-Netzwerk umgewandelt werden. Im Delta-Netzwerk wird der Wert jedes Widerstands bestimmt, indem alle möglichen Produkte von Y-Widerständen summiert werden, die jeweils zwei genommen werden, und dann durch den gegenüberliegenden Y-Widerstand dividiert wird.
Für ein ausgeglichenes Netzwerk mit gleichen Widerständen in Y- und Delta-Konfigurationen vereinfacht sich die Umrechnungsformel.

delta- und y-netzwerke

Bei der Schaltungsanalyse treten oft Situationen auf, in denen Widerstände weder in Reihen- noch in Parallelschaltungen vorliegen. Um solche Szenarien anzugehen, kommen dreipolige äquivalente Netzwerke wie das Stern- (Y) (Figure 1 (a)) oder T- und das Dreieck- (Δ) (Figure 1 (b)) oder Pi-Netzwerke zum Einsatz. Diese Netzwerke bieten vielseitige Lösungen und finden häufig Anwendung in verschiedenen Bereichen, einschließlich Drehstrom-Elektriksystemen, elektrischen Filtern und Anpassungsnetzwerken. <img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;"> Das Wesen dieser Netzwerke liegt in ihrer Anpassungsfähigkeit. Sie können einzeln eingesetzt oder in komplexere Schaltungen integriert werden. Wenn man beispielsweise mit einem Dreiecksnetzwerk arbeitet, es aber bequemer findet, mit einem Sternnetzwerk zu arbeiten, kann ein Sternnetzwerk auf die bestehende Dreieckskonfiguration überlagert werden. Um die äquivalenten Widerstände innerhalb des Sternnetzwerks zu bestimmen, ist es entscheidend, dass der Widerstand zwischen jedem Paar von Knoten im Dreiecksnetzwerk gleich dem Widerstand zwischen demselben Paar von Knoten im Y- (oder T-) Netzwerk ist. Der Umwandlungsprozess zwischen diesen Netzwerken beinhaltet mathematische Beziehungen, die sich auf die Widerstände beziehen. Die Umwandlung wird erleichtert, indem ein zusätzlicher Knoten 'n' eingeführt und die Umwandlungsregel beachtet wird: Im Y-Netzwerk ist jeder Widerstand das Produkt der Widerstände in den zwei angrenzenden Δ-Zweigen, geteilt durch die Summe der drei Δ-Widerstände. Umgekehrt, um ein Sternnetzwerk in ein äquivalentes Dreiecksnetzwerk umzuwandeln, kann man die folgende Umwandlungsregel verwenden: Jeder Widerstand im Netzwerk ist die Summe aller möglichen Produkte von Y-Widerständen, genommen jeweils zwei auf einmal, geteilt durch den gegenüberliegenden Y-Widerstand. Diese Umwandlungsformeln vereinfachen sich für ausgeglichene Netzwerke, bei denen die Widerstände in beiden Y- und Δ-Konfigurationen gleich sind. Diese Transformation beinhaltet weder das Hinzufügen noch das Entfernen von Komponenten aus der Schaltung, sondern ersetzt mathematisch äquivalente dreipolige Netzwerkmuster. Sie verwandelt effektiv eine Schaltung und ermöglicht es, Widerstände so zu analysieren, als wären sie entweder in Serie oder parallelgeschaltet, was die Berechnung des äquivalenten Widerstands bei Bedarf erleichtert.

Delta- und Y-Netzwerke

Praktische Anwendungen, wie z. B. Drehstromgetriebe und Motoren, verwenden interkonvertierbare Y- oder T-Netze mit drei Anschlüssen sowie Delta- oder Pi-Netzwerke.
...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

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Basics of Electric Circuits

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KEY TERMS AND CONCEPTS

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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

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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