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

三相送電やモーターなどの実際のアプリケーションでは、インターコンバーチブルの3端子YまたはT、およびデルタまたはpiネットワークを使用します。
3つの抵抗で構成されるデルタネットワークを考えてみましょう。Y ネットワークへの変換には、中央ノードを追加して、対応する Y ネットワークをデルタ ネットワークにオーバーレイすることが含まれます。
デルタ ネットワーク内のノードの各ペア間の抵抗は、Y ネットワーク内の同じペア間の抵抗と同等であるため、3 つの方程式のセットが確立されます。これらの方程式を解くと、Y ネットワークの抵抗が得られます。
Yネットワークでは、各抵抗の値は、隣接する2つのデルタ分岐の抵抗を3つのデルタ抵抗の合計で割った積です。
同様に、Y ネットワークは同等のデルタ ネットワークに変換できます。デルタネットワークでは、各抵抗の値は、一度に2つのY抵抗のすべての可能な積を合計し、次に反対側のY抵抗で除算することによって決定されます。
Y 構成とデルタ構成の両方で抵抗が等しい平衡型ネットワークの場合、変換式は簡略化されます。

デルタと y ネットワーク

回路解析では、抵抗が直列構成でも並列構成でもない状況がよく発生します。このようなシナリオに取り組むには、Y（ワイ）、Δ（デルタ）、およびπ（パイ）などの3端子等価ネットワークは、三相電気システムや電気フィルターなど様々なアプリケーションにおいて、その柔軟性から頻繁に用いられます。これらのネットワークは多用途のソリューションを提供し、三相電気システム、電気フィルター、整合ネットワークなどのさまざまなアプリケーションで頻繁に使用されます。

<img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;">

これらのネットワークの本質は、その適応性にあります。これらは個別に使用することも、より複雑な回路に統合することもできます。たとえば、デルタ ネットワークを扱っているが、Y ネットワークを使用するほうが便利であると判断した場合、既存のデルタ構成に Y ネットワークを重ね合わせることができます。 Y ネットワーク内の等価抵抗を決定するには、デルタ ネットワークの各ノード ペア間の抵抗が Y (または T) ネットワークの同じノード ペア間の抵抗と等しいことを確認することが重要です。

これらのネットワーク間の変換プロセスには、抵抗に関連する数学的関係が含まれます。変換は、追加のノード「n」を導入し、変換ルールに従うことで容易になります。Y ネットワークでは、各抵抗は、2 つの隣接する Δ (デルタ) ブランチの抵抗の積を 3 つの Δ の合計で割ったものです。抵抗器。逆に、Y ネットワークを等価なデルタ ネットワークに変換するには、次の変換ルールを使用できます。ネットワーク内の各抵抗は、一度に 2 つずつ取られた Y 抵抗の可能なすべての積の合計を、反対側の Y 抵抗で割ったものです。

これらの変換式は、Y 構成と Δ 構成の両方の抵抗が等しい平衡ネットワークを簡素化します。この変換には、回路へのコンポーネントの追加や削除は含まれませんが、数学的に等価な 3 端子ネットワーク パターンを置き換えます。これは回路を効果的に変換し、抵抗を直列または並列であるかのように解析できるようにし、必要に応じて等価抵抗の計算を容易にします。

デルタと Y ネットワーク

三相送電やモーターなどの実際のアプリケーションでは、インターコンバーチブルの3端子YまたはT、およびデルタまたはpiネットワークを使用します。
...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Basics of Electric Circuits

電気回路の基礎

KEY TERMS AND CONCEPTS

主要用語および概念

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

Electric charge in circuits explains how charged particles behave in matter and how current is produced. Everyday static effects, like a wool sweater sticking to the body or a shock from a carpet, show charge in action. Charge is an inherent property of atomic particles and is measured in coulombs (C). Matter is made of atoms with electrons, protons, and neutrons. Electrons carry a negative charge (-e), and protons carry a positive charge (+e). These two charges have the same magnitude. An...

voltage

Voltage in Electric Circuits

Voltage in electric circuits is the energy needed to move electric charge between two points. It is also called electromotive force, or EMF. In most circuits, an external force such as a battery provides this energy for electron movement in a conductor. The voltage between points a and b is written as v_ab. It is defined as the work, or energy, needed to move a unit charge from point a to point b. In the equation, w is the energy in joules and q is the charge in coulombs. Voltage is measured...

power and energy

Circuit Power, Absorption, and Supply

Circuit power, absorption, and supply explain how much energy an element uses or delivers in an electric circuit. These ideas matter in electrical engineering because power and energy calculations help describe circuit behavior. A 100-watt light bulb, for example, emits more light than a 60-watt bulb, so wattage is a useful measure in real devices. Power is the time rate of expending or absorbing energy. It is measured in watts, written as W. The relation between power and energy uses the...

electric circuit elements

Circuit Elements: Passive, Active, and Linear

Circuit elements are the building blocks of an electric circuit. An electric circuit is the connection of these elements. In this context, circuit elements are often grouped by how they behave and whether they supply energy. One major group is passive elements. These elements do not generate energy. Common passive elements include resistors, capacitors, and inductors. The other group is active elements, which can generate energy. Generators, batteries, and operational amplifiers are typical...

circuit terminology

Circuit Parts: Branches, Nodes, and Loops

Circuit parts like branches, nodes, loops, and meshes help describe how electrical networks work. An electrical network is a system of connected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, a network does not have to form a closed path. A circuit is also made of connected electrical elements, but it must include one or more closed paths. These loops let current flow continuously, which is what makes the circuit operate. Because of this,...

independent and dependent sources

Circuit Source Symbols and Controls

Circuit sources in electrical circuits can be independent or dependent. They provide the power a circuit needs to operate. Independent voltage sources supply a fixed voltage, and independent current sources supply a fixed current. Their output does not change because of other parts in the circuit. These sources use standard symbols in circuit diagrams. An independent voltage source is shown with + and - signs to mark the potential difference. An independent current source is shown with an...

ohm's law

Resistance and Conductance in Circuits

Resistance and conductance help explain how electric current moves through a circuit. Resistors are basic circuit parts made from metallic alloys or carbon compounds. They are used to model how a material resists current and to control and regulate electrical power in a circuit. Ohm's law describes the link between voltage and current across a resistor. The voltage across a resistor is directly proportional to the current through it. The constant that sets this relationship is resistance.

kirchhoff's current law

Kirchhoff's Current Law at Circuit Nodes

Kirchhoff's Current Law explains how current behaves at a circuit node. A node is the point where two or more circuit elements meet. The law says the current entering a node equals the current leaving it. That balance follows the rule of charge conservation, which means electric charge is not lost at the junction. When applying KCL, currents entering the node are treated as positive and currents leaving the node are treated as negative. The currents can be added algebraically at the node, and...

kirchhoff's voltage law

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

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Delta-Wye Network Conversion

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