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

3상 전기 전송 및 모터와 같은 실제 응용 분야는 상호 변환 가능한 3단자 Y 또는 T와 델타 또는 파이 네트워크를 사용합니다.
3개의 저항으로 구성된 델타 네트워크가 있다고 가정하겠습니다. Y 네트워크로의 변환에는 중앙 노드를 추가하여 해당 Y 네트워크를 델타 네트워크에 오버레이하는 작업이 포함됩니다.
델타 네트워크의 각 노드 쌍 간의 저항은 Y 네트워크의 동일한 쌍 간의 저항과 동일하기 때문에 세 가지 방정식 세트가 설정됩니다. 이러한 방정식을 풀면 Y 네트워크에 대한 저항이 산출됩니다.
Y 네트워크에서 각 저항기의 값은 인접한 두 델타 분기의 저항을 세 델타 저항기의 합으로 나눈 곱입니다.
마찬가지로, Y 네트워크는 동등한 델타 네트워크로 변환될 수 있습니다. 델타 네트워크에서 각 저항의 값은 한 번에 두 개씩 취한 Y 저항의 가능한 모든 곱을 합산한 다음 반대쪽 Y 저항으로 나누어 결정됩니다.
Y 및 델타 구성 모두에서 동일한 저항을 갖는 균형 잡힌 네트워크의 경우 변환 공식이 단순화됩니다.

델타와 y 네트워크

회로 분석에서 저항이 직렬이나 병렬 구성이 아닌 상황이 자주 발생합니다. 이러한 시나리오를 해결하기 위해 와이(Y)(Figure 1(a)), 티(T) 및 델타(Δ)(Figure 1(b)) 또는 파이(π) 네트워크와 같은 3단자 등가 네트워크가 사용됩니다. 이러한 네트워크는 다양한 솔루션을 제공하며 3상 전기 시스템, 전기 필터 및 매칭 네트워크를 포함한 다양한 애플리케이션에서 자주 사용됩니다.

<img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;">

이러한 네트워크의 본질은 적응성에 있습니다. 이는 개별적으로 사용되거나 보다 복잡한 회로에 통합될 수 있습니다. 예를 들어, 델타 네트워크를 다루지만 wye 네트워크를 사용하는 것이 더 편리하다고 생각하는 경우 wye 네트워크를 기존 델타 구성에 중첩할 수 있습니다. 와이 네트워크 내에서 등가 저항을 결정하려면 델타 네트워크의 각 노드 쌍 사이의 저항이 Y(또는 T) 네트워크의 동일한 노드 쌍 사이의 저항과 동일한지 확인하는 것이 중요합니다.

이러한 네트워크 간의 변환 과정에는 저항과 관련된 수학적 관계가 포함됩니다. 변환은 추가 노드 'n'을 도입하고 변환 규칙을 준수함으로써 촉진됩니다. Y 네트워크에서 각 저항은 두 개의 인접한 Δ(델타) 가지에 있는 저항의 곱을 세 개의 Δ의 합으로 나눈 값입니다. 저항기. 반대로, Wye 네트워크를 동등한 델타 네트워크로 변환하려면 다음 변환 규칙을 사용할 수 있습니다. 네트워크의 각 저항은 한 번에 두 개씩 취한 Y 저항의 가능한 모든 곱의 합을 반대 Y 저항으로 나눈 값입니다.

이러한 변환 공식은 Y 및 Δ 구성의 저항이 동일한 균형 잡힌 네트워크에 대해 단순화됩니다. 이 변환에는 회로의 구성요소를 추가하거나 제거하는 작업이 포함되지 않지만 수학적으로 동등한 3단자 네트워크 패턴을 대체합니다. 이는 회로를 효과적으로 변환하여 저항기를 직렬 또는 병렬인 것처럼 분석할 수 있도록 하며 필요한 경우 등가 저항 계산을 용이하게 합니다.

델타와 Y 네트워크

3상 전기 전송 및 모터와 같은 실제 응용 분야는 상호 변환 가능한 3단자 Y 또는 T와 델타 또는 파이 네트워크를 사용합니다.
...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Basics of Electric Circuits

전기 회로의 기초

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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,...

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Circuit Source Symbols and Controls

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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 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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