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

יישומים מעשיים, כגון תמסורת חשמל תלת פאזית ומנועים, משתמשים בשלושה הדקים Y או T הניתנים להמרה הדדית, ורשתות דלתא או פאי.
חשבו על רשת דלתא המורכבת משלושה נגדים. הפיכתה לרשת Y כרוכה בכיסוי רשת Y המתאימה לרשת הדלתא על ידי הוספת צומת מרכזי.
מכיוון שההתנגדות בין כל זוג צמתים ברשת הדלתא שקולה להתנגדות בין אותו זוג ברשת Y, נוצרת קבוצה של שלוש משוואות. פתרון משוואות אלה מניב את ההתנגדויות עבור רשת Y.
ברשת Y, ערכו של כל נגד הוא מכפלה של ההתנגדויות בשני ענפי הדלתא הסמוכים, חלקי סכום שלושת נגדי הדלתא.
באופן דומה, רשת Y יכולה להפוך לרשת דלתא מקבילה. ברשת הדלתא, ערכו של כל נגד נקבע על ידי סיכום כל המכפלות האפשריות של נגדי Y שנלקחו שניים בכל פעם ולאחר מכן התחלקו בנגד Y הנגדי.
עבור רשת מאוזנת עם התנגדויות שוות הן בתצורת Y והן בתצורת דלתא, נוסחת ההמרה מפשטת.

רשתות דלתא ו- y

<div style="direction:rtl">בניתוח מעגלים, לעתים קרובות נוצרים מצבים שבהם נגדים אינם בתצורות סדרה או מקבילות. כדי להתמודד עם תרחישים כאלה, נכנסות לפעולה רשתות מקבילות לשלושה טרמינלים כמו רשת wye (Y) (Figure 1 (א)) או טי (T) ו-delta (Δ) (Figure 1 (ב)) או pi (π). רשתות אלו מציעות פתרונות מגוונים והן נתקלות לעתים קרובות ביישומים שונים, לרבות מערכות חשמל תלת פאזיות, מסננים חשמליים ורשתות תואמות. <img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;"> המהות של רשתות אלו טמונה בכושר ההסתגלות שלהן. ניתן להשתמש בהם בנפרד או לשלבם במעגלים מורכבים יותר. לדוגמה, כאשר עוסקים ברשת דלתא אך מוצאים את זה יותר נוח לעבוד עם רשת wye, ניתן להצמיד רשת wye על תצורת הדלתא הקיימת. כדי לקבוע את ההתנגדויות המקבילות בתוך רשת wye, חשוב לוודא שההתנגדות בין כל זוג צמתים ברשת הדלתא שווה להתנגדות בין אותו זוג צמתים ברשת Y (או T). תהליך ההמרה בין הרשתות הללו כולל יחסים מתמטיים המתייחסים להתנגדויות. הטרנספורמציה מתאפשרת על ידי הכנסת צומת 'n' נוסף והקפדה על כלל ההמרה: ברשת Y, כל נגד הוא מכפלת הנגדים בשני ענפי Δ (דלתא) הסמוכים, חלקי סכום שלושת ה- Δ נגדים. לעומת זאת, כדי להמיר רשת wye לרשת דלתא שווה ערך, אפשר להשתמש בכלל ההמרה הבא: כל נגד ברשת הוא סכום כל התוצרים האפשריים של נגדי Y שנלקחו שניים בכל פעם, חלקי נגד Y הנגדי. נוסחאות ההמרה הללו מפשטות עבור רשתות מאוזנות שבהן ההתנגדויות בתצורות Y ו- Δ שוות. טרנספורמציה זו אינה כוללת הוספה או הסרה של רכיבים מהמעגל אלא מחליפה תבניות רשת מקבילות מתמטית של שלושה טרמינלים. הוא הופך למעשה מעגל, ומאפשר לנתח נגדים כאילו היו בסדרה או מקבילה, מה שמקל על חישוב ההתנגדות המקבילה במידת הצורך.</div>

רשתות דלתא ו- Y

יישומים מעשיים, כגון תמסורת חשמל תלת פאזית ומנועים, משתמשים בשלושה הדקים Y או T הניתנים להמרה הדדית, ורשתות דלתא או פאי.
...

Education

JoVE Core

Electrical Engineering

הנדסה חשמלית

Unit 1

יחידה 1

Basics of Electric Circuits

יסודות מעגלים חשמליים

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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 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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