Name: matching load impedance for maximum power
Uploaded: 2024-07-08T13:19:54.000Z
Duration: 1 min 20 s
Channel: JoVE

חשבו על מעגל AC ליניארי המחובר לעומס, המיוצג על ידי המקבילה שלו לתבנין.
הזרם הזורם דרך העומס נקבע באמצעות הצורה המלבנית של עכבת התבנין והעומס.
ההספק הממוצע המועבר לעומס מתקבל מהביטוי הנוכחי.
כדי לקבוע את התנגדות העומס להספק מרבי, נגזרת הכוח ביחס להתנגדות להספק מרבי נקבעת כאפס.
באופן דומה, תגובת העומס עבור כוח מרבי מתקבל.
לכן, עבור העברת כוח ממוצעת מקסימלית, התגובה של עכבת העומס היא השלילית של התגובה של עכבת תבנין, וההתנגדות שלה שווה להתנגדות של עכבת תבנין.
על ידי החלפת ערכים אלה, הכוח המרבי מתקבל.
על פי משפט ההספק הממוצע המרבי, עכבת העומס שווה למצומד המרוכב של עכבת תבנין.
עבור עומסים התנגדותיים בלבד, העברת הכוח הממוצעת המרבית מתרחשת כאשר עכבת העומס שווה לגודל עכבת תבנין.
בתקשורת אלחוטית, עכבת האנטנה מותאמת לעכבה של קו השידור או מעגל המקלט, ממקסמת את העברת הכוח, מבטיחה עוצמת אות אופטימלית ומשפרת את איכות התקשורת ואת טווחה.

משפט העברת ההספק המקסימלי

<div style="direction:rtl">

שקול מעגל שווה ערך AC תבנין ליניארי המחובר לעכבת עומס.

<img alt="Equation 1" src="/files/ftp_upload/15125/15125_Equation_1.svg" style="text-align: center; height: 16px;">

העומס המחובר שואב את הזרם, והמעגל מספק את ההספק לעומס. זרם החילופין הזורם דרך העומס נקבע באמצעות הצורה המלבנית של מתחים, זרמים, עכבת רשת ועכבת עומס. ההספק הממוצע המסופק לעומס מתקבל מהמכפלה של ריבוע הזרם והתנגדות העומס.

<img alt="Equation 1" src="/files/ftp_upload/15125/15125_Equation_1.svg" style="text-align: center; height: 16px;">

<img alt="Equation 2" src="/files/ftp_upload/15125/15125_Equation_2.svg" style="text-align: center; height: 16px;">

העברת ההספק המקסימלי המסופק לעומס נקבעת על ידי חישוב נגזרת ההספק ביחס להתנגדות העומס. לאחר מכן, הנגזרת מושווית לאפס עבור התנאי המקסימלי. לכן, עבור העברת הספק ממוצע מקסימלי, ההיגב של עכבת העומס הוא השלילי של ההיגב של עכבת תבנין, וההתנגדות שלה שווה להתנגדות של עכבת תבנין. כאשר תנאים אלה מתקיימים, אומרים שעכבת העומס היא הצמוד המרוכב של עכבת תבנין של המעגל. ההספק המקסימלי מתקבל כאשר עכבת העומס עומדת בתנאי 

שהוזכר לעיל.

<img alt="Equation 3" src="/files/ftp_upload/15125/15125_Equation_3.svg" style="text-align: center; height: 44px;">

<img alt="Equation 4" src="/files/ftp_upload/15125/15125_Equation_4.svg" style="text-align: center; height: 36px;">

<img alt="Equation 5" src="/files/ftp_upload/15125/15125_Equation_5.svg" style="text-align: center; height: 16px;">

על פי משפט ההספק הממוצע המקסימלי, עכבת העומס שווה לצמוד המרוכב של עכבת תבנין. עבור עומסים התנגדותיים טהורים, העברת הספק ממוצע מקסימלי מתרחשת כאשר עכבת העומס שווה לגודל עכבת תבנין.

בתקשורת אלחוטית, העכבה של האנטנה מותאמת לעכבה של קו השידור או מעגל המקלט, מגדילה את העברת ההספק, מבטיחה עוצמת אות מיטבית ומשפרת את איכות וטווח התקשורת.

</div>

חשבו על מעגל AC ליניארי המחובר לעומס, המיוצג על ידי המקבילה שלו לתבנין.
הזרם הזורם דרך העומס נקבע באמצעות ...

Education

JoVE Core

Electrical Engineering

הנדסה חשמלית

Unit 1

יחידה 1

AC Steady State Power

הספק זרם חילופין במצב רגוע

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

The Maximum Power Transfer Theorem

matching load impedance for maximum power

Maximum power transfer in an AC circuit depends on matching the load impedance to the Thevenin equivalent of the source network. The load draws current, and the circuit delivers power to that load. To analyze the current, the voltages, currents, network impedance, and load impedance are written in rectangular form.

The average power delivered to the load comes from the square of the current multiplied by the load resistance. To find the condition for maximum power, the power is differentiated with respect to the load resistance. That derivative is then set equal to zero.

For maximum average power transfer, the load reactance must be the negative of the Thevenin reactance. The load resistance must also equal the Thevenin resistance. When both conditions are met, the load impedance is the complex conjugate of the circuit's Thevenin impedance.

For a purely resistive load, maximum average power transfer occurs when the load impedance equals the magnitude of the Thevenin impedance. This idea is used in wireless communications, where an antenna is matched to a transmission line or receiver circuit. Good matching improves power transfer, signal strength, communication quality, and range.

Matching Load Impedance for Maximum Power

matching-load-impedance-for-maximum-power

instantaneous power

AC Power and Phase Shift

Instantaneous power in an electrical circuit comes from the voltage across an element and the current through it. It is written as p(t) and follows the passive sign convention. For sinusoidal input, this product helps show how power changes at each moment. When instantaneous power is expanded, it has two parts. One part is constant and depends on the phase difference between voltage and current. The other part is a sinusoidal term that varies at twice the frequency of the voltage or current. <br...

average power

Power Consumption in AC Circuits

Power consumption in AC circuits is often described with average power. In practical electrical work, the changing value of instantaneous power is less useful than the average over a time period. Average power is found by integrating instantaneous power over that time and then dividing by the duration. The time-domain expression for average power comes from simplifying the equation for instantaneous power. In that form, one cosine term averages to zero over a complete cycle. The result does...

effective value of a periodic waveform

RMS Value for AC Power Measurement

The RMS value, or effective value, helps measure how much power a periodic voltage or current can deliver. It is the direct current, or DC, value that gives the same average power to a resistor as the periodic signal does. This idea is especially important in AC circuits. To find the effective value of current, calculate the root mean square, or RMS, current. First square the instantaneous current values over one period. Then find the mean of those squared values and take the square root. The...

complex power

Power Triangle in AC Circuits

Power triangle and complex power help describe how an AC load uses energy. Engineers use complex power to capture the combined effect of parallel loads. It gives a full picture of the power consumed by a specific load. Complex power is found by multiplying voltage by the complex conjugate of current. Using rms values, it is written with the rms voltage phasor and the complex conjugate of the rms current phasor. It can also be written in terms of load impedance. The magnitude of complex power...

conservation of ac power

AC Power in Series and Parallel Circuits

AC power in series and parallel circuits follows a power preservation rule. In AC circuits, the complex power, real power, and reactive power produced by the source are equal to the total complex, real, and reactive powers absorbed by the loads. When two load impedances are connected in parallel to an AC source V, the source power can be written as the sum of the complex powers delivered to loads Z1 and Z2. If those same loads are connected in series with the voltage source, the complex power...

power factor

Power Factor and AC Load Behavior

Power factor describes how voltage and current behave in an AC load. It is the ratio of average, or active, power to apparent power. The power factor angle is the phase difference between voltage and current, and the cosine of that angle gives the power factor. It also matches the angle of the load impedance. Power factor shows how much apparent power becomes real, or average, power. Its value ranges from zero to one. When a load is purely resistive, voltage and current are in phase. In that...

power factor correction

Reducing Reactive Power in AC Loads

Power factor correction helps AC systems use electrical power more efficiently. In a factory circuit, transmitted power includes apparent power, which is made of active power and reactive power. Power factor is the ratio of real power, measured in kW, to apparent power, measured in kVA. It shows how much of the supplied power becomes useful work. A low power factor often happens when an inductive load draws too much reactive power. This creates a lagging power factor. It can also cause large...

the power superposition principle

Power from Multiple AC Sources

Power from multiple AC sources is found by adding the effects of each source separately. In a circuit with two sinusoidal voltage sources, each source acts independently. The superposition principle says the total current is the sum of the currents produced by each source alone. If those currents are labeled i1 and i2, they combine to give the total current. Instantaneous power is the power at one moment in time. In this circuit, it equals the square of the instantaneous current times the...

the maximum power transfer theorem

Maximum power transfer in an AC circuit depends on matching the load impedance to the Thevenin equivalent of the source network. The load draws current, and the circuit delivers power to that load. To analyze the current, the voltages, currents, network impedance, and load impedance are written in rectangular form. The average power delivered to the load comes from the square of the current multiplied by the load resistance. To find the condition for maximum power, the power is differentiated...

key terms and concepts

Learn how AC load impedance matching and complex conjugate conditions help maximize power transfer in Thevenin equivalent circuits and wireless communication.

Matching Load Impedance for Maximum Power | 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.

electrical engineering

Matching Load Impedance for Maximum Power

Description

Transcript