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

Thevenin eşdeğeri ile temsil edilen bir yüke bağlı doğrusal bir AC devresi düşünün.
Yükten geçen akım, Thevenin'in dikdörtgen formu ve yük empedansı kullanılarak belirlenir.
Yüke iletilen ortalama güç, akım ifadesinden elde edilir.
Maksimum güç için yük direncini belirlemek için, maksimum güç için dirence göre gücün türevi sıfır olarak ayarlanır.
Benzer şekilde, maksimum güç için yük reaktansı elde edilir.
Bu nedenle, maksimum ortalama güç aktarımı için, yük empedansının reaktansı, Thevenin empedansının reaktansının negatifidir ve direnci, Thevenin empedansının direncine eşittir.
Bu değerlerin yerine konarak maksimum güç elde edilir.
Maksimum ortalama güç teoremine göre, yük empedansı, Thevenin empedansının karmaşık eşleniğine eşittir.
Tamamen dirençli yükler için, yük empedansı Thevenin empedansının büyüklüğüne eşit olduğunda maksimum ortalama güç aktarımı gerçekleşir.
Kablosuz iletişimde, antenin empedansı, iletim hattı veya alıcı devresinin empedansı ile eşleştirilir, güç aktarımını en üst düzeye çıkarır, optimum sinyal gücü sağlar ve iletişim kalitesini ve menzilini artırır.

 maksimum güç transferi teoremi

Yük empedansına bağlı doğrusal bir AC Thevenin eşdeğer devresini düşünün.

<img alt="Equation 1" src="/files/ftp_upload/15125/15125_Equation_1.svg" style="height: 18px;">

Bağlanan yük akımı çekerken devre de gücü yüke iletir. Yükten akan alternatif akım, gerilimlerin, akımların, ağ empedansının ve yük empedansının dikdörtgen biçimi kullanılarak belirlenir. Yüke iletilen ortalama güç, akımın ve yük direncinin karesinin çarpımından elde edilir.

<img alt="Equation 1" src="/files/ftp_upload/15125/15125_Equation_1.svg" style="height: 18px;">

<img alt="Equation 2" src="/files/ftp_upload/15125/15125_Equation_2.svg" style="height: 18px;">

Yüke iletilen maksimum güç aktarımı, yük direncine göre güç türevinin hesaplanmasıyla belirlenir. Türev daha sonra maksimum koşul için sıfıra eşitlenir. Dolayısıyla, maksimum ortalama güç aktarımı için yük empedansının reaktansı, Thevenin empedansının reaktansının negatifidir ve direnci, Thevenin empedansının direncine eşittir. Bu koşullar karşılandığında yük empedansının devrenin Thevenin empedansının karmaşık eşleniği olduğu söylenir. Yük empedansı yukarıda belirtilen koşulu karşıladığında maksimum güç elde edilir.

<img alt="Equation 3" src="/files/ftp_upload/15125/15125_Equation_3.svg" style="height: 46px;">

<img alt="Equation 4" src="/files/ftp_upload/15125/15125_Equation_4.svg" style="height: 38px;">

<img alt="Equation 5" src="/files/ftp_upload/15125/15125_Equation_5.svg" style="height: 18px;">

Maksimum ortalama güç teoremine göre yük empedansı, Thevenin empedansının karmaşık eşleniğine eşittir. Tamamen dirençli yükler için, maksimum ortalama güç aktarımı, yük empedansı Thevenin empedansının büyüklüğüne eşit olduğunda meydana gelir.

Kablosuz iletişimde, antenin empedansı iletim hattının veya alıcı devresinin empedansıyla eşleştirilerek güç aktarımı en üst düzeye çıkarılır, optimum sinyal gücü sağlanır ve iletişim kalitesi ve menzili artırılır.

 Maksimum Güç Transferi Teoremi

Thevenin eşdeğeri ile temsil edilen bir yüke bağlı doğrusal bir AC devresi düşünün.
Yükten geçen akım, ...

Education

JoVE Core

Electrical Engineering

Elektrik Mühendisliği

Unit 1

Ünite 1

AC Steady State Power

AC Kararlı Durum Gücü

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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 Elektrik Mühendisliği, devre analizi teknikleriyle birlikte elektrik devrelerinin temel kavramlarını kapsayan, anlaşılması kolay animasyonlu videolar sunar. Operasyonel amplifikatörler ve devre dönüşümü kavramlarını kullanarak birinci dereceden ve ikinci dereceden devreleri içerir. Pratik tasarım örneklerinin ve gerçek dünya uygulamalarının bilim insanlarınca hazırlanan videolar aracılığıyla dahil edilmesi, karmaşık kavramları erişilebilir hale getirerek önemli bir eğitim değeri katmaktadır.

electrical engineering

Matching Load Impedance for Maximum Power

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