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

テブナン等価物で表される負荷に接続された線形AC回路を考えてみましょう。
負荷を流れる電流は、テブナンと負荷インピーダンスの長方形を使用して決定されます。
負荷に供給される平均電力は、電流式から得られます。
最大電力の負荷抵抗を決定するために、最大電力の抵抗に対する電力の微分をゼロに設定します。
同様に、最大電力の負荷リアクタンスが得られます。
したがって、最大平均電力伝送の場合、負荷インピーダンスのリアクタンスはテブナンインピーダンスのリアクタンスの負であり、その抵抗はテブナンインピーダンスの抵抗と等しくなります。
これらの値を代入することにより、最大電力が得られます。
最大平均電力定理によれば、負荷インピーダンスはテブナンインピーダンスの複素共役に等しくなります。
純粋な抵抗性負荷の場合、最大平均電力伝送は、負荷インピーダンスがテブナンインピーダンスの大きさに等しいときに発生します。
無線通信では、アンテナのインピーダンスが伝送線路または受信回路のインピーダンスに一致しているため、電力伝送が最大化され、最適な信号強度が確保され、通信品質と範囲が向上します。

最大電力伝送定理

負荷インピーダンスに接続された線形 AC テブナン等価回路を考えてみましょう。
<img alt="Equation 1" src="/files/ftp_upload/15125/15125_Equation_1.svg" style="height: 18px;">
接続された負荷が電流を流し、回路が負荷に電力を供給します。負荷を流れる交流電流は、電圧、電流、ネットワークのインピーダンス、負荷インピーダンスの直角形式を使用して決定されます。負荷に供給される平均電力は、電流と負荷抵抗の 2 乗の積から得られます。
<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;">
負荷に供給される最大電力伝送は、負荷抵抗に対する電力導関数を計算することによって決定されます。次に、導関数は最大条件でゼロに等しくなります。したがって、最大平均電力伝送の場合、負荷インピーダンスのリアクタンスはテブナンの定理におけるインピーダンスのリアクタンスの負数であり、その抵抗はテブナンの定理におけるインピーダンスの抵抗に等しくなります。これらの条件が満たされると、負荷インピーダンスは回路のテブナン定理におけるインピーダンスの複素共役になります。負荷インピーダンスが上記の条件を満たすと、最大電力が得られます。
<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;">

最大平均電力定理によると、負荷インピーダンスはテブナンの定理におけるインピーダンスの複素共役に等しくなります。純粋な抵抗負荷の場合、最大平均電力伝送は、負荷インピーダンスがテブナンの定理におけるインピーダンスの大きさに等しいときに発生します。

無線通信では、アンテナのインピーダンスが伝送線または受信回路のインピーダンスに一致し、電力伝送が最大化され、最適な信号強度が確保され、通信品質と範囲が向上します。

テブナン等価物で表される負荷に接続された線形AC回路を考えてみましょう。
負荷を流れる電流は、...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

AC Steady State Power

交流定常状態電力

KEY TERMS AND CONCEPTS

主要用語と概念

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 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。

electrical engineering

Matching Load Impedance for Maximum Power

Description

Transcript

Tags