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

Si consideri un circuito CA lineare collegato a un carico, rappresentato dal suo equivalente Thevenin.
La corrente che scorre attraverso il carico viene determinata utilizzando la forma rettangolare del Thevenin e l'impedenza del carico.
La potenza media erogata al carico si ottiene dall'espressione corrente.
Per determinare la resistenza di carico per la massima potenza, la derivata della potenza rispetto alla resistenza per la massima potenza è impostata su zero.
Allo stesso modo, si ottiene la reattanza di carico per la massima potenza.
Quindi, per il massimo trasferimento di potenza media, la reattanza dell'impedenza di carico è il negativo della reattanza dell'impedenza di Thevenin e la sua resistenza è uguale alla resistenza dell'impedenza di Thevenin.
Sostituendo questi valori si ottiene la massima potenza.
Secondo il teorema della massima potenza media, l'impedenza di carico è uguale al coniugato complesso dell'impedenza di Thevenin.
Per carichi puramente resistivi, il trasferimento di potenza medio massimo si verifica quando l'impedenza di carico è uguale all'entità dell'impedenza di Thevenin.
Nelle comunicazioni wireless, l'impedenza dell'antenna è abbinata all'impedenza della linea di trasmissione o del circuito del ricevitore, massimizzando il trasferimento di potenza, garantendo una potenza del segnale ottimale e migliorando la qualità e la portata della comunicazione.

il teorema del massimo trasferimento di potenza

Considera un circuito equivalente AC Thevenin lineare collegato a un'impedenza di carico.

<img alt="Equation 1" src="/files/ftp_upload/15125/15125_Equation_1.svg" style="height: 18px;">

Il carico collegato assorbe la corrente e il circuito fornisce energia al carico. La corrente alternata che scorre attraverso il carico viene determinata utilizzando la forma rettangolare di tensioni, correnti, impedenza di rete e impedenza di carico. La potenza media erogata al carico si ottiene dal prodotto del quadrato della corrente e della resistenza del carico.

<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;">

Il massimo trasferimento di potenza erogato al carico viene determinato calcolando la derivata della potenza rispetto alla resistenza del carico. La derivata è quindi pari a zero per la condizione di massimo. Pertanto, per il massimo trasferimento di potenza medio, la reattanza dell'impedenza di carico è il negativo della reattanza dell'impedenza di Thevenin e la sua resistenza è uguale alla resistenza dell'impedenza di Thevenin. Quando queste condizioni sono soddisfatte, si dice che l'impedenza di carico è il complesso coniugato dell'impedenza di Thevenin del circuito. La potenza massima si ottiene quando l'impedenza di carico soddisfa la condizione sopra menzionata.

<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;">

Secondo il teorema della potenza media massima, l'impedenza di carico è uguale al complesso coniugato dell'impedenza di Thevenin. Per carichi puramente resistivi, il trasferimento di potenza medio massimo si verifica quando l'impedenza di carico è uguale all'impedenza di Thevenin.

Nelle comunicazioni wireless, l'impedenza dell'antenna è adattata all'impedenza della linea di trasmissione o del circuito del ricevitore, massimizzando il trasferimento di potenza, garantendo una potenza ottimale del segnale e migliorando la qualità e la portata della comunicazione.

Il teorema del massimo trasferimento di potenza

Si consideri un circuito CA lineare collegato a un carico, rappresentato dal suo equivalente Thevenin.
La corrente che scorre attraverso il carico è determinata utilizzando il ...

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

AC Steady State Power

Potenza in regime stazionario CA

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

Tags