Name: load matching in thevenin circuits
Uploaded: 2024-04-11T12:48:31.000Z
Duration: 1 min 16 s
Channel: JoVE

In practical applications, a circuit is designed to deliver maximum power from a source to a load.
A Thevenin equivalent circuit can determine the maximum power that a linear circuit can deliver.
The delivered power is the product of the load resistance and the square of the current. It varies as the load resistance changes.
To identify the load resistance value that maximizes power, differential calculus is used. Simplifying this equation provides the optimal load resistance value.
This resistance value is substituted into the second derivative of power, resulting in a negative value, confirming the condition for maximum power.
The obtained resistance value allows the calculation of the maximum power. If the load resistance does not match the Thevenin resistance, the actual power delivered will deviate from this maximum.
According to the Maximum Power Transfer Theorem, the highest power transfer occurs when the load resistance matches the Thevenin resistance.
Consider a battery of known parameters, connected with two resistors of known values. The resistance that matches the internal resistance of the battery receives the maximum power.

maximum power transfer

Numerous practical applications within engineering disciplines, such as telecommunications, necessitate optimizing power delivery to a connected load. This pursuit, however, entails inherent internal losses, which can either equal or exceed the power supplied to the load. The Thevenin equivalent circuit is helpful in finding the maximum power a linear circuit can deliver to a load. It is assumed in this context that the load resistance can be adjusted.
By substituting the entire circuit with its Thevenin equivalent while preserving the load as shown in Figure 1,
<img alt="Thevenin equivalent circuit diagram with voltage source, resistor, and current flow analysis." src="/files/ftp_upload/15055/15055_PT_Figure_1.svg" style="text-align: center; height: 140px;" data-altupdatedat="1761830439000" data-alt="Figure1" />
Figure 1:Circuit used for maximum power transfer
 the power delivered to the load is given by
<img alt="Static equilibrium diagram; forces &#931;Fx=0 mechanism analysis." src="/files/ftp_upload/15055/15055_PT_Equation_1.svg" style="text-align: center; height: 40px;" data-altupdatedat="1761830439000" data-alt="Equation1" />.................(1)
For a given circuit, Thevenin equivalent resistance and voltage are fixed. The variation of power delivered to the load with load resistance is small for small or large values of load resistance but maximum for some value load resistance between zero and infinity. The maximum power occurs when the load resistance equals the Thevenin's resistance expressed as
<img alt="Static equilibrium; &#931;Fx=0, &#931;Fy=0 diagram; forces and vectors labeled; physics concepts" src="/files/ftp_upload/15055/15055_PT_Equation_2.svg" style="text-align: center; height: 14px;" data-altupdatedat="1761830439000" data-alt="Equation2" />.................(2)
This is known as the maximum power transfer theorem. Using equations 1 and 2, the expression for maximum power transferred is obtained and is expressed as
<img alt="Statics diagram showing force equilibrium with vectors and &#931;Fx=0 equation." src="/files/ftp_upload/15055/15055_PT_Equation_3.svg" style="text-align: center; height: 40px;" data-altupdatedat="1761830439000" data-alt="Equation3" />..................(3)
This Equation applies only when equation 2 is valid, otherwise, the power delivered to the load is determined using Eq. 1.

Maximum Power Transfer

In practical applications, a circuit is designed to deliver maximum power from a source to a load.
A Thevenin equivalent circuit can determine the maximum ...

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load matching in thevenin circuits

Load matching in Thevenin circuits helps a source deliver the most power to a connected load. This matters in engineering fields such as telecommunications, where power delivery must be optimized. Even then, internal losses can be significant and may equal or exceed the power sent to the load.

The Thevenin equivalent circuit is a useful way to study this situation. It replaces the full linear circuit with a simpler source and resistance while keeping the load in place. In this setup, the load resistance is assumed to be adjustable, so the power delivered to it can be tested across different values.

For a fixed circuit, the Thevenin equivalent voltage and resistance do not change. The load power changes only a little when the load resistance is very small or very large. It reaches a maximum at one value between zero and infinity.

The maximum power occurs when the load resistance equals the Thevenin resistance. This condition is called the maximum power transfer theorem. Using the load-power equation and this matching rule, the maximum transferred power can be found. If the matching condition is not met, the load power is determined from the general power equation instead.

Load Matching in Thevenin Circuits

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Load matching in Thevenin circuits helps a source deliver the most power to a connected load. This matters in engineering fields such as telecommunications, where power delivery must be optimized. Even then, internal losses can be significant and may equal or exceed the power sent to the load. The Thevenin equivalent circuit is a useful way to study this situation. It replaces the full linear circuit with a simpler source and resistance while keeping the load in place. In this setup, the load...

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Learn how Thevenin equivalent circuits predict maximum power transfer when load resistance matches Thevenin resistance in linear circuits.

Load Matching in Thevenin Circuits | 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

Load Matching in Thevenin Circuits

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