Maximum Power Transfer

Maximum Power Transfer occurs when the resistance value of the load is equal to the value of the internal resistance of voltage sources, which allows maximum power to be provided.

In general, this welding resistance or even impedance has a constant value in Ohm when it comes to inductors or capacitors.

However, when we connect an R L load resistance along the output terminals of the power supply, the impedance of the load will change from an open circuit state to a short circuit state, resulting in the dependence of power absorbed by the load.Then, in order for the load resistance to absorb the maximum possible power, it must be "Compatible" with the impedance of the power supply, which forms the basis of the Maximum Power Transfer.

When the maximum power transfer theorem is the value of load resistance equal to full power supply resistance, the maximum amount of power, the relationship between the load impedance and the internal impedance of the energy source will give the power in the load.Consider the circuit below.

Thevenin Equivalent Circuit

Maximum Power Transfer

In our equivalent circuit of thevenin above, the maximum power transfer theorem states that " maximum power will be expended in load resistance if the power-feeding network is equal in value to Thevenin or Norton weld resistance ".

In other words, the load resistance that causes the greatest power loss should be equal to the equivalent Thevenin welding resistance, then R L = R S but if the load resistance is lower or higher than the source resistance of the vein of the network, the spent power will be less than the maximum.

For example, find the load resistance R L value that will give the maximum power transfer in the following circuit.

Maximum Power Transfer Question Sample 1

Maximum Power Transfer

Then, using the following Ohm's Law equations:

Maximum Power Transfer

We can now complete the table below to determine the current and power in the circuit for different load resistance values.

Current Table Against Power

Maximum Power Transfer

Using the data in the table above, we can chart the P load resistance graph against R L power for different load resistance values.Also note that the power for the open circuit (zero current state) as well as the short circuit (zero voltage state) is zero.

Power Chart Against Load Resistance

Maximum Power Transfer

From the table and chart above, when the load resistance, R L, equals the welding resistance, we can see that the Maximum Power Transfer occurs in the load , R S , that is: R S = R L = 25Ω .This is called the "compatible state", and as a general rule, when the impedance of the external device exactly matches the impedance of the source, maximum power is transferred from an active device such as a power supply or battery to an external device.

A good example of impedance compatibility is between a sound amplifier and a speaker. The output impedance of the amplifier can be given between Z OUT 4Ω and 8Ω, while the nominal input impedance of the speaker, Z IN can only be given as 8Ω.

Then, if an 8Ω speaker is installed on the amplifier output, the amplifier sees the speaker as an 8Ω load.Connecting two 8Ω speakers in parallel is equivalent to the amplifier driving a 4Ω speaker, and both configurations are within the amplifier's output capabilities.

Improper impedance pairing can cause excessive power loss and heat dissipation.But how can you pair the impedance of an amplifier and speaker with very different impedances?There are existing speaker impedance matching transformers that can change from impedances.

Transformer Impedance Pairing

Signal transformers are used to match the higher or lower impedance value of the speakers to the amplifier's output impedance to achieve maximum audio power output.These sound signal transformers are called "compatible transformers" and connect the load to the amplifier output, as shown below.

Transformer Impedance Pairing

Maximum Power Transfer

Maximum power transfer can be achieved even if the output impedance is not the same as the load impedance.This matches the ratio of primary rotations to secondary rotations as a resistance on one side of the transformer, using a suitable "rotation rate" on the transformer, the corresponding ratio of the load impedance, Z LOAD – output impedance, Z OUT. the transformer changes to a different value in the other.

If the load impedance, Z LOAD is fully resistant and the welding impedance is fully resistant, the equation to find the maximum power transfer of Z OUT is given as follows:

Maximum Power Transfer

Where: N P is the number of primary turns, and N S is the number of secondary rotations in the transformer.Then, by changing the value of the rotational ratios of transformers, the output impedance can be "paired" with the welding impedance to achieve maximum power transfer.For example

Maximum Power Transfer Question Sample 2

8Ω speaker 1000 to be connected to an amplifier with an output impedanceΩ calculate the rate of transformer mapping rotations required to ensure the maximum power transfer of the audio signal.Suppost that the amplifier welding impedance is Z 1, the return rate of the load impedance given as N is Z 2.

Maximum Power Transfer
Maximum Power Transfer

In general, small high frequency audio transformers used in low-power amplifier circuits are almost always considered ideal for simplicity, so any loss can be ruled out.

In the next lesson on DC circuit theory, we will look at the equivalent delta of balanced star-linked circuits and the Star Delta Transformation, which allows us to do the opposite.