Linggo, Oktubre 12, 2014

Week 12: Maximum Power Transfer

Maximum Power Transfer

What is Maximum Power Transfer?
-In electrical engineering, the maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals. Moritz von Jacobi published the maximum power (transfer) theorem around 1840; it is also referred to as "Jacobi's law".

The theorem results in maximum power transfer, and not maximum efficiency. If the resistance of the load is made larger than the resistance of the source, then efficiency is higher, since a higher percentage of the source power is transferred to the load, but the magnitude of the load power is lower since the total circuit resistance goes up.
If the load resistance is smaller than the source resistance, then most of the power ends up being dissipated in the source, and although the total power dissipated is higher, due to a lower total resistance, it turns out that the amount dissipated in the load is reduced.
The theorem states how to choose (so as to maximize power transfer) the load resistance, once the source resistance is given. It is a common misconception to apply the theorem in the opposite scenario. It does not say how to choose the source resistance for a given load resistance. In fact, the source resistance that maximizes power transfer is always zero, regardless of the value of the load resistance.

Procedures in applying Maximum Power Transfer:
·        * Apply Thevenin’s Theorem on a circuit
·        *  Solve for VTh and RTh

·        * Apply the power delivered to the load resistance (RL) and RL = RTh, The formula for power delivered to RL is:

* To find the maximum power, differentiate the above expression with respect to resistance RL and equate it to zero. Thus,
Thus in this case, the maximum power will be transferred to the load when load resistance is just equal to internal resistance of the battery.

Example:
Find the power dissipated by the 0.8 resistor.  
With this value of load resistance, the dissipated power will be 39.2 watts:
If we were to try a lower value for the load resistance (0.5 Ω instead of 0.8 Ω, for example), our power dissipated by the load resistance would decrease:
Power dissipation increased for both the Thevenin resistance and the total circuit, but it decreased for the load resistor. Likewise, if we increase the load resistance (1.1 Ω instead of 0.8 Ω, for example), power dissipation will also be less than it was at 0.8 Ω exactly:

Reflection:
The Maximum Power Transfer Theorem is not so much a means of analysis as it is an aid to system design. Simply stated, the maximum amount of power will be dissipated by a load resistance when that load resistance is equal to the Thevenin/Norton resistance of the network supplying the power. In solving for problems like these, It is very important that we have a correct Thevenin/Norton equivalent circuit because if Vth and Rth is wrong, then the power dissipated by the load resistance (RL) will also be wrong.

Video(s):
Video that will explain more about the derivation in the procedure


Maximum Power Transfer

“Every idea is in the soul of its owner. No other power can shift it to another soul, that is why we have the telephone, aircraft, etc, each having its unique inventor.”
― Michael Bassey Johnson

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