# Why maximum power transfer condition is suitable for communication system but not for transmission of electricity?

A fundamental concept that i have learned from basic electrical circuit study is to receive maximum power by a load of resistance RL from a source the necessary condition is RL = Rin where Rin is the input resistance seen by the load. This is called maximum power transfer theorem. But the efficiency in this condition is 50%.

Then it is said that, the maximum power transfer condition is the best choice to transmit signal in communication system. Since we need the signal with maximum strength at the receiving end.

But in power transmission we target to receive as much higher efficiency as possible. That's why maximum power transfer condition is not a desirable feature in this case.

My question is, whether the above two paragraphs are true or not? If true then, why maximum receiving power wouldn't be a desirable feat for electricity transmission?

Those statements are true. But I see what bothers you. You have to imagine it like this:

In Wireless transmission one wants to make the highest loss possible since this loss will actually be the power of the transmitted signal. This is a very easy optimization problem which will lead to the fact you have stated $$R_L = R_{in}.$$

In power transmission however the goal is to be as efficient as possible. This will still lead to the fact that the highest power output is achieved with $$R_L = R_{in}.$$ But thats the maximum you could get out e.g. of a transformer. You don't want it to operate in this point. Instead you lay out your transformer in such a way that it won't reach this point. Then the efficiency is much higher but you won't be using its full potential.

You might have noticed this when e.g. trying to charge a tablet with phone charger. It may works and the charger maxes out, but it gets hot since much energy is converted to heat because of the high internal loss. (Keep in mind that a phone charger is not only a transformer). You take a bigger charger which won't max out, is may oversized but has a higher efficiency.

The theorem was originally misunderstood (notably by Joule) to imply that a system consisting of an electric motor driven by a battery could not be more than 50% efficient since, when the impedances were matched, the power lost as heat in the battery would always be equal to the power delivered to the motor.

This is also good explained in Wikipedia:

In 1880 this assumption was shown to be false by either Edison or his colleague Francis Robbins Upton, who realized that maximum efficiency was not the same as maximum power transfer.

• I see, so maximum power transfer gives you the maximum power that you can absorb from source but in that case you loose half of your generated power. But when RL >> Rin, then you won't achieve that max power but your absorb power will be nearly equal to the generated power and hence less loss in the transmission process. Is that it? – Sabbir Ahmed Nov 26 '18 at 14:46
• @SabbirAhmed yes you got it :) – Mr.Sh4nnon Nov 26 '18 at 14:48
• @Mr.: There's something not quite right about the sentence "... the efficiency is much higher but you won't be using its full potential." The transformer magnetics and wire gauge will be close to maxed out at rated output power so we've pretty much used up all its potential. I can't think of a better wording though. Can you? – Transistor Nov 26 '18 at 16:53
• @Transistor nope your right. That sound way better! – Mr.Sh4nnon Nov 26 '18 at 16:56

In "maximum power transfer theorem" you model a system with a power source $$\V_s\$$ and a $$\R_{in}\$$ and $$\R_{load}\$$.

we can generate a source with low $$\R_{in}\$$ and we can get high current and neglect the internal power dissipation.

Wiki: https://en.wikipedia.org/wiki/Maximum_power_transfer_theorem As the link said when Rs -> 0 then the efficiency is "1"

But many communication circuits are distributed circuits not lumped circuits. For an antenna with $$\R_{Antenna}\$$ if the source impedance is not as same as the source impedance, this causes reflection.

As wiki said "the result being very sensitive to the electrical length of the transmission line. " Wiki: https://en.wikipedia.org/wiki/Standing_wave_ratio

In receive mode, we get a signal from an antenna with $$\R_{Antenna}\$$ and the antenna is the source $$\V_s\$$. The theory said that for best detection the SNR should be as high as possible. so we need impedance matching.