Obtaining maximum "benefit" from power source

[chuackl]

In Thevenin maximum power transfer theorem it state that the load resistance,RL must be equal to internal resistance of the source,Rin. However, the efficiency of the circuit is just 50%. At here, can i say i use power source in a more effective way if be able to have an output of higher efficiency and at the same time considerable high output voltage but this output voltage will be slightly lower abit than when RL=Rin. The efficinecy will be higher alot if using RL>>Rin but the amount of output voltage will be extremely low. So in order to choose a load resistor give optimization to power saving and total output power, can consider it as a product of efficiency and total oputput power?

here i let X=efficiency*output power and consider a voltage source connected in series with an internal resistance and a load resistance,nRin where n is the value to be find.

efficiency=Pout/Pin=V^2[(nRin)/(Rin+nRin)^2]/V^2(nRin+Rin)=n/(1+n)
output power=v^2(nRin)/(n+1)^2Rin^2)=(V^2/Rin)(n/(n+1)^2)

hence X=n^2/(n+1)^3[V^2/Rin]
differentiate it with respect to n using UV method will finally get
dx/dn=[n/(n+1)^3][2-[3n/(n+1)]]
when dx/dn=0 n=0(rejected) and n=2
so at here, can i say if i take into consideration of power saving and the amount of output power dissipated, taking n=2 will give me what i want? a desirable high efficinecy and high output power.

 

[FvM]

I don't understand, what you want to calculate.

Thevenin's theorem is giving the unique power transfer maximum. If the voltage source's Rin is given, maximum efficiency will be achived at RL = inifinity (no load), because eta = f(RL) is monotone. A reasonable problem would be e.g. to calculate RL for a specified efficiency value.

 

[chuackl]

As i mention above if putting load resistance which is very large, the efficiency of course will reach almost 100% but the output power is extremely small. I just considering in finding a suitable load resistance value that will give optimization in power saving and output power. Using this method to find it is not correct? Higher efficiency also mean it is more power saving in a circuit correct? Well let's say in a circuit the output performance is related by factor A,factor B and factor C. For factor A and B the higher the value the better while for factor C it is a factor that we don't want. There is a set of value given to A, B and C. When come to comparison which set of value is better isn't we can formulate the performance as (A*B)/C? while the set of value that can provide biggest value of (A*B)/C is the best choice for us or it can also put it this way something like i "sacrifice" some output power(putting higher load resistance) but i get a large increase in efficiency. However after some point i "sacrifice" the output power(putting larger and larger resistance) it only cause the efficiency to increase a bit only which is not worth to be consider. So where is the optimum point in power saving at the same time giving high output power(of course power will be lower abit than thevenin maximum power transfer theorem). So differentiate it with respect to the product of efficiency and output power is not something to be consider?

 

[FvM]

What do you think is the physical meaning of the product Pout*efficiency? I don't see any, i think it's just an arbitray quantity and maximizing the value is simply meaningless.

 

[chuackl]

hmm, may be you are right but i just considering the case for a pure resistor network a heater(load resistance) and a internal resistance connected in series. Lets say i put different load resistance, load A may be giving me an efficiency of X and output power of Z, load B may be giving an efficiency of C and output power of D and etc. If i consider from the spec of saving power and the power output provided the calculation have nothing to do with it?

 

[snafflekid]

the maximum power transfer theorem shows how to the the maximum amount of power from the source into the load. Transferring the power efficiently is not a requirement of the theorem.

Search the term "maximum power transfer"

 

[FvM]

the maximum power transfer theorem shows how to the the maximum amount of power from the source into the load. Transferring the power efficiently is not a requirement of the theorem.

This has been taken as granted by the original poster...