.Maximum Power Transfer Theorem

Maximum Power Transfer Theorem 

Although applicable to any or all branches of engineering, this theorem is especially helpful for analysing communication networks. the general potency of a network activity most power to any branch is fifty per cent.  For this reason, the applying of this theorem to power transmission and distribution networks is proscribed as a result of, in their case, the goal is high potency and not most power transfer.

However, within the case of electronic and communication networks, very often, the goal is either to receive or transmit most power (through at reduced efficiency) specially once power concerned is just a couple of milliwatts or microwatts.  Frequently, the matter of most power transfer is of crucial significance within the operation of transmission lines and antennas.

As applied to d.c. networks, this theorem is also expressed as follows :

 A resistive load can abstract most power from a network once the load resistance is adequate to the resistance of the network as viewed from the output terminals, with all energy sources removed dropping their internal resistances.

 In Fig. 2.230 (a), a load resistance of RL is connected across the terminals A and B of a network that consists of a generator of e.m.f.  E and internal resistance Rg and a series resistance R that, in fact, represents the lumped resistance of the connecting wires.  Let Ocean State = Rg + R = internal resistance of the network as viewed from A and B.

 In keeping with this theorem, RL can abstract most power from the network once RL = Ocean State.

It is value noting that underneath these conditions, the voltage across the load is hold the open-circuit voltage at the terminals A and B.

Let us think about Associate in Nursing a.c. supply of internal electrical phenomenon (R1 + j X1) activity power to a load electrical phenomenon (RL + jXL).  It are often well-tried that most power transfer can come about once the modules of the load electrical phenomenon is capable the modulus of the supply electrical phenomenon i.e. | ZL | = | Z1 |

Where there's a very free selection concerning the load, the utmost power transfer is obtained once load electrical phenomenon is that the advanced conjugate of the supply electrical phenomenon. for instance, if supply electrical phenomenon is (R1 + jX1), then most transfer power happens, once load electrical phenomenon is (R1 − jX1).  It are often shown that underneath this condition, the load power is = E2/4R1.