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ECE 3144 Lecture 23

ECE 3144 Lecture 23. Dr. Rose Q. Hu Electrical and Computer Engineering Department Mississippi State University. Method of finding Thevenin equivalent Circuit. Method of finding Norton equivalent Circuit. Maximum Power Transfer.

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ECE 3144 Lecture 23

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  1. ECE 3144 Lecture 23 Dr. Rose Q. Hu Electrical and Computer Engineering Department Mississippi State University

  2. Method of finding Thevenin equivalent Circuit

  3. Method of finding Norton equivalent Circuit

  4. Maximum Power Transfer • Many applications of circuits require that the maximum power available from a source be transferred to a load resistor RL. • Consider the circuit network A, terminated with load RL. A can represent any circuit network, say power utility systems. Power utility systems are designed to transport the power to the load RL with the greatest efficiency by reducing the losses on the power lines and power sources themselves. • How to calculate the maximum power efficiency? We know that the general circuit A can be reduced to its Thevenin (Norton) circuit. i A

  5. Maximum Power Transfer • For the given general circuit, we wish to what is the power delivered to the load resistor RL. • Since current i is • The power delivered to RL is • Since VTH and RTH are fixed for a given source, the power delivered is a function of load resistor RL. To find RL that maximizes the power, we differentiate the power with respect to RL: => =>

  6. Maximum Power transfer • Confirm that RTH= RL gives the maximum power transfer instead of the minimum power transfer. We know that • If RL = 0 => p = i2RL = 0 => p is minimum in this case • if RL =  =>p = vi = 0 => p is also minimum in this case. • So RTH=RLgives maximum power transfer. • The maximum power achieved when RTH = RL • The maximum power transfer theorem states that the maximum power delivered by a source represented by its Thevenin circuit (Norton circuit) is attained when the load is equal to the Thevenin (Norton) resistance RTH (RN). • The maximum power delivered is v2TH /4RL for Thevenin equivalent source The power attained as RL varies is shown as Where

  7. Efficiency of power transfer • The efficiency of power transfer is defined as the ratio of the power delivered to the load, pout, to the power supplied by the source, pin. Therefore we have the efficiency  as • In the ideal source case, all the power supplied by the source is absorbed by the load =>=1. • For practical sources we have discussed, the maximum power transfer happened when RL = RTH. • For the maximum case, power supplied by the source pin and the power absorbed by the load pout are • Therefore only 50% efficiency can be achieved at maximum power transfer conditions

  8. Maximum power transfer for Norton Equivalent circuits io • We may also use Norton circuit to represent circuit A A => Maximum power occurs when RN = RL = RTH The maximum power delivered is

  9. Examples • Provided in the class.

  10. Homework for Lecture 23 • Problems 4.70, 4.71, 4.72, 4.73 • Due March 18

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