Lesson 25AC ThèveninMax Power Transfer

Learning Objectives Explain under what conditions a source transfers

maximum power to a load. Determine the value of load impedance for which

maximum power is transferred from the circuit.

Determining ETh Remove the load (open-circuit) and measure the

resulting voltage.

Review

Eth = open ckt voltage

Determining ZTh With the load disconnected, turn off all

independent sources. Voltage sources – 0 V is equivalent to a short-circuit. Current sources – 0 A is equivalent to a open-circuit.

ZTh is the equivalent resistance looking into the “dead” circuit through terminals a-b.

Zth

Review

Example Problem 1

Convert the source below into a Thévenin equivalent and determine the power dissipated by the load.

Conjugates

The conjugate of C is written as C*, which has the same real value but the opposite imaginary part:

a jb C

a jb C

C

C

Review

Maximum power transfer theorem Maximum power is transferred to the load

when RLD = RTh.

2

4Th

MAX

Th

PRE

Review

In AC circuits, max power transfer occurs when load impedance (ZL) is the complex conjugate of the Thévinin equivalent impedance (ZTh).

This means the load has a capacitor if the Thèvenin impedance includes an inductor

XLD cancels out XTH!

Max Power Transfer in AC Circuits

TH TH TH LD LD LDR jX R jX Z Z

Since RLD=RTH, and the reactances cancel out, the resulting PMAX equation is the same as with DC!

Max Power Transfer in AC Circuits

2 2

22

2

( ) ( )

2

2 4

4

LD LD LD TH TH TH

Th ThL

Th LD Th LD Th LD

Th Th ThTh LD

Th LD Th Th Th

Th ThL L LD LD Th

Th Th

Th

Th

R jX R jX

R R j X X

R RR R R R R

E EP I R R R

R R

E

R

Z Z

E EI

Z Z

E E E

since

#1 Mistake with AC Max Power is not using the REAL value of resistance when calculating Pmax

Transform ZTH into rectangular form to determine RTH

Max Power Transfer in AC Circuits

2

max 4

TH TH TH

ThLD T

T

h

H

Th

R jX

E

R

Z

P

Z

Z Z when

X

Example Problem 2

Determine the load ZLOAD that will allow maximum power to be delivered to the load the circuit below. Find the power dissipated by the load.

Example Problem 3Determine the load ZLD that will allow maximum power to be delivered to the load the circuit below. Frequency is 191.15 Hz. Find the maximum power. What will happen to power if the frequency is changed to 95.575?