lesson 25 ac thèvenin max power transfer. learning objectives explain under what conditions a...
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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?