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EECS 314 Fall 2006 HW 07 Problem 1
Student's name ___________________________
(Last name, first name,
IN INK)
The big picture
Transformers can help match
the source and load
impedances and thus achieve
the maximal power transfer
from the given source to the
given load.
Read the lecture notes and
section 7.3 in Rizzoni’s text
for discussion and examples.
Problem
Consider an audio amplifier as the voltage source
V
T
= (80 V)
⋅
cos(
ω
t)
with the equivalent impedance (equivalent resistance)
Z
T
= R
T
= 60
Ω
, and the speaker as a load with
Z
LOAD
= 8
Ω
.
Hints:
A.
In each part of the problem, use the formulas for the average AC power. Notice
that, although you do NOT need phasors (there is no phase shift between the
voltage and the current in this circuit), the voltage is sinusoidal (not DC) thus you
have to use the formulas for AC voltage and average power (not for DC voltage
and DC power).
B.
In each part 2, 3 of the problem, reduce the original circuit (top diagram) to its
equivalent (bottom diagram) and determine the apparent load impedance.
C.
In Part 2, you know the apparent load impedance: it must equal the complex
conjugate of the source impedance: since the source impedance is pure resistance,
the load impedance is also pure resistance (the phase shift between the voltage
and current is zero).
D.
In Part 3, a very good replacement ensures power transfer (relative to the
maximal) of 90% and above, a good replacement ensures 80% and above, and an
acceptable replacement ensures 70% and above.
Part 1
Consider the circuit with the given source and the given load, connected directly, without
any transformer. Calculate the average power
P
1
in watts transferred to the load.
The problem is continued on the next page
© 2006 Alexander Ganago
Page 1 of 2
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View Full DocumentEECS 314 Fall 2006 HW 07 Problem 1
Student's name ___________________________
(Last name, first name,
IN INK)
Part 2
Consider the circuit with the same source and the same load, connected through a
transformer, which is specially chosen to achieve maximal power transfer. The
transformer has
n
1
= 1000
turns in its primary coil. Calculate the number of turns
n
2
in the secondary coil and the average power
P
MAX
in watts transferred to the load.
Calculate the ratio of powers
P
1
/ P
MAX
Part 3
Assume that you found a transformer that has
300
turns in one coil and
600
turns in the
other coil, and decided to use it in this circuit for impedance matching.
Which coil would you use as the primary?
What average power
P
3
in watts is transferred to the load in a circuit with this
transformer?
Calculate the ratio of powers
P
3
/ P
MAX
Write a brief conclusion on whether this transformer is a good replacement for the perfect
transformer discussed in Part 2 (see Hint D above).
Write your results below.
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 Fall '09
 Ganago
 Impedance

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