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+
V g
–
R s
512 �
120 V
Solutions:
a. The source current:
Is � � � �230.8 mA
The power to the speaker:
P � I 2 R � (230.8 mA) 2 E 120 V 120 V
� �� �
RT 512 ��8 � 520 �
⋅ 8 ��426.15 mW � 0.43 W
or less than half a watt.
b. Zp � a 2 ZL a � � � 8
and Zp � (8) 2 8 ��512 �
which matches that of the source. Maximum power transfer conditions
have been established, and the source current is now determined
by
Is � � � �117.19 mA
The power to the primary (which equals that to the secondary for the
ideal transformer) is
P � I 2 R � (117.19 mA) 2 Np 8
� �
Ns 1
E 120 V 120 V
� �� �
RT 512 ��512 � 1024 �
512 ��7.032 W
The result is not in milliwatts, as obtained above, and exceeds 7 W,
which is a significant improvement.
c. Comparing levels, 7.032 W/426.15 mW � 16.5, or more than 16
times the power delivered to the speaker using the impedance matching
transformer.
Another important application of the impedance matching capabilities
of a transformer is the matching of the 300-� twin line transmission
line from a television antenna to the 75-� input impedance of
today’s televisions (ready-made for the 75-� coaxial cable), as shown
in Fig. 21.9. A match must be made to ensure the strongest signal to the
television receiver.
Using the equation Zp � a 2 ZL we find
300 ��a 2 75 �
IMPEDANCE MATCHING, ISOLATION, AND DISPLACEMENT ⏐⏐⏐ 945
8 �
Zp (a) (b)
+
V g
–
FIG. 21.8
Example 21.5.
R s
512 �
120 V
8 : 1
8 �
300 �:75 �
75 �
TV input
FIG. 21.9
Television impedance matching transformer.