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946 ⏐⏐⏐ TRANSFORMERS
Public address
system
Very low output impedance
+
70.7 V
–
and a �
300 �
� ��75 �
� �4� � 2
with N p : N s � 2 : 1 (a step-down transformer)
EXAMPLE 21.6 Impedance matching transformers are also quite evident
in public address systems, such as the one appearing in the 70.7-V
system of Fig. 21.10. Although the system has only one set of output
terminals, up to four speakers can be connected to this system (the
number is a function of the chosen system). Each 8-� speaker is connected
to the 70.7-V line through a 10-W audio-matching transformer
(defining the frequency range of linear operation).
FIG. 21.10
Public address system.
8 � 10 W
matching audio
transformers
8 � speakers
a. If each speaker of Fig. 21.10 can receive 10 W of power, what is the
maximum power drain on the source?
b. For each speaker, determine the impedance seen at the input side of
the transformer if each is operating under its full 10 W of power.
c. Determine the turns ratio of the transformers.
d. At 10 W, what are the speaker voltage and current?
e. What is the load seen by the source with one, two, three, or four
speakers connected?
Solutions:
a. Ideally, the primary power equals the power delivered to the load,
resulting in a maximum of 40 W from the supply.
b. The power at the primary:
Pp � VpIp � (70.7 V) Ip � 10 W
10 W
and Ip ��� 141.4 mA
70.7 V
70.7 V
so that Zp � � � �� � 500 �
Ip 141.4 mA
c. Z p � a 2 Z L ⇒ a � �� � �� � �6�2�.5� � 7.91 � 8:1
V p
V p
Zp �
ZL
500 �
�
8 �
70.7 V
d. Vs � VL � � ��� 8.94 V � 9 V
a 7.91