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dB
XLmid � 2pfLmid � 2p(1 kHz)(270 mH) � 1.696 �
1
1
XCmid ������ �3.386 �
2pfCmid 2p(1 kHz)(47 mF)
(ZR �0°)(Vi �0°) (8 � �0°)(4 V �0°)
Vo ��� �����
ZT
8 ��j 1.696 ��j 3.386 �
� 3.94 V �11.93°
XChigh � � �40.81 �
Vo � �
� 0.77 V �78.91°
Using the basic power equation P � V 2 /R, thepower to the woofer is
Plow � � �0.259 W
to the midrange speaker,
Pmid � � �1.94 W
and to the tweeter,
(0.77 V)
Phigh � � �0.074 W
resulting in a power ratio of 7.5�1 between the midrange and the
woofer and 26�1 between the midrange and the tweeter. Obviously, the
response of the midrange speaker will totally overshadow the other two.
2
V
��
8 �
2
(3.94 V)
�
R
2
V
��
8 �
2
(1.44 V)
�
R
2
V
��
8 �
2
1
1
�� ���
2pfChigh 2p(1 kHz)(3.9 mF)
(ZR �0°)(Vi �0°) (8 � �0°)(4 V �0°)
�� ���
ZT
8 ��j 40.81 �
�
R
23.16 APPLICATIONS
Attenuators
Attenuators are, by definition, any device or system that can reduce the
power or voltage level of a signal while introducing little or no distortion.
There are two general types: passive and active. The passive type
uses only resistors, while the active type uses electronic devices such as
transistors and integrated circuits. Since electronics is a subject for the
courses to follow, our attention here will be only on the resistive type.
Attenuators are commonly used in audio equipment (such as the
graphic and parametric equalizers introduced in the previous chapter),
antenna systems, AM or FM systems where attenuation may be
required before the signals are mixed, and any other application where
a reduction in signal strength is required.
The unit of Fig. 23.84 has coaxial input and output terminals and
switches to set the level of dB reduction. It has a flat response from dc
to about 6 GHz, which essentially means that its introduction into the
network will not affect the frequency response for this band of frequencies.
The design is rather simple with resistors connected in either a tee
(T) or a wye (Y) configuration as shown in Figs. 23.85 and 23.86,
respectively, for a 50-� coaxial system. In each case the resistors are
APPLICATIONS ⏐⏐⏐ 1075
50-ohm coax attenuator
IN 1 dB 3 dB 10 dB
2 dB 5 dB 20 dB
FIG. 23.84
Passive coax attenuator.
R 1
R 2
R 1
OUT
Attentuation R 1 R 2
1 dB
2 dB
3 dB
5 dB
10 dB
20 dB
2.9 Ω
5.7 Ω
8.5 Ω
14.0 Ω
26.0 Ω
41.0 Ω
FIG. 23.85
Tee (T) configuration.
433.3 Ω
215.2 Ω
141.9 Ω
82.2 Ω
35.0 Ω
10.0 Ω