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1036 ⏐⏐⏐ DECIBELS, FILTERS, AND BODE PLOTS
1
0.707
0
90°
45°
0
A v = V o
V i
Low-pass
f c = 6631.46 Hz f (log scale)
1
1
Av � � �—— ���
2 �1� �� (�2�) �
�1� � ��� �4 2� 0
0� k
k� �
Vo 1
� ——
2
Vi
� �1� ���� �X �
���
�
v � tan �1
1
���0.4472 �5�
X C
� R
� tan �1
R� C ��� 2
40 k�
� 20 k�
V o
� tan �1 2 � 63.43°
and Av ��� 0.4472 �63.43°
Vi
23.7 PASS-BAND FILTERS
1
0.707
A v = V o
V i
High-pass
dB
0 f c = 6631.46 Hz f (log scale)
FIG. 23.26
Normalized plots for a low-pass and a high-pass filter using the same elements.
� θ (Vo lags Vi )
� θ (Vo leads Vi )
Low-pass
f c = 6631.46 Hz f (log scale)
90°
45°
0
High-pass
FIG. 23.27
Phase plots for a low-pass and a high-pass filter using the same elements.
f c = 6631.46 Hz f (log scale)
A number of methods are used to establish the pass-band characteristic
of Fig. 23.7(c). One method employs both a low-pass and a high-pass
filter in cascade, as shown in Fig. 23.28.
The components are chosen to establish a cutoff frequency for the
high-pass filter that is lower than the critical frequency of the low-pass
filter, as shown in Fig. 23.29. A frequency f 1 may pass through the low-
+
V i
–
High-pass
filter
FIG. 23.28
Pass-band filter.
Low-pass
filter
+
V o
–