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dB
0.707
0.5
23.6 R-C HIGH-PASS FILTER
1
A v = V o
V i
0.954
318.31 kHz
0.305
10 kHz 100 kHz fc 1 MHz 10 MHz f (log scale)
FIG. 23.18
Normalized plot of Fig. 23.17.
As noted early in Section 23.5, a high-pass R-C filter can be constructed
by simply reversing the positions of the capacitor and resistor, as shown
in Fig. 23.19.
At very high frequencies the reactance of the capacitor is very small,
and the short-circuit equivalent can be substituted, as shown in Fig.
23.20. The result is that V o � V i.
+
V i
–
R
+
V o = 0 V
FIG. 23.20
R-C high-pass filter at very high frequencies.
At f � 0 Hz, the reactance of the capacitor is quite high, and the
open-circuit equivalent can be substituted, as shown in Fig. 23.21. In
this case, V o � 0 V.
A plot of the magnitude versus frequency is provided in Fig. 23.22,
with the normalized plot in Fig. 23.23.
V o = V i
V o = 0.707V i
0
V o
Stop-band
fc Pass-band
FIG. 23.22
V o versus frequency for a high-pass R-C filter.
–
f (log scale)
At any intermediate frequency, the output voltage can be determined
using the voltage divider rule:
V o � R �0° V i
��
R � jXC
+
V i
–
+
V i
–
R-C HIGH-PASS FILTER ⏐⏐⏐ 1033
C
R
FIG. 23.19
High-pass filter.
R
+
–
+
V o
–
V o = 0 V
FIG. 23.21
R-C high-pass filter at f � 0 Hz.