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HIGH PASS FILTER
In a similar approach, one can derive the transfer function of
a high pass filter. A typical first order high pass filter is shown
below:
FIGURE 5. Highpass FIlter
Writing the KCL for this circuit :
(V
denotes the voltage between C and R
1
Solving these two equations to find the transfer function and
using:
(high frequency gain)
Which results:
Looking at the transfer function, it is clear that when f/f
small, the capacitor is open and hence no signal is getting in
to the amplifier. As the frequency increases the amplifier
starts operating. At f = f
the capacitor behaves like a short
O
circuit and the amplifier will have a constant, high frequency,
gain of H
. Figure 6 shows the transfer function of this high
O
pass filter:
20039654
)
1
(12)
(13)
and
(14)
is
O
FIGURE 6. Highpass Filter Transfer Function
BAND PASS FILTER
FIGURE 7. Bandpass Filter
Combining a low pass filter and a high pass filter will generate
a band pass filter. In this network the input impedance forms
the high pass filter while the feedback impedance forms the
low pass filter. Choosing the corner frequencies so that f
f
, then all the frequencies in between, f
2
through the filter while frequencies below f
be cut off.
The transfer function can be easily calculated using the same
methodology as before.
Where
The transfer function is presented in the following figure.
15
20039658
20039660
<
1
≤
≤
f
f
, will pass
1
2
and above f
will
1
2
(15)
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