High Pass Filter

The transfer function of a high pass filter can be derived in

much the same way as the previous example. A typical first

order high pass filter is shown below:

Writing the KCL for this circuit :

(V

(12)

(13)

Solving these two equations to find the transfer function and

using:

(high frequency gain)

and

Which gives:

(14)

Looking at the transfer function, it is clear that when f/f

small, the capacitor is open and therefore, no signal is

getting to the amplifier. As the frequency increases the am-

plifier starts operating. Atf=f

short circuit and the amplifier will have a constant, high

frequency gain of H

of this high pass filter.

Band Pass Filter

Combining a low pass filter and a high pass filter will gener-

ate a band pass filter. Figure 11 offers an example of this

type of circuit.

In this network the input impedance forms the high pass filter

while the feedback impedance forms the low pass filter. If the

designer chooses the corner frequencies so that f

all the frequencies between, f

1

≤ f ≤ f

filter while frequencies below f

The transfer function can be easily calculated using the

same methodology as before and is shown in Figure 12.

(15)

20179559

FIGURE 8. Low Pass Filter Transfer Function

20179560

FIGURE 9. High Pass Filter

20179564

FIGURE 10. High Pass Filter Transfer Function

20179566

FIGURE 11. Band Pass Filter

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