LMV771 datasheet(14/21 Pages) NSC

14 / 21 page

Application Note (Continued)

ACTIVE FILTER

Active Filters are circuits with amplifiers, resistors, and ca-

pacitors. The use of amplifiers instead of inductors, which

are used in passive filters, enhances the circuit performance

while reducing the size and complexity of the filter.

The simplest active filters are designed using an inverting op

amp configuration where at least one reactive element has

been added to the configuration. This means that the op amp

will provide "frequency-dependent" amplification, since reac-

tive elements are frequency dependent devices.

LOW PASS FILTER

The following shows a very simple low pass filter.

The transfer function can be expressed as follows:

By KCL:

(7)

Simplifying this further results in:

(8)

(9)

Now, substituting

ω=2πf, so that the calculations are in f(Hz)

and not

ω(rad/s), and setting the DC gain

and

(10)

Set:

(11)

Low pass filters are known as lossy integrators because they

only behave as an integrator at higher frequencies. Just by

looking at the transfer function one can predict the general

form of the bode plot. When the f/f

O ratio is small, the

capacitor is in effect an open circuit and the amplifier be-

haves at a set DC gain. Starting at f

O, −3dB corner, the

capacitor will have the dominant impedance and hence the

circuit will behave as an integrator and the signal will be

attenuated and eventually cut. The bode plot for this filter is

shown in the following picture:

20039673

FIGURE 2. CMRR vs. Frequency

20039647

FIGURE 3.

20039653

FIGURE 4.

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