LMV771 datasheet(17/21 Pages) NSC

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Application Note (Continued)

This relationship depends on the output of all the filters. The

input-output relationship for A

2 can be expressed as:

And finally this relationship for A

3 is as follows:

Re-arranging these equations, one can find the relationship

between V

O and VIN (transfer function of the lowpass filter),

O1 and VIN (transfer function of the highpass filter), and VO2

and V

IN (transfer function of the bandpass filter) These rela-

tionships are as follows:

Lowpass filter

Highpass filter

Bandpass Filter

The center frequency and quality factor for all of these filters

is the same. The values can be calculated in the following

manner:

A design example is shown here:

Designing a bandpass filter with center frequency of 10kHz

and Quality factor of 5.5

To do this, first consider the quality factor. It is best to pick

convenient values for the capacitors. C

2 =C3 = 1000pF.

Also, choose R

1 =R4 = 30k

Ω. Now Values of R

5 and R6

need to be calculated. With the chosen values for the ca-

pacitors and resistors, Q reduces to:

5 = 10R6

6 = 1.5k

Ω

5 = 15k

Ω

Also, for f = 10kHz, value of center frequency is

c =2

πf=

62.8kHz.

Using the expressions above, the appropriate resistor values

will be R

2 =R3 = 16k

Ω.

The following graphs show the transfer function of each of

the filters. The DC gain of this circuit is:

20039690

The following graphics show the frequency response of each

of the stages when using LMV774 as the amplifier:

20039691

FIGURE 10. Lowpass Filter Frequency Response

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