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

input-output relationship for A

And finally this relationship for A

Re-arranging these equations, one can find the relationship

between V

V

and V

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

Also, choose R

Ω. Now Values of R

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

pacitors and resistors, Q reduces to:

or

R

R

Ω

R

Ω

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

ω

πf=

62.8kHz.

Using the expressions above, the appropriate resistor values

will be R

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

www.national.com

17