Low Pass Filter

(20)

High Pass Filter

(21)

Band Pass Filter

(22)

The center frequency and Quality Factor for all of these

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

following manner:

(23)

Designing a band pass filter with a center frequency of 10

kHz 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:

(24)

or

R

R

Ω

R

Ω

(25)

Also,

forf=10

kHz,

the

center

frequency

is

ωc=2πf = 62.8 kHz.

Using the expressions above, the appropriate resistor values

will be R

Ω.

The DC gain of this circuit is:

(26)

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