Active filtering

RHF310

18/22

Doc ID 15577 Rev 3

7

Active filtering

Figure 27.

Low-pass active filtering, Sallen-Key

classic non-inverting amplification configuration.

The response of the system is assumed to be:

The cut-off frequency is not gain-dependent and so becomes:

The damping factor is calculated using the following expression.

The higher the gain, the more sensitive the damping factor. When the gain is higher than 1,

it is preferable to use very stable resistor and capacitor values. In the case of R1=R2=R:

Due to a limited selection of capacitor values in comparison with the resistors, you can set

C1=C2=C, so that:

+

_

R

G

IN

R

fb

1 k

Ω

OUT

R1

R2

C2

C1

AM00843

A

V

g1

R

fb

R

g

--------

+

==

T

j

ω

Vout

j

ω

Vin

j

ω

------------------

g

12

ζ jω

ω

c

------

j

ω

()

2

ω

c

2

-------------

++

-------------------------------------------

==

ω

c

1

R1R2C1C2

-------------------------------------

=

ζ

1

2

---

ω

C

C

C

–

++

()

=

ζ

2C

2

C

1

R

fb

R

g

--------

–

2C

---------------------------------

=

ζ

2R

2

R

1

R

fb

R

g

--------

–

2R

---------------------------------

=