RHF330

Active filtering

Doc ID 15576 Rev 3

19/22

8

Active filtering

Figure 33.

Low-pass active filtering, Sallen-Key

inverting amplification configuration.

We assume the following expression is the response of the system.

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

The damping factor is calculated by the following expression.

The higher the gain, the more sensitive the damping factor is. 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, we can set

C1=C2=C, so that:

+

_

R

G

IN

R

fb

100

Ω

OUT

R1

R2

C2

C1

AM00840

A

V

g1

R

fb

R

g

--------

+

==

T

j

ω

Vout

j

ω

Vin

j

ω

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

g

12

ζ

j

ω

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

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

=