Active filtering

TSH350

18/22

8

Active filtering

Figure 35.

Low-pass active filtering, Sallen-Key

inverting amplification configuration:

We assume the following expression as 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 some very stable resistor and capacitor values. In the case of

R1=R2=R:

Due to a limited selection of values of capacitors in comparison with resistors, we can set

C1=C2=C, so that:

+

_

R

G

IN

910

100

OUT

+

_

R

G

IN

910

100

OUT

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

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

=