Active Filtering

TSH350

17/21

8 Active Filtering

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:

Figure 35: Low-pass active filtering, Sallen-Key

+

_

IN

100

Ω

OUT

+

_

IN

100

Ω

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

R1R2C 1C2

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

=

ζ

1

2

---

ω

c

C

1

R

1

C

1

R

2

C

2

R

1

C

1

R

1

g

–

++

()

=

ζ

2C2 C1

R

fb

R

g

----------

–

2C

1

C

2

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

=