TSH310

Active Filtering

16/19

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:

Due to a limited selection of values of capacitors in comparison with resistors, we can fix C1=C2=C, so

that:

Figure 31: Low-pass active filtering, Sallen-Key

+

_

IN

1k

Ω

OUT

+

_

IN

1k

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

R1 R2C1C2

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

=

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

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

=

ζ

2R2 R1

R

fb

R

g

----------

–

2R

1

R

2

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

=