Active filters can generate gains greater than one and are easier to interconnect than passive filters by using operational amplifiers with resistors and capacitors. The linear models for operational amplifier circuits remain valid if the resistors are replaced with impedances. Examples show how inverting and non-inverting amplifiers can be used to create basic filters, including low-pass and second-order filters.

1. ACTIVE NETWORK

2. ACTIVE FILTERS
Passive filters have several limitations
1. Cannot generate gains greater than one
2. Loading effect makes them difficult to interconnect
3. Use of inductance makes them difficult to handle
Using operational amplifiers one can design all basic filters, and more,
with only resistors and capacitors
The linear models developed for operational amplifiers circuits are valid, in a
more general framework, if one replaces the resistors by impedances
Ideal Op-Amp
These currents are
zero

3. Basic Inverting Amplifier
0V
  VVgainInfinite
0V
0 II-impedanceinputInfinite
1
1 2
0OVV
Z Z
 
2
1
1
O
Z
V V
Z
 
Linear circuit equivalent
0I
1
2
Z
Z
G 
1
1
1
Z
V
I 

4. EXAMPLE USING INVERTING AMPLIFIER
LOW PASS FILTER

5. Basic Non-inverting amplifier
1V
1V
0I 
1
1
2
10
Z
V
Z
VV


1
1
12
0 V
Z
ZZ
V


1
2
1
Z
Z
G 
01 I

6. EXAMPLE USING NON INVERTING CONFIGURATION

7. EXAMPLE SECON ORDER FILTER
2
( )V s
22 2 2
1 1 2 3
0
1/
OIN
V VV V V V
R C s R R

   
2
2 2
0
1/
O
VV
R C s
  