Datasheet

1
1 + j (f/f
o
)
H = H
O
H = H
O
1
j2SfcR
2
+1
R
1
1
jwcR
2
+1
-R
2
V
i
V
O
=
V
O
=
V
i
R
1
1
jwcR
2
+1
-R
2
- -
-V
i
R
1
V
O
R
2
= O
V
O
1
jwc
V
i
R
1
R
2
+
-
V
OUT
C
LMV771, LMV772, LMV774
SNOSA04F –MAY 2004–REVISED SEPTEMBER 2010 www.ti.com
ACTIVE FILTER
Active filters are circuits with amplifiers, resistors, and capacitors. The use of amplifiers instead of inductors,
which are used in passive filters, enhances the circuit performance while reducing the size and complexity of the
filter.
The simplest active filters are designed using an inverting op amp configuration where at least one reactive
element has been added to the configuration. This means that the op amp will provide "frequency-dependent"
amplification, since reactive elements are frequency dependent devices.
LOW PASS FILTER
The following shows a very simple low pass filter.
Figure 7. Lowpass Filter
The transfer function can be expressed as follows:
By KCL:
(9)
Simplifying this further results in:
(10)
or
(11)
Now, substituting ω=2πf, so that the calculations are in f(Hz) and not ω(rad/s), and setting the DC gain H
O
=
−R
2
/R
1
and H = V
O
/V
i
(12)
Set: f
o
= 1/(2πR
1
C)
(13)
Low pass filters are known as lossy integrators because they only behave as an integrator at higher frequencies.
Just by looking at the transfer function one can predict the general form of the bode plot. When the f/f
O
ratio is
small, the capacitor is in effect an open circuit and the amplifier behaves at a set DC gain. Starting at f
O
, −3dB
corner, the capacitor will have the dominant impedance and hence the circuit will behave as an integrator and
the signal will be attenuated and eventually cut. The bode plot for this filter is shown in the following picture:
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