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
SM73308
SNOSB90B –JUNE 2011–REVISED APRIL 2013 www.ti.com
Figure 44. 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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