Datasheet

j (f/f
o
)
1 + j (f/f
o
)
H = H
O
H
O
=
-R
2
R
1
H =
V
O
V
i
f
O
=
1
2SR
1
C
=
V
-
+ V
O
R
2
V
-
+ V
1
R
1
=
V
1
- V
-
R
1
V
1 -
V
i
1
jwC
V
i
R
1
R
2
+
-
V
OUT
C
dB
0
f = f
o
-20dB/dec
f (Hz)
|H|
|H
O
|
LMV771, LMV772, LMV774
www.ti.com SNOSA04F –MAY 2004–REVISED SEPTEMBER 2010
Figure 8. Lowpass Filter Transfer Function
HIGH PASS FILTER
In a similar approach, one can derive the transfer function of a high pass filter. A typical first order high pass filter
is shown below:
Figure 9. Highpass FIlter
Writing the KCL for this circuit :
(V
1
denotes the voltage between C and R
1
)
(14)
(15)
Solving these two equations to find the transfer function and using:
(16)
(high frequency gain) and
Which results:
(17)
Looking at the transfer function, it is clear that when f/f
O
is small, the capacitor is open and hence no signal is
getting in to the amplifier. As the frequency increases the amplifier starts operating. At f = f
O
the capacitor
behaves like a short circuit and the amplifier will have a constant, high frequency, gain of H
O
. Figure 10 shows
the transfer function of this high pass filter:
Copyright © 2004–2010, Texas Instruments Incorporated Submit Documentation Feedback 17
Product Folder Links: LMV771 LMV772 LMV774