© National Instruments
|
4-5
One-Pole Lowpass RC Filter
Figure 4-8 shows the transfer function of a simple series circuit consisting of a resistor (
R
) and
capacitor (
C
) when the voltage across
R
is assumed to be the output voltage (
V
m
).
Figure 4-8.
Simple RC Lowpass Filter
The transfer function is a mathematical representation of a one-pole lowpass filter, with a time
constant of:
Use Equation 4-1 to design a lowpass filter for a simple resistor and capacitor circuit, where the
values of the resistor and capacitor alone determine
f
c
:
(4-1)
where
G
is the DC gain and
s
represents the frequency domain.
Selecting Components for Lowpass Filtering
To determine the value of the components in the circuit, fix
R
(10 k
Ω
is reasonable) and isolate
C
from Equation 4-1 as follows:
(4-2)
The cut-off frequency in Equation 4-2 is
f
c
.
For best results, choose a resistor that has the following characteristics:
•
Low wattage of approximately 0.125 W
•
Precision of at least 5%
•
Temperature stability
•
Tolerance of 5%
•
AXL package (suggested)
•
Carbon or metal film (suggested)
R
C
V
in
V
m
1
2
π
RC
---------------
T s
( )
G
1
2
π
RC
(
)
s
+
-------------------------------
=
C
1
2
π
Rfc
---------------
=
