2-22
|
ni.com
Chapter 2
Analog Input and Temperature Sensor Measurements
Figures 2-16 and 2-17 show the Bode Plots for the ideal filter and the real filter, respectively, and
indicate the attenuation of each transfer function.
Figure 2-16.
Transfer Function Attenuation for an Ideal Filter
Figure 2-17.
Transfer Function Attenuation for a Real Filter
The cut-off frequency,
f
c
, is defined as the frequency beyond which the gain drops 3 dB.
Figure 2-16 shows how an ideal filter causes the gain to drop to zero for all frequencies greater
than
f
c
. Thus,
f
c
does not pass through the filter to its output. Instead of having a gain of absolute
zero for frequencies greater than
f
c
, the real filter has a transition region between the passband
and the stopband, a ripple in the passband, and a stopband with a finite attenuation gain.
Real filters have some nonlinearity in their phase response, causing signals at higher frequencies
to be delayed longer than signals at lower frequencies and resulting in an overall shape distortion
of the signal. For example, when the square wave, shown in Figure 2-18, enters a filter, an ideal
filter smooths the edges of the input, whereas a real filter causes some ringing in the signal as
the higher frequency components of the signal are delayed.
P
assba
nd
S
top
ba
nd
Log Fre
qu
ency
G
a
in
f
c
P
assba
nd
S
top
ba
nd
Log Fre
qu
ency
G
a
in
f
c
Tr
a
n
s
ition
Region
