Biomedical Engineering Reference
In-Depth Information
possible, it is important to verify that the magnitude-frequency response stays at
20 dB per decade
for frequencies less than 0.01 radians/s to the limits of the recording instrumentation.
For frequencies in the range of 2 to 1,000 radians/s, the slope of the gain-frequency graph is
40 dB per decade. Since a pole has already been identified in the previous frequency interval,
it is reasonable to conclude that there is another pole in this interval. Other possibilities exist
such as an additional pole and a zero that are closely spaced, or a complex pole and a zero.
However, in the interests of simplicity and because these possibilities are not evident in the
graphs, the existence of a pole is all that is required to describe the data.
Summarizing at this time, the model contains a pole at the origin and another pole somewhere
in the region above 1 radians/s. It is also safe to conclude that the model does not contain heavily
damped complex poles since the slope of the gain-frequency graph is accounted for completely.
To estimate the unknown pole, straight lines are drawn tangent to the magnitude-frequency
curve as shown in Figure 13.63. The intersection of the two lines gives the break frequency for
the pole at approximately 2 radians/s. Notice that the actual curve is approximately 3dB below
the asymptotes as discussed previously and observed in the following figure.
80
60
40
40 dB/dec
Intersection
20
20 dB/dec
0
0.01
0.1
1
10
100
1000
- 20
-
40
- 60
- 80
-
100
- 120
Frequency (rad/s)
FIGURE 13.63
Straight-line approximations for Example Problem 13.9.
The model developed thus far is
1
G ð j
o
Þ¼
j o
2 þ
jw
1
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