07.02.1
07.02
Trapezoidal Rule for Integration-More Examples
Electrical Engineering
Example 1
All electrical components, especially off-the-shelf components do not match their nominal
value.
Variations in materials and manufacturing as well as operating conditions can affect
their value. Suppose a circuit is designed such that it requires a specific component value,
how confident can we be that the variation in the component value will result in acceptable
circuit behavior? To solve this problem a probability density function is needed to be
integrated to determine the confidence interval.
For an oscillator to have its frequency within
5% of the target of 1 kHz, the likelihood of this happening can then be determined by finding
the total area under the normal distribution for the range in question:
dx
e
x
2
9
.
2
15
.
2
2
2
1
1
a)
Use single segment Trapezoidal rule to find the frequency.
b)
Find the true error,
t
E
, for part (a).
c)
Find the absolute relative true error for part (a).
Solution
a)
2
b
f
a
f
a
b
I
, where
15
.
2
a
9
.
2
b
2
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- Spring '08
- Kaw,A
- Normal Distribution, 5%, 100 %, true error, 1.4276 %, 88.304 %
-
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