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mws_ele_int_txt_simpson13_examples

# mws_ele_int_txt_simpson13_examples - Chapter 07.03 Simpsons...

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07.03.1 Chapter 07.03 Simpson’s 1/3 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 Simpson’s 1/3 Rule to find the frequency. b) Find the true error, t E , for part (a). c) Find the absolute relative true error, t , for part (a). Solution a) ) ( 2 4 ) ( 6 1 b f b a f a f a b 15 . 2 a 9 . 2 b 37500 . 0 2 b a 2 2 2 1 ) ( x e x f 2 15 . 2 2 2 1 15 . 2 e f 039550 . 0 2 9 . 2 2 2 1 9 . 2 e f 0059525 . 0

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07.03.2 Chapter 07.03  2 375 . 0
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mws_ele_int_txt_simpson13_examples - Chapter 07.03 Simpsons...

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