mws_ele_int_txt_romberg_examples

# mws_ele_int_txt_romberg_examples - Chapter 07.05 Romberg...

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07.05.1 Chapter 07.05 Romberg 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 Table 1 Values obtained for Trapezoidal rule. n Trapezoidal Rule 1 0.11489 2 0.99637 4 0.96969 8 0.97901 a) Use Richardson’s extrapolation formula to find the frequency. Use the 2-segment and 4-segment Trapezoidal rule results given in Table 1.

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