Exam3_Info.pdf - ECE 2210 Exam 3 Useful Information Bode Plots Look for places in |H(s)| where a real number and a jω or jf term are added Set real =

# Exam3_Info.pdf - ECE 2210 Exam 3 Useful Information Bode...

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ECE 2210 Exam 3 Useful Information Bode Plots Look for places in | H(s) | where a real number and a j ϖ or jf term are added. Set real = |imaginary| to find poles and zeroes. Slopes: -20, 0, or +20 dB/decade Poles come from denominator of transfer function, zeroes from numerator. dB is . 20 log 10 ( ) H ( ) ϖ Divide frequencies into regions & find approx | H(s) | in each region by simplifying each (real + imaginary) to just the largest part. cut corners by . 3 dB 2nd order tran. Overdamped b 2 . 4 k > 0 s 1 and s 2 are real and negative X ( ) t = X ( ) . B e . s 1 t . D e . s 2 t X ( ) 0 = X ( ) B D d d t X ( ) 0 = . B s 1 . D s 2 Critica lly damped b 2 . 4 k = 0 s 1 = s 2 = b 2 = s s 1 and s 2 are real, equal and negative X ( ) t = X ( ) . B e . s t . . D t e . s t B = X ( ) 0 X ( ) D = d d t X ( ) 0 . B s Underdamped b 2 . 4 k < 0 s = α + j ϖ complex s 1 and s 2 X ( ) t = X ( ) . e . α t ( ) . B cos ( ) . ϖ t . D sin ( ) . ϖ t B = X ( ) 0 X ( ) D = d d t X ( ) 0 . B α ϖ d d t i L ( ) 0 = v L ( ) 0 L d d t v C ( ) 0 = i C ( ) 0 C Final Conditions, or "after a long time"
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