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# set18new - ECE3050 Assignment 18 1 Sketch and label the...

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ECE3050 Assignment 18 1. Sketch and label the Bode magnitude and phase plots for the transfer functions given. Use log- log scales for the magnitude plots and linear-log scales for the phase plots. On the magnitude plots, label the slopes of all asymptotes in dec/dec, label the break frequencies in rad/s, label the gain magnitude on all zero-slope asymptotes, and label the approximate gain magnitude for the actual plot at the break frequencies. You can check your plots with a convenient computer program, e.g. PSpice , Mathcad, MatLab, etc., to obtain computer generated plots. An example PSpice deck is given for one of the transfer functions. The output voltage is V(2) , i.e. the voltage at node 2 . It is obtained by the LAPLACE statement, which multiplies the voltage V(1) by the transfer function after the word LAPLACE .They -ax isinthe PSpice Probegraph icsrout inemustbechangedtoalogsca letoseethecorrects lopesontheBode magnitude plot. The number of decades displayed on the y-axis should be changed to no more than 3 or 4 to get the best looking plot. T ( s )=10 1 1+ s/ 100 T ( s )=10 s/ 100 1+ s/ 100 T ( s )= 10 (1 + s/ 100) (1 + s/ 1000) T ( s )=10 ( s/ 1000) 2 (1 + s/ 100) (1 + s/ 10000) T ( s )= 10 ( s/ 100) 2 +2( s/ 100) + 1 T ( s )=10 ( s/ 100) 2 ( s/ 100) 2 +2( s/ 100) + 1 T ( s ) = 100 2( s/ 100) ( s/ 100) 2 +2( s/ 100) + 1 T ( s )=10 ( s/ 100) 2 +1 ( s/ 100) 2 +2( s/ 100) + 1 T ( s )=10 1 ( s/ 100) 2 + 2( s/ 100) + 1 T ( s )=10 ( s/ 100) 2 ( s/ 100) 2 + 2( s/ 100) + 1 T ( s ) = 100 2( s/ 100) ( s/ 100) 2 + 2( s/ 100) + 1 T ( s )=10 ( s/ 100) 2 +1 ( s/ 100) 2 + 2( s/ 100) + 1 T ( s )=10 1 ( s/ 100) 2 +0 . 5( s/ 100) + 1 T ( s )=10 ( s/ 100) 2 ( s/ 100) 2 +0 . 5( s/ 100) + 1 T ( s ) = 100 0 . 5( s/ 100) ( s/ 100) 2 +0 . 5( s/ 100) + 1 T ( s )=10 ( s/ 100) 2 +1 ( s/ 100) 2 +0 . 5( s/ 100) + 1 T ( s )=10 s/ 10 1 s/ 10 + 1 T ( s )=10 ( s/ 100) 2 2( s/ 100) + 1 ( s/ 100) 2 + 2( s/ 100) + 1 EXAMPLE TRANSFER FUNCTION BODE PLOT VS10AC1 E1 2 0 LAPLACE {V(1)}={10*PWR(S/100,2)/(PWR(S/100,2)+SQRT(2)*S/100+1)} .AC DEC 50 1 100K .PROBE .END 2. The f gure shows an RLC circuit. Show that the voltage gain transfer function is of the form T ( s )= ( s/ω 0 ) 2 ( s/ω 0 ) 2 +

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where you must give the equations for ω 0 and Q .F o r Q =0 . 5 , show that the transfer function becomes T ( s )= ( s/ω 0 ) 2 ( s/ω 0 +1) 2 For Q< 0 . 5 , show that the transfer function becomes T ( s )= s/ω 1 s/ω 1 +1 s/ω 2 s/ω 2 +1 where ω 1 , 2 = ω 0 1 2 Q ± s μ 1 2 Q 2 1 Sketch the Bode magnitude and phase plots as a function of ω for the cases Q< 0 . 5 , Q =0 . 5 , and Q> 0 .
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## This note was uploaded on 05/25/2011 for the course ECE 3050 taught by Professor Hollis during the Summer '08 term at Georgia Tech.

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set18new - ECE3050 Assignment 18 1 Sketch and label the...

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