ECE2100 Section 7 Spring2012_solutions

E to determine the constant out front of the

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e) To determine the constant “out front” of the expression involving poles and zeroes, use any “flat spot” on the plot (no slope). Then for frequencies within the range in the “flat spot”, determine whether the corresponding s or ( p,z ) dominates each term. Cancel what you can and find the value of 2 | ) ( | s H for the flat spot (inverse of db value) and then find | ) ( | s H . Evaluate the constant.
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3 2. Find the transfer function H ( s ) = V 2 / V 1 for the circuit shown below. Use the poles and zeroes of H ( s ) to construct a Bode plot for A db ( ω ) = 20log |H ( j ω ) | . Evaluate |H ( j ω ) | as ω . At what value of ω will |H ( j ω ) | be 2 / 1 times its maximum value? Let ) 2 / 1 ( 0 RC = ω where R = 40 k//40 k. 2RC 1
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4 3. Consider the transfer function: ( )( ) + + = 7 3 9 10 10 10 ) ( s s s s H Sketch the asymptotic Bode plot for ( ) 2 ω j H . 4. A certain transfer function is ( ) ( ) ( ) + + + = 5 3 10 10 10 100 ) ( s s s s s H For the corresponding frequency response, complete the following: a) The magnitude at ω 0 will be: 0 ) 0 ( = H b) The magnitude at ω →∞ will be: 100 ) ( = H c) The magnitude at ω = 10 3 will be:
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5 Make the asymptotic Bode plot of 2 | ) ( | ω j H for the transfer function. Compare the plot to the exact magnitudes evaluated at ω = 0, 10, and 10 3 rad/sec and as ω that you found previously. 5. For the asymptotic Bode plot shown below, find the corresponding transfer function H ( s ). (Assume real poles and zeroes and that the constant multiplier is real. Note that A db ( ω ) = 20log 10 | H ( s )|.
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