midterm2.solutions.2008 - 1 Find the transfer function that...

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Unformatted text preview: 1. Find the transfer function that maps + to for the figure below. Σ - SOLUTION 2. Suppose Starting with the definition of the Laplace transform, compute that the Laplace transform of and the region of convergence. DO NOT use the tables, and DO show all your work. Solution There is no restriction on required to evaluate the integral, so the region of convergence is the entire complex plane. 3. A simple RC low‐pass filter has transfer function of this circuit, when in the input is answer should be a function of time. SOLUTION . Compute , the output volts. There are no initial conditions. Your 4. Consider a circuit described by the differential equation where the initial conditions are all zero. The input is and the output is steady‐state output ( ) of this circuit when the input is ? Solution , Using the final value theorem, Since 5. Find all values of for which the system shown below BIBO stable? + . What is the Σ - SOLUTION The transfer function for the system is For BIBO stability, the pole of the transfer function should have negative real part. Thus we require ...
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