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ee541F11HWSolutions03

# ee541F11HWSolutions03 - EE 541 University of Southern...

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EE 541 University of Southern California Viterbi School of Engineering Choma Solutions, Homework #03 35 Fall Semester, 2011 U U U niversity of S S S outhern C C C alifornia USC Viterbi School of Engineering Ming Hsieh Department of Electrical Engineering EE 541: Solutions, Homework #03 Fall, 2011 Due: 09/20/2011 Choma Solutions Problem #12: In the filter of Figure (P12), the inductance, L , is chosen in accordance with the constraint, 2 o L R C , L C R o R o R o V s V o Z in Figure (P12) where R o is the resistance terminating the output port of the filter, as well as representing the Thévenin resistance of the signal source applied to the filter input port. In addition, note that a resistance of value R o shunts inductance L in the filter. (a). Determine the input port scattering parameter, S 11 , referred to a characteristic impedance of R o . The input impedance, Z in , of the filter is 3 o a o o o in 2 o a o o o o 2 o o o o R sL R sR C R Z R sL 1 sR C 1 sR C R sR C R sR C R . 1 sR C (P12-1) Thus, because the filter is terminated in the reference resistance, R o , scattering parameter S 11 is null; that is, in o 11 in o Z R S 0 . Z R (P12-2) (b). How must inductance L or capacitance C be chosen to ensure that the voltage transfer function, V o /V s , of the filter establishes a radial 3-dB bandwidth of B ? An inspection of the schematic diagram of the filter reveals that its voltage transfer function is

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