EE 541 University of Southern California Viterbi School of Engineering Choma Solutions, Homework #03 35Fall Semester, 2011 UUUniversity of SSSouthern CCCalifornia 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, 2oLR C ,LCRoRoRoVsVoZinFigure (P12) where Rois 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 Roshunts inductance Lin the filter. (a).Determine the input port scattering parameter, S11, referred to a characteristic impedance of Ro. The input impedance, Zin, of the filter is 3oaoooin2oaoooo2ooooRsLRsR CRZRsL1sR C1sR CRsR CRsR CR.1sR C(P12-1) Thus, because the filter is terminated in the reference resistance, Ro, scattering parameter S11is null; that is, ino11inoZRS0 .ZR(P12-2) (b).How must inductance Lor capacitance Cbe chosen to ensure that the voltage transfer function, Vo/Vs, of the filter establishes a radial 3-dBbandwidth of B? An inspection of the schematic diagram of the filter reveals that its voltage transfer function is
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