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ee541F11HW03

# ee541F11HW03 - EE 541 USC Viterbi School of Engineering J...

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EE 541 USC Viterbi School of Engineering J. Choma Homework #03 30 Fall Semester, 2011 U niversity of S outhern C alifornia USC Viterbi School of Engineering Ming Hsieh Department of Electrical Engineering EE 541: Homework Assignment #03 Fall, 2011 Due: 09/20/2011 Choma Problem #12: In the filter of Figure (P12), the inductance, L , is chosen in accordance with the constraint, 2 o L RC, 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 . (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 ? (c). Determine the transducer power gain, G T , as a function of signal frequency . (d). The so-called “insertion loss,” IL , of a filter is expressed in decibels and has been defined (albeit controversially) as T 10 2 11 G IL (dB) 10 . 1S log    (i). What is the engineering significance of an insertion loss of 0 dB ? (ii). What is the engineering significance of an insertion loss that equals the decibel value of the transducer power gain? Problem #13: If a second order, passive notch filter, such as the abstraction in Figure (P13), displays a symmetrical frequency response (identical very low and very high frequency gains),

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EE 541 USC Viterbi School of Engineering J. Choma Homework #03 31 Fall Semester, 2011 its transfer function is the form, 2 o n o 2 s nn s H1 ω V H(s) . V ss 1 Q ωω      In this transfer relationship, H o , is the gain at both very low and very high frequencies. In a pas- sive filter, the magnitude of H o is less than unity. Moreover, Q
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ee541F11HW03 - EE 541 USC Viterbi School of Engineering J...

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