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ee541F10FinalSolution

# ee541F10FinalSolution - EE 541 University of Southern...

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EE 541 University of Southern California Viterbi School of Engineering J. Choma. Final Examination Solutions 1 Fall Semester, 2010 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: Final Examination 14 December 2010 (SOLUTIONS) 11:00 -to- 1:00 Problem #1: Solution (25%) The circuit shown in Figure (E1) is a simplified model of a MOSFET technology amplifier that combines shunt peaking via the inductance L 1 with series peaking through induc- tance L 2 to achieve a broadbanded network. The two inductances utilized in the circuit are un- coupled. The input signal is the voltage, V s , while the output response to this signal is voltage V o . It can be demonstrated that the input/output voltage transfer function, H n (p) , normalized to the voltage gain realized at zero frequency is of the form, 2 n 2 2 1 kQ p H (p) , 1 p Q p + = + + where “p” is complex frequency “s” normalized to the uncompensated circuit bandwidth, say B u . Specifically, B u represents the radial 3-dB bandwidth that is realized when L 1 = L 2 = 0 . g V m s L 1 L 2 R L C L V o Figure (E1) (a). Determine parameter “k” in terms of the two inductances, L 1 and L 2 . The input/output (I/O) transfer function, H(s) = V o /V s , is easily confirmed to be ( ) ( ) ( ) 1 L 1 L o L m m L 2 s L L 1 2 L L 1 2 L 1 sL R sL 1 sC V R H(s) g g R , 1 V 1 sR C s L L C R sL sL sC + + = = − = − + + + + + + (E1-1) where the zero frequency value, say H(0) , of the I/O voltage gain is clearly seen to be –(g m R L ) . Moreover, we note that when L 1 = L 2 = 0 , the transfer relationship in (E1-1) reduces to 1 2 L L 0 L L H(0) H(s) , 1 sR C = = = + (E1-2) which clearly projects an uncompensated 3-dB bandwidth, B u , (i.e. the bandwidth of the circuit with the inductors replaced by short circuits) of

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