ee541F10HW03-04

ee541F10HW03-04 - U niversity of S outhern C alifornia U SC...

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U niversity of S outhern C alifornia USC Viterbi School of Engineering Ming Hsieh Department of Electrical Engineering EE 541: Homework Assignment #03-#04 Fall, 2010 Due: 09/28/2010 Choma Problem #10: A lossless, lowpass, filter boasting a 3-dB bandwidth of 2 GHz is to be used to couple a 50 Ω load (R l ) to a 50 source (R s ) , as is abstracted in the diagram of Figure (P10). It has been determined that the desired filter must be a 4 th order Butterworth (maximally flat magnitude) structure for which the desired transfer function of the entire system, (with load and source terminations) is + Lossless Lowpass Filter V 2 V 1 V s R l R s Z (s) in Figure (P10) v 2 v 23 4 s A(0 ) V( s ) A (s) , V(s ) 1a sb s a s s == ++ + + where normalizations with respect to a 50 impedance and the 3-dB bandwidth of 2 GHz have been exploited in this mathematically delineated transfer characteristic. Moreover (and as will be investigated later in class), a = 2.6131 and b = 3.4142 . It should be noted that for this 4 th or- der Butterworth filter, 2 2 v vv v 8 ) A (s) A (s)A (-s) . 1s + (a). Determine the normalized driving point input impedance, Z in (s) , that necessarily supports the indicated voltage transfer function. (b). Design the filter. Submit a network topology that shows the normalized values of all branch elements, as well as a topology for which de-normalization has been executed. (c). Simulate the finalized network topology on HSPICE or equivalent circuit analysis soft- ware. What 3-dB bandwidth and zero frequency voltage gain are projected by the simu- lated frequency response? Problem #11: Convert the finalized filter topology developed in Problem #10 to a notch circuit architecture for which the notched frequency is 800 MHz and the filter Q is 10 . Simulate the final design on HSPICE or on equivalent circuit analysis software.
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EE 541 University of Southern California Viterbi School of Engineering Choma Homework #03-04 26 Fall Semester, 2010 Problem #12: With reference to the system diagram of Figure (P10), let the normalized driving point input impedance, Z in (s) , be 2 in 23 s 1s 2 Z (s) , 7s s s 1 363 ++ = + where the normalizing impedance is 50 Ω , and the normalizing frequency is 2 GHz . Synthesize the structure in both normalized and de-normalized formats, and determine the normalized sys- tem transfer function, V 2 (s)/V s (s)
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ee541F10HW03-04 - U niversity of S outhern C alifornia U SC...

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