ee541F11HWSolutions03

ee541F11HWSolutions03 - EE 541 University of Southern...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
EE 541 University of Southern California Viterbi School of Engineering Choma Solutions, Homework #03 35 Fall Semester, 2011 U niversity of S outhern 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 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 . The input impedance, Z in , of the filter is   3 oa oo o in 2 o o 2 o o Rs L R C R Z R s L 1s R C 1s R C R C R C R. R 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 ZR S0 .  (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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
EE 541 University of Southern California Viterbi School of Engineering Choma Solutions, Homework #03 36 Fall Semester, 2011  oo o 3 oa s o 2 a o o 2 o RR 11 1s R C 2 21s R C V Rs L V R R C R C R s L R C R sR C R 22 , R C R C      (P12-3) which renders transparent the fact that the radial 3-dB bandwidth, B , is o o R 1 B , R CL (P12-4) where the given information, L = R o 2 C has been used. Either answer in (P12-4) is valid. (c). Determine the transducer power gain, G T , as a function of signal frequency ω . The transducer power gain of the filter is the ratio of the output power -to- the maximum available signal source power. Accordingly, s 2 o 2 T s o o V RV 1 G4 . V V 1 ω RC 4R (P12-5) (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? An insertion loss of 0 dB requires 2 T1 1 G1 S.  (P12-6) Since the transducer power gain, G T , is the squared magnitude of S-parameter S 21 , (P12-6) is equivalent to 11 21 SS 1 ,  (E2-7) which is satisfied only if the network for which parameters S 11 and S 21 are evaluated or meas- ured is a lossless architecture. Thus, the engineering significance of a 0 dB insertion loss is its implication that the network undergoing investigation is lossless .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/22/2011 for the course EE 541 at USC.

Page1 / 16

ee541F11HWSolutions03 - EE 541 University of Southern...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online