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midterm2

# midterm2 - l(30 points For the resonant circuit shown...

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Unformatted text preview: l. (30 points) For the resonant circuit shown: Y(s) -> C :7 a) Find the impedance, 2(3). b) Given that the capaacitor has a value C = 8 1.1 farads (8 x 105), what values of L and R will result in: resonate frequency: 0)., = 20,000 radlsec quality factor: Q = 5 c) What is mom expression at the circuit resonant frequency. Zﬁmo) ? 1'me d) With Q = 5, what is the phase of 20600) at the circuit resonant frequency ? I ﬂ' ' L a ()3 2(5); 1 :- | L LC514EC .1 LC, 1 S4 LS4R + C8 LSiR L3”; 5 . LCS1‘RCs-I" L94 2 I <7 4 t: I. (I) : LLB-Le: E 4 ' = (E 1;) L a I 4 LS LC) (3 4 \$1.34 I: L{Door}, :‘+Oooy 3129a: . 9D. '1 F. + 3.1755- , . _‘ , . =- 31. )5 ~61 1 KE-L (106 £\1+ Lilli-HCMS 9 5-44 35; 1,) Sg- NFL-AU?" . Q L C “3+ 3“,“, ECE-S304. midterm #2 page 2 August I6, 2006 2. (25 pts) The following is the transfer function for a continuous system: s3+sz+6s+gK+32 H(s)= 34+ 533+553+ Ks+(K-4) a) Determine all the necessary conditions on "K" using Routh-Hurwitz for system stability. b) Using part a) ﬁnd and sketch the over-all range of "K" for system stability. c) What value of “K" will cause the system to oscillate ? what is the frequency of oscillation "too" ?_ G gig-ma. g _K PAC") c; 7 2"? (ﬁg-hill “340(5) _ Leg-k1- ELEM ‘29 — g e_________________ 4c _\-‘-_—--_-__—-'-'—-_—-—u 1 l;- 2-ng ;_K +1001 5 3 —k_"+loo "”1 5* 15-14 __ _ 25-; (“ii M W .-KZ.'-‘+Ioo ‘j/J‘l/ mm ' / 2§~K 1C) % i139 ZG-Kﬁeo \$V+¥7S =5 k419/ (9 ”PHDO 9.0 => k1 .900.» Kilo) K 10 ltvblzo :5 Kzzii/ m \W-(P‘bkl; Art's.- E-k ' ' 7" 3~K Zo _ “’0 0 NE). (W: km) K £3 E’s-to ‘U/ A.)- is V 3. (25 pts) Given the network function: /‘ m3) = 631% :1) Plot the individual asymptotes and the resultant asymptote of the Bode magnitude in dB on the semi-log graph provided (see the next page). ‘h) Plot the individual asymptotes and the resultant asymptote of the phase in degrees on the semi-log grapl provided (see the next page). c) From the Bode plots of parts a) and b), determine the magnimde and phase of the network function at (0 = 20 rad/sec. Show (circle) these points on the Bode plots. its—ND) l-MM' ”but: (70*) mu a. \$1233 frequency in rad/sec frequency in rad/sec 3. (20 pm) For the vector matrix differential equation: a -2 l 2 x(t) =Ax(t)+Bu(t); A=[ ]; B{] 0 3 0 3) Take the Laplace Transform of me vector matrix differential equation and solve for X03). b) Find ¢(s)= (sI - A)" which is the state transfer function (resolvant) matrix. c) Find the state-transition matrix Mt) = e"M = L- I[¢(s)]. 0k) 9%,) XIO) ~ AWE? Eu“ 1/ (SIMXIS)-A%@)1PM(3) L/ I. (cLWkH my ([email protected]+gu(s))‘ m ®(S)=E1-AY[§ °122JEO 3/ d )= @@ EOE-5304. midterm #2 page 5 August 16. 2006 ...
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midterm2 - l(30 points For the resonant circuit shown...

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