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# midtermsol - \$élcetti’l/U ECE433-Exam 1 6:00-7:45 PM...

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Unformatted text preview: \$élcetti’l/U ECE433-Exam 1, February 18, 2011, 6:00-7:45 PM Name: PUID: Note: For each question, you have to develop the mathematical equations and show the comprehensive work to get the credit. Do not write any final equation without showing the procedure. Otherwise, you do not get the credit. 1) True/False (Brieﬂy explain your answer) (10 points): a) In a DC-DC converter under steady-state conditions, the net change of inductor . . . p 7 '1) . ‘ . ltage 0 er 0 e full sw1t hlng cycle 18 zero. FCZ/i/il {i '— | — ‘ neﬁ FM amp/e, l2?» a M amydriéf WWI L2,» 01 e, I 4 «Ct (DIS a UL: Vlh'l/(I'zzf: .2; \ ‘3 Ml: w «r - _ ., ‘ ,_* I. . mmmm 49‘ 5619’) m / 080503? 'UL — W »' 47;?th ‘ b) In a DC-DC converter under steady-state conditions, the net change of inductor current over one full switching cycle is zero. WE _ .. 773,; is ﬁle 19mm 0f- the WWW/f watt, fee. eegawf/m . Ma ‘ LLCRTS'): LLQII , 5 ' (UL U (“+0 ("M 5 , >- “‘3 ~14 hits] M n‘Ts (“H x (175 L- hTs 31 M} L c) In a DC—DC converter under ste y-state conditions, the net change of capacitor rent 0v ron full witchi cycle is zero. 2 3,”: ~ , v . Rot“ cwémpleﬁfar 6L to? game/r 2°} ‘5 h elm 4 cf (WW #4013 ,3 £5, 5 e “(if LC” '3 "‘9 mﬁwt W” 6W J‘Iéii‘w‘iﬁ Vgggi’ ‘ V -7 r (> . ,' . - ~' ' . CL ‘ (2 f5 [wt 5&9. d) In a DC-DC converter under steady-state conditions, the net change of capacitor voltage over one full switching cycle is zero. T171 {1 Whig. is the. harm; a)? he \Ciméjﬁor‘ bdlzmég {m m} 1,5 , j w ' £6“ iscc M: 'S 740113) ECU”, q H \k g W 7:. :9 n7] ﬁzﬁ/(dt th C: a. VG -“* T ) \ l _ :Dej‘ln"aDQé-§C*converter, bﬂéﬁgging the switching frequency, the average value of the inductor current and the amplitude of the inductor current ripple will be decreased. r . The. ail/em e: Um 67/3 7/49 Cami/Lt 1,5 Inchgm/eet M9- 'r‘n’e rafﬂe/Leg. The ripp/e @Irwﬂﬂa‘af is Bra/gum? {/(gﬂfﬁéjﬁi' ml 4L3 ﬁe sex/Mtg ilk/Wag mama, 2 2—a) For an ideal buck converter, derive the value forfswCCH-t) in terms of duty cycle, switching frequency, and load, at the boundary of DCM and CCM. fswmit) refers to the value of switching frequency for which the converter operates in the boundary of DCM and CCwIO points). 4f WWWg 41 56/14 gt Dal/z fL: ALLng Meal 4? We. IL (yALL . mum} (QrﬂfF, ow) V": “UL: l V "LVL’. 3 T’Uc K g ’ULrl/g-’0mt?¢ l/g'Vm UL: vvazzt~—L’Ezzf t _ ", . r ‘ N - M’ r (0" 2’; [Q'Vw “41.1: ; JUth : »V&ct,t 75 y T L- df ’75: “T . ‘ "6 * m—v wru— & :0 Wong? E (Digit/d Wow J m) V27 - Vmi ~0~D)T (n- vow." _ V. 3 2-b) For an ideal boost converter, derive the equation for the inductor current ripple and output voltage ripple and express them in terms of duty cycle, capacitance, switching frequency,Eductance, and load resistance (10 points). Wok ,0 % Jﬁ (1)1103 )+ 0/? MM) @4927) .— a :aWké’f‘g-t— 2L) 3 L, T5 ‘ , n V mm) D L ML, ~ ~—- ~ ., , , g M i . A ’ 1L“ ' Tr: L e LL» 2% eff Ts r ,J/wtm’ W e ﬂaw/7%:- SWWJ , M‘ . f: ' 1 . ,. V. r 5—.— r 7‘ \ < ‘ J g 4 3) Assuming that the following converter is ideal and operates in CCM, determine the voltage conversion ration of the converter Q1 switches ON and OFF with a switching frequency of f5W and with a duty cycle of D (15 points). 4) For the given converter, Vg = 50V,L = 5mH,C = 20yF,R = 20,0 = 0.2,fsw = 100kHz. a) Assume that the MOSFET has a voltage drop of VTon during conduction. Determine the voltage conversion ratio (5 points). b) Determine the efficiency of the converter under the condition of part b) (4 points). c) Determine the rating values (voltage and current) of the MOSFET and diode (4 points). d) Assume VTon = 1V, plot the voltage and current of each individual component, i.e. switch, diode, inductor, and capacitor in steady-state. Determine ML and AVC and include them on the graphs (for each graph show the numerical values for magnitude and time information) (12 points). 04t- (DIS (m at) , 0, roar) 030505 {(156%) r). :m) up + V1": +(ijcycgi L59“??? ._,. » ([7- 7;] - Dari. " lL"i‘Z/€%- ((161) :st (DTg IL) :DiL #9 5% W WA +a WW6 IL. (elL »— (LC>T5;0 :7) Jﬁ,(DlT5(—_V%§)+U-D)T5 —7a” A a 1L: your ? ml? :75? RU—D) “0 X QALL. : “V72” AL :: : qlgx 7&3 /T:’ ‘4 L , ~3 9 - A do»: Magma : mamas” ) : '53 w Pm @061): wwfaawi 9 9’1: 106%}: ’, FELL-R: W W“ w 1/“? (A VD Hw : Viz?“ fl 1 (mm: Kw; : w? +cq,zx153):7 be 4 l/&L{h “HM M43 ; [ﬁg/5,th 5&442237; éz-ZYV“ [cammm wean {fa/t6) 5 EHALL: ¥ééﬂ ‘ 44V \ ‘ . “i: ...
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midtermsol - \$élcetti’l/U ECE433-Exam 1 6:00-7:45 PM...

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