12/13/2002 D. Zhou, Ph.D.EE136 Final Exam11. (10 pts) In a boost converter, Vo=15V, Vd=12V, Io=250mA, L=1mH,C=470µF, and fs=20kHz, calculate duty ratio D and ∆Vo(peak-peak).2. (10 pts) A 75W DC-DC converter has input voltage Vd=127V and output voltage Vout=19.5V, original design has 8mF output capacitance. The worst case load is at constant rated current. What is the hold-up time of the converter if input line losses power? If an additional 10ms hold up time is required, additional capacitors can be added either on input or output side. Calculate their capacitances needed to support such function. Which approach do you prefer, adding input side capacitor or increasing the output capacitance?mVHzFACfDIVoperationecontinuousAAIDIIIIAHzHVLfDVLDTVIVVVVVVDDVVoperationcontinuousAssumesooLoLLLsdsdLododo32.51020104702.025.0.mod,02525.0212.02.0125.021212.010201012.0122.0151215,1136min33=••••==∆>=−−=∆−−=∆−==••••===∆=−=−=−=−−inputatFJVECoroutputatcecapaciadditionalmFJVECrequireswhichJmsATIVEcaseworstatenergystoredaddtionalrequirestimeupholdadditionalmsmsAVIVETtimeupholdloadcurrenttconsWithJFeCVEcapoutputatenergystoredInitialAVWVPIcurrentcaseWorstdinoutoutooutooutupholdoutoutoµ1.93127751.0*22,tan95.35.19751.0*22751.010*85.3*5.19103.2085.3*5.19521.1,tan521.15.19*38*5.02185.35.1975222222===∆===∆==∆=∆====−=====−12/13/2002 D. Zhou, Ph.D.EE136 Final Exam23. (10pts) A forward converter with a demagnetizing winding is designed to operate with a maximum duty ratio Dmaxof 0.5. Calculate the voltage rating of the diode D3in terms of the input voltage Vd.4. (10pts) In a regulated flyback converter with a 6:1 turns ratio, Vo=19.5V, Vdis 127V, Ploadis 6W, and the switching frequency fs=200kHz. Calculate the maximum value allowed for magnetizing inductance Lmsuch that the converter is operating in a complete demagnetization (equivalent to a discontinuous-conduction) mode at this operating point..2215.05.01,,113max,3maxmax13max13maxtimeonswitchduringVVVNNVVDDNNThusDNNDddddD==+===−==−mHAHzVLVVVDVVwithAVWVPIIfNDDVNLVNVNVNDthusDDNNVVeconductioncriticalDuringmdoooosdmdoodo54.1308.010200*12)48.01(48.0127*6,48.01275.19*65.19*6,127308.05.196,2)1(,,1,mod32121112=•••−••≤=+=====−≤+=−=12/13/2002 D. Zhou, Ph.D.EE136 Final Exam35. (10pts) A MOSFET has a switching waveform as shown on the right. Vd=50V, Rdson=0.1Ω, Id=10A, ton=100ns, toff=200ns and neglect its leakage current during off time. It is switching at 100kHz.(a). Calculate its switching losses;(b). If the switch duty ratio is 0.5, calculate its on state loss;(c). If the switch is the only significant lossycomponent, calculate the circuit efficiency.6. (10pts) A 100µF capacitor is used as the output component of a DC-DC converter. The part has a constant tanδ=0.12 across its frequency spectrum, calculate its ESR at 100kHz switching frequency. %952505.122505.1255.72505.0*10*50)(55.0*1.0*10)(5.755.253100*9200*10*50*5.0215.23100*9100*10*50*5.021)(______22_=−=−==+=+======−=Ω===+=+=−=−==−=−==WWWPPPefficiencyWWWPPPlossTotalWAVDIVIVIVPclossstateonforWDRIPblossswitchingforWWWPPPlossoffturnforWHzeseAVftIVPlossonturnforWHzeseAVftIVPaaverageinlossaverageinstateonswlossddaverageindaverageininaverageindsondstateonoffonswsoffddoffsonddonηΩ=−== mFeHzeCESR 91.16100*3100*212.0tanπωδ12/13/2002 D. Zhou, Ph.D.EE136 Final Exam47. (10 pts) Three components R=10Ω, Lr=1mH and Cr=1mF can be used to form either series resonant circuit in 2a or a parallel one as in 2b.(a). What are their resonant frequencies ωo?(b). Calculate their quality factors;(c). Calculate their characteristics impedances.2a2bTcTjPlossRθ,jc8. (10 pts) A Power MOSFET power loss is 4W. Its junction temperature is limited to 150°C while maximum case temperature can reach 70°C. What is the design restriction for its junction to case thermal resistance?Ω=−−=====Ω−===−−==13131)(101.01031*/1000)(/100031*3111)(FeHeCLZcLRQHesradRLQbsradFeHeCLarroroprosrroωωωWCWCCPTTRRTTPlosscjjcjccjloss/20470150,,ooo=−=−≤−≤θθ12/13/2002 D. Zhou, Ph.D.EE136 Final Exam59. (20pts) A DC source supplying an inverter with a bipolar PWM is 96V. The PWM output has a spectrum as listed on the right table. The output has a fundamental frequency of 50Hz.(a). If the output fundamental voltage is required as 67.9V, what is the amplitude modulation ratio;(b). Calculate the first 5 harmonic voltages if the frequency modulation ratio is 21;(c). Calculate the voltage THD if any higher harmonics beyond the first 5 are neglected;(d). If the load is an R-L-C series combination with R=10Ω, L=1mH and C=1mF, calculate the fundamental and first 5 harmonic currents;(e). What is the current THD if higher harmonics are neglected;(f). With still higher harmonics neglected, calculate real and apparent power, power