Topic 11Main contentsLast lecture review Principles of DC-AC converter
Main contents • Last lecture review • Principles of DC-AC converter Topic 11
1.4Problems10-1A 12-Vregulated linearpowersupplyof thetypeshown in Fig. 10-1a designed to operate with a 60-Hz acvoltage in range of 120V (+10%~-25%).At the maximumload, the peak-to-peak ripple in the capacitor voltage is 1.oVThe power supply is designed such that Vd.min-V。=0.5V inFig.10-1b.IoCalculate the loss of大3BaseErrotNefficiency due to powercontrolimpLine input0.or3-Vo,r60-HzlossesinthetransistorattransformerRectifierFiltercapacitor(a)full load, with the inputvoltage at its maximum.Ud(t)range(Hint: Approximate thecapacitorvoltagewaveformwithstraight-linesegments.)(b)Figure 10-1 Linear power supply: (a) schematic, (b) selection of transformer turns ratioso that Vd.min>V,bya small margin
3 10-1 A 12-V regulated linear power supply of the type shown in Fig. 10-1a designed to operate with a 60-Hz ac voltage in range of 120V (+10%~-25%). At the maximum load, the peak-to-peak ripple in the capacitor voltage is 1.0V. The power supply is designed such that Vd,min-Vo=0.5V in Fig.10-1b. Calculate the loss of efficiency due to power losses in the transistor at full load, with the input voltage at its maximum. (Hint: Approximate the capacitor voltage waveform with straight-line segments.) 1.4 Problems
10-2Aflybackconverterisoperatinginacompletedemagnetization mode. Derive the voltage transfer ratioV.N.in terms of the load resistance R, switching frequencyfs, transformer inductance Lm, and duty ratio D
4 10-2 A flyback converter is operating in a complete demagnetization mode. Derive the voltage transfer ratio Vo /Vd in terms of the load resistance R, switching frequency fs , transformer inductance Lm, and duty ratio D
Problem10-4Aflybackconverterisoperatinginanincompletedemagnetization mode with a duty ratio of 0.4. in the sameapplication, another option may be to parallel two half-sizeflyback converters as shown in Fig. 10-9b. Compare theripple in the input current ig and the output stage current i.waveforms in these two options, assuming a very largeoutput capacitor such that vo(t)=Vo.(a)(b)Figure 10-9 Other flyback topologies: (a) two-transistor flyback converter; (b) parallledflyback converters
5 10-4 A flyback converter is operating in an incomplete demagnetization mode with a duty ratio of 0.4. in the same application, another option may be to parallel two half-size flyback converters as shown in Fig. 10-9b. Compare the ripple in the input current id and the output stage current io waveforms in these two options, assuming a very large output capacitor such that vo (t)≈Vo . Problem
Problem10-5 A switch-mode power supply is to be designed with thefollowingspecifications:Va=48V±10%,V.=5V,f.=100kHzPjoad is 15~50W.A forward converter operating in acontinuous-conduction mode with a demagnetizing winding(N3=Ny) is chosen. Assume all components to be idealexcept the presence of transformer magnetizationinductance,VI(a) Calculate Na/N if this+NNIN,本Dturnsratio is desired to be asVasmall as possible(b) Calculate the minimumyalue of thefilterinductancePracticalforwardconverter5
inductance. + Vd - + Vo - 1 L iL + vL - D2 T N1N3 N2 i i i D2 1 3D3 Practical forward converter 5 (a) Calculate N2/N1 if this turns ratio is desired to be as small as possible. (b) Calculate the minimum value of the filter inductance. Problem 10-5 A switch-mode power supply is to be designed with the following specifications: Vd =48V±10%, Vo=5V, fs=100kHz, Pload is 15~50W. A forward converter operating in a continuous-conduction mode with a demagnetizing winding (N3=N1 ) is chosen. Assume all components to be ideal except the presence of transformer magnetization
Problem10-6 A forward converter with demagnetizing winding isdesired to operate wit a maximum duty ratio Dmax of 0.7.calculate the voltage rating of the switching in terms of theinput voltage Vd
7 10-6 A forward converter with demagnetizing winding is desired to operate wit a maximum duty ratio Dmax of 0.7. calculate the voltage rating of the switching in terms of the input voltage Vd . Problem
Problem10-7 In the circuit of Fig. 10-12b with two parallel forwardconverter, draw the input current ia and i, waveforms if eachconverter is operating at a duty ratio of o.3 in a continuous-conduction mode.Comparethesetwo waveformswiththose ifa singleforwardconverter (withtwicethe powerrating but with the same valueoftheoutputfilterinductance asinFig.10-12b)is used.Assuming V。(t)=V。V1(b)Figure 10-12 Other topologies of forward converter: (a) two-switchforward converter; (b) parallelled forward converters
8 10-7 In the circuit of Fig. 10-12b with two parallel forward converter, draw the input current id and iL waveforms if each converter is operating at a duty ratio of 0.3 in a continuousconduction mode. Compare these two waveforms with those if a single forward converter (with twice the power rating but with the same value of the output filter inductance as in Fig. 10-12b) is used. Assuming vo (t)≈Vo . Problem
Problem10-8 In the push-pull converter of Fig.10-13a,assume thelosses to be zero and each switch duty ratio to be 0.25. Thetransformer has a finite magnetizing inductance and im isthe magnetizing currentiDi(a) At a large load whereiL(N2/N,)>>im, draw the im, ip1,and ip2 waveform.Figure10-13Push-Fullconverter
9 10-8 In the push-pull converter of Fig. 10-13a, assume the losses to be zero and each switch duty ratio to be 0.25. The transformer has a finite magnetizing inductance and im is the magnetizing current. (a) At a large load where iL (N2 /N1 )>>im, draw the im, iD1, and iD2 waveform. Problem
ProblemStep-downconverters7-1 In a step-down converter, consider all components to beideal. Let v=V.be held constant at 5V by controlling theswitch duty ratio D. calculate the minimum inductance Lrequired to keep the converter operation in a continuous-conduction mode under all conditions if V.is 10~40V,P。>=5W,and f,=50kHz.idioYYL+1oVL大VdC.1.(a)O
Problem Step-down converters 7-1 In a step-down converter, consider all components to be ideal. Let vo=Vo be held constant at 5V by controlling the switch duty ratio D. calculate the minimum inductance L required to keep the converter operation in a continuousconduction mode under all conditions if Vd is 10~40V, Po>=5W, and fs=50kHz. + Vd - + vL - R + C vo=Vo - + voi - (a) L i i L d io 9
Problem7-2 Consider all components to be ideal. Assume V。=5V,f.=20kHz, L=1mH,and C=470μF.Calculate △V。(peak-peak)if Va=12.5V,and l.=200mA.7-3 In Problem 7-2, calculate the rms value of the ripplecurrent through L and, hence, through C.10
Problem 10 7-2 Consider all components to be ideal. Assume Vo=5V, fs=20kHz, L=1mH, and C=470µF. Calculate ΔVo (peak-peak) if Vd=12.5V, and Io=200mA. 7-3 In Problem 7-2, calculate the rms value of the ripple current through L and, hence, through C