05272095 Buck Converter

2106 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 8, AUGUST 2010

Mix-Voltage Conversion for Single-InductorDual-Output Buck Converters

Chun-Shih Huang, Student Member, IEEE, Dan Chen, Fellow, IEEE,Ching-Jan Chen, Student Member, IEEE, and Kwang H. Liu

AbstractA single-inductor dual-output (SIDO) buck converterhas recently found applications in hand-held battery-powered elec-tronic devices. The circuit operation and the functional interdepen-dencies among basic converter parameters such as dc voltage gains,transistor duty cycles, and load current levels are much more com-plicated than those of the single-output counterpart. In this paper, arigorous analysis was conducted to develop dc equations in steady-state operation for SIDO converters. More importantly, from theanalysis results, a possibility of a new mode of operation, dubbedmix-voltage operation, will be pointed out. In the so-called mix-voltage operation, the converter is capable of working even whenthe input voltage is lower than one of the two output voltages.In the past, a SIDO buck converter has been used for providingpure-buck outputs, i.e., both output voltages are lower than theinput voltage. Therefore, this possibility not only opens up new ap-plications but also extends the operating battery range in existingapplications. Experimental results confirmed the dc equations andthe mix-voltage conversion of SIDO buck converters.

Index TermsDCDC power converters, mix-voltage conver-sion, single-inductor dual-output (SIDO).

I. INTRODUCTION

A SINGLE-inductor dual-output (SIDO) buck converter hasrecently found applications in hand-held battery-poweredelectronic devices, which require dual outputs but no electricalisolation [1][3]. The main attraction of a SIDO lies in the factthat dual regulated outputs can be provided with relatively lowcost and small size. Fig. 1 shows the power circuit diagram of aSIDO buck converter [4]. The circuit diagram may look simplebut the circuit operation and the functional interdependenciesamong basic converter parameters such as dc voltage gains, tran-sistor duty cycles, and load current levels are much more com-plicated than the counterparts of a conventional single-outputbuck converter.

In this paper, a rigorous analysis in steady-state operationwould be conducted to develop useful equations for design pur-poses. More importantly, from the analysis results, a possibilityof a new mode of operation, dubbed mix-voltage operation,

Manuscript received May 6, 2009; revised July 24, 2009; accepted September14, 2009. Date of current version July 16, 2010. This paper was presented at theIEEE Energy Conversion Congress and Exposition, San Jose, CA, September2024, 2009. This work was supported by the National Science Council, Taiwan,under Grant NSC-96-2221-E-002-292-MY2. Recommended for publication byAssociate Editor M. Alonso.

C.-S. Huang, D. Chen, and C.-J. Chen are with the Department of ElectricalEngineering, National Taiwan University, Taipei 106, Taiwan, R.O.C. (e-mail:[email protected]; [email protected]; [email protected]).

K. H. Liu is with the Green Mark, Inc., Sindian City, Taipei 231, Taiwan,R.O.C. (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2009.2033070

Fig. 1. SIDO buck converter circuit diagram.

would be pointed out. In the so-called mix-voltage operation,the input voltage can be lower than one of the output voltages, asopposed to conventional pure-buck operation in which inputvoltage must be higher than both output voltages. This impliesthat the input battery may operate down to a voltage level lowerthan previously thought possible. This may also mean that asingle battery, instead of two in series, is sufficient in someapplications.

In the paper, a basic review of SIDO buck converter willbe given first. Analytical equations relevant to continuous anddiscontinuous conduction mode, dc voltage gains, and duty cy-cles will be developed for both the pure-buck and the mix-voltage operations. An equation will also be derived to estimatewhether a mix-voltage conversion is possible for given speci-fications. Since a SIDO buck converter is mostly used in low-voltage applications, semiconductor switch conduction voltagedrops will be included in the analysis for accuracy. Experimen-tal results will also be shown to validate the analytical resultsand the mix-voltage conversion.

II. DESCRIPTION OF THE OPERATION OF A SIDOBUCK CONVERTER

A SIDO buck converter can be operated in both the contin-uous conduction mode (CCM) [2], [5][10] and discontinuousconduction mode (DCM) [11], [12], just like a conventionalsingle-output buck converter. Fig. 2 shows the waveforms ofthe inductor current and transistor duty cycles with a time-multiplexing control scheme [13] for both the CCM and DCMoperations. According to the relative magnitude of transistorQ1 duty cycle D1 and transistor Q2 duty cycle D2 , the wave-forms are given for three cases: Case A (D1 < D2), Case B(D1 = D2), and Case C (D1 > D2). In the CCM operation,there are three periods: T1 is the duration when both transistorsQ1 and Q2 are ON. During this period, diodes Da and Db are

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HUANG et al.: MIX-VOLTAGE CONVERSION FOR SINGLE-INDUCTOR DUAL-OUTPUT BUCK CONVERTERS 2107

Fig. 2. Operating waveforms of a SIDO buck converter for both the CCMand DCM operations: (a) Case A (D1 < D2 ); (b) Case B (D1 = D2 ); and(c) Case C (D1 > D2 ).

OFF and the power is provided to VO1 only. The period T2 is theperiod when only one of the transistors is in conduction. If Q1 ,instead of Q2 , is in conduction, then the inductor current flowsthrough Db and the power is provided to VO2 only. Otherwise,it flows through Da and the power is provided to VO1 only. Theperiod T3 is the period when both transistors are OFF. The induc-tor current is then flowing through Da and Db , and the poweris provided only to VO2 . Notice that D1 is, therefore, equal toT1/TS or (T1 + T2)/TS , where TS is the conversion switchingperiod, depending upon whether it is Case A, B, or C. The samesituation applies to D2 . It is also clear that there is no T2 periodfor Case B. All of these are shown along with the waveforms inFig. 2. For the DCM operation, there is an additional period Tdwhen the inductor current stays at zero and none of the switchesis on. The duty cycle Dd is defined as Td/TS . Just like a single-

Fig. 3. Illustration of current flow for Case A of CCM.

output counterpart, a SIDO operation is moving from CCM to-ward DCM as load current levels are reduced or input voltage isincreased.

III. SIDO BUCK CONVERTER DC EQUATIONS

In this section, dc equations of the SIDO converters in steady-state operation will be derived. The derivation starts with aninductor current waveform that varies according to the case ofconverter operation described in Section II. Only Case A willbe used as an example for detailed derivation. As mentionedearlier, semiconductor switch conduction voltage drops will beincluded in the derivation.

A. Derivation for the DC Equations in CCM

Fig. 3 shows the inductor current waveform of Case A ofCCM. From the waveform, the input average current Iin is theaverage of the Q1 current, i.e., the area below the inductorcurrent waveform during the T1 period divided by the totalperiod TS . This leads to (1). Similarly, (2) can be obtained byequating the output current IO1 to the average of the inductorcurrent of the Q2 current. And (3) can be obtained by equatingthe output current IO2 to the average of the Db current. In theequations,Vin is the input voltage,VD andVDS are, respectively,the conduction voltage drops of diodes and transistors, and VO1and VO2 are the output voltages. IX is the valley of the inductorcurrent as shown in Fig. 3, and TS is the conversion switchingperiod

Iin =TS2L

(Vin 2VDS VO1)D21 + IXD1 (1)

IO1 =TS2L

[VinD1 (2D2 D1) VO1D22 + VDS (D21

2D1D2 D22 ) VD (D2 D1)2 ] + IXD2 (2)

IO2 =TS2L

(VO2 + 2VD ) (1D2)2 + IX (1D2) . (3)


TABLE IGROUPING OF SYMBOLS

Using the principle of conservation of energy, (4) can beobtained, where the left-hand side is the total input power, thefirst two terms of the right-hand side represent the total outputpower, and the remaining two terms are the power losses of theMOSFET and diode switches

VinIin = VO1IO1 + VO2IO2 + VDS (Iin + IO1)

+ VD (2IO2 + IO1 Iin) . (4)

From the four simultaneous equations (1)(4), the two vari-ables IX and Iin can be eliminated. Two independent equationsremain. These two independent equations can be simplified fur-ther using (5), which can be obtained from a consideration ofthe inductor volt-second balance in the steady state

(Vin VO1 2VDS )D1 = (VO1 + VDS + VD ) (D2 D1)+ (VO2 + 2VD ) (1D2) . (5)

DC equations for Case A of CCM can then be obtained as (6)and (7). A grouping of symbols is shown in Table I.

Group I in CCM consists of variables VO1 , VO2 , D1 , andD2 ; Group II consists of converter component values VD , VDS ,and L; and Group III consists of converter operating conditionsTS , IO1 , IO2 , and Vin . Normally, the values of the latter twogroups are given. The values D1 and D2 can then be foundby solving the two simultaneous (6) and (7), if the values ofVO1 and VO 2 are specified. On the other hand, the values VO1and VO2 can be found by solving the same set of equations,if the values D1 and D2 are specified. The DC equations forthe other two Cases of CCM operation can be obtained in asimilar fashion. The results are listed in Table II. It should bepointed out that besides the equation complexity, the voltagegains in a SIDO converter depend not only on duty cycles butalso on inductor value, load currents, and switching period.That is very different from a conventional single-output buckconverter.

B. Derivation for the DC Equations in DCM

The DC equations of a SIDO converter in DCM operationwill be derived as follows. Case A will be used for the il-lustration of detailed derivation. Fig. 4 shows the waveformsof such a case. Compared to a CCM operation, there are twodifferences in writing the equations for DCM operation. First,IX is zero and an additional variable, duty cycle Dd , is in-volved. Setting IX equal to zero and including the variable

Dd in (2) and (3) leads, respectively, to (10) and (11) asshown in Table III. From the consideration of the inductor volt-second balance in the steady-state DCM operation, (12) can beobtained.

Again, a grouping of symbols is helpful. Compared to theCCM operation, the grouping in DCM is identical except thatin Group I, there is an additional variable Dd involved, asshown in Table I. Therefore, there are five variables in Group I,namely VO1 , VO2 , D1 , D2 , and Dd . The parameters/conditionsin Groups II and III are normally given. If two of the five vari-ables in Group I are specified, the other three can be found out bysolving the three simultaneous equations (10)(12). For exam-ple, if VO1 and VO2 in Group I and all the parameters in GroupII and III are specified, then all the duty cycle information canbe found. Table III lists the DC equations for the three Cases ofDCM operation.

C. Algorithm for Determining the SIDO Buck-Operating Modeand Duty Cycle Values

Normally, converter component values (Group II parameters)and operating conditions (Group III parameters) are given. Fromthe equations in Tables II and III, one can see that if duty cyclesD1 , D2 , and Dd are known, then proper Case and, therefore,proper equations can be selected to solve for the output voltagesVO1 and VO2 . However, it is more difficult to do that the otherway around, that is, to determine the duty cycle values fromthe specified output voltage values. This is because, to use theproper equations, one needs to know in advance in which mode(CCM or DCM) and in which Case (A, B, or C) the converter isbeing operated. This information can only be found out with anelaborate procedure. Fig. 5 shows a proposed algorithm to dothat.

Refer to the flowchart in Fig. 5. In the top block, a set ofvalues including output voltages, component values, switchingperiod, and input voltage are given. In Step 1, one assumes thatthe converter operates in Case C of DCM, and therefore, usesthe corresponding equations to find out the values D1 , D2 , andDd . In Step 2, Dd is used to determine the converter operationmode. If Dd is within the range of [0, 1], then it is a DCMoperation. If not, then it is a CCM operation. In Step D3, theduty cycle D1 and D2 values are checked to see if they stay inproper boundary. Obviously, they cannot be a complex numberand have to be within the range of [0, 1-Dd ]. If not, then there isno answer to the given set of starting parameters. In other words,it is not possible for a SIDO converter to provide the specifiedVO1 and VO2 under the specified conditions and parameters asindicated by Step D7. If otherwise, go to Step D4. In Step D4, itmust be checked if D1 > D2 (Case C) because it was initiallyassumed to be Case C in Step 1. If the answer is yes, then thevalues D1 , D2 and Dd obtained in Step 1 are the final answers.Otherwise, go to Step D6 and use Case A or B equations tofind out the duty cycle values. The discussion that took placeearlier applies to the situation if the decision in Step 2 is yes.If the decision in Step 2 is no, then go through the CCMpath to Step C3 and first assume it is in Case C and solve forthe duty cycles. The rest of the path follows the same logic as


TABLE IIDC EQUATIONS OF A SIDO BUCK CONVERTER IN CCM

Fig. 4. Illustration of current flow for Case A of DCM.

used in the DCM path. At the end, either an answer can befound or it is not possible to meet the beginning specificationsof the SIDO converter. This flowchart will be used in the nextsection to illustrate the search of the possibility of mix-voltageconversion.

IV. Mix-VOLTAGE CONVERSION FOR SIDO BUCK CONVERTER

Three examples will be given to illustrate the use of theflowchart in Fig. 5. From the results, one can also see if mix-voltage conversion is possible for the specifications.

Example 1: Converter specifications are given in thefollowing.VO1 = 1.8V, VO2 = 3.3V, IO1 = 500mA, IO2 = 200mA,

L = 10 H, VDS = 0.01 V, VD = 0.4 V, and TS = 5 s.The maximum input voltage Vin max = 5 V. Find the dutycycle information and the minimum operable input voltageVin min .

Step 1: Vin is first set at 5 V and proceeded as follows: Twosets of solutions are obtained using (13)(15). (D1 ,D2 ,Dd) ={(0.6763,0.7931, 2.255) and (0.6763, 0.7931, 0.2546)}.

MATHCAD software was used for solving the simultaneousequations.

Step 2: Since Dd is outside the range of [0, 1] for bothsolutions, the converter works in CCM; therefore, go toStep C3.

Step C3: One set of solution is obtained (D1 ,D2) = (0.5335,0.6478) using (8) and (9).

Step C4: D1 and D2 stay within boundary.Step C5: Need to check if D1 > D2 . It turns out D1 is less

thanD2 . This means the assumption in Step C3 and the equationused to obtain D1 and D2 were incorrect. Therefore, go to StepC7. The duty cycles need to be recalculated.

Step C7: Solving for D1 and D2 using (6) and (7). (D1 ,D2)= (0.5268, 0.6670).

The data given earlier were obtained for Vin = 5 V. For eachselected Vin value, the operating duty cycle values can be foundas described earlier. It turns out that the converter operates inthe CCM for the entire input range. Fig. 6 shows the plot ofthe resultant duty cycle values versus Vin . As Vin is decreased,the D1 curve intersects with the D1 = 1 line at Vin min . Thiscrossover point is the minimum input voltage that the converterspecifications can still be met by the converter because D1 mustbe no more than unity. From the figure, Vin min is about 2.36 V,which lies between VO1 and VO2 . So, mix-voltage conversionexists in this example. This example shows that the converter iscapable of operating even when the input battery voltage is wellbelow VO2 value of 3.3 V.

Example 2: The converter specifications are the same as thoseof Example 1 with the exception of the load current values:IO1 = 100 mA and IO2 = 500 mA.

One can go through the flowchart of Fig. 5 and the resultis shown in Fig. 7. In this case, the converter operates in theCCM also for the entire input voltage range. However, Vin minis greater than both output voltages, which implies that mix-voltage conversion is not possible.

Example 3: The converter specifications are the same as thoseof Example 1 except that the load current levels are smaller:IO1 = 50 mA and IO2 = 20 mA.

By applying the same procedure, it was found that thisis a DCM case. For DCM operation, Vin min occurs at theintersecting voltage of the D1 curve and (1Dd) curve.


Fig. 5. Proposed algorithm to determine the converter operating mode and duty cycles.

Fig. 6. Plots of duty cycle values versus Vin for Example 1.


Fig. 8 shows the plot of D1 , D2 and (1Dd). In this case,mix-voltage conversion is possible, as it can be seen thatVin min < VO2 .


A. Determination of the Minimum Operable Input Voltage

Section IV includes three examples of plotting the vari-ous duty cycle values versus the input voltage for given con-verter specifications of output variables (VO1 , VO2 , IO1 , andIO2), power stage component values (VD , VDS and L), andthe conversion switching period (TS ). From the examples, onecan find out the converter operating mode (CCM or DCM),the various duty cycle values, and the minimum operableinput voltage Vin min . However, it would be much more con-venient to the designers if Vin min can be calculated by an an-alytical expression. The following paragraph will discuss thisissue.

For the first two examples, both of the CCM operations,Vin min occur when D1 is equal to unity. Therefore, by settingD1 = 1 in (8) and (9) and eliminating D2 for the two equations,


TABLE IIIDC EQUATIONS OF A SIDO BUCK CONVERTER IN DCM

(16) can be obtained

Vin min = VO1 + VDS +(VO2 + VD VO1 VDS ) IO2

IO1 + IO2.

(16)Equations (8) and (9), instead of (6) and (7), are used be-

cause D1 > D2 under this condition. Similarly, for example 3, aDCM operation, Vin min occurs when the curve of D1 intersects(1Dd). Therefore, by using (13)(15) and D1 = (1Dd)and by eliminating D2 and Dd from the three equations, onecan obtain Vin min . It turns out, surprisingly, that (16) applies toboth the CCM and DCM operations. That cannot be a coinci-dence. Therefore, a separate approach described in the followingparagraph will be used to confirm the result.

By rearranging (4), which is derived from the principle ofconservation of energy, (17) can be obtained

(Vin + VD VDS ) Iin = VO1IO1 + VO2IO2 + VDS IO1+ VD (2IO2 + IO1) . (17)

For the given converter specifications, the right-hand sideof (17) is fixed, regardless of the Vin value. Therefore, as Vinis reduced, the Iin value should increase. However, it will beproved later that the maximum input average current Iin maxis equal to (IO1 + IO2). Therefore, Vin min can be obtainedby substituting the Iin in (17) for Iin max , which is equal to(IO1 + IO2). The result is identical to (16) obtained earlierusing different approaches. In the following paragraph, it willbe proved that Iin max is indeed equal to (IO1 + IO2) for alloperating cases and for both the CCM and DCM operations.

B. Physical Explanation for the Derivation of MinimumOperable Input Voltage

In this paragraph, it will be proved that Iin max is equal to(IO1 + IO2). Referring to the inductor current waveforms inFig. 2, assume that the area under the waveform of periods T1 ,T2 , andT3 are, respectively,A1 , A2 , andA3 . From Fig. 1 and thedescription of the converter operation given in Section II, onecan see that the inductor current flows to VO1 or VO2 and returnsthrough Q1 or Da . Current flows to VO1 during Q2 ON timeand to VO2 during Q2 OFF time, and the input current flowsduring Q1 ON time. Consider Case A of CCM as an example.Then IO1 is equal to (A1 +A2)/TS ; IO2 is equal to A3/TS ;

Fig. 9. Inductor current waveforms under the minimum operable input voltageVin m in in (a) CCM operation; and (b) DCM operation.

and Iin is equal to A1/TS . Therefore, (IO1 + IO2) is equal to(A1 +A2 +A3)/TS , which is always larger than or equal to Iin .They are equal only when D1 = 1, i.e., when the input currentflows for the entire period. Fig. 9(a) shows the waveform undersuch conditions for the CCM operation. It can be seen from thefigure that Iin is equal to (A1 +A2)/TS , IO1 is equal toA1/TS ,and IO2 is equal toA2/TS . Therefore, under such conditions, Iinis the maximum and is equal to (IO1 + IO2). The conclusiondrawn earlier was for Case A of CCM operation. The same


TABLE IVSPECIFICATIONS OF THE SIDO BUCK CONVERTER

Fig. 10. Photo of the prototype.

conclusion applies to the other two cases because (IO1 + IO2)also covers the area under the inductor current waveform forthe entire period, while Iin covers only part of the total periodexcept when D1 = 1. For a DCM operation, the situation issimilar, i.e., Iin is always less than (IO1 + IO2), except whenD1 = (1Dd), which implies that Q1 conduction time alsocovers the whole inductor current conduction time. Therefore,Iin max is also equal to (IO1 + IO2) for a DCM operation.Fig. 9(b) shows the waveforms for such a case.

V. EXPERIMENTAL RESULTS

A prototype of the SIDO buck converter was implemented toverify the analytical results. The prototype specifications for thethree examples are listed in Table IV, and a photo of the proto-type is shown in Fig. 10. In the prototype, a voltage-mode feed-back control was used. The same small signal model presentedin [2] applies to both the pure-buck and mix-voltage operations.Fig. 11 shows the measured waveforms for Example 1. The re-sults confirm the theoretical results of Fig. 6. Fig. 11(a) and (b)is the pure-buck mode, and Fig. 11(c) is the mix-voltage

Fig. 11. Measured waveforms of Example 1 for different input voltage values:(a) Vin = 5 V; (b) Vin = 3.5 V; and (c) Vin = 2.4 V (iL : 250 mA/div.,VGS1 : 10 V/div., VGS2 : 10 V/div., time: 1 s/div.).

mode; therefore, mix-voltage conversion is achieved under thisoperating condition. Fig. 11(c) also reveals the duty cycle D1as it approaches unity, while the converter works in CCM andthe input voltage is the minimum value. When the input voltagedropped below 2.36 V, the converter ceased to function properlyas (16) predicts.

Fig. 12 shows the measured waveforms for Example 2. How-ever, the converter can only work in the pure-buck mode andno mix-voltage conversion exists under this operating condi-tion. The converter ceased to regulate properly when the inputvoltage dropped below 3.4 V.

Fig. 13 shows the measured waveforms for Example 3. Thewaveforms reveal the three cases of duty cycles in DCM underdifferent input voltage values, and mix-voltage conversion can


Fig. 12. Measured waveforms of Example 2 for different input voltage values:(a) Vin = 5 V; and (b) Vin = 3.4 V (iL : 250 mA/div., VGS1 : 10 V/div.,VGS2 : 10 V/div., time:1 s/div).

TABLE VMINIMUM OPERABLE INPUT VOLTAGE UNDER DIFFERENT LOADS

be achieved under this operating condition. Moreover, whenthe converter operates in DCM under minimum operable inputvoltage, D1 is equal to (1Dd) as shown in Fig. 13(c). Theconverter ceased to regulate when the input voltage droppedbelow 2.36V.

Table V shows the predicted converter minimum operableinput voltage with and without considering the semiconductorswitch conduction voltage drops. It can be seen that a significanterror occurs if the switch voltage drops were ignored.

Fig. 13. Measured waveforms of Example 3 for different input voltage values:(a) Vin = 5 V; (b) Vin = 3.5 V; and (c) Vin = 2.4 V (iL : 100 mA/div.,VGS1 : 10 V/div., VGS2 : 10 V/div., Time: 1 s/div.).

VI. CONCLUSION

A SIDO buck converter was analyzed for steady-state oper-ation. The various operating modes were explored and designequations were developed. These equations allow the designer tofind out intricate relationships among output voltages, transistorduty cycles, and output currents. From the results, a mix-voltageoperation was pointed out and demonstrated. This new mode ofoperation opens up new applications and may also extend theinput battery operable range for existing applications.


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Chun-Shih Huang (S09) was born in Kaohsiung,Taiwan, R.O.C., in 1982. He received the B.S. de-gree in electrical engineering from National ChungCheng University, Chiayi, Taiwan, R.O.C., in 2005.He is currently working toward the Ph.D. degree inelectrical engineering with the Department of Electri-cal Engineering, National Taiwan University, Taipei,Taiwan, R.O.C.

His current research interests include modelingand control of switching dcdc converters and elec-tromagnetic interference in switching power supplies.

Dan Chen (S72M75SM83F02) received theB.S.E.E. degree from National Chiao Tung Univer-sity, Hsinchu, Taiwan, R.O.C., in 1969, and the Ph.D.degree in electrical engineering from Duke Univer-sity, Durham, NC, in 1975.

From 1975 to 1979, he was with the GE Cor-porate Research Center, Schenectady, NY, where hewas engaged in power electronic applications includ-ing electric car and electronic ballast applications.From 1979 to 2003, he was with the Department ofElectrical Engineering, Virginia Polytechnic Institute

and State University, Blacksburg, and was a core Professor with the NationalScience Foundations Center for Power Electronic Systems, Blacksburg. SinceSeptember 2003, he has been a Professor with the Department of ElectricalEngineering, National Taiwan University, Taipei, Taiwan, R.O.C. In 1986, healso co-founded Motion Control System, Inc, a company dedicated to brushlessdc motor and control, in Dublin, VA, and served as the companys Chief Consul-tant until 2003. His current research interest includes power conversion systems,power semiconductor device characterization, electromagnetic interference inswitching circuits, and more recently, power ICs. He is the author or coauthorof numerous papers, held nine U.S. patents, and coedited an IEEE-Press bookon Power Transistors and their Applications, in 1984.

Dr. Chen coreceived the IEEE Aerospace Society Barry Carlton Award, in1975, the NASA Invention Award, in 1986, and the IEEE Power ElectronicsSociety Best Paper Award, in 1998.

Ching-Jan Chen (S08) was born in Taipei, Taiwan,R.O.C., in 1984. He received the B.S. degree in elec-trical engineering from National Taiwan University,Taipei, in 2006. He is currently working toward thePh.D. degree with the Department of Electrical En-gineering, National Taiwan University.

His current research interests include modelingand design and analysis of dcdc power converters,especially for CPU power applications.

Kwang H. Liu received the B.S. degree from Na-tional Taiwan University, Taipei, Taiwan, R.O.C, andthe M.S. and Ph.D. degrees from Virginia Polytech-nic Institute and State University, Blacksburg, allin electrical engineering, in 1976, 1982, and 1986,respectively.

He has been in the power electronics and power ICindustry since 1986. He was with ITT Power Systems,Delta Research Laboratory, Momenta Computer,Siliconix, O2 Micro, and Arques Technology. He iscurrently President with the Green Mark, Inc., Sin-

dian City, Taipei, a power IC company. He holds more than 15 U.S. patents.His research interests include high-efficiency power conversion, synchronousrectifier control, light-emitting diode lighting control, solar power system, solarinverter, vehicle power control, brushless dc motor control, dc servo system,and fast charger for electrical vehicle.

05272095 Buck Converter

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