Multiphase Buck Converter With Minimum Time Control .
Multiphase buck converter with minimum timecontrol strategy for RF envelope modulationP. M. Cheng, M. Vasic, O. Garcia, J. A. Oliver, P. Alou. J. A. CobosCentro de Electrónica Industrial, Universidad Politécnica de MadridMadrid, Spainpengming.cheng@upm.esAbstract—Power amplifier supplied with constant supply voltagehas very low efficiency in the transmitter. A DC-DC converter inseries with a linear regulator can be used to obtain voltagemodulation. Since this converter should be able to change theoutput voltage very fast, a multiphase buck converter with aminimum time control strategy is proposed. To modulate supplyvoltage of the envelope amplifier, the multiphase converter workswith some particular duty cycle (i/n, i l, 2 . n, n is the number ofphase) to generate discrete output voltages, and in these dutycycles the output current ripple can be completely cancelled. Thetransition times for the minimum time are pre-calculated andinserted in a look-up table. The theoretical background, the systemmodel that is necessary in order to calculate the transition timesand the experimental results obtained with a 4-phase buckprototype are given.I.INTRODUCTIONThe solutions for the high frequency power amplifierscan be classified two different families of power amplifiers:linear and nonlinear. The linear power amplifiers (classes A,B or AB) are known to be highly linear, but inefficientsolutions. On the other hand, the nonlinear power amplifiershave high power efficiency and their output is a sinusoidalsignal with constant envelope. They are based on the idea touse transistors as switches instead as a current source. In thatway the power losses of the devices are lower and theseamplifiers are presented with classes C, D, E and F.In order to increase the spectral efficiency the moderntelecommunication systems use complex modulations thatare based on multicarrier signals and result in complexenvelopes that require high linearity. These envelopes havehigh peak to average power ratio and the linear poweramplifiers, due to this signal property, have extremely lowefficiency. Because of the low efficiency of the linearsolutions there has been a lot of research with the idea toextend the area of application of highly efficient non linearclasses. This topic became important especially with the fastdevelopment of the digital wide bandwidth applicationswhere the non constant envelope signals are applied and thenecessary linearity of the power amplifier is very highUntil now, several techniques have been used in order toincrease the linearity: Back-Off, predistortion, Doherty,Outphasing, Khan's technique (Envelope Elimination andThis work has been supported by the Ministry of Education and Science ofSpain for the project TEC2009-14307-C02-01Restoration, EER), etc. Almost all of these techniques havenot been able to provide high linearity and high efficiency inthe complete range of the transmitted signal. Only theKahn's technique has showed that it is capable to linearizehighly non linear power amplifier (for example class E) andto provide relatively high efficiency. This technique is basedon the use of one highly efficient, but non linear poweramplifier that is used for the phase modulation, together withan envelope amplifier that has to have high efficiency andprovide envelope modulation by modulating the voltagesupply of the non linear power amplifier. Simplified blockschematic of one Kahn's transmitter can be seen in Fig.l.Basically, this technique exploits the fact that any narrowband signal can be correctly defined by knowing its envelopeand phase.Although the Kahn's technique is very well known sincethe 50's of the last century there have been various issuesthat have stopped this technique to be massively exploited.Some of these problems are the limited bandwidth of the dcdc converters that are normally employed as the solution forthe envelope amplifier and the impossibility for thesemiconductor devices to operate at high frequencies andwide bandwidths due to the technology limits that arereflected as the maximal voltages, parasitic capacities, riseand fall times of the devices and parasitic effects of thepackage where the transistors are placedSimilar approach for the reduction of the energyconsumption is envelope tracking (ET). In this technique theenvelope amplifier is used to supply a linear power amplifierwith minimal needed voltage. Figure 2 shows a blockphasereference ,.inputcouplerJN o n linear RFPAill ili Ml i # #Power SupplyInputdetectorrr\EnvelopeAmplifierFigure 1. Block schematic of a tranismitter based on Kahn's technique
schematic of this approach.In the state of the art, several solutions for the envelopeamplifier can be found, such as a simple buck converter in[1], multiphase buck converter in [2], and three-levelconverter in [3]. In all these solutions the employedswitching dc-dc converters operate using PWM and thislimits the possible bandwidth of the envelope amplifier,because for the high bandwidth envelope it is needed toapply high switching frequency that leads to heavy switchinglosses. In [4], the idea is to employ a buck converter that useslow switching frequency in parallel with a linear regulator. Inthis case it is possible to obtain high efficiency because themajor part of the output power is managed by the buckconverter, while the fast dynamic response is guaranteed bythe linear regulator. A solution that exhibits a fast dynamicresponse and high output power is presented in [5, 6]. Themain idea is to exploit good dynamic characteristics of themultilevel converter and to increase its efficiency. Fig. 3shows relevant time diagrams. In this solution a multilevelconverter is put in series with a linear regulator, and themultilevel converter can be implemented by using differentconcepts, independent voltage cells [5], independent voltagesources [6] or multiphase topology that employs specialPWM modulation [7]. A similar solution that employs amultilevel converter in parallel with a linear regulator hasbeen presented in [8]. The multilevel converter isimplemented as an 8-phase buck converter that operates withduty cycles that provide current ripple cancelation in order todecrease the value of the output capacitor.In this paper an approach to implement a multilevelconverter that can be combined with a linear regulator inE-nlryvFigure 2. Block schematic based on envelope trackingorder to modulate the power supply of envelope amplifier inEER or ET is presented. Like the method in [8], themultilevel converter is implemented using an N-phase buckconverter, like it is shown in Figure 4, but the voltagetransients are obtained by employing the minimum timecontrol that has been used in several applications[9, 10]. In[9], it is used to implement a fast power supply that can beused for Dynamic Voltage Scaling (DVS) applications. Thecapacitor-charge balance algorithm is explained in [10],which is suitable for load step and has good current balanceduring the transient and after that. In this paper a simple andsimple hardware implementation control strategy with lookup table to control the transient is proposed. Only severaldiscrete voltage levels will be permitted. The converter willonly work at fixed duty cycles (i/n, i l, 2 . n, n is thenumber of phase) to take advantage of current ripplecancellation and provide easier calculation of the minimumtime transient. It is compatible with the envelope amplifier in[5].II.MINIMUN TIME CONTROL IN A MULTIPHASEBUCK CONVERTERA.Review of the minimun time control lawThe minimum time control is a control based on theMaximum Principle or Pontriagyn's Principle [9]. In the caseof a buck converter this theorem provides means to changethe buck's output voltage in the minimum time bycontrolling the on and off states of the buck's switches. Evenmore, it can be shown that this voltage transient can beobtained by closing and opening the main switch just once.The idea in this paper is to use a multiphase converterwith fixed duty cycles. When it is necessary to change theoutput voltage level, The pre-calculated on and off times forthe main switch are applied in order to change it in theminimum time without voltage over/under shoot. Each phasehas its own on and off times to assure that the circuit will beclose to the new steady-state condition after the transient.The transient starts when one of the phases finishes its PWMcycle. In order to do it is necessary to calculate the chargeflow through the inductors precisely. An approximation ismade by assuming that the output voltage is changedlinearly. Another important issue is that it is necessary toinclude the information regarding the current ripple of theeach phase in the calculus in order to avoid the errors. Thecomplete methodology for the calculation of the transienttime is presented in the following section.1 i-'1 if W . iii'j;irT li c)Figure 3. Time waveforms of the envelope amplifier based on Ímultilevel converter in series with a linear regulator MT. .-.i:i. -1-Ü-. : --1!" Figure 4. Multiphase buck converter in series with a linear regulator
B. Control strategy in multiphase buck converterIn order to calculate the minimum time and the intervalsduring which the main switch in the buck converter is turnedon and off in multiphase buck converter, it is necessary toanalyze the charge flow in each one phase of the multiphasebuck converter.where AI¡ is the difference of the phase current after andbefore the transient (Fig.5). Equation (6) leads tot0„j KAt The assumption that the output voltage changes linearlyduring the transient is made:K„.t(t) :V,V 1 t—t(1)Where Vi is the buck's output voltage before thetransient starts, At is the duration of the transient and AV isthe voltage difference of the output's voltage after and beforethe transient. During the transient time, from initial voltage(Vi) to the final voltage (V2), the output capacitor willreceive the charge ofe c C ( V 2 - V 1 ) C-AV -K2At2 1¡¿LOADAt-"-LOADiAU(3)'Here it is assumed that the load is a current source (if theload is a linear regulator and the voltage change issufficiently fast so that the load's current is constant, i.e. theenvelope is not changed significantly). All that charge willcome from the converter's inductors and it can be calculatedas:IUI0LI QC QLOAD¿2A/,.2 2KL t t , A/A/,.Vl(8)(9)Combining equations (7-9) it can be obtainedY*J0 nKAt(10) C 2A/2 111 (IDinSince the parameters of the converter and the transientvoltages (Vi, V2) are known, 2 ¡ i i c a n t e calculated.By using (4), (5), (10) and (11), the following equation isobtainedCAV IloadAt At2(-2L Atl„-nK22V„(4)where QLi is the charge provided by each phase of themultiphase converter. If it is assumed that the voltage changeis linear, which is close to the actual response, the charge ofone phase, QLi, can be calculated as:vjON,AtAVAt2-At2QL --IAt(5)2L "" 2LL6Lthwhere L is the 1 inductor's current before the transient,toN.i is the time interval during which the main switch of the1th phase is turned on and L is the value of the inductor ineach phase. It can be seen that the charge through each phasedepends on the current through each phase before thetransient. When the equation (5) is substituted in equation (4)it is clear that the total charge depends on the sum of thephase currents. If the duty cycle of the multiphase converteris chosen as i/n (i l.n, n is the number of the converters)the sum of phase currents is always equal to the load'scurrent, otherwise there will always be a small portion of thecurrent that goes to the capacitor due to the voltage ripple.Therefore, by selecting the duty cycles of i/n not only theoutput voltage has lower ripple, but the calculation of thetransient time is more exact.(7)V„1 0(2)v K--AVIt can be shown that for the selected duty cycles thefollowing equation always holds thatwhere C is the value of the output capacitor. During thesame time the load will receive the charge of:OK LAIi -nK2LAVn)6L- z r iA/,2(12)From this quadratic equation, the transition time, At, canbe calculated and then the turn on interval of each phase isobtained by using (7).It is important to notice that the transition time inequation (12) does not depend on the load current, but onlyon the difference of the current.Fig. 5 shows one voltage transition and one phase current.Some of the earlier mentioned values like AL or It can beobserved.r' ! ' . . . H i .VlÍjT- Vi jyVt 1. .1 r x III I I - **iFor each phase it can be written:LAI, VJ„ V,1At--AVAt2(6)Figure 5. Simplified waveforms of the buck's output voltage and thecurrent through one phase
Fig. 6 shows simulated gate signals in a 4-phase converterwhen the transition from 0.5Vm to 0.75Vm is performed. Itcan be observed that in order to avoid any oscillation, itcontinues with PWM keeping the corresponding phasedelays between the phases after the transient.,,„., \Fig. 7 shows the simulated output voltage and phasecurrents during the transient. The simulation has beenperformed in MATLAB and the input voltage of theconverter is 20V, the transition is from 10V to 15V, theinductor per each phase is 1 luH, while the output capacitoris 1 luF.:I ,M .-Table 1 shows the calculated times for each phase anddifferent transitions for the same converterC. Filter design constraintFor the given filter parameters (L, C), the transient timecan be calculated. This transient time restrict the maximumfrequency of the envelope that the converter can modulate.However, the design way is usually inversed. The maximumtransient time is fixed by the application, then there are aplenty of possibilities for the filter parameters (L, C). Theinductor limits the slew rate of current through the outputcapacitor, and the output capacitance value determines thecharge that has to be delivered during the transient time tochange the output voltage. Designing for very fast outputvoltage transient, a high ratio between L and C is suitable forcharging output capacitor very fast. And it makes inductorsize large. But the good regulation under the load currentchange requires a low ratio between L and C. It reduces thesize of inductor, but increase the inductor current ripple andoutput voltage ripple as well.If the maximal slope of the envelope signal is known theselection of the L and C can be made by using thisinformation and the equations from section B. It can beshown that there is a following relationship between theconverter's parameters:: 11; 1 -- -1Figure 6. Control strategy for the voltage transition from 0.5VIN to0.75VINA "Figure 7. Simulation results for the voltage transition from 0.5VIN to0.75VINT A B L E I.C - ( Ó F ¡ „ « Í : - 3 « F 1 - « A F - 3 « Í : V ¡ „ ) — - — V f A/f n 3)y6Lm22VinkV 'Transientwhere m is the maximal slew rate of the buck's outputvoltage. Obviously the solution in this paper takes advantageof multiphase converter's feature, if it works in someparticular duty cycles, which make completely ripplecancellation on output capacitor. With this feature, it allowsto design the filter with low value of inductor and relativelyhigh value of capacitor complying with the maximumtransient time without suffering from the output voltageripple. However, this analysis is outside the scope of thispaper and it will be detail presented in one of the futurepapers.FromIII.0.25ViNto0.5VJNFrom 0 . 5 V I Nto0.75ViNFrom0.75ViNto0.5VJNEXPERIMENTAL RESULTSA 4-phase prototype is used to validate the implementationof this minimum-time control strategy. The converterparameters are, VIN 20V, L 11UH and C lluF. The state{ mFrom 0 . 5 V I Nto0.25ViNTRANSIENT TIME FOR EACH PHASES FOR DIFFERENTTRANSITIONSPhasetoN [US]toFF [US]At 523M3.763.767.524th3.134.397.52
TFig. 8 output voltage step from 5V to 10V at 1A load current, 100kHzFig. 10 output voltage step from 5V to 10V and from 10V to 15V at 1Aload, 100kHzTABLE II.TransientFrom0.25VINto 0.5VINTHE EXPERIMENT TRANSIENT TIMEPhase1 st2 nd3 rd4thFrom0.5ViNto0.75VIN1 st2 nd3 rd4thFromFig. 9 output voltage step from 5V to 10V at 2A load current, lOOkFIztransient can be output voltage from 5V to 10V (25% dutycycle to 50% duty cycle), from 10V to 15V (50% duty cycleto 75% duty cycle) in Fig. 8, Fig. 9 and Fig. 10. The otherparameter of the state should be inductor current. Thanks tomultiphase with ripple cancellation, it is not necessary toknow the inductor current value before and after thetransient, but to know the difference of the current is enough.It can be seen from the equations in section II. The sum ofthe initial current can be cancelled by load current. Thisindicates that the control strategy is not influenced by thecurrent unbalance.0.75VINto 0.5VIN1 st2 nd3 rd4thFrom0.5ViNto0.25VIN1 st2 nd3 rd4tht0N 82.51.823.983.15t0FF 24.184.862.73.53At [us]6.686.686.686.68777777776.686.686.686.68The control strategy is implemented on FPGA. Fourcounters are used in the program to generate PWM signal.With different initial counter value, four PWM can work ininterleaved way. There is a process in the program tosynchronize the transient with one of the PWM signal by thecounter. At the end of the transient time, the new initial valuehas to be given to the counter. The on-time and off-time inthe transient required are in the look-up table in the program.The control is tested in open-loop, to validate the idea of theminimum time control.Table II shows the experimental transient time.Comparing with table 1, there are some differences, becausethe model is idea one and it introduces some errors.However, it still makes a good starting point to find realtransient time. More accurate model including the parasiticFig. 11 The prototype of the 4-phase buck converterresistance needed to calculate the transient time, which canbe the following work.
IV.The concept of the minimum time transient will beapplied for the envelopes with high slew rate. In order toachieve it, it is necessary to use significantly higherfrequency so that the output filter can be small, because thetransient time is directly proportional to its value. Fig. 11shows a photograph of the prototype that has been developedand the switching frequency that is applied is 2MHz.Another important issue of the future prototypes is thenumber of the phases that are used. To optimize the numberof the phases has been considered for the desired voltageslew rate, complexity of the system and its size.V.REFERENCESFUTURE WORKCONCLUSIONSModulating the envelope to improve the efficiency in RFsystem is an active research topic. There are a lot ofchallenges to optimize the performance of envelopemodulator. In this paper, the envelope amplifier includes anopen-loop multiphase buck converter in series with a linearregulator. The multiphase buck converter is analyzed to meetthe requirement for the variations of output voltage. Themethodology of calculating the parameters for this controlhave been presented. The theoretical results are verified inpractice using a 4-phase multiphase converter. The minimumtime control strategy can be obtain by transient model of themultiphase converter. This control strategy has simpletransient time calculation and easy hardware implementation.The trade-off between the transient time and the output filterparameters is considerate also. In the design, the relativelylow switching frequency and low value of inductor can beused without the problem of ripple, because of interleavedmultiphase converter and the particular duty cycles that areused.[1]V. Yousefzadeh, N. Wang, "A digitally controlled DC/DC converterfor an RF power amplifier", IEEE Transactions on Power Electronics,Volume 21, No. 1, January 2006, Pages: 164-172.[2] A. Soto, J.A. Oliver, J.A. Cobos, J. Cezon, F. Arevalo, "Power supplyfor a radio transmitter with modulated supply voltage", AppliedPower Electronics Conference, APEC '04, Volume: 1, Feb. 2004Pages:392-398.[3] V. Yousefzadeh, E. Alarcon, D. Maksimovic, "Three-level buckconverter for envelope tracking in RF power amplifiers," IEEE Trans,on Power Electronics, Volume:21, Issue: 2, March 2006, Pages:549 552.[4] V. Yousefzadeh, E. Alarcon, D. Maksimovic, "Band separation andefficiency optimization in linear-assisted switching poweramplifiers", IEEE Power Electronics Specialists Conference, 2006Pages: 1-7.[5] M. Vasic, O. Garcia, J.A. Oliver, P. Alou, D. Diaz, J.A. Cobos,"Multilevel Power Supply for High Efficiency RF Amplifier", Proc.of the 24th Annual IEEE Applied Power Electronics Conference,APEC '09, February 2009.[6] M. Vasic, O. Garcia, J.A. Ohver,P. Alou, D. Diaz, J.A. Cobos,"Switching capacities based envelope amplifier for high efficiency RFamplifiers" Proc. of the 25th Annual IEEE Applied Power ElectronicsConference, pp.723-728[7] M.C. Gonzalez, M. Vasic, P. Alou, O. Garcia, J.A. Oliver, J.A.Cobos, "Power Analog to Digital Converter for Voltage ScalingApplications", Proc. of the 25th Annual IEEE Applied PowerElectronics Conference, Feb. 2010 Pages:271 - 276.[8] M. Rodríguez, PE. Miaja, J. Sebastián, D. Maksimovic, "Mismatcherror noise-shaping based digital multiphase modulator", IEEECOMPEL Conference, June. 2010.[9] A. Soto, P. Alou, J.A Cobos, J. Uceda, "Analysis of the buckconverter for Scaling the supply voltage of digital circuits", IEEETransactions on Power Electronics, Volume 22, 6, November 2007Page(s):2432-2440.[10] J. Alico, A. Prodic, "Multiphase optimal response mixed-signalcurrent-programmed mode controller", IEEE Applied PowerElectronics Conference, Feb. 2010 Pages:1113 - 1118.
Multiphase buck converter in series with a linear regulator . B. Control strategy in multiphase buck converter In order to calculate the minimum time and the intervals during which the main switch in the buck converter is turned on and o
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Fig 1. Multiphase synchronous buck topology. One important operating parameter in the multiphase buck converter topology is called the duty cycle D. For buck converter, the ideal duty cycle when operated in continuous conduction mode (continuous inductor current) is the ratio of the output voltage
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