Author name used in this publication: S. C. WongAuthor name used in this publication: C. K. TseRefereed conference paper2003-2004 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe

Tang, KC

Tse, CKM

Wong, SC

Author name used in this publication: S. C. WongAuthor name used in this publication: C. K. TseRefereed conference paper2003-2004 > Academic research: refereed > Refereed conference paperVersion of RecordPublishedVoR allowe

PolyU Institutional Repository

2004 351h Annual IEEE Power Elecrronics Specialists Conference Aachen, Germany, 2004 Dual Current-Mode Control for Single-Switch Two-Output Switching Power Converters S. C. Wong, C. K. Tse and K. C. Tang Department of Electronic and Information Engineering Hong Kong Polytechnic University, Hunghom, Hong Kong, China Abstract-A novel method for programming current in dddc converters operating in discontinuous conduction mode is de- scribed in this paper. The control variable is the pmduct of the square of the duty cyle and the switching period, i.e., D'T, which is directly proportional to input and output currents of a discontinuousmode converter. A method of controlling D 'T is applied to converters that utilize one switch (or one set of synchronous switches) for achieving two control functions. In  particular a single-switch two-output boost converter, in which a continuous-mode converter and a discontinuous-mode converter share one active switch, is studied. In this system, current-mode control is used to regulate the output voltage of the continuous- mode converter and the proposed D 'T control is used to regulate the other discontinuous-mode converter. The result is a generic current-mode controlled dual-output converter. Keywords-Current-mode control, dddc converter, dual-output converter, discontinuous conduction mode. I. INTRODUCTION This paper describes a single-switch two-output regulator which comprises two boost converters, one operating in contin- uous conduction mode (CCM) and the other i n  discontinuous conduction mode (DCM) [I],  [2]. Previously reported control methods take advantage of the insensitivity of the CCM converter to switching frequency, and apply duty-cycle control to regulate the CCM converter while regulating the DCM converter by frequency modulation 131, [4]. In this paper, we consider application of generic current-mode control to both converters in  order to achieve faster transient responses [5].  Specifically, we use a standard current programming for the CCM converter and a novel D2T control for regulating the DCM converter. We will also discus:; the local stability of the combined current-mode and DZT control scheme, and present a practical circuit implementation of the controller. 11. OUTLINE OF THE PROPOSED CONTROL Inspired by its averaged behaviour model, the DCM con- verter can he controlled by varying the control quantity D Z T  which is proportional to the output current [6] .  In principle, if the quantity D2T is adjusted via a feedback mechanism, the output load voltage can he regulated. A special but practically important case is when either the omtime or off-time duration is already determined by another control law. We shall make reference to a single-switch two-output boost converter later in  the paper. Suppose the duty cycle is D, and the period begins with the switch turned off. Thus, after a duration of (1 - D)T ,  the switch is turned on; and after another duration of DT,  the switch is turned off again, completing one cycle. Our objective .is to derive a scheme, whereby the off-time duration (1 - D)T is pre-determined and the period T is adjusted to give the desired value of D'T. The proposed 0 W D ) T  1switchd"vinifij ti ~ off-time on-time off-time on-time 1 restart  switching cycle s = I for on time s = 0 for off time (b) Fiq. I .  (a) Waveforms of the parabolic and ramp generators in the conceptual D T control scheme; (b) conceptual implementation. controller consists of a periodic parabola generator p ( t )  and a ramp generator r(t): p ( t )  = a(t - to)' ( 1 )  r(t) = b ( t - t b )  ( 2 )  where to and tb are arbitrary start instants for the two generators, and a and b can be considered as constant for the time being. Fig. 1 (a) shows these generator waveforms. At the start of the switching cycle, say t = 0, the ramp generator is triggered to start. At t = (1 - D)T  (which is determined externally), the switch is turned on. At the same time, the parabola generator is triggered to start from zero. As soon as the outputs of the generators are equal, the switch is turned off whereby spawning a new cycle. Clearly, this 0-7803-8399-0/04/$20.00 82004 IEEE. 23' Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on December 16, 2008 at 01:24 from IEEE Xplore.  Restrictions apply.2004 351h A n n u l  IEEE Power Elecrronics Specialists Conference Aachen. Germany, 2004 I I I 4 b I I bl T2 TI Fig. 2. Inductor cunent waveform for stability analysis. rent-mode co"tmlJ Fig. 3. mode D2T convol. Details of the D2T control block is shown in Fig. 4. Schematic of dual-output boost regulator under combined current- condition forces in  a typical continuous-mode dcldc converter under current- mode control, the turn-off instant is determined by comparing the inductor current with a reference level. Thus, effectively, this conventional scheme is controlling the on-time duration. In our scheme, however, we control the off-time duration instead. As we will see, this has an important implication on the stability. In brief, the switch is turned on at the instant the inductor current descends to a reference level. The turn- off instant, moreover, is determined by our proposed D2T control. In other words, the repetition period is controlled by the D2T controller. The stability issue therefore involves the consideration of the stability of the current-mode control with off-time duration being pre-determined and the period being controlled by the D2T scheme. First, referring to Fig. 2, we can write the inductor current values at the start and end of a period as (4) i l  = Jref + (mc + mz)Tz i 2  = Zref + m,Tz + mlT1 where TI is the on-time duration, T2 is the off-time duration, ml is the on-time inductor current slope, m2 is the off- time inductor current slope, and m, is the compensation slope. Note that we consider here the general case where a compensation slope is included in the current-mode control. Upon differentiating (4). we get Let us now introduce the D2T control to the abovementioned current-mode controlled converter. In the steady state, the aim is to fix the value of D'T, i.e., T: = constant, TI + Tz where the constant in the RHS is equal lo the steady-state value of D'T. Thus, differentiating (6). we get 6T1 D bT2 2 -  D - (7) (3) Hence, the quantity D2T can be made controllable by varying Hence, from (5 ) ,  and using mlD = mz(1 - D),  we have p(DT) = r(T) + a(DT)' = bT + D2T = b/a. D (8 )  biz m , + m l ~ - m , + m z ~  6i1 m, +mz mc + m2 - - bJa. A conceptual implementation of this control scheme is shown in Fig. 1 (b). In this scheme, the off-time duration is -- - . .  externally determined, and the control circuit in turn produces a pulse to set the period. Thus, the proposed control can be viewed as a modulator which, for each cycle, maintains a constant DZT. If the current sources (i.e., a and Local stability requires that the magnitude of the above expression be less than 1. Thus, we can see that stability is guaranteed for all since (9) b) are controllable, the quantity D2T can be modulated via 1 - D  1 O < -  < - for all D E (0, l) ,  2 - 0  2 feedback. 111. LOCAL STABILITY OF COMBINED CURRENT-MODE which implies 16~~,6i~l < 1 for all 0 < It is interesting to note that the stability of the system is unaffected even when the compensation ramp is zero. In other words, the DZT control inherently stabilizes the current-mode control, eliminating the need for ramp compensation. < 1, A N D  D2T CONTROL Our interest in this section is to study the local stability of the proposed control scheme when the off-time duration is pre-determined by a current-mode control scheme. Essentially, 24 Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on December 16, 2008 at 01:24 from IEEE Xplore.  Restrictions apply.2004 3Sth Annual IEEE Power Electrvnics Specialists Conference Aachen, Germany, 2004 I ItlufR) ("e) UCd QPP (ncxyz) Reset - - Fig. 4. Derailed circuit schematic of the D2T control. IV. EXPERIMENTAL VERIFICATION consists of a CCM boost converter and a DCM boost converter, sharing one common switch. The circuit design aspect has been studied extensively by Sebastian et al. [l], [3]. Here, we focus on the application of the proposed combined current- mode and DZT control for simultaneous regulation of the two outputs, and verify the control function with an experimental In this section we present a single-switch two-output boost regulator, as outlined previously in the Introduction. Figs. 3 and 4 show the schematic of the system and the detailed circuit of the D2T controller, respectively. In brief, this regulator 25 Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on December 16, 2008 at 01:24 from IEEE Xplore.  Restrictions apply.2004 351h Annual IEEE Power Elecrronics Specialists Conference Aachen. Germany. 2004 output 2 ( IXMi 45' 40 - - - - . - - - - . - - -  ;" 1-1 0 40 35 30 25 20 15 10 5 I " d  ill outpu, I IQ) J" oulpul I (CCM) 25 20 '; 1-1 O40 60 80 100 120 140 load at output 2 IQ) Fig. 5. Experimentally measured steady-state output voltages versus load variation in output 1. with load at outpul 2 fixed at 60 R; (b) steadystate output voltages versus load variation in output 2, with load at output I fixed at 10 R; (c) mnsient responses for step changing loads with R ol changing from 10 R to 35 R at t = 4 ms. and back to 10 R at t = 14 ms; (d) transient responses for step changing loads with R ,z changing from 50 R to 100 R at t = 4.2 ms, and back to 50 Rat  t = 14.2 ms. Venical scale: 10 Vldiv and 2 Ndiv.  Horizontal scale: 2 inddiv. TABLE I COMPONENT A N D  PARAMRTBRVA1.UF.S OF BXPERIMBNTAI. PROTOTYPE Componentlparameter Value Inductance I (CCM). L I  100 pH Inductance 2 (DCM). LZ 20 pH Output capacitance I, CI 41  YF Output capacitance 2, Cz 100 p F  Input voltage. Vi. I2 to 16 V Load resistance I, R,,  10to40R Load resistance 2,  R,z 40 to 147 R Power MOSFET IRFP 360 Frequency 20 to IW kHz prototype. In the experiment, discrete components are used to construct the the D2T control block, as shown in Fig. I (b). Component and parameter values of the prototype are summarized in Table 1. Of the CCM converter is referenced at  the turn-on instant, and hence its peak is generally unlimited (actually determined by the DZT control). It is thus necessary to impose a peak limiter to limit the maximum switching period. This arrangement has been incorporated in our study. Several tests have been performed to verify the operation of the proposed control. First of all, the steady-state output char- acteristics characteristics have been obtained by plotting the output voltages against load variations. Measured results are Fig. 6.  Oulput tmnsienl responses for step changing inpul voltage. At t = 6 ms, V,. steps up from 12 V to 16 V. and at t = 14 ms. it steps down back to 12 V. Vertical scale: 10 Vldiv and 2 Ndiv.  Horizontal scale: 2 msldiv. shown in Figs. 5 (a) and (b). Then, the transient performance has been evaluated, including input regulation, load regulation and cross regulation. Results are shown in Figs. 5 ( c H d )  and 6. In Figs. 5 (cHd) ,  the transient responses are recorded when the load resistances are stepped. Note that Figs. 5 ( c H d )  reflect very satisfactory self load regulation performance as well as cross regulation performance, i.e., transient of u,i (or It is noting that the inductor 26 Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on December 16, 2008 at 01:24 from IEEE Xplore.  Restrictions apply.2004 35rh A n n u l  IEEE Power Elecrrvnics Specialists Conference Aochen. German>,, 2004 v,2) when R,z (or RO1) is stepped. In Fig. 6, the transient responses are recorded when the input voltage is stepped. I ,  V. CONCLUSION /. * In a dual-output voltage regulator, where two dcldc convert- ers (one operating in CCM and the other in  DCM) are sharing one switch, generic current-mode control can be achieved by applying conventional current-mode control to the CCM converter and a DZT programming control to the DCM converter. In  this paper we propose a strategy for control- ling the D2T quantity, whereby both outputs can be tightly regulated. Satisfactory cross regulation is possible by virtue of the CCM converter being insensitive to frequency changes and the DCM converter being directly current-programmed. Clearly, the concept of direct DZT control can also be applied to other applications where one switch is required to achieve two functions, e.g., in  single-switch single-stage PFC power supplies. ACKNOWLEDGMENT This work is supported by Hong Kong Polytechnic Univer- sity under Grant G-T662. REFERENCES [ I ]  J. Sebastian and J. Uceda. ”Double converter: a fully regulated two output dc-to-dc canvener.”lEEE PESC Rec., pp. 117-126. 1985 [2] J. Sebastib, J. Uceda. M. Rico. M.A. Perez and E Aldana. “A com- plete study of the double forward-flyback convener:’ IEEE PESC Rec., pp. 142-149. 1988. 131 T. Charanasamban. M.J. Devaney and R.G. Hofl, “Single switch dual output ddde  converterpelfomwnce:’lEEE T r m .  Power Electmn., vol. 5,  no. 2, pp. 241-245. 1990. [4] ET. Tang and C.K. Tse, “Design and implementation of a fully-regulated four-output wo-switch one-controller power module:’ lEEE PESC Rec., pp. 823-828. June 1996. 151 R. Redl and N.O. Sokal, “Cumnt-mode control. five different types. used with the three basic classes of Dower converten,” lEEE PESC R e t ,  pp. 771-775. 1985. [6] PR. Severns and E.J. Blwm, Modern Switching DC-to-DC Power Con- verter Circuils, New York: Van Nostrand, 1985. 21 Authorized licensed use limited to: Hong Kong Polytechnic University. 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Dual current-mode control for single-switch two-output switching power converters

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