the fast response double buck dc\u0026#8211;dc converter (frdb): operation and output filter...

$: The Fast Response Double Buck DC\u0026#8211;DC Converter (FRDB): Operation and Output Filter Influence$
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 20, NO. 6, NOVEMBER 2005 1261

The Fast Response Double Buck DC–DC Converter(FRDB): Operation and Output Filter InfluenceAndrés Barrado, Member, IEEE, Antonio Lázaro, Member, IEEE, Ramón Vázquez, Vicente Salas, and

Emilio Olías, Member, IEEE

Abstract—The fast response double buck (FRDB) dc–dc con-verter was presented like a low output voltage dc–dc converterwith fast transient response, in order to feed devices such as mi-croprocessors and digital signal processors (DSPs). The topologyof the FRDB is composed of two buck converters connected inparallel, each one of them with different features and aims, andcontrolled by means of the novel linear-non-linear (LnL) control.

In this paper, the topology, the control strategy and the operationprinciple are shown. Finally, experimental results in different pro-totypes are presented to show both, the transient response and therecovery time when these prototypes are subjected to load currentsteps, and the influence of the output filter on these parameters.

Index Terms—Digital signal processors (DSPs), fast responsedouble buck (FRDB) dc–dc converter, linear-non-linear (LnL)control, voltage regulator module (VRM).

I. INTRODUCTION

I N RECENT years, different strategies and power topologieshave been presented in order to feed previous generations

of microprocessors and digital signal processors (DSPs). Thesetypes of devices need power supplies with low output voltage,high output current, and the main challenge of fast transient re-sponse [1]–[4].

Different techniques have been used in order to improve thetransient response of these types of power supplies: some ofthem improve the control block like hysteretic control orcontrol [5]–[7]; others modify the topology like the voltage reg-ulator module (VRM) with interleaving techniques [8], [9]; andother solutions, like the hybrid sources [10], [11] have mademodifications on both the control and the topology. VRMs arehaving a fast evolution since they present important featuressuch as robustness and versatility. In fact, many industrial ap-plications have been developed based on VRM solutions.

The fast response double buck converter (FRDB converter)was presented like a dc–dc switching converter, which can beconsidered an alternative to the VRM converters in some ap-plications [12]. This type of converter is composed of two buckconverters connected in parallel, each one of them with differentfeatures and aims. Moreover, the FRDB converter is controlledby means of the linear-non-linear (LnL) control. The goal ofthis converter is to reduce the recovery time of the output

Manuscript received August 5, 2004; revised January 14, 2005. This workwas supported by the Ministry of Science and Technology, Spain, under Re-search Project ALDIRA (Code PN: DPI2001-0748). Recommended by Asso-ciate Editor C. K. Tse.

The authors are with the Departamento de Tecnología Electrónica, Uni-versidad Carlos III de Madrid, Leganés 28911, Madrid, Spain (e-mail:[email protected]).

Digital Object Identifier 10.1109/TPEL.2005.854017

voltage when the converter operates under load current steps,limiting, at the same time, the variation of the output voltage( Vomax) and guaranteeing the stability of the converter.

The FRDB converter combines two strategies. The first one,from a topological point of view, is in the way of the solutionsproposed in [13] and [14]. In these two solutions the transient re-sponse is only improved during negative load current steps, andthey use a nonlinear control based on threshold logic, similarto hysteretic control. However, in the FRDB converter the tran-sient response is improved for positive and negative load currentsteps, and the nonlinear control used presents different featuresand implementation.

The second strategy, in this case from the control point ofview, is in the same manner as that of the solutions proposedin [15] and [16], although the FRDB converter presents impor-tant differences, such as the fact that the LnL control used in theFRDB converter is asynchronous. Therefore, the duty cycle sat-uration is instantaneous, once the load current step is produced;the LnL control allows obtaining a 100% duty cycle during sev-eral consecutive switching periods; the control error signal inthe non-linear block of the LnL control is not filtered, and there-fore, delays are not produced in the transmission of this signal,facilitating a very fast response; and with the LnL control theduty cycle can be saturated (100% or 0%) even if the controlerror signal of the linear block, in the LnL control, is betweenthe maximum and minimum values of the ramp signal in themodulator.

In this paper, once the operation principle of the FRDB con-verter is revised and experimentally shown, the influence ofthe output filter values will be also experimentally shown. Toachieve these experimental results, several prototypes has beendesigned and built. Finally, some conclusions will be deduced.

II. FRDB TOPOLOGY

Fig. 1 shows the block diagram of the FRDB converter.The topology of this converter is composed of two switchingconverters (in this case both of them with buck topology [seeFig. 2]) connected in parallel. It is very important to take intoaccount the fact that although both converters are connectedin parallel, they have to be designed with different purposes,and therefore , the operation does not match a typical paralleloperation.

In the FRDB converter, the main switching converter must bedesigned to work in steady-state operation, and therefore with agood stability and a low output voltage ripple, but consequentlywith slow response. On the contrary, the auxiliary switchingconverter must be designed to work in transient operation. The

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1262 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 20, NO. 6, NOVEMBER 2005

Fig. 1. Basic structure and operation of the FRDB converter.

Fig. 2. Simplified diagram of a FRDB converter.

main aim of the auxiliary converter is to provide the requiredhigh current slew rate and fast transient response. However, lowoutput voltage ripple is not a requirement for the auxiliary con-verter.

Fig. 2 shows the simplified diagram of the FRDB converter.In this figure, two buck topologies have been used to design theauxiliary and main converter. Both of them feed the output inparallel. Furthermore, a control block can be noticed. Basically,the control block is composed of a linear control, a non-linearcontrol, and finally, a multiplexer (MUX).

In short, and from a topological point of view, the principleoperation is based on keeping the main switching converter op-erating all the time, connecting the auxiliary switching converteronly at the edges of the load current steps. In this way, the aux-iliary converter completes the main converter performances inorder to fulfill the requirements.

III. CONTROL STRATEGY

LnL control is used to regulate the FRDB converter [17]. Thestability of this type of control was study in [18] using the de-scribing transfer function. From a general point of view, thestability of a non-linear control applied to dc–dc converter isdemonstrated using the Lyapunov’s method in [19].

The LnL control is based on the utilization of a threshold band(see Fig. 3). This band presents two limits, a higher

threshold (HT, ) and a lower threshold (LT, )

Fig. 3. FRDB converter waveforms: (a) load current steps, (b) output voltage,(c) duty cycle, (d) L/NL and E/D selection inputs, and (e) injected current bythe auxiliary converter.

[see Fig. 3(b)]. If the output voltage is within the threshold band,only the main switching converter operates, and therefore theFRDB operates like a typical buck converter with linear con-trol. If output voltage goes out the threshold band, the auxiliaryswitching converter and the non-linear control are connected(E/D and L/NL inputs are set to 1 [see Figs. 2 and 3(d)]).

The threshold logic and the duty cycle saturation and resetlogic, in non-linear control (see Fig. 2) are used to detect if theoutput voltage is within the threshold band, above the higherthreshold or below the lower threshold.

The LnL selection input of the multiplexer (MUX) selectseither the linear control output, with low level, when outputvoltage is within the threshold band, or the non linear controloutput, with high level, when output voltage is out the thresholdband.

The input E/D of the driver, in auxiliary converter, is used toenable (set to 1) or to disable (set to 0) the driver.

The operation principle is shown in Fig. 3. In steady-stateoperation, the output voltage is within the threshold band, grayarea in Fig. 3(b); the main buck converter works with linearcontrol and almost constant duty cycle [see Fig. 3(c)]; the L/NLinput is at low level to select linear control [see Fig. 3(d)]; andthe auxiliary converter injects no current [see Fig. 3(e)], sinceE/D input is set to 0 like L/NL input.

When a load current step occurs, if output voltage exceedsthe thresholds, the input L/NL and E/D are set to 1. Then, theauxiliary buck converter starts to work, and the main converteris controlled by means of the nonlinear control, Fig. 3(d). Theduty cycle saturation and reset logic block forces of the dutycycle to 1 if the lower threshold is surpassed, or it set the dutycycle to 0 if the output voltage is above the higher threshold [seeFig. 3(c)].

At the same time, the auxiliary converter injects current tothe output, if the output voltage is below the lower threshold, or

BARRADO et al.: FAST RESPONSE DOUBLE BUCK DC–DC CONVERTER 1263

Fig. 4. Main theoretical current waveforms comparison: (a) typical buckconverter, (b) two buck converters in parallel with linear control, and (c) FRDBconverter.

it takes the current out from the output if the output voltage isabove the higher threshold [see Fig. 3(e)]. Therefore, the auxil-iary converter forces the output voltage to be within the thresh-olds [see Fig. 3(b)].

It is important to emphasize that the nonlinear control andthe linear control are independent. Thus, no instabilities are pro-duced when the output voltage returns into the threshold bandand the linear control has to regulate the converter.

Also, it is advisable to take into account that in real proto-types, the used threshold band has to be lower than the max-imum output voltage ripple indicated in the specifications.

IV. MAIN THEORETICAL CURRENT WAVEFORMS COMPARISON

The FRDB converter combines two different actions to getfast transient response. One of them is to provide or to take outcurrent from the output, when the output voltage exceeds thethresholds [see Fig. 3(e)]. Another one is to change the con-trol of the main converter from linear control to non linear con-trol, also when the output voltage exceeds the thresholds [seeFig. 3(d)].

It very important to know the effects of each action on themain waveforms, such as the output voltage ripple, the dutycycle, and the current provided by the main and auxiliary con-verter.

The main theoretical current waveforms are shown in Fig. 4.Fig. 4(a) shows the output current and the current pro-vided by the main converter , when the power supply isonly composed of a buck converter with linear control (typicalbuck converter). Fig. 4(b) shows the output current , the cur-rent provided by the main converter and the current pro-vided by the auxiliary converter , when the power supply iscomposed of two buck converters connected in parallel, and themain converter is always controlled by means of a linear con-trol. Finally, Fig. 4(c) shows the output current , the current

Fig. 5. BL: Conventional Buck converter with linear control.

Fig. 6. BLnL: Buck converter with LnL control.

provided by the main converter and the current providedby the auxiliary converter , when the power supply is com-posed of two buck converters connected in parallel, and the mainconverter is controlled with a LnL control (FRDB converter).

In Fig. 4(b), it is possible to notice, in comparison with thecurrent waveforms shown in Fig. 4(a), that the current providedby the auxiliary converter completes the current provided by themain converter in order to supply the output current. However,the evolves slower than in Fig. 4(a). This is because theauxiliary converter provides or takes out current from the output,since the output voltage is closed to the threshold limits. As aconsequence, the error seen by the linear control in the outputvoltage of the main converter is small, and therefore, the changein the main converter is slow.

In Fig. 4(c), this problem has been removed. At the same timethat the auxiliary converter is connected, the control of the mainconverter is changed to non linear control. As a consequence,the duty cycle is saturated (set to 1 or to 0), getting the fastestresponse of the main converter. This fact reduces the energyprovided by the auxiliary converter.

V. EXPERIMENTAL RESULTS

In order to check the features of the FRDB, several prototypeshave been designed and built. These prototypes can be classifiedas follows.

• A conventional Buck Converter with linear control: BL[see Fig. 5].

• A Buck converter with LnL control: BLnL [see Fig. 6].• Two Buck converters connected in parallel, in which the

auxiliary converter works when the output voltage goes


Fig. 7. BBL: Two Buck converters connected in parallel, in which the auxiliaryconverter works when the output voltage goes out the threshold band, and themain converter is always controlled by means of a linear control.

Fig. 8. FRDB: Two Buck converters connected in parallel with LnL control.

out the threshold band, and the main converter is alwayscontrolled by means of a linear control: BBL [see Fig. 7].

• Two Buck converters connected in parallel with LnL con-trol: FRDB [see Fig. 8].

Based on these prototypes two different sets of testing havebeen implemented. The first one tries to check the operationanalysis, the transient response, and the recovery time, amongothers; the second one tries to show the output filter influence.Both types of testing are summarized as follows.

A. Operation Analysis and Features

In order to check the operation and the features of the FRDB,four prototypes have been designed and built according to thespecifications shown in Table I.

Each prototype belongs to one of the four types of converterspreviously described: BL, BLnL, BBL, and FRDB.

These four prototypes have been tested and compared underthe same conditions. Also, the same main buck converter hasbeen used to make the switching block of the four prototypes. In

TABLE IMAIN DESIGN PARAMETERS OF THE PROTOTYPES

Fig. 9. Prototype 1- BL: Typical Buck converter with linear control, undera 16-A load current step. Ch1: �V , output voltage ripple (100 mV/div, accoupling). Ch2: I , load current (20 A/div). Ch3: I , output current of themain Buck converter (20 A/div). Ch4: I , output current of the auxiliary Buckconverter (20 A/div). Time base 200 �s/div.

this way, the differences that could appear between the studiedsystems due to their assemblies have been minimized.

1) Main Waveforms: Figs. 9 and 10 show the transient re-sponse of a typical buck converter with linear control and theFRDB converter, respectively.

It can be seen how both the time in which the output voltageis kept out of the threshold band , recovery time) and theoutput voltage variation are drastically reduced in theFRDB converter. This is due to the extra current delivered bythe auxiliary converter to the output, and the used LnL control.Therefore, the transient response obtained in the new supply ismuch faster.

Figs. 9–12 show the influence of the LnL control in compar-ison with the Linear control. It can be seen in Figs. 9 and 11,that the current slew rate of the main converter is higherusing LnL control (see Fig. 11) than using linear control (seeFig. 9). Also, by means of Figs. 10 and 12, it is possible to seethat the current provided by the auxiliary converter , as wellas its operation time, are drastically reduced using LnL control(FRDB includes LnL control).

2) Output Voltage Recovery Time and Current Slew RateComparison: Figs. 13–18 show, in detail, the transient re-sponse of the built converters. In these figures, four waveformscan be seen, the output voltage ripple , the gate-sourcevoltage applied to the forward switch, , in the main con-verter , the output current of the main Buck converter

, and the output current of the auxiliary Buck converter.


Fig. 10. Prototype 1- FRDB converter under a 16-A load current step. Ch1:�V , output voltage ripple (100 mV/div, ac coupling). Ch2: I , load current(20 A/div). Ch3: I , Output Current of the Main Buck Converter (20 A/div).Ch4: I , output current of the auxiliary Buck converter (20 A/div). Time base200 �s/div.

Fig. 11. Prototype 1- BLnL: Buck converter with LnL control under a 16-Aload current step. Ch1: �V , output voltage ripple (100 mV/div, ac coupling).Ch2: I , load current (20 A/div). Ch3: I , output current of the main Buckconverter (20 A/div). Ch4: I , output current of the auxiliary Buck converter(20 A/div). Time base 200 �s/div.

Figs. 13–15 show the response of the converters under a 16-Apositive load current step and, Figs. 16–18 show the responseunder a 16-A negative load current step.

By means of these figures, four parameters can be compared:the recovery time in the waveform, the saturation (set to 0or to 1) of the signal control in the waveform, the currentslew rate of the main converter in the waveform, and thecurrent provided by the auxiliary converter in the waveform.

In Figs. 13–15, it can be seen that the recovery time is dras-tically reduced using two buck converters connected in parallel(BBL and FRDB converters). This time is reduced from 147 sto 4 s.

Furthermore, Fig. 15 shows how the LnL control saturatesthe duty cycle to 1, when the output voltage go below the lowerthreshold, and the saturation is maintained until the outputvoltage go back the threshold band (take into account thatthe threshold band is lower than 30 mV). This saturation

Fig. 12. Prototype 1- BBL: Two Buck converters with linear control undera 16-A load current step. Ch1: �V , output voltage ripple (100 mV/div, accoupling). Ch2: Io, load current (20 A/div). Ch3: I , output current of themain Buck converter (20 A/div). Ch4: I , output current of the auxiliary Buckconverter (20 A/div). Time base 200 �s/div.

Fig. 13. Prototype 1- BL: output voltage recovery time under a 16-A positiveload current step. Ch1: �V , output voltage ripple (100 mV/div, ac coupling).Ch2: V , MOSFET M (20 V/div). Ch3: I , output current of the mainBuck converter (20 A/div). Ch4: I , output current of the auxiliary Buckconverter (20 A/div). Time base 50 �s/div.

allows for getting the highest current slew rate that the mainconverter can present. Finally, comparing Figs. 14 and 15, animportant reduction of the current and the energy provided bythe auxiliary converter is achieved, due to the LnL control.

Figs. 16–18 show similar conclusions to the previous ones.But in this case, the LnL control saturates the signal controlto 0, when the output voltage goes above the higher threshold.Also, the reduction obtained in the recovery time has beendrastic, from 175 s to 15 s.

It is important to take into account that the FRDB, thanks tothe LnL control, keeps a fast response independent of the ampli-tude of the load current step, as long as the output voltage goesout the threshold band, unlike the buck converter with linearcontrol in which its response is very dependent on the load cur-rent step and the regulator gain.

3) Efficiency: Finally, the efficiency of the prototypes as afunction of the applied load current steps frequency is shown inFig. 19.


Fig. 14. Prototype 1- BBL: output voltage recovery time under a 16-Apositive load current step. Ch1: �V , output voltage ripple (100 mV/div, accoupling). Ch2: V , MOSFET M (20 V/div). Ch3: I , output current ofthe main Buck Converter (20 A/div). Ch4: I , output current of the auxiliaryBuck converter (20 A/div). Time base 50 �s/div.

Fig. 15. Prototype 1- FRDB: output voltage recovery time under a 16-Apositive load current step. Ch1: �V , output voltage ripple (100 mV/div, accoupling). Ch2: V , MOSFET M (20 V/div). Ch3: I , output current ofthe main Buck converter (20 A/div). Ch4: I , output current of the auxiliaryBuck converter (20 A/div). Time base 50 �s/div.

In Fig. 19, the relative efficiencies relationship is more impor-tant than the absolute values. This is due to the fact that the usedmeasurement equipment has limited its bandwidth to 50 kHz,therefore, for higher frequencies the error in the measurementis also higher.

It can be seen that the buck converter, with linear-nonlinearcontrol, presents the best efficiency, even higher than buck con-verter with linear control. This is because the BLnL converterpresents lower switching power losses when the duty cycle issaturated. On the contrary, the BBL converter has shown theworst efficiencies, since this topology delivers more energy bythe auxiliary converter.

However, with the utilization of the LnL control, in theFRDB, the differences among efficiencies of the BBL con-verter, in respect to the typical buck converter, have beensignificantly reduced.

Fig. 16. Prototype 1- BL: output voltage recovery time under a 16-A negativeload current step. Ch1: �V , output voltage ripple (100 mV/div, ac coupling).Ch2: V , MOSFET M (20 V/div). Ch3: I , output current of the mainBuck converter (20 A/div). Ch4: I , output current of the auxiliary Buckconverter (20 A/div). Time base 50 �s/div.

Fig. 17. Prototype 1- BBL: output voltage recovery time under a 16-Anegative load current step. Ch1: �V , output voltage ripple (100 mV/div, accoupling). Ch2: V , MOSFET M (20 V/div). Ch3: I , output current ofthe main Buck converter (20 A/div). Ch4: I , output current of the auxiliaryBuck converter (20 A/div). Time base 50 �s/div.

Therefore, from this point of view, the converters with LnLcontrol present a better efficiency than the same converters usinglinear control, besides improving its transient response.

B. Output Filter Influence

In order to check the output filter influence on the FRDB con-verters, three different design parameters, shown in Table II,have been applied in two types of prototypes.

• A conventional Buck converter with linear control: BL,Fig. 5.

• Two Buck converters connected in parallel with LnL con-trol: FRDB, Fig. 8.

In both cases, the same prototype has been built with differentoutput filter values and tested and compared under different loadcurrent steps amplitude.

The experimental results of the Prototype 1-BL and Prototype1-FRDB, both designed with the parameters at 1 of Table II,were shown in Figs. 9 and 10, respectively. This is because the


Fig. 18. Prototype 1- FRDB: output voltage recovery time under a 16-Anegative load current step. Ch1: �V , output voltage ripple (100 mV/div, accoupling). Ch2: V , MOSFET M (20 V/div). Ch3: I , Output current ofthe main Buck converter (20 A/div). Ch4: I , output current of the auxiliaryBuck converter (20 A/div). Time base 50 �s/div.

Fig. 19. Efficiency of the prototypes as a function of the applied load currentsteps frequency.

design parameters shown in Table I coincide with the designparameters at 1 in Table II.

Therefore, Fig. 9 shows the transient response of a typicalbuck converter (linear control) with the design parameters at 1(Prototype 1-BL), and Fig. 10 shows the FRDB converter withthe design parameters at 1 (Prototype 1-FRDB).

It can be seen that once a 16-A load current step has beenapplied, the time in which the output voltage is kept out thethreshold band (recovery time), and the outputvoltage variation are drastically reduced in the FRDBconverter. This is because, as previously indicated, of the extracurrent delivered to the output by the auxiliary converter, andthe used LnL control.

In the design parameters at 2, the output filter values in mainswitching converter has been reduced ( 2.5 H C4.7 mF). The output inductance value in auxiliary switching

Fig. 20. Prototype 2-BL: Typical Buck converter with linear control, undera 32-A load current step. Ch1: �V , output voltage ripple (200 mV/div, accoupling). Ch2: I , Output Current of the Main Buck Converter (23 A/div).Ch3: I , Output Current of the Auxiliary Buck Converter (13 A/div). Ch4: Io,load current (27 A/div). Time base 200 �s/div.

Fig. 21. Prototype 2-FRDB converter under a 32-A load current step. Ch1:�V , output voltage ripple (200 mV/div, ac coupling). Ch2: I , outputcurrent of the main Buck converter (23 A/div). Ch3: I , output current of theauxiliary Buck converter (13 A/div). Ch4: I , load current (27 A/div). Timebase 200 �s/div.

TABLE IIMAIN DESIGN PARAMETERS OF THE PROTOTYPES

converter has been not modified. Furthermore, a 32-A load cur-rent step has been applied in these prototypes.

The obtained experimental results have been shown inFigs. 20 (Prototype 2-BL) and 21 (Prototype 2-FRDB). Again,the FRDB converter presents a better response than the BL one.


TABLE IIIMEASUREMENTS OBTAINED OF THE PROTOTYPES

Fig. 22. Prototype 3-FRDB converter under a 32-A load current step. Ch1:�V , output voltage ripple (100 mV/div, ac coupling). Ch2: I , outputcurrent of the main Buck converter (23 A/div). Ch3: I , output current of theauxiliary Buck converter (27 A/div). Ch4: I , load current (27 A/div). Timebase 200 �s/div.

Recovery times and maximum output voltage variations havebeen significantly reduced even with double load current stepsamplitude, in comparison to Figs. 9 and 10.

Fig. 22 (Prototype 3-FRDB) shows the waveforms obtainedwith design parameters at 3, when 32-A load current steps areapplied in its output. In this prototype, the inductance value ofthe output inductor in an auxiliary switching converter has beenreduced to 0.11 H (from 0.63 H). The output capacitor isthe same as that in prototypes 2 (Prototype 2-BL and Prototype2-FRDB).

In this case, the obtained waveforms are very similar to Pro-totype 2-FRDB. A more precise measurement shows some dif-ferences (see Table III).

Figs. 23 and 24 show the waveforms obtained with design pa-rameters at 3, when an 11-A output current step is applied. It canbe seen that if the topology works like a typical buck converterwith linear control (see Fig. 23) (Prototype 3-BL), the outputvoltage variation go out the specification . However,if FRDB is implemented, Fig. 24 (Prototype 3-FRDB), the vari-ation of output voltage is within the threshold band, and it fulfillsspecifications. Again, the FRDB converter presents a better re-sponse than the other analyzed topologies.

Fig. 23. Prototype 3-BL: Typical Buck converter with linear control, underan 11-A load current step. Ch1: �V , output voltage ripple (50 mV/div, accoupling). Ch2: I , output current of the main Buck converter (10 A/div). Ch3:I , output current of the auxiliary Buck converter (10 A/div). Ch4: I , loadcurrent (10 A/div). Time base 200 �s/div.

Fig. 24. Prototype 3-FRDB converter under an 11-A load current step.Ch1: �V , output voltage ripple (50 mV/div, ac coupling). Ch2: I , outputcurrent of the main Buck converter (10 A/div). Ch3: I , output current of theauxiliary Buck converter (10 A/div). Ch4: I , load current (10 A/div). Timebase 200 �s/div.

In Table III, the main measurements obtained with regard tothe output voltage variation and the recovery times have beensummarized. If BL and FRDB are compared, in all cases the


Fig. 25. Top side of a prototype.

Fig. 26. Bottom side of a prototype.

experimental results obtained in FRDB converters are signifi-cantly better than the experimental results obtained when pro-totypes work like a typical buck converter with linear control(BL).

Comparing the prototypes 1 with the prototypes 2, it can bededuced that with lower output filter values in a main Buckconverter, the transient response obtained is much better, evenif load current steps amplitude is double. However, the com-parison of the prototypes 2 and prototypes 3 shows that, if theoutput filter inductance value of the auxiliary converter is re-duced six times (from 0.63 H to 0.11 H), the maximum vari-ation of the output voltage is not affected, and the recovery time

is reduced slightly more than in the previous case.These experimental results indicate that there is an optimum

output filter inductance value for the auxiliary buck converter;and, there is an optimum relationship between the output filterinductance value of the auxiliary and main buck converter.

If 11-A load current steps are applied in Prototype 3-FRDB,the output voltage variation does not exceed the specifications,

30 mV, and therefore the recovery time is zero.In general, the obtained results show that the LnL control al-

lows for reducing the output filter requirements. This can beeasily seen by comparing Figs. 9 and 11. Prototype 1-BL needsharder output filter requirements than the Prototype 1-BLnL toget the same recovery time and output voltage variation.

Finally, Figs. 25 and 26 show the top and bottom side, respec-tively, for one of the built prototypes.

VI. CONCLUSION

Fast response double Buck converters (FRDB) are composedof two buck converters connected in parallel, and controlled by

the novel LnL control. This solution significantly reduces therecovery time and the output voltage variation incomparison with a classical buck converter, when a load currentstep has been demanded.

In this paper, the operation principle of the FRDB converterhas been revised and experimentally shown. The main advan-tages and features of the FRDB converter has been deduced bya comparison with other topologies: a conventional Buck con-verter with linear control: BL (see Fig. 5); a Buck converter withLnL control: BLnL (see Fig. 6); and two Buck converters con-nected in parallel, in which the auxiliary converter works whenthe output voltage goes out the threshold band, and the mainconverter is always controlled by means of a linear control: BBL(see Fig. 7).

Also, the influence of the output filter values in both themain Buck converter and the auxiliary Buck converter has beenproven. By means of a smaller output filter in the main buckconverter, a better transient response can be reached, althoughthe output voltage ripple also increases. However, a muchsmaller output filter inductor in the auxiliary Buck converterdoes not affect the maximum variation of the output voltage,and although the recovery time is reduced, this reductionis not much higher than using a six time higher inductancevalue in the output filter of the auxiliary buck converter.

Finally, the FRDB converter, thanks to the LnL control, keepsa fast response independently of the amplitude of the load cur-rent step, as long as the output voltage goes out the thresholdband, unlike the buck converter with linear control in which itsresponse is very dependent on the load current step and the reg-ulator gain. Also, this type of control allows for reducing theoutput filter requirements.

Although some of next features are not shown in this paper,one can remember that the FRDB converter presents a very goodstability, due to the LnL control, keeping a low output voltageripple and fast transient response. Also, it allows for reducingthe steady-state switching frequency affecting the EMI and theswitching losses.

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Andrés Barrado (M’02) was born in Badajoz,Spain, in 1968. He received the M.Sc. degree in elec-trical engineering from the Universidad Politécnicade Madrid, Madrid, Spain, in 1994, and the Ph.D.degree from the University Carlos III, Madrid, in2000.

Since 1994, he has been an Associate Professorat the University Carlos III. His research interests isfocus in switching-mode power supplies, multipleoutput dc–dc converters, modeling of dc–dc andac–dc converters, low-voltage fast transient response

dc–dc converters, EMC, ballasts and high power factor rectifiers.

Antonio Lázaro (M’04) was born in Madrid, Spain,in 1968. He received the M.Sc. degree in electricalengineering from the Universidad Politécnica deMadrid, Madrid, in 1995 and the Ph.D. degree inelectronic engineering from the Universidad CarlosIII de Madrid in 2003.

He has been an Assistant Professor of the Uni-versidad Carlos III de Madrid since 1995. He hasbeen involved in power electronics since 1994,participating in more than ten research and devel-opment projects and he has published nearly 40

papers in IEEE conferences. His research interest is switching mode powersupplies, power factor correction, modeling of dc–dc and ac–dc converters, andlow-voltage fast transient response dc/dc converters.

Ramón Vázquez was born in Placetas, Cuba, in1962. He received the M.Sc. degree in electronicengineering from the Polytechnical Institute of Baku,Baku, Azerbaijan, in 1986 and the Ph.D. degree fromthe University Carlos III, Madrid, Spain, in 2003.

From 1986 to 1994, he was a Researcher in thefield of semiconductor technology. Since 1994, hisresearch interest is in switching-mode power suppliesand low voltage dc/dc converters.

Vicente Salas was born in Madrid, Spain, in 1970.He received the M.Sc. degree in physics from theComplutense University of Madrid, in 1996 and thePh.D. degree from the University Carlos III, Madridin 2005.

His research interests are maximum power pointtrackers (MPPT), hybrid power systems, photo-voltaic energy, and switching-mode photovoltaicpower supply.

Emilio Olías (M’02) received the M.S. and Ph.D. de-grees in industrial engineering from the UniversidadPolitécnica de Madrid, Madrid, Spain, in 1981 and1983, respectively.

Since 1996, he has been a Professor in the De-partment of Electronic Technology, UniversidadCarlos III de Madrid, heading the Power ElectronicsSystems Group and collaborating with PowerElectronics Companies in different subjects aroundresearch projects, financed by private and publicfounds. He is working on power electronics (dc–dc

converters with new topologies, control strategies and power factor correction),alternative energy systems (photovoltaic and hybrid systems), and electromag-netic compatibility. Also, he is interested in CAD tools applied to the designand analysis of power systems operating in low and medium frequency. InUniversidad Carlos III de Madrid, he is Staff Member of Escuela PolitécnicaSuperior, High Polytechnic School. Named First Vice-dean in 2000, he hasthe educational and administrative competences in relation with the Industrialengineering studies in Universidad Carlos III, Madrid.

the fast response double buck dc\u0026#8211;dc converter (frdb): operation and output filter...

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