design of an ultraprecise 127-mw/3 - hpe - high power ......stability measurements. they show that...

Design of an Ultraprecise 127-MW/3 – us Solid-State Modulator With Split-Core Transformer

D. Gerber, J. Biela Power Electronic Systems Laboratory, ETH Zürich

Physikstrasse 3, 8092 Zürich, Switzerland

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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 44, NO. 5, MAY 2016 829

Design of an Ultraprecise 127-MW/3-μs Solid-StateModulator With Split-Core Transformer

Dominic Gerber and Juergen Biela, Member, IEEE

Abstract— This paper presents the design of an ultraprecise127-MW/3-µs solid-state modulator with split-core transformer.The modulator consists of a power supply, 12 pulse generatormodules with active core reset, and a split-core transformer withsix cores. In addition, an LC bouncer could be used to compen-sate the droop of the pulse. This paper includes the design andanalysis of the pulse transformer. A volume minimal transformeris investigated for different load capacitances to investigate theachievable rise time and the parameters which can be usedto adjust the damping. In addition, the influence of the pulsetransformer on the synchronization of the switches is investigatedusing an enhanced reluctance model. In addition, an LC bouncercircuit is investigated. A multiobjective optimization is performedwhich shows the required energy of the bouncer for a certainpulse ripple. The flat-top ripple of the presented modulator canbe reduced to 0.2%. Because the bouncer degrades the flat-topstability, the bouncer is not implemented. Measurements of theoverall system include short-circuit measurements and flat-topstability measurements. They show that the modulator is short-circuit capable. Furthermore, the flat-top stability is determinedto be less than 10 ppm at an output voltage of 360 kV.

Index Terms— Power electronics, pulse generation, pulse powersystems, pulse transformers, semiconductor switches, trans-former cores.

I. INTRODUCTION

A COMPACT and cost-effective X-ray free-electron lasersystem (SwissFEL) is currently built at the Paul Scherrer

Institute in Switzerland [1]. This laser system requires modu-lators with a pulse power of 127 MW for 3 μs and a flat-topstability of 10 ppm (Table I).

A concept for solid-state modulator has been investigatedfor SwissFEL. The usage of semiconductor switches offers alonger lifetime than other types of switches as, for example,gas switches. Furthermore, they are turn-OFF capable whatallows an adjustable pulselength and a lower short-circuitenergy.

There are two feasible concepts for a solid-state modulatorwith the requirements shown in Table I: a Marx generatorand a pulse-transformer-based solution. A pulse-transformer-based solution is chosen, because the voltage can be adjusted

Manuscript received December 31, 2015; accepted March 11, 2016. Date ofpublication April 6, 2016; date of current version May 6, 2016. This work wassupported in part by Ampegon AG, in part by Ampegon Puls PlasmatechnikGmbH, in part by ABB Switzerland Ltd., and in part by the Paul ScherrerInstitute.

The authors are with the Laboratory for High Power Electronic Sys-tems, ETH Zurich, Zurich 8092, Switzerland (e-mail: [email protected];[email protected]).

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

Digital Object Identifier 10.1109/TPS.2016.2543304

TABLE I

SPECIFICATIONS OF THE MODULATOR FOR SwissFEL

Fig. 1. Picture of the modulator (Ampegon AG).

to the semiconductors. In addition, less switches are required,because there is no series connection necessary to achieve theoutput voltage. The modulator is shown in Fig. 1.

Pulse-transformer-based modulators can be divided intothree different categories: transformers with a single core,transformers with multiple cores, and transmission-line trans-formers. A single-core transformer consists of one magneticcore and two or more windings. Transformers with multiplecores are realized in different configurations. The most simplesolution is connecting multiple transformers in series or inparallel. A parallel connection of multiple pulse transformersdoes not result in any benefit compared with a solution, wheremultiple switches are connected in parallel on the primary sideof a single-core transformer. Connecting multiple transformersin series is more useful. The load current is equally sharedbetween the semiconductor switches. The current on theprimary side is given by the current on the secondary side andthe turns ratio. The series connection guarantees equal currentson the secondary side of all transformers, resulting in equalcurrents on the primary side if the transformers have the same

0093-3813 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

830 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 44, NO. 5, MAY 2016

Fig. 2. Structure of a pulse-transformer-based modulator, including powersupplies.

turns ratio. The series connection of multiple transformerscan be improved by enclosing all cores with one secondarywinding, instead of an individual secondary winding for eachtransformer.

The third possible structure is a transmission-line trans-former. In such transformers, multiple transmission lines areconnected to a common source at one end and in series atthe other end of the line [2]. Often, coaxial cables are usedas transmission lines. To improve the low-frequency response,the cables are wound around a magnetic core. The impedanceof the transmission lines and the load have to be matched toachieve an optimal gain.

The structure of the modulator is shown in Fig. 2. It consistsof commercially available galvanically isolated ac/dc convert-ers with power factor correction, an ultraprecise charging unitconsisting of two interleaved boost converters, pulse generatorswith core reset circuit, and the transformer. Furthermore, abouncer circuit can be added to compensate the droop duringthe flat-top.

The parts of the modulator have been previously described.The gate unit for the used Insulated-Gate Bipolar Transis-tor (IGBTs), including short-circuit measurements, is shownin [3]. A detailed analysis of the capacitor charger has beendone in [4], and the interleaving is shown in [5].

In this paper, the parts of the system which have not beenpreviously described are presented. In Section II, the basicstructure of the modulator is shown. Then, in Section III, thepulse transformer is presented. It includes an investigationof the interlaminate voltage as well as an optimization ofa volume minimal transformer to show the achievable risetime. Furthermore, the influence of the transformer on the syn-chronization of the switches is investigated with an enhancedreluctance model. An LC bouncer circuit is investigatedin Section IV. Finally, measurements, including the flat-topstability, are shown in Section V.

II. MODULATOR

A power modulator typically consists of four main parts:a supply, which charges the energy storage, the energy storage,a switching element, and in most cases, a pulse-shaping net-work. The presented modulator has a capacitive energy storageand thus requires a closing switch. Among the suitable switchtypes, a semiconductor switch is used. They achieve the lowestblocking voltages and currents, but they have a much longerlifetime, and some types are turn-OFF capable. The turn-OFF

capability is particulary useful under short-circuit conditions.Among the different semiconductor switch types, IGBTs are

the most suitable solution for a solid-state modulator at thisoutput power level. They offer a higher blocking voltage andcurrent-carrying capability than MOSFETs which reduces thenumber of switches.

There are two basic topologies suitable for the presentedcase: the Marx generator and the pulse-transformer-basedmodulators. A pulse-transformer-based solution with a split-core transformer is selected (Fig. 2), since it requires lessswitches than the Marx generator. Furthermore, the inputvoltage can be adjusted to the semiconductor switches. Thesplit-core transformer allows an operation of the switches at amuch lower voltage than the output voltage. This in turn resultsin high currents at the primary side. Since the pulselength ismuch shorter than the time between two consecutive pulses,the switches can be operated at higher currents than incontinuous applications. The resulting high-current transientsduring turn-ON and turn-OFF require a low inductive pack-age. Furthermore, the package-related inductances of parallel-connected chips need to match as good as possible to assureequal currents during switching transients. This is particularlycritical during fault conditions. Thus, modules with bond wiresare not well suited for high pulsed currents [6]. Press-packsolutions provide a better current sharing between the chips [7]and are well suited for pulsed power applications [8].

A press-pack solution with 4.5-kV IGBTs is selected forthe modulator (ABB 5SNA1250B450300), because they offera good compromise between blocking voltage, current, andswitching speed. Each press pack contains 20 IGBTs and4 diode chips. It has a continuous current rating of 1250 A.Because of the low repetition rate and short pulselength,thermal issues are not critical due to the relatively largethermal capacitance. Although the switch is rated for 1250 Aand 4.5 kV, it is operated at 3 kV and 4 kA. Each switchis, therefore, capable of switching 12-MW pulsed power. Fora pulse power of 127 MW, ten switches would be required,resulting in a transformer with five cores. Because of the lownumber of primary turns, the magnetizing current per corecan be a few 100 A or more. Thus, 12 switches are requiredwith a transformer consisting of six cores. In addition,an LC bouncer can be added to compensate the droop of theenergy storage capacitors.

In order to achieve a symmetric flux swing, a core resetcircuit is required. A commonly used circuit is a dc resetcircuit. Such a reset circuit is a current source connectedto an auxiliary winding. This generates a dc magnetic fluxin the core. However, such a reset circuit is very inefficientfor a short-pulse modulator, since it is also active during thebreaks between the pulses. This means that the core bias is notrequired during more than 99.9% of the time for the presentedmodulator.

A much better method is an active reset circuit with orwithout flux swing control shown in [9]. It is a self-stabilizingcircuit as long as the losses in the transformer or the remanenceflux density are low enough. If this is not the case, thecapacitor Cr has to be charged, such that a symmetrical fluxswing is achieved. The peak magnetizing current is halvedcompared with the dc reset circuit because of the bipolarvoltage applied at the primary side. The circuit does not

GERBER AND BIELA: DESIGN OF AN ULTRAPRECISE 127-MW/3-μs SOLID-STATE MODULATOR 831

require an additional primary winding (see Fig. 3). Anotherfeature of this circuit is that a reverse voltage is applied at theprimary side during short-circuit conditions at the secondaryside. The parts of the remaining energy in the system are,therefore, transferred to Cr . With the dc reset circuit, only theforward voltage drop of the free-wheeling diode is applied atthe primary side. This voltage is much smaller than the voltageacross Cr , thus resulting in a longer time until the current isreduced to zero. The remaining energy is dissipated in thediode. Both effects result in an increased stress during short-circuit conditions. As a disadvantage, the active reset circuitrequires a switch with the same blocking voltage as the mainswitch.

The capacitors are charged with two interleaved boostconverters. A detailed description and investigations of theconverter, including a charging precision analysis, are donein [4]. The interleaving is described in detail in [5].

The detailed structure of the modulator is shown in Fig. 3.In the following, the pulse transformer and the bouncer aredescribed.

III. TRANSFORMER

The transformer of a power modulator is used to step thevoltage on the primary side up to the desired load voltage.In addition, it serves as the pulse-forming network. In thissection, the pulse transformer is investigated and described.First, possible core materials are presented and analyzed.In order to investigate the achievable rise time and the designmethod, a volume optimized transformer is designed based onanalytical formulas. Furthermore, the synchronization is inves-tigated using a detailed reluctance model of the transformer.The Section III is concluded with the final transformer designand measurements.

A. Core Material

The key component of a pulse transformer is the magneticcore. The selection of the material determines the size, weight,and losses of the core. There are four key requirements for thematerial: 1) high saturation flux density; 2) low remanence fluxdensity; 3) high relative permeability; and 4) low losses.

There are four different classes of materials suitable forpulse transformer cores: silicon–iron (SiFe)-based alloys,cobalt–iron (CoFe)-based alloys, amorphous alloys, andnanocristalline alloys.

The CoFe-based alloys have the highest saturation flux den-sity of all listed materials, but it is, in general, too expensive(25× SiFe).

Cores manufactured of these material classes are manufac-tured as laminated cores. They consist of thin tapes whichare electrically insulated between each other. This reducesthe eddy-current losses. Thinner ribbons reduce the losses atthe cost of a higher price. SiFe is typically available in theribbon thicknesses of 25, 50, and 100 μm. Thicker tapes arealso available, but they are not suitable for pulse transformercores. Amorphous alloys are typically produced with a ribbonthickness of 25 μm and nanocristalline cores with 18 μm.

In [10], measurements with rectangular pulse shape anddifferent materials have been performed (Table II). The lowest

Fig. 3. Modulator structure with six cores, including an LC bouncer andtwo reset circuits per core.

TABLE II

COMPARISON OF DIFFERENT CORE MATERIALS FOR A PULSELENGTH

OF 5 μS WITH 10-μS ACTIVE PREMAGNETIZATION [10]

losses per volume are achieved with nanocristalline materials(Finemet F3CC). The drawback of these materials is the lowsaturation induction which leads to a higher core volume.An SiFe core with 50 μm would result in high core losses,although it has the best saturation induction.

As a conclusion, it can be stated that the selection of thecore material is a compromise between the resulting systemvolume, losses, and costs. If a low volume is required, theSiFe- or CoFe-based cores are the best choice at the cost


Fig. 4. Model of a laminated core to determine the interlaminate voltagewith (a) one core and (b) two cores enclosed by a winding.

of higher losses and a higher price. The lowest losses areachieved with nanocristalline materials. Amorphous alloys area compromise between cost, volume, and losses.

B. Interlaminate Voltage

The insulation between the ribbons is important, since abreakdown between the tapes results in higher eddy-currentlosses and decreases the inductance. Hence, the interlaminatevoltage has to be considered for the transformer design andthe selection of the material.

The time-varying flux density results in an eddy elec-trical field. This electrical field induces a voltage betweenthe ribbons in laminated cores. If this voltage exceeds thebreakdown voltage of the insulating material, the ribbons areshort-circuited. In order to determine the voltage between tworibbons (interlaminate voltage), the Maxwell–Faraday equationis used in its integral form∮

∂�

�E d�l = − d

dt

∫∫�

�B d �S = −dφ

dt(1)

where ∂� is the boundary of a surface �.It is assumed that there is a flux φr inside each ribbon

and a flux φins inside each insulator between two ribbons[Fig. 4(a)]. The core is enclosed by a winding with Np turnsand an applied voltage v p . Four integration paths are definedat the boundary of the ribbon. It is assumed that the electricfield inside the ribbon is symmetric for a ribbon inside thecore. This reduces the integration paths to γa and γb. Theinterlaminate voltage is given by the integration path γc.

The induced voltage of one ribbon is obtained by integratingalong γa and γb and is given by

2∫

γa

�E d�l + 2∫

γb

�E d�l = −dφr

dt. (2)

The induced voltage in a core with a total flux φcore and Nr

ribbons consists of two paths γa , 2Nr paths γb, and 2(Nr −1)paths γc

2∫

γa

�E d�l + 2Nr

∫γb

�E d�l + 2(Nr −1)

∫γc

�E d�l = − d

dtφcore.

(3)

The permeability of the ribbons is much higher than thepermeability of the insulator, since they consist of magneticmaterial. Furthermore, the total area of the ribbons is greaterthan the area of the insulator. Hence, the flux inside theribbons φr is much larger than the flux inside the insulatingmaterial φins. The total flux is approximated by

φcore = Nr φr + (Nr − 1)φins ≈ Nr φr . (4)

The interlaminate voltage is calculated by integrating over theelectric field along path γc. The flux can be eliminated of theequations by substituting (2) into (3) and using approxima-tion (4)

vl =∫

γc

�E d�l =∫

γa

�E d�l. (5)

The integration path γb is much shorter than the path γa ,since the ribbon thickness is between 25 and 100 μm. There-fore, the voltage drop across γb is much lower, since theelectric field strength is assumed to be in the same order ofmagnitude as along the path γa . The total induced voltageis equal to the induced voltage in one turn of the windingenclosing the core and is

vind = 2∫

γa

�E d�l + 2(Nr − 1)

∫γc

�E d�l = 2Nr vl = v p

Np. (6)

The interlaminate voltage vl for a core, therefore, is

vl = v p

2Np Nr. (7)

Another approach to estimate the interlaminate voltageis to assume that the conductivity of the core material ismuch better than the conductivity of the insulating material.In that case, the voltage drop across γa is much smaller thanthe voltage drop across the insulation between the ribbons.By assuming an equal voltage drop across the 2(Nr −1) gaps,the interlaminar voltage for a large number of ribbons is

vl = v p

2Np(Nr − 1)≈ v p

2Np Nr(8)

which is the same as the result given in (7).There are two possibilities to reduce the interlaminar volt-

age. The first one is increasing the number of turns Np .In the case of a pulse transformer with fast rise time, thisis in most cases not desirable. A larger number of primaryturns result in a larger leakage inductance and, therefore, in aslower rise time. In addition, the number of ribbons is possiblyreduced, because less core area is required to achieve thedesired pulselength. The second possibility is splitting the corein multiple cores with lower depth [Fig. 4(b)]. The numberribbons is not affected, but the flux in one core is reduced,resulting in a lower induced voltage per core.

Because of the high-induced voltage per turn, the inter-laminar voltage might exceed the breakdown voltage. Thebreakdown voltage depends on the magnetic material and theinsulating material. In [11], different alloys and insulationmaterials have been tested. The SiFe-based cores were testedwith interlaminar voltages up to 11 V without breakdown.In the case of 2605SA1, a breakdown occurred at 0.5 V inone case.


Fig. 5. Geometrical parameters for a volume optimized transformer.

The core of the considered modulator consists of approxi-mately 2087 ribbons. This results in an interlaminar voltageestimated to 1.39 V for one primary turn and 3000 V primaryvoltage.

For pulse power applications with high d B/dt , the inter-laminar voltages may be higher than the average interlaminarvoltage due to the slow propagation speed of magnetizationwaves.

C. Volume Optimal Transformer

In order to investigate the achievable rise time and the damp-ing of the pulse, a volume optimal transformer is designed fora load capacitance up to 100 pF. The parasitic elements of thetransformer are calculated according to the equations for theleakage inductance and the distributed capacitance presentedin [12] and [13].

The geometrical parameters necessary for the calculationsare shown in Fig. 5. The core width and the core depth as wellas the height of the secondary winding have to be chosen, suchthat the pulse is optimally damped and the rise time is minimal.To investigate the theoretically achievable rise time with a min-imal volume transformer, an optimization is performed. Thealgorithm calculates the leakage inductance and the distributedcapacitance of the transformer for a given geometry. Then,the output pulse is calculated with those values. The solutionis considered as optimal when the rise time is minimal andthe pulse has no overshoot. A flowchart of the optimizationis shown in Fig. 6. The parameters for the optimization areshown in Table III. The isolation thickness diso is set to 0,since it has a negligible influence on the transformer design.The turn-ON time of the switches is set to 0. The damping isadjusted, such that the resulting pulse has no overshoot.

When only the space between the primary winding andthe secondary winding is considered for the capacitance andinductance calculation, the damping is not affected by theaverage turn length, since Lσ and Cd are scaled with the samevalue. The rise time on the other hand depends on theturn length. Therefore, the transformer geometry has to be

Fig. 6. Flowchart of the transformer optimization.

TABLE III

FIXED PARAMETERS OF THE VOLUME OPTIMIZED TRANSFORMER

chosen, such that the average turn length is minimal, which isthe case for a square-shaped turn. As shown in [12] and [13],the regions outside the area between the primary winding andthe secondary winding also contribute significantly to Cd butnot to Lσ . In addition, there is also an additional amount ofcapacitance Csec connected to the secondary winding of thetransformer, e.g., the klystron or a capacitive voltage divider.On the other hand, the pulse generators on the primary side adda certain amount of inductance. The total inductance relevantfor the pulse rise and the fall time, therefore, consists of Lσ

and the pulse generator inductance. This means that the totalcapacitance does not scale with the same ratio as the totalinductance depending on the average turn length. Therefore,a rise-time-optimized transformer without overshoot is notnecessarily an average turn length optimized transformer.

There are four degrees of freedom to adjust the damping.These are the height of the secondary winding hw, the dis-tance dw1, the number of primary turns, and an additionalinductor on the primary side or secondary side. The additionalinductor is implemented by increasing the pulse generatorinductance Lgen. The core area is adjusted depending on the


Fig. 7. Rise time depending on Csec for a volume optimized transformerwith the specification given in Table III.

Fig. 8. hw depending on Csec for a volume optimized transformer with thespecification given in Table III.

Fig. 9. dw1 depending on Csec for a volume optimized transformer with thespecification given in Table III.

number of primary turns, such that the resulting flux in the coreremains the same. All measures except the adjustment of hw

results in a higher Lσ Cd product. The lower boundary for hw

is set to dw and to 70 nH for the pulse generator inductance.The resulting rise time for all the cases is shown in Fig. 7.

With dw1 as a free parameter, the optimization algorithmkeeps hw always at the lower bound (Fig. 8). It adjusts thedamping only by adjusting dw1 (Fig. 9). The achieved risetime is longer than with an unbounded hw as expected. Therise time starts to significantly increase for a load bigger than80 pF, since dw1 reaches the upper bound. The only way toachieve the desired damping is by increasing Lgen.

For a transformer with two primary turns, the resulting dw1is always at the lower bound. The damping is adjusted byvarying hw . The resulting rise time is the worst for allconsidered cases.

Adding an external inductance does not result in a betterrise time as long as hw and dw1 are not at their bounds.

Summarizing these results, the damping can be welladjusted by increasing or decreasing hw. When hw reachesthe lower bound, dw1 is used to adjust the damping. If the

Fig. 10. Optimal rise time for Np = 1 and Np = 2 for a lower limitof 70 mm of hw .

desired damping is still too high, the number of primary turnsor an external inductance has to be added. The best rise timeis achieved for a single primary turn transformer with dw1 atthe lower limit. Increasing dw1 results in a longer rise time.Using a higher number of primary turns increases the rise timesignificantly.

To show the different measures to adjust the damping overa certain span of Csec, the lower limit of hw is decreasedto 70 mm. The transformer is then optimized for Np = 1and Np = 2. The resulting rise time is shown in Fig. 10.First, the results for Np = 1 are discussed. Below Csecof 15 pF, the best rise time is achieved by adjusting hw only.All other parameters are kept at their lower limits. Between15 and 135 pF, hw is kept at the lower limit and dw1 is usedto adjust the damping. For Csec > 150 pF, it is not possible toachieve the desired damping by adjusting hw and dw1, sincethey are at their bounds. Hence, the only way to increase theinductance is increasing the generator inductance.

For Np = 2, it is always possible to achieve the desireddamping by adjusting hw. The optimization results show thata transformer with two primary turns is always slower than antransformer with one primary turn for the investigated rangeof Csec. For larger load capacitances, a transformer with twoprimary turns might become better than a transformer withone primary turn, because hw is reduced further. This resultsin a lower Cd at larger Csec. If the desired damping canonly be achieved by increasing the generator inductance, Cd

remains constant. Hence, increasing the number of primaryturns becomes more beneficial at a larger Csec.

D. Switch Synchronization

The two switches driving the same core are electrically con-nected in parallel. Nonequal leakage inductances and differentturn-ON delays could result in unbalanced currents throughthese switches. The switch which carries more current isthermally more stressed than the other one. To avoid theexcessive stress, the currents need to be balanced.

In order to investigate the synchronization of the switches,an enhanced reluctance model of the transformer is used. Sucha model for a split-core transformer is given in [14]. Dueto the parallel connection of the secondary windings, onlyone MMF source is used in [14] for the secondary windings.To obtain a more accurate model, each winding is modeledwith one MMF source, resulting in two sources per core


Fig. 11. Reluctance model for one core with two primary and two secondarywindings.

Fig. 12. Equivalent circuit during the pulse with the transformer reluctancemodel.

for the primary windings and two sources for the secondarywindings. In addition, the space between the secondary turnsis modeled by an additional leakage reluctance. The resultingmodel is shown in Fig. 11 and the corresponding circuitin Fig. 12. This model can be extended to multiple cores,since all cores share the MMF sources for the secondarywindings. The reluctance Rσ,5 results in a weaker couplingbetween the windings on different legs of the core. Theleakage reluctances Rσ,1 and Rσ,2 as well as Rσ,3 and Rσ,4are connected in parallel. Therefore, the model can be reducedfrom five to three leakage reluctances. The circuit, includingthe reluctance model for the transformer, is shown in Fig. 12with Rσ,6 = Rσ,1||Rσ,2 and Rσ,7 = Rσ,3||Rσ,4.

The reluctance Rσ,5 only influences the current balancing ofthe secondary windings. The equivalent model for Rσ,5 = 0 istwo transformers connected in parallel. In this case, the ratioof the currents in the secondary windings matches the ratio ofthe load currents of the primary windings. For Rσ,5 → ∞, theflux in both the secondary windings is equal. Since they areconnected to the same load, this results in equal currents inthe secondary windings. For a finite value of Rσ,5, balancedcurrents on the secondary side help to balance the current onthe primary side, since the couplings between the windingsdepend on their position on the core.

A simulation with two cores and the values given inTable IV is performed to investigate the current balancing.The switches connected to the first core are labeled as Sm,1and Sm,2, the ones of the second core as Sm,3 and Sm,4. Sm,1and Sm,3 are enclosed by the same secondary winding, andSm,2 and Sm,4 are enclosed by the second one. The turn-ON

TABLE IV

CIRCUIT VALUES USED FOR CIRCUIT SIMULATIONS WITH A MATRIXTRANSFORMER CONSISTING OF TWO CORES

Fig. 13. (a) Switch currents and (b) currents in the secondary windings fora turn-ON delay of 100 ns of Sm,1.

time instance of Sm,1 is delayed by 100 ns. The resultingswitch currents are shown in Fig. 13. As expected, iSm,2is significantly higher than iSm,1. In addition, the currentbalancing of the second core is slightly influenced, i.e., iSm,3is slightly lower than iSm,4. The chosen value of Rσ,5 resultsin a better coupling between Sm,1 and Sm,3 than between Sm,2and Sm,3. This effect can also be observed in the currentsthrough the secondary windings. Current is,1 is significantlylower than is,2.

The results of the simulation indicate that balancing the cur-rents on the secondary side by a filter or common-mode chokeimproves the current balancing on the primary side. However,a significant improvement is only observed when Rσ,5 is smallenough, which is not the case for the presented transformer.

As a conclusion, the synchronization of the main switchesis critical. The matrix transformer significantly influences thebalancing of the currents in the primary windings. Dependingon the coupling of the windings on different legs of thesame core, a delayed turn-ON not only influences the currentsin the switches connected to the same core, it also resultsin unbalanced currents in the switches connected to anothercore. This also results in unbalanced currents in the secondarywindings.

In [10], a method to balance the currents is shown. The cur-rent of the switches connected to the same core is synchronizedby aligning the current edges. In addition, the voltage edgesof the cores have to be aligned, since a pure current edge


Fig. 14. Measured and simulated output voltage with 12 pulse generators.

Fig. 15. Currents through the main capacitor of two pulse generatorsconnected to the same core.

alignment does not guarantee synchronized currents due tothe split-core transformer design and the additional leakageinductance Rσ,5.

E. Measurements

The optimal values of the leakage inductance and thedistributed capacitance of the transformer are calculated withan finite element method simulation. In order to verify thetransformer parameters, test with a 1-k� load connected inseries with a diode is made. Fig. 14 shows the measuredand simulated output voltage at 300 kV. The predicted andmeasured waveform matches well. Hence, the transformerparameters are close to their predicted values.

The current balancing of the main switches is measured byplacing Rogowski coils around the main capacitors. Fig. 15shows the measured current of two switches connected to thesame core with three cores. The main capacitors are chargedto 3 kV. The difference between the currents is ∼150 Awithout current or voltage edge synchronization. Hence, thecurrents are balanced well enough. Thus, the switches do notneed to be synchronized. The current balancing is better thanexpected. The capacitors of the pulse generator are looselycoupled to each other. Therefore, the capacitor which carriesmore current is discharged faster. A lower voltage resultsin a lower di/dt and thus improves the current balancing.In addition, the magnetizing current starts to discharge theoutput capacitance of the main switches as soon as the resetswitch is turned OFF. This can be observed by a slowlyincreasing voltage at the output before the main switches areturned ON.

Fig. 16. Bouncer model, including pulse transformer, reset circuit, andklystron load.

Fig. 17. Pareto front with the initial bouncer energy and flat-top ripple fora fixed flat-top length of 3 μs.

IV. BOUNCER

The droop of the main capacitor voltage during the pulsecan be compensated with a bouncer. A simple method isan L R bouncer. It does not require any active components,but the resistor generates additional losses. A more efficientmethod is an LC bouncer, as presented in [15]. This type ofbouncer requires a switch to initiate the resonant transition.The inductor of this bouncer can be built as a transformerwhat allows to adapt the required initial voltage to the switch.

In order to design the bouncer circuit, the model shown inFig. 16 is used. It includes the core reset circuit and the pulsetransformer.

In order to analyze the required initial bouncer energyfor a certain flat-top ripple, a multiobjective optimization ismade. The optimization includes component tolerances andcalculates the worst case ripple. The capacitor tolerances areset to ±10%, and the inductor tolerance is set to ±20%. Theresulting Pareto front for the presented modulator is shownin Fig. 17. It shows a constant slope for a ripple of lessthan 0.22%. Below this value, the required energy starts toincrease significantly. The minimum ripple of 0.2% is achievedwith an initial energy of 7 J. These results show that the flat-top ripple can be significantly reduced with an LC bouncer.The amount of initial energy is far below the required pulseenergy, thus the bouncer volume does not contribute much tothe system volume.

A critical parameter of the bouncer is the switching signaljitter of the bouncer switch. Since the bouncer compensates the


Fig. 18. Output voltage and current with short circuit on the secondary side.

Fig. 19. IGBT current with short circuit on the secondary side.

droop of the main capacitor, the turn-ON time instance directlyaffects the output voltage amplitude. For example, a droopof 2% during a 3 μs flat-top results in the slope of 2.5 kV/μs.The slope of the bouncer output voltage is not affected bythe time instance when it is turned ON for a small switchingsignal jitter. However, the absolute voltage at the beginningof the flat-top is affected. If the switching signal is delayedby 1 ns, the bouncer voltage is shifted by 2.5 V. Hence, theflat top is also shifted by 2.5 V, which is an amplitude jitterof 7 ppm. Therefore, a bouncer is not used in the system, sincea high flat-top stability is more important than a low flat-topripple.

V. MEASUREMENTS

Different measurements have been performed with theoverall system. First, short-circuit tests at the load side areperformed, since these are part of the normal operation whenthe klystron is arcing. To do so, a triggered spark gap is used.Fig. 18 shows the measured voltage and the current on thesecondary side with a short circuit during the flat-top. Theoscillations in the current are caused by reflections at the shortcircuit and the transformer. The initial peak of the currentis caused by the discharge of the transformer capacitance.As soon as the main switches have turned OFF, the remainingenergy in the transformer is transferred into the capacitor ofthe premagnetization circuit. The measurements show that theshort-circuit current reaches zero after approximately 10 μs.

Fig. 20. Modulator output voltage with klystron load at a flat-top lengthof 3.8 μs.

Fig. 21. Windows P1–P6 used to measure the flat-top stability.

The corresponding IGBT current is shown in Fig. 19. Themaximum IGBT current of 6.7 kA is reached 300 ns after theshort circuit. The IGBTs are turned OFF within less than 1 μs.

After the successful short-circuit tests, the ohmic load isreplaced with a klystron. A typical pulse is shown in Fig. 20.The 10%–90% rise time is 700 ns. The flat-top is reached after1.8 μs and after the main switches are turned ON. The flat-topripple is 1.9%. The slow voltage rise at the beginning of thepulse (t = 0.1 μs) is caused by the magnetizing current whichdischarges the output capacitance of the main switches duringthe interlocking interval.

Finally, the flat-top stability is measured by splitting the flat-top into windows of 0.5 μs (Fig. 21). This results in six win-dows for a flat-top length of 3 μs. The mean value of theoutput current within each window is recorded over a period of10 min. The rms stability is calculated over a moving windowof 100 pulses. The output current is measured with a differen-tial amplifier, and the mean values inside the windows P1–P6are recorded with an oscilloscope. An additional windowoutside the pulse is used to measure the noise of the differ-ential amplifier. These measurements show that the flat-topstability at 360 kV is below the targeted 10 ppm in allsix windows.

VI. CONCLUSION

This paper presents the design of an ultraprecise 127-MW3-μs solid-state modulator with split-core transformer. Themodulator consists of a power supply, twelve pulse generatormodules with active core reset, and a split-core transformerwith six cores. In addition, an LC bouncer could be used tocompensate the droop of the pulse.

The pulse transformer design is shown. Different corematerials are analyzed. Furthermore, the interlaminate voltageis investigated and calculated for the presented modulator.


In addition, a volume minimal transformer is investigateddepending on different load capacitances to investigate theachievable rise time and the parameters which can be used toadjust the damping. The optimization shows that a rise timeof 700 ns can be achieved for a load capacitance of 100 pF.The best rise time is achieved by adjusting the height of thesecondary winding to achieve the desired damping.

In addition, the influence of the pulse transformer onthe synchronization of the switches is investigated using anenhanced reluctance model. It is shown that the transformercurrent balancing of the secondary winding influences thecurrent balancing of the switches connected to the same core.Measurements with the constructed transformer show that asynchronization of the switches is not necessary, since thecurrent sharing is good enough without it.

In addition, an LC bouncer circuit is investigated. A multi-objective optimization is performed which shows the requiredenergy of the bouncer for a certain pulse ripple. The minimumachievable ripple is determined to be 0.2% with an energyof 7 J. However, the bouncer is not included in the system,because its switching signal jitter degrades the flat-top stability.

Measurements of the overall system include short-circuitand flat-top stability measurements. They show that the modu-lator is short-circuit capable. Furthermore, the flat-top stabilityis determined to be less than 10 ppm at an output voltageof 360 kV.

REFERENCES

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Dominic Gerber received the M.Sc. degree in elec-trical engineering and information technology fromETH Zurich, Zurich, Switzerland, in 2010, wherehe is currently pursuing the Ph.D. degree with theLaboratory for High Power Electronic Systems.

He focused on power electronics, drive systems,and high voltage technology, during his M.Sc. stud-ies. His work focused on solid-state modulators, highaccurate capacitor charging, and current measure-ment based on the Faraday effect. He has been aPost-Doctoral Fellow with the Laboratory for High

Power Electronic Systems, ETH Zurich, since 2016. His current researchinterests include high accurate capacitor charging and field-programmable gatearray-based control of converter systems.

Juergen Biela (S’04–M’06) received the Diploma(Hons.) degree from Friedrich-Alexander-UniversitätErlangen-Nürnberg, Nuremberg, Germany, in 1999,and the Ph.D. degree from the Power ElectronicSystems (PES) Laboratory, Swiss Federal Instituteof Technology (ETH) Zurich, Zurich, Switzerland, in2006, with a focus on optimized electromagneticallyintegrated resonant converters.

He joined the Research Department, SiemensA&D, Erlangen, Germany, in 2000, where he hasbeen involved in inverters with very high switching

frequencies, SiC components, and electromagnetic compatibility. He was aPost-Doctoral Fellow with the PES Laboratory and a Guest Researcher withthe Tokyo Institute of Technology, Tokyo, Japan, from 2006 to 2007. He was aSenior Research Associate with the PES Laboratory, ETH Zurich, from 2007to 2010, where he has been an Associate Professor of High-Power ElectronicSystems since 2010. His current research interests include design, modeling,and optimization of power factor correction, DC/DC, and multilevel converterswith an emphasis on passive components, the design of pulsed-power systems,and power electronic systems for future energy distribution.

design of an ultraprecise 127-mw/3 - hpe - high power ......stability measurements. they show that...

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