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

Transcription

1 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 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of ETH Zürich s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permission@ieee.org. By choosing to view this document you agree to all provisions of the copyright laws protecting it.

2 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 44, NO. 5, MAY Design of an Ultraprecise 127-MW/3-μs Solid-State Modulator With Split-Core Transformer Dominic Gerber and Juergen Biela, Member, IEEE Abstract This paper presents the design of an ultraprecise 127-MW/3-µs solid-state modulator with split-core transformer. The modulator consists of a power supply, 12 pulse generator modules with active core reset, and a split-core transformer with six cores. In addition, an LC bouncer could be used to compensate the droop of the pulse. This paper includes the design and analysis of the pulse transformer. A volume minimal transformer is investigated for different load capacitances to investigate the achievable rise time and the parameters which can be used to adjust the damping. In addition, the influence of the pulse transformer on the synchronization of the switches is investigated using an enhanced reluctance model. In addition, an LC bouncer circuit is investigated. A multiobjective optimization is performed which shows the required energy of the bouncer for a certain pulse ripple. The flat-top ripple of the presented modulator can be reduced to 0.2%. Because the bouncer degrades the flat-top stability, the bouncer is not implemented. Measurements of the overall system include short-circuit measurements and flat-top stability measurements. They show that the modulator is shortcircuit capable. Furthermore, the flat-top stability is determined to be less than 10 ppm at an output voltage of 360 kv. Index Terms Power electronics, pulse generation, pulse power systems, pulse transformers, semiconductor switches, transformer cores. TABLE I SPECIFICATIONS OF THE MODULATOR FOR SwissFEL I. INTRODUCTION A COMPACT and cost-effective X-ray free-electron laser system (SwissFEL) is currently built at the Paul Scherrer Institute in Switzerland [1]. This laser system requires modulators with a pulse power of 127 MW for 3 μs and a flat-top stability of 10 ppm (Table I). A concept for solid-state modulator has been investigated for SwissFEL. The usage of semiconductor switches offers a longer lifetime than other types of switches as, for example, gas switches. Furthermore, they are turn-off capable what allows an adjustable pulselength and a lower short-circuit energy. There are two feasible concepts for a solid-state modulator with the requirements shown in Table I: a Marx generator and a pulse-transformer-based solution. A pulse-transformerbased solution is chosen, because the voltage can be adjusted Manuscript received December 31, 2015; accepted March 11, Date of publication April 6, 2016; date of current version May 6, This work was supported in part by Ampegon AG, in part by Ampegon Puls Plasmatechnik GmbH, in part by ABB Switzerland Ltd., and in part by the Paul Scherrer Institute. The authors are with the Laboratory for High Power Electronic Systems, ETH Zurich, Zurich 8092, Switzerland ( gerberdo@ethz.ch; jbiela@ethz.ch). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TPS 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 the output voltage. The modulator is shown in Fig. 1. Pulse-transformer-based modulators can be divided into three different categories: transformers with a single core, transformers with multiple cores, and transmission-line transformers. A single-core transformer consists of one magnetic core and two or more windings. Transformers with multiple cores are realized in different configurations. The most simple solution is connecting multiple transformers in series or in parallel. A parallel connection of multiple pulse transformers does not result in any benefit compared with a solution, where multiple switches are connected in parallel on the primary side of a single-core transformer. Connecting multiple transformers in series is more useful. The load current is equally shared between the semiconductor switches. The current on the primary side is given by the current on the secondary side and the turns ratio. The series connection guarantees equal currents on the secondary side of all transformers, resulting in equal currents on the primary side if the transformers have the same IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

3 830 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 44, NO. 5, MAY 2016 Fig. 2. Structure of a pulse-transformer-based modulator, including power supplies. turns ratio. The series connection of multiple transformers can be improved by enclosing all cores with one secondary winding, instead of an individual secondary winding for each transformer. The third possible structure is a transmission-line transformer. In such transformers, multiple transmission lines are connected to a common source at one end and in series at the other end of the line [2]. Often, coaxial cables are used as transmission lines. To improve the low-frequency response, the cables are wound around a magnetic core. The impedance of the transmission lines and the load have to be matched to achieve an optimal gain. The structure of the modulator is shown in Fig. 2. It consists of commercially available galvanically isolated ac/dc converters with power factor correction, an ultraprecise charging unit consisting of two interleaved boost converters, pulse generators with core reset circuit, and the transformer. Furthermore, a bouncer circuit can be added to compensate the droop during the flat-top. The parts of the modulator have been previously described. The gate unit for the used Insulated-Gate Bipolar Transistor (IGBTs), including short-circuit measurements, is shown in [3]. A detailed analysis of the capacitor charger has been done in [4], and the interleaving is shown in [5]. In this paper, the parts of the system which have not been previously described are presented. In Section II, the basic structure of the modulator is shown. Then, in Section III, the pulse transformer is presented. It includes an investigation of the interlaminate voltage as well as an optimization of a volume minimal transformer to show the achievable rise time. Furthermore, the influence of the transformer on the synchronization of the switches is investigated with an enhanced reluctance model. An LC bouncer circuit is investigated in Section IV. Finally, measurements, including the flat-top stability, 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 network. The presented modulator has a capacitive energy storage and thus requires a closing switch. Among the suitable switch types, a semiconductor switch is used. They achieve the lowest blocking voltages and currents, but they have a much longer lifetime, 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 this output power level. They offer a higher blocking voltage and current-carrying capability than MOSFETs which reduces the number of switches. There are two basic topologies suitable for the presented case: the Marx generator and the pulse-transformer-based modulators. A pulse-transformer-based solution with a splitcore transformer is selected (Fig. 2), since it requires less switches than the Marx generator. Furthermore, the input voltage can be adjusted to the semiconductor switches. The split-core transformer allows an operation of the switches at a much lower voltage than the output voltage. This in turn results in high currents at the primary side. Since the pulselength is much shorter than the time between two consecutive pulses, the switches can be operated at higher currents than in continuous applications. The resulting high-current transients during turn-on and turn-off require a low inductive package. Furthermore, the package-related inductances of parallelconnected chips need to match as good as possible to assure equal currents during switching transients. This is particularly critical during fault conditions. Thus, modules with bond wires are not well suited for high pulsed currents [6]. Press-pack solutions 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 for the modulator (ABB 5SNA1250B450300), because they offer a good compromise between blocking voltage, current, and switching speed. Each press pack contains 20 IGBTs and 4 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 large thermal capacitance. Although the switch is rated for 1250 A and 4.5 kv, it is operated at 3 kv and 4 ka. Each switch is, therefore, capable of switching 12-MW pulsed power. For a pulse power of 127 MW, ten switches would be required, resulting in a transformer with five cores. Because of the low number of primary turns, the magnetizing current per core can be a few 100 A or more. Thus, 12 switches are required with a transformer consisting of six cores. In addition, an LC bouncer can be added to compensate the droop of the energy storage capacitors. In order to achieve a symmetric flux swing, a core reset circuit is required. A commonly used circuit is a dc reset circuit. Such a reset circuit is a current source connected to an auxiliary winding. This generates a dc magnetic flux in the core. However, such a reset circuit is very inefficient for a short-pulse modulator, since it is also active during the breaks between the pulses. This means that the core bias is not required during more than 99.9% of the time for the presented modulator. A much better method is an active reset circuit with or without flux swing control shown in [9]. It is a self-stabilizing circuit as long as the losses in the transformer or the remanence flux density are low enough. If this is not the case, the capacitor C r has to be charged, such that a symmetrical flux swing is achieved. The peak magnetizing current is halved compared with the dc reset circuit because of the bipolar voltage applied at the primary side. The circuit does not

4 GERBER AND BIELA: DESIGN OF AN ULTRAPRECISE 127-MW/3-μs SOLID-STATE MODULATOR 831 require an additional primary winding (see Fig. 3). Another feature of this circuit is that a reverse voltage is applied at the primary side during short-circuit conditions at the secondary side. The parts of the remaining energy in the system are, therefore, transferred to C r. With the dc reset circuit, only the forward voltage drop of the free-wheeling diode is applied at the primary side. This voltage is much smaller than the voltage across C r, thus resulting in a longer time until the current is reduced to zero. The remaining energy is dissipated in the diode. Both effects result in an increased stress during shortcircuit conditions. As a disadvantage, the active reset circuit requires a switch with the same blocking voltage as the main switch. The capacitors are charged with two interleaved boost converters. A detailed description and investigations of the converter, including a charging precision analysis, are done in [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 are described. III. TRANSFORMER The transformer of a power modulator is used to step the voltage on the primary side up to the desired load voltage. In addition, it serves as the pulse-forming network. In this section, 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 design method, a volume optimized transformer is designed based on analytical formulas. Furthermore, the synchronization is investigated using a detailed reluctance model of the transformer. The Section III is concluded with the final transformer design and measurements. A. Core Material The key component of a pulse transformer is the magnetic core. The selection of the material determines the size, weight, and losses of the core. There are four key requirements for the material: 1) high saturation flux density; 2) low remanence flux density; 3) high relative permeability; and 4) low losses. There are four different classes of materials suitable for pulse transformer cores: silicon iron (SiFe)-based alloys, cobalt iron (CoFe)-based alloys, amorphous alloys, and nanocristalline alloys. The CoFe-based alloys have the highest saturation flux density of all listed materials, but it is, in general, too expensive (25 SiFe). Cores manufactured of these material classes are manufactured as laminated cores. They consist of thin tapes which are electrically insulated between each other. This reduces the eddy-current losses. Thinner ribbons reduce the losses at the cost of a higher price. SiFe is typically available in the ribbon thicknesses of 25, 50, and 100 μm. Thicker tapes are also available, but they are not suitable for pulse transformer cores. Amorphous alloys are typically produced with a ribbon thickness of 25 μm and nanocristalline cores with 18 μm. In [10], measurements with rectangular pulse shape and different materials have been performed (Table II). The lowest Fig. 3. Modulator structure with six cores, including an LC bouncer and two 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 low saturation 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 the core material is a compromise between the resulting system volume, losses, and costs. If a low volume is required, the SiFe- or CoFe-based cores are the best choice at the cost

5 832 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 44, NO. 5, MAY 2016 The permeability of the ribbons is much higher than the permeability of the insulator, since they consist of magnetic material. Furthermore, the total area of the ribbons is greater than the area of the insulator. Hence, the flux inside the ribbons φ r is much larger than the flux inside the insulating material φ ins. The total flux is approximated by φ core = N r φ r + (N r 1)φ ins N r φ r. (4) Fig. 4. Model of a laminated core to determine the interlaminate voltage with (a) one core and (b) two cores enclosed by a winding. of higher losses and a higher price. The lowest losses are achieved with nanocristalline materials. Amorphous alloys are a compromise between cost, volume, and losses. B. Interlaminate Voltage The insulation between the ribbons is important, since a breakdown between the tapes results in higher eddy-current losses and decreases the inductance. Hence, the interlaminate voltage has to be considered for the transformer design and the selection of the material. The time-varying flux density results in an eddy electrical field. This electrical field induces a voltage between the ribbons in laminated cores. If this voltage exceeds the breakdown voltage of the insulating material, the ribbons are short-circuited. In order to determine the voltage between two ribbons (interlaminate voltage), the Maxwell Faraday equation is used in its integral form E d l = d Bd S = dφ (1) dt dt where is the boundary of a surface. It is assumed that there is a flux φ r inside each ribbon and a flux φ ins inside each insulator between two ribbons [Fig. 4(a)]. The core is enclosed by a winding with N p turns and an applied voltage v p. Four integration paths are defined at the boundary of the ribbon. It is assumed that the electric field inside the ribbon is symmetric for a ribbon inside the core. This reduces the integration paths to γ a and γ b.the interlaminate voltage is given by the integration path γ c. The induced voltage of one ribbon is obtained by integrating along γ a and γ b and is given by 2 Ed l + 2 Ed l = dφ r γ a γ b dt. (2) The induced voltage in a core with a total flux φ core and N r ribbons consists of two paths γ a,2n r paths γ b,and2(n r 1) paths γ c 2 Ed l + 2N r Ed l + 2(N r 1) Ed l = d γ b dt φ core. γ a γ c (3) The interlaminate voltage is calculated by integrating over the electric field along path γ c. The flux can be eliminated of the equations by substituting (2) into (3) and using approximation (4) v l = Ed l = Ed l. (5) γ c γ a The integration path γ b is much shorter than the path γ a, since the ribbon thickness is between 25 and 100 μm. Therefore, the voltage drop across γ b is much lower, since the electric field strength is assumed to be in the same order of magnitude as along the path γ a. The total induced voltage is equal to the induced voltage in one turn of the winding enclosing the core and is v ind = 2 Ed l + 2(N r 1) γ a γ c The interlaminate voltage v l for a core, therefore, is Ed l = 2N r v l = v p N p. (6) v l = v p. (7) 2N p N r Another approach to estimate the interlaminate voltage is to assume that the conductivity of the core material is much better than the conductivity of the insulating material. In that case, the voltage drop across γ a is much smaller than the voltage drop across the insulation between the ribbons. By assuming an equal voltage drop across the 2(N r 1) gaps, the interlaminar voltage for a large number of ribbons is v p v l = 2N p (N r 1) v p (8) 2N p N r which is the same as the result given in (7). There are two possibilities to reduce the interlaminar voltage. The first one is increasing the number of turns N p. In the case of a pulse transformer with fast rise time, this is in most cases not desirable. A larger number of primary turns result in a larger leakage inductance and, therefore, in a slower rise time. In addition, the number of ribbons is possibly reduced, because less core area is required to achieve the desired pulselength. The second possibility is splitting the core in multiple cores with lower depth [Fig. 4(b)]. The number ribbons 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 interlaminar voltage might exceed the breakdown voltage. The breakdown voltage depends on the magnetic material and the insulating material. In [11], different alloys and insulation materials have been tested. The SiFe-based cores were tested with interlaminar voltages up to 11 V without breakdown. In the case of 2605SA1, a breakdown occurred at 0.5 V in one case.

6 GERBER AND BIELA: DESIGN OF AN ULTRAPRECISE 127-MW/3-μs SOLID-STATE MODULATOR 833 Fig. 5. Geometrical parameters for a volume optimized transformer. The core of the considered modulator consists of approximately 2087 ribbons. This results in an interlaminar voltage estimated to 1.39 V for one primary turn and 3000 V primary voltage. For pulse power applications with high db/dt, the interlaminar voltages may be higher than the average interlaminar voltage due to the slow propagation speed of magnetization waves. Fig. 6. Flowchart of the transformer optimization. TABLE III FIXED PARAMETERS OF THE VOLUME OPTIMIZED TRANSFORMER C. Volume Optimal Transformer In order to investigate the achievable rise time and the damping of the pulse, a volume optimal transformer is designed for a load capacitance up to 100 pf. The parasitic elements of the transformer are calculated according to the equations for the leakage inductance and the distributed capacitance presented in [12] and [13]. The geometrical parameters necessary for the calculations are shown in Fig. 5. The core width and the core depth as well as the height of the secondary winding have to be chosen, such that the pulse is optimally damped and the rise time is minimal. To investigate the theoretically achievable rise time with a minimal volume transformer, an optimization is performed. The algorithm calculates the leakage inductance and the distributed capacitance of the transformer for a given geometry. Then, the output pulse is calculated with those values. The solution is considered as optimal when the rise time is minimal and the pulse has no overshoot. A flowchart of the optimization is shown in Fig. 6. The parameters for the optimization are shown in Table III. The isolation thickness d iso 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 is adjusted, such that the resulting pulse has no overshoot. When only the space between the primary winding and the secondary winding is considered for the capacitance and inductance calculation, the damping is not affected by the average turn length, since L σ and C d are scaled with the same value. The rise time on the other hand depends on the turn length. Therefore, the transformer geometry has to be chosen, such that the average turn length is minimal, which is the case for a square-shaped turn. As shown in [12] and [13], the regions outside the area between the primary winding and the secondary winding also contribute significantly to C d but not to L σ. In addition, there is also an additional amount of capacitance C sec connected to the secondary winding of the transformer, e.g., the klystron or a capacitive voltage divider. On the other hand, the pulse generators on the primary side add a certain amount of inductance. The total inductance relevant for the pulse rise and the fall time, therefore, consists of L σ and the pulse generator inductance. This means that the total capacitance does not scale with the same ratio as the total inductance depending on the average turn length. Therefore, a rise-time-optimized transformer without overshoot is not necessarily an average turn length optimized transformer. There are four degrees of freedom to adjust the damping. These are the height of the secondary winding h w, the distance d w1, the number of primary turns, and an additional inductor on the primary side or secondary side. The additional inductor is implemented by increasing the pulse generator inductance L gen. The core area is adjusted depending on the

7 834 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 44, NO. 5, MAY 2016 Fig. 7. Rise time depending on C sec for a volume optimized transformer with the specification given in Table III. Fig. 10. Optimal rise time for N p = 1andN p = 2 for a lower limit of 70 mm of h w. Fig. 8. h w depending on C sec for a volume optimized transformer with the specification given in Table III. Fig. 9. d w1 depending on C sec for a volume optimized transformer with the specification given in Table III. number of primary turns, such that the resulting flux in the core remains the same. All measures except the adjustment of h w results in a higher L σ C d product. The lower boundary for h w is set to d w and to 70 nh for the pulse generator inductance. The resulting rise time for all the cases is shown in Fig. 7. With d w1 as a free parameter, the optimization algorithm keeps h w always at the lower bound (Fig. 8). It adjusts the damping only by adjusting d w1 (Fig. 9). The achieved rise time is longer than with an unbounded h w as expected. The rise time starts to significantly increase for a load bigger than 80 pf, since d w1 reaches the upper bound. The only way to achieve the desired damping is by increasing L gen. For a transformer with two primary turns, the resulting d w1 is always at the lower bound. The damping is adjusted by varying h w. The resulting rise time is the worst for all considered cases. Adding an external inductance does not result in a better rise time as long as h w and d w1 are not at their bounds. Summarizing these results, the damping can be well adjusted by increasing or decreasing h w.whenh w reaches the lower bound, d w1 is used to adjust the damping. If the desired damping is still too high, the number of primary turns or an external inductance has to be added. The best rise time is achieved for a single primary turn transformer with d w1 at the lower limit. Increasing d w1 results in a longer rise time. Using a higher number of primary turns increases the rise time significantly. To show the different measures to adjust the damping over a certain span of C sec, the lower limit of h w is decreased to 70 mm. The transformer is then optimized for N p = 1 and N p = 2. The resulting rise time is shown in Fig. 10. First, the results for N p = 1 are discussed. Below C sec of 15 pf, the best rise time is achieved by adjusting h w only. All other parameters are kept at their lower limits. Between 15 and 135 pf, h w is kept at the lower limit and d w1 is used to adjust the damping. For C sec > 150 pf, it is not possible to achieve the desired damping by adjusting h w and d w1,since they are at their bounds. Hence, the only way to increase the inductance is increasing the generator inductance. For N p = 2, it is always possible to achieve the desired damping by adjusting h w. The optimization results show that a transformer with two primary turns is always slower than an transformer with one primary turn for the investigated range of C sec. For larger load capacitances, a transformer with two primary turns might become better than a transformer with one primary turn, because h w is reduced further. This results in a lower C d at larger C sec. If the desired damping can only be achieved by increasing the generator inductance, C d remains constant. Hence, increasing the number of primary turns becomes more beneficial at a larger C sec. D. Switch Synchronization The two switches driving the same core are electrically connected in parallel. Nonequal leakage inductances and different turn-on delays could result in unbalanced currents through these switches. The switch which carries more current is thermally more stressed than the other one. To avoid the excessive 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. Such a model for a split-core transformer is given in [14]. Due to the parallel connection of the secondary windings, only one MMF source is used in [14] for the secondary windings. To obtain a more accurate model, each winding is modeled with one MMF source, resulting in two sources per core

8 GERBER AND BIELA: DESIGN OF AN ULTRAPRECISE 127-MW/3-μs SOLID-STATE MODULATOR 835 TABLE IV CIRCUIT VALUES USED FOR CIRCUIT SIMULATIONS WITH A MATRIX TRANSFORMER CONSISTING OF TWO CORES Fig. 11. Reluctance model for one core with two primary and two secondary windings. Fig. 12. model. Equivalent circuit during the pulse with the transformer reluctance for the primary windings and two sources for the secondary windings. In addition, the space between the secondary turns is modeled by an additional leakage reluctance. The resulting model is shown in Fig. 11 and the corresponding circuit in Fig. 12. This model can be extended to multiple cores, since all cores share the MMF sources for the secondary windings. The reluctance R σ,5 results in a weaker coupling between the windings on different legs of the core. The leakage reluctances R σ,1 and R σ,2 as well as R σ,3 and R σ,4 are connected in parallel. Therefore, the model can be reduced from five to three leakage reluctances. The circuit, including the reluctance model for the transformer, is shown in Fig. 12 with R σ,6 = R σ,1 R σ,2 and R σ,7 = R σ,3 R σ,4. The reluctance R σ,5 only influences the current balancing of the secondary windings. The equivalent model for R σ,5 = 0is two transformers connected in parallel. In this case, the ratio of the currents in the secondary windings matches the ratio of the load currents of the primary windings. For R σ,5,the flux in both the secondary windings is equal. Since they are connected to the same load, this results in equal currents in the secondary windings. For a finite value of R σ,5, balanced currents on the secondary side help to balance the current on the primary side, since the couplings between the windings depend on their position on the core. A simulation with two cores and the values given in Table IV is performed to investigate the current balancing. The switches connected to the first core are labeled as S m,1 and S m,2, the ones of the second core as S m,3 and S m,4. S m,1 and S m,3 are enclosed by the same secondary winding, and S m,2 and S m,4 are enclosed by the second one. The turn-on Fig. 13. (a) Switch currents and (b) currents in the secondary windings for a turn-on delay of 100 ns of S m,1. time instance of S m,1 is delayed by 100 ns. The resulting switch currents are shown in Fig. 13. As expected, i Sm,2 is significantly higher than i Sm,1. In addition, the current balancing of the second core is slightly influenced, i.e., i Sm,3 is slightly lower than i Sm,4. The chosen value of R σ,5 results in a better coupling between S m,1 and S m,3 than between S m,2 and S m,3. This effect can also be observed in the currents through the secondary windings. Current i s,1 is significantly lower than i s,2. The results of the simulation indicate that balancing the currents on the secondary side by a filter or common-mode choke improves the current balancing on the primary side. However, a significant improvement is only observed when R σ,5 is small enough, which is not the case for the presented transformer. As a conclusion, the synchronization of the main switches is critical. The matrix transformer significantly influences the balancing of the currents in the primary windings. Depending on the coupling of the windings on different legs of the same core, a delayed turn-on not only influences the currents in the switches connected to the same core, it also results in unbalanced currents in the switches connected to another core. This also results in unbalanced currents in the secondary windings. In [10], a method to balance the currents is shown. The current of the switches connected to the same core is synchronized by aligning the current edges. In addition, the voltage edges of the cores have to be aligned, since a pure current edge

9 836 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 44, NO. 5, MAY 2016 Fig. 14. Measured and simulated output voltage with 12 pulse generators. Fig. 16. Bouncer model, including pulse transformer, reset circuit, and klystron load. Fig. 15. Currents through the main capacitor of two pulse generators connected to the same core. alignment does not guarantee synchronized currents due to the split-core transformer design and the additional leakage inductance R σ,5. E. Measurements The optimal values of the leakage inductance and the distributed capacitance of the transformer are calculated with an finite element method simulation. In order to verify the transformer parameters, test with a 1-k load connected in series with a diode is made. Fig. 14 shows the measured and simulated output voltage at 300 kv. The predicted and measured waveform matches well. Hence, the transformer parameters are close to their predicted values. The current balancing of the main switches is measured by placing Rogowski coils around the main capacitors. Fig. 15 shows the measured current of two switches connected to the same core with three cores. The main capacitors are charged to 3 kv. The difference between the currents is 150 A without current or voltage edge synchronization. Hence, the currents are balanced well enough. Thus, the switches do not need to be synchronized. The current balancing is better than expected. The capacitors of the pulse generator are loosely coupled to each other. Therefore, the capacitor which carries more current is discharged faster. A lower voltage results in a lower di/dt and thus improves the current balancing. In addition, the magnetizing current starts to discharge the output capacitance of the main switches as soon as the reset switch is turned OFF. This can be observed by a slowly increasing voltage at the output before the main switches are turned ON. Fig. 17. Pareto front with the initial bouncer energy and flat-top ripple for a fixed flat-top length of 3 μs. IV. BOUNCER The droop of the main capacitor voltage during the pulse can be compensated with a bouncer. A simple method is an LR bouncer. It does not require any active components, but the resistor generates additional losses. A more efficient method is an LC bouncer, as presented in [15]. This type of bouncer requires a switch to initiate the resonant transition. The inductor of this bouncer can be built as a transformer what allows to adapt the required initial voltage to the switch. In order to design the bouncer circuit, the model shown in Fig. 16 is used. It includes the core reset circuit and the pulse transformer. In order to analyze the required initial bouncer energy for a certain flat-top ripple, a multiobjective optimization is made. The optimization includes component tolerances and calculates the worst case ripple. The capacitor tolerances are set to ±10%, and the inductor tolerance is set to ±20%. The resulting Pareto front for the presented modulator is shown in Fig. 17. It shows a constant slope for a ripple of less than 0.22%. Below this value, the required energy starts to increase significantly. The minimum ripple of 0.2% is achieved with an initial energy of 7 J. These results show that the flattop ripple can be significantly reduced with an LC bouncer. The amount of initial energy is far below the required pulse energy, thus the bouncer volume does not contribute much to the system volume. A critical parameter of the bouncer is the switching signal jitter of the bouncer switch. Since the bouncer compensates the

10 GERBER AND BIELA: DESIGN OF AN ULTRAPRECISE 127-MW/3-μs SOLID-STATE MODULATOR 837 Fig. 20. Modulator output voltage with klystron load at a flat-top length of 3.8 μs. Fig. 18. Output voltage and current with short circuit on the secondary side. Fig. 21. Windows P1 P6 used to measure the flat-top stability. Fig. 19. IGBT current with short circuit on the secondary side. droop of the main capacitor, the turn-on time instance directly affects the output voltage amplitude. For example, a droop of 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 by the time instance when it is turned ON for a small switching signal jitter. However, the absolute voltage at the beginning of the flat-top is affected. If the switching signal is delayed by 1 ns, the bouncer voltage is shifted by 2.5 V. Hence, the flat top is also shifted by 2.5 V, which is an amplitude jitter of 7 ppm. Therefore, a bouncer is not used in the system, since a high flat-top stability is more important than a low flat-top ripple. V. MEASUREMENTS Different measurements have been performed with the overall system. First, short-circuit tests at the load side are performed, since these are part of the normal operation when the klystron is arcing. To do so, a triggered spark gap is used. Fig. 18 shows the measured voltage and the current on the secondary side with a short circuit during the flat-top. The oscillations in the current are caused by reflections at the short circuit and the transformer. The initial peak of the current is caused by the discharge of the transformer capacitance. As soon as the main switches have turned OFF, the remaining energy in the transformer is transferred into the capacitor of the premagnetization circuit. The measurements show that the short-circuit current reaches zero after approximately 10 μs. The corresponding IGBT current is shown in Fig. 19. The maximum IGBT current of 6.7 ka is reached 300 ns after the short circuit. The IGBTs are turned OFF within less than 1 μs. After the successful short-circuit tests, the ohmic load is replaced with a klystron. A typical pulse is shown in Fig. 20. The 10% 90% rise time is 700 ns. The flat-top is reached after 1.8 μs and after the main switches are turned ON. The flat-top ripple is 1.9%. The slow voltage rise at the beginning of the pulse (t = 0.1 μs) is caused by the magnetizing current which discharges the output capacitance of the main switches during the interlocking interval. Finally, the flat-top stability is measured by splitting the flattop into windows of 0.5 μs (Fig. 21). This results in six windows for a flat-top length of 3 μs. The mean value of the output current within each window is recorded over a period of 10 min. The rms stability is calculated over a moving window of 100 pulses. The output current is measured with a differential amplifier, and the mean values inside the windows P1 P6 are recorded with an oscilloscope. An additional window outside the pulse is used to measure the noise of the differential amplifier. These measurements show that the flat-top stability at 360 kv is below the targeted 10 ppm in all six windows. VI. CONCLUSION This paper presents the design of an ultraprecise 127-MW 3-μs solid-state modulator with split-core transformer. The modulator consists of a power supply, twelve pulse generator modules with active core reset, and a split-core transformer with six cores. In addition, an LC bouncer could be used to compensate the droop of the pulse. The pulse transformer design is shown. Different core materials are analyzed. Furthermore, the interlaminate voltage is investigated and calculated for the presented modulator.

11 838 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 44, NO. 5, MAY 2016 In addition, a volume minimal transformer is investigated depending on different load capacitances to investigate the achievable rise time and the parameters which can be used to adjust the damping. The optimization shows that a rise time of 700 ns can be achieved for a load capacitance of 100 pf. The best rise time is achieved by adjusting the height of the secondary winding to achieve the desired damping. In addition, the influence of the pulse transformer on the synchronization of the switches is investigated using an enhanced reluctance model. It is shown that the transformer current balancing of the secondary winding influences the current balancing of the switches connected to the same core. Measurements with the constructed transformer show that a synchronization of the switches is not necessary, since the current sharing is good enough without it. In addition, an LC bouncer circuit is investigated. A multiobjective optimization is performed which shows the required energy of the bouncer for a certain pulse ripple. The minimum achievable ripple is determined to be 0.2% with an energy of 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-circuit and flat-top stability measurements. They show that the modulator is short-circuit capable. Furthermore, the flat-top stability is determined to be less than 10 ppm at an output voltage of 360 kv. REFERENCES [1] (Mar. 2014). SwissFEL. [Online]. Available: [2] J. Qiu, K. Liu, and Y. Wu, A pulsed power supply based on power semiconductor switches and transmission line transformer, IEEE Trans. Dielectr. Electr. Insul., vol. 14, no. 4, pp , Aug [3] D. Gerber, T. Guillod, R. Leutwyler, and J. Biela, Gate unit with improved short-circuit detection and turn-off capability for 4.5-kV press-pack IGBTs operated at 4-kA pulse current, IEEE Trans. Plasma Sci., vol. 41, no. 10, pp , Oct [4] D. Gerber and J. Biela, Charging precision analysis of a 40-kW 3-kV soft-switching boost converter for ultraprecise capacitor charging, IEEE Trans. Plasma Sci., vol. 42, no. 5, pp , May [5] D. Gerber and J. Biela, Interleaving of a soft-switching boost converter operated in boundary conduction mode, IEEE Trans. Plasma Sci., vol. 43, no. 10, pp , Oct [6] R. L. Cassel and M. N. Nguyen, A new type short circuit failures of high power IGBT s, in Proc. Pulsed Power Plasma Sci. (PPPS), vol.1. Jun. 2001, pp [7] A. Müsing, G. Ortiz, and J. W. Kolar, Optimization of the current distribution in press-pack high power IGBT modules, in Proc. Int. Power Electron. Conf. (IPEC), Jun. 2010, pp [8] S. Scharnholz, R. Schneider, E. Spahn, A. Welleman, and S. Gekenidis, Investigation of IGBT-devices for pulsed power applications, in Proc. 14th IEEE Int. Pulsed Power Conf., vol. 1. Jun. 2003, pp [9] D. Bortis, J. Biela, and J. W. Kolar, Design and control of an active reset circuit for pulse transformers, IEEE Trans. Dielectr. Electr. Insul., vol. 16, no. 4, pp , Aug [10] D. Bortis, 20 MW Halbleiter-Leistungs modulator-system, Ph.D. dissertation, Dept. Inf. Technol. Elect. Eng., ETH Zurich, Zürich, Switzerland, [11] A. W. Molvik and A. Faltens, Induction core alloys for heavyion inertial fusion-energy accelerators, Phys. Rev. ST Accel. Beams, vol. 5, p , Aug [Online]. Available: doi/ /physrevstab [12] D. Bortis, G. Ortiz, J. W. Kolar, and J. Biela, Design procedure for compact pulse transformers with rectangular pulse shape and fast rise times, IEEE Trans. Dielectr. Electr. Insul., vol. 18, no. 4, pp , Aug [13] J. Biela, D. Bortis, and J. W. Kolar, Modeling of pulse transformers with parallel- and non-parallel-plate windings for power modulators, IEEE Trans. Dielectr. Electr. Insul., vol. 14, no. 4, pp , Aug [14] D. Bortis, J. Biela, and J. W. Kolar, Transient behavior of solid-state modulators with matrix transformers, IEEE Trans. Plasma Sci., vol. 38, no. 10, pp , Oct [15] D. Bortis, J. Biela, and J. W. Kolar, Optimal design of a two-winding inductor bouncer circuit, in Proc. IEEE Pulsed Power Conf. (PPC), Jun./Jul. 2009, pp Dominic Gerber received the M.Sc. degree in electrical engineering and information technology from ETH Zurich, Zurich, Switzerland, in 2010, where he is currently pursuing the Ph.D. degree with the Laboratory for High Power Electronic Systems. He focused on power electronics, drive systems, and high voltage technology, during his M.Sc. studies. His work focused on solid-state modulators, high accurate capacitor charging, and current measurement based on the Faraday effect. He has been a Post-Doctoral Fellow with the Laboratory for High Power Electronic Systems, ETH Zurich, since His current research interests include high accurate capacitor charging and field-programmable gate array-based control of converter systems. Juergen Biela (S 04 M 06) received the Diploma (Hons.) degree from Friedrich-Alexander-Universität Erlangen-Nürnberg, Nuremberg, Germany, in 1999, and the Ph.D. degree from the Power Electronic Systems (PES) Laboratory, Swiss Federal Institute of Technology (ETH) Zurich, Zurich, Switzerland, in 2006, with a focus on optimized electromagnetically integrated resonant converters. He joined the Research Department, Siemens A&D, Erlangen, Germany, in 2000, where he has been involved in inverters with very high switching frequencies, SiC components, and electromagnetic compatibility. He was a Post-Doctoral Fellow with the PES Laboratory and a Guest Researcher with the Tokyo Institute of Technology, Tokyo, Japan, from 2006 to He was a Senior Research Associate with the PES Laboratory, ETH Zurich, from 2007 to 2010, where he has been an Associate Professor of High-Power Electronic Systems since His current research interests include design, modeling, and optimization of power factor correction, DC/DC, and multilevel converters with an emphasis on passive components, the design of pulsed-power systems, and power electronic systems for future energy distribution.