„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 promo-tional 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.”

BOUNCER CIRCUIT FOR A 120 MW/370 KV SOLID STATE MODULATOR

D. Gerber, J. Biela Laboratory for High Power Electronic Systems

ETH Zurich, Physikstrasse 3, CH-8092 Zurich, Switzerland Email: gerberdo@ethz.ch

BOUNCER CIRCUIT FOR A 120 MW/370 KV SOLID STATE MODULATOR

D. Gerber, J. BielaLaboratory for High Power Electronic Systems

ETH Zurich, Physikstrasse 3, CH-8092 Zurich, SwitzerlandEmail: gerberdo@ethz.ch

Abstract

In this paper, a bouncer circuit for a 120 MW/370 kVmodulator is described. The bouncer circuit is a two-winding inductor bouncer which reduces the output voltagedroop. The bouncer circuit is described and investigatedin detail. Also, the influence of component tolerances isinvestigated. Finally, the benefit of using a bouncer circuitis shown by presenting the same modulator without andwith bouncer circuit. The amount of stored energy wasreduced by a factor of 3.3 which reduces the overall systemvolume significantly.

I. INTRODUCTION

In application areas as e.g. radar systems, cancer treatmentor particle accelerators, more and more pulse modulatorsare based on modern solid state modulator systems. Theseoffer the advantages of a variable pulse length/amplitudeand a higher life-time of the semiconductor switches, whichdecreases the system operation costs. In addition the solidstate modulators offer the benefit that they can be turned offduring the pulse in case of a failure as e.g. short circuit inorder to protect the system and/or the load (e.g. a klystron).

At the PSI in Switzerland a compact and cost effectiveX-ray free electron laser facility for a wavelength range of0.1 to 10 nm is designed [1] (SwissFEL). This laser requiresa solid state modulator to drive the klystron. The parametersof this modulator are shown in tab. I.

TABLE ISPECIFICATIONS OF THE SOLID STATE MODULATOR FOR SWISSFEL

DC link voltage 3 kVOutput Voltage 370 kVOutput Power 120 MW

Repetition Rate 100 HzMaximum Droop <0.5 %

Rise/Fall Time <1 µsPulse Length 3 µs

Repetition Accuracy < 10−5

To achieve a voltage droop ∆ of the pulse flat top of0.5 %, the stored energy ECin has to be 100 times higherthan the pulse energy Ep if only a capacitor is discharged.This huge amount of stored energy is a disadvantage asmore stored energy always implies a bigger system volumeand more difficult error handling.

The amount of stored energy and therefore also the systemvolume can be substantially reduced by bouncer circuits.However, with the classical RL bouncer in series with thepulse transformer high additional losses are generated – inthe considered case up to a few kilowatts. A more efficientand compact solution is obtained with an LC bouncer,which uses an LC resonance for droop compensation.

Bouncer

Pulse GeneratorPulse Transformer

Load

CinSm

Sr

Cr

Active Reset Circuit

Fig. 1. Schematic of the modulator based on a split core transformerwith 6 cores, an active pre-magnetization circuit as well as a two-windinginductor bouncer.

There, an additional switch is required for starting theoscillation before the pulse. In [2] an improved two-winding inductor bouncer is presented, which enables toadapt the bouncer operating voltage to the blocking voltageof available semiconductors. In [2] also a design methodand an optimization procedure for determining the bouncerparameters is presented. However, in the optimization proce-dure only ideal components without tolerances are includedand only a limitation for the peak current in the bouncerswitch is considered. Limitations of other components, asfor example the voltage rating of the bouncer capacitor, areneglected.

Therefore, in this paper an improved design and opti-mization procedure is presented and applied to the designof a bouncer circuit for the 120 MW/370 kW solid statemodulator. First, the basic schematic of the modulator withbouncer is described in section II. Afterwards, the bouncercircuit is described in detail in section III and the influenceof the different bouncer parameters on the output waveformis discussed in section IV. Finally, a design method for the120 MW/370 kW solid state modulator is presented.

II. MODULATOR DESCRIPTION

In the following, the three basic modulator components– generator circuit, pulse transformer, bouncer circuit – asshown in fig. 1 are shortly discussed, because they are

important for understanding the derivation of the bouncermodel.

A. Pulse Generator

The pulse generator circuit consists of an input capacitorCin, which serves as energy storage, a semiconductor switchSm and the pre-magnetization circuit (Sr and Cr). Theconsidered modulator with the specifications in tab. I isbased on 12 such generator circuits, which are connected tothe primary windings of the pulse transformer as discussedbelow.

Since the voltage Vpri on the transformer primary sideis unipolar during the pulse, a pre-magnetization circuitis required to achieve a symmetrical flux swing in thetransformer core and fully utilize the transformer core.Further details on the operation principle of the active resetcircuit is given in [3].

B. Split Core Pulse Transformer

The pulse transformer is a key element of the modulatorsince it significantly influences the pulse shape and enablesto adapt the input voltage to the blocking voltage of semi-conductor switches. Additionally, a single semiconductorswitch is not capable to provide sufficient output power,so that a series and/or a parallel connection of switches isnecessary.

In case of a series connection, the balancing of the switchvoltage must be guaranteed, and in case of a parallel con-nection, the currents through the switches must be equallydistributed. By utilizing a split core/matrix transformer theseproblems can be solved, since such a transformer providesinherent current balancing between switches connected towindings on different cores, e.g. Npri,1 and Npri,n (cf.fig. 3) as explained in [5]. The current between the pairof switches connected to the same core is not inherentlybalanced. To achieve the current balancing for these pairsof switches, an active gate control can be used as describedin [4].

C. Bouncer Circuit

The bouncer circuit is basically an LC resonant circuit,which could be either placed on the primary side or onthe secondary side of the pulse transformer. If the bouncer

Vout

t

t

t

t

Sr

Sb

Sm

VCc0’VCr’

Fig. 2. Output voltage during one pulse cycle.

Vsek

Nsek

Vpri,1

Vpri,n

Npri, 1

Npri, n

Vpri,1

Vpri,n

Npri, 1

Npri, n

Fig. 3. Split-core/matrix-transformer with n cores, 2 primary windingsper core and 2 parallel connected secondary windings.

is placed on the primary side, the current through theswitch of the bouncer must be higher than the currentthrough the main switch during the pulse. On the otherhand, for a bouncer on the secondary side, the currentthrough the bouncer switch is lower than for a bouncer onthe primary side, but the switch voltage is much higher. Inboth cases, the design and the maximum voltage droop, thatcan be compensated, could be significantly limited by thesemiconductors which are available.

For this reason in [2], a two winding inductor bounceris presented, where the bouncer inductance is replaced bya two-winding inductor, which is basically a transformerwhere the magnetizing inductance is used as an inductor. Afurther degree of freedom is available with the turns ratioin the bouncer design process, that enables to use a singlesemiconductor switch for the bouncer because the bounceroperating voltage and current can be adjusted to availableswitches.

III. BOUNCER CIRCUIT OPERATION

To explain the operation of a bouncer circuit, the matrix-transformer is first simplified to a transformer with one coreand one primary/secondary winding. Then, the componentsof the generator and the bouncer are transformed to thesecondary side as shown in fig. 4. The pre-magnetizationcircuit is not included in the model as it does not influencethe basic operation of the bouncer if the pre-magnetization isproperly designed. In the following, the resonant transitionof the bouncer is split into three time intervals T1 to T3 –refer also to the waveforms in fig. 5 and 6.

a) T1: At the beginning of a pulse cycle, the two capac-itors C ′

in and C ′c are charged to V ′

Cin0 and V ′Cc0 and both

switches are open. To initialize the pulse cycle, the bouncerswitch Sb is closed, so that capacitor C ′

c starts to dischargeand the current i′Lc in the bouncer inductor L′

c rises.b) T2: At the beginning of T2, switch Sm is closed and

the load current starts to flow. The load current has to flowthrough capacitor C ′

c because the current in the bouncerinductance has to be continuous. The voltage across thebouncer capacitor still drops as long as the load current issmaller than the current through the bouncer inductance.Because the output pulse is centered around TB

4 , whereTB is the period of one resonant transition of the bouncercircuit, the voltage of the bouncer capacitor swings froma positive voltage to a negative voltage with applying thesame peak value. Since, vout(t) = v′Cin(t) + v′Cc(t), thevoltage across the load vout(t) is reduced by the bouncerat the beginning of the pulse and raised at the end of the

Cin’

Cc’ Lc’

Rl

VCin0’

VCc0’

VCin0 Cin

VCc0 Cc

Rl

iCc

iin

iin’

iCc’ iLc’

Modulator with Matrix Transformer andTwo-Winding Inductor Bouncer

Circuit with simplified Matrix Transformer Simplified Circuit without Galvanic Insulation, Values refered to Secondary Side

Sm

Sbvout

vLc’

Fig. 4. Simplification of the modulator – first the matrix transformer is replaced a transformer with a single core and then all components are transferredto the secondary side of the transformer.

pulse. This results in a more or less constant voltage acrossthe load during the pulse.

c) T3: At the beginning of T3, the main switch Sm isopened, so that the bouncer is a pure parallel LC resonantcircuit again. The bouncer capacitor voltage swings backto a voltage close to its initial voltage at the beginning ofthe pulse. At this point, switch Sb is turned off to stop theoscillation at the zero crossing of the bouncer current.

t3

T/2T/4

Tp/2

t

VCc0’

vCc’iLc’ iCc’

T1 t10 t2T2 T3

TB

Fig. 5. Voltage and current waveforms of bouncer circuit shown in fig. 4.

Bouncer Model: The bouncer circuit can be describedwith three simple differential equation systems, one for eachof the three time intervals T1 to T3. During time interval T1,switch Sm is opened and switch Sb is closed. Capacitor C ′

c

is charged to V ′Cc0 and there is no current flowing through

the bouncer inductor L′c. Therefore, the equation system is:

Droop without BouncerDroop with Bouncer

t

Output Voltage without BouncerOutput Voltage with Bouncer

Fig. 6. Output waveform with bouncer circuit.

i′Cc(t) = C ′c

dv′Cc(t)

dtv′Lc(t) = L′

c

di′Lc(t)

dtv′Lc(t) = v′Cc(t) i′Cc(t) = −i′Lc(t) (1a)

with the initial conditions:

v′Cc(0) = V ′Cc0 i′Lc(0) = 0 (1b)

For the second time interval, both switches are closed.The initial conditions are given by the solution at t = t1 ofthe differential equation system for the time interval T1.

i′Cc(t) = C ′c

dv′Cc(t)

dt−i′in(t) = C ′

Cin ·dv′Cin(t)

dt

v′Lc(t) = L′c ·di′Lc(t)

dt

i′in(t) =vout(t)

Rli′Cc(t) = i′in − i′Lc(t)

v′Cin(t) = vout(t) + v′Lc(t) v′Lc(t) = v′Cc(t) (2a)

with the initial conditions:

v′Cc(t1) = V ′Cc1 i′Lc(t1) = I ′Lc1

v′Cin(t1) = V ′Cin1 = V ′

Cin0 (2b)

The equation system during T3 is basically the same asfor T1, but the initial conditions are given by the solutionof the differential equations at the end of T2:

i′Cc(t) = C ′c ·dv′Cc(t)

dtv′Lc(t) = L′

c ·di′Lc(t)

dtv′Lc(t) = v′Cc(t) i′Cc(t) = −i′Lc(t) (3a)

with the initial conditions:

v′Cc(t2) = V ′Cc2 i′Lc(t2) = I ′Lc2 (3b)

The algorithm for calculating the waveforms and thedroop of the pulse is graphically described in fig. 7a.

Equations 1a0≤t<t1

Equations 2at1≤t<t2

Equations 3at2≤t<t3

Droop ∆

Initial Conditions 2b

Initial Conditions 1b

Initial Conditions 3b

(a) Calculation of the bouncerresponse.

Optimize Lc’ for∆=0.5% and VCc0’ = VCc0,max

Optimize Lc’ for∆=0.5% and ICc,peak = ICc,max

Lc,minOptimize Lc’ for

∆min=0.5% with 2π√LcCc≥2Tp

Lc,max,VCc’

Lc,max,ICc

Set Cc’

(b) Calculation of circuit value limi-tations.

Fig. 7. Algorithms used for calculations.

IV. BOUNCER PARAMETERS

The two-winding inductor bouncer has four degrees offreedom: Bouncer capacitance Cb, bouncer inductance Lc,initial bouncer voltage VCc0 and turns ratio of the two-winding inductor (bouncer transformer). The turns ratio isonly used to adjust the current and voltage of the bouncerto values suitable for semiconductor switches at the end ofthe design process. Therefore, in a first step, all componentsare transferred to the secondary side of bouncer transformerand the bouncer transformer is replaced by an equivalentinductor in order to simplify the calculations. The turns ratiois only considered when the component limitations are takeninto account as discussed later in detail.

A. Initial Bouncer Capacitor Voltage

The pulse droop is compensated with the bouncer capaci-tor voltage. The initial value V ′

Cc0 determines the amplitudesof v′Cc and i′Lc for a given set of component values. If V ′

Cc0is set too low, v′Cc is too small at t = t1 and the outputvoltage is not reduced enough by the bouncer. Therefore,the droop compensation is too small (undercompensated).If the initial capacitor voltage is set too high, v′Cc is toohigh at t = t1 and the bouncer compensates more droopthan necessary (overcompensated). Consequently, there is anoptimal voltage V ′

Cc0 to achieve exactly the targeted droopas can be seen in fig. 8.

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

0.5

1

1.5

2

2.5

3

3.5

VCc0’ (V)

Droop (%)

Undercompensated Overcompensated

Fig. 8. Droop as a function of V ′Cc0 for C′in = 121 nF, C′c = 1 µF,L′c = 1 µH.

The optimal V ′Cc0 results in a minimum amount of stored

energy if it is in the undercompensated region.

B. Bouncer Capacitor

For considering the influence of the bouncer capacitancevalue on the droop, it is interesting to fix the inductancevalue and calculate the optimal initial capacitor voltage forthe considered bouncer capacitance. For such a case, thedroop of the output pulse is shown in fig. 9. The voltagedroop is becoming smaller and smaller with increasingcapacitance values. The reason is that the minimum droop isgiven by the ripple of the capacitor voltage v′Cc during thepulse. By increasing C ′

c the resonant period TB of the LC-bouncer increases, so that the voltage drop across C ′

c duringthe output pulse becomes more and more linear. However,the peak amplitude of the bouncer current increases alsowith C ′

c and the bouncer components/switches must bedesigned for this current.

In fig. 9 also the optimal V ′Cc0 is given, which has a clear

minimum. For large values of C ′c, a high initial voltage

V ′Cc0 is required, since the resonant current in the bouncer

must increase in order to obtain a sufficient change ofv′Cc during the pulse. For small C ′

c values also V ′Cc0 must

increase to obtain a high enough amplitude of i′Lc, so thatthe influence of the load current, which flows also throughC ′

c, is compensated.

10 -8 10 -7 10 -66065707580859095100

Cc' (F)

V Cc0

' (kV

)

10-8 10 -7 10-60

0.5

1

1.5

Cc' (F)

Dro

op (%

)

(a) (b)

Fig. 9. Minimum droop (a) and initial capacitor voltage (b) dependingon bouncer capacitor value C′c for C′in = 121 nF and L′c = 10 µH.

C. Bouncer Inductor

The influence of the bouncer inductance value L′c is

similar to the influence of the bouncer capacitance value.Again, the initial capacitor voltage has to be increased foran increasing L′

c to get a high enough capacitor current.A bigger inductance also results in a longer period whichreduces the minimum droop.

D. Component Tolerances

Besides the component values themselves, also the tol-erances of the values influence the achievable droop ifthe initial conditions and/or the point of time, when Sb

is switched, is adapted to the modified component values.In worst case, the droop requirements might not be metbecause the real circuit values are not the same as thecalculated ones. Therefore, the component tolerances mustbe taken into account during the design process, to makesure that the maximum droop is always below the maximumallowed one.

V. BOUNCER DESIGN

Based on the bouncer operation and the influence of thebouncer parameters explained in the previous section, theinfluence of circuit limitations is discussed and a designstrategy is presented in the following.

A. Design Constraints

Besides the droop requirements, also some design con-straints must be considered. First, the resonance frequencyof the bouncer circuit must meet the following criteria,because the output pulse is centered around TB

4 .

TB4>Tp2→ TB > 2 · Tp, (4)

where TB = 1/fB is the period of the LC bouncer and Tpis the length of the output pulse including rise and fall time.

Second, the maximum allowed voltage V ′Cc0 is limited

by the klystron load, because the klystron usually hasa maximal allowed reverse voltage, which must not beexceeded. Since the bouncer voltage swings from V ′

Cc0 to−V ′

Cc0 and back to V ′Cc0, the initial voltage V ′

Cc0 must besmaller than the maximum allowed klystron inverse beamvoltage. In the considered case, the pre-magnetization alsoresults in a negative output voltage. It has to be operated insuch a way, that the resulting voltage on the secondary sideis half of the maximum inverse beam voltage to achieve themaximum possible bouncer output voltage swing (cf. fig2). Therefore, the maximum VCc0 is half of the maximuminverse beam voltage.

Third, the bouncer semiconductor switch limits the max-imum bouncer voltage/current. With the turns ratio ofthe bouncer transformer, the peak voltage/current can beadapted to to the switch, however, the product voltage ×current must be kept below the limits of the switch. In theconsidered system a press-pack IGBT is used, which has amaximum blocking voltage of 3 kV and a maximum currentof 4 kA.

B. Design Room

With the discussed design constraints and the limit for theoutput pulse droop, a design room for the bouncer circuitis determined and only certain sets L′

c, C ′c and V ′

Cc0 willmeet these constraints. The limits of the design room canbe calculated with optimization algorithms like the gradientdescent method. An example for such an algorithm is shownfig. 7b for a given C ′

in. The resulting curves are shown infig. 10.

For each point on a specific limiting curve, the droopis exactly the maximum allowed droop and the respectivelimiting parameter is also exactly at its limit. During de-termining the limiting curves, it has to be assured, that thebouncer is always in the undercompensated region. Other-wise, it would be possible to reduce V ′

Cc0 and therefore alsothe switch current. This might lead to a solution with thesame droop without violating the given limitations.

The design room itself depends on the input capacitanceC ′

in. For a decreasing C ′in, the design room is getting

smaller. Below a certain C ′in, it is not possible to design

a bouncer without violating at least one of the givenlimitations.

10 -8 10 -7 10 -6 10 -510-8

10-7

10-6

10-5

10-4

10-3

10-2

Cc‘ (F)

Lc’ (H)

Limited by maximum VCc0’Limited by maximum Switch Current

Limited by minimum Droop

Design Room

Limited by minimum Resonant Transition Time

Fig. 10. Design room for an input capacitance C′in of 181 nF

Because there is no unique solution, it is possible tooptimize the bouncer for various criteria. In [2], it wasoptimized for minimum volume. Other optimizations arepossible, like minimum stored energy, minimum bouncerinductor volume or repetition accuracy.

When performing an optimization, it has to be takeninto account, that all components of the bouncer andthe pulse generator have tolerances. Such tolerances aree.g. component tolerances or jitter of the switches. If thebouncer is optimized for a certain droop, it might notalways meet the requirements because of these tolerances.One possibility to solve this problem would be to set themaximum allowed droop lower than the required maximumdroop. However, the solution found with this method mightlead to a bouncer which meets the requirements even withcomponent tolerances, but it is not guaranteed that this isthe optimal solution.

A better way to take various uncertainties into account isto calculate the worst case droop instead of the ideal droop.There, for a given set of L′

c, C ′c and V ′

Cc0 the worst casedroop is calculated by maximizing the droop for the givencomponent tolerances.

VI. PROTOTYPE SYSTEM

To show the benefits of the bouncer circuit and the effectof tolerances, a bouncer circuit for the 120 MW pulsemodulator with the specifications given in tab. I has beendesigned. In a first step, the initial bouncer capacitor voltageis adjusted to meet the worst case droop requirements. Then,the initial capacitor voltage is calculated to meet the drooprequirements with ideal circuit elements and finally, thesetwo bouncers are simulated and compared with a modulatorwithout bouncer.

For illustrating the influence of the tolerances, the bouncercircuit parameters in the two right columns of tab. II areconsidered. If ideal components without tolerances are as-sumed an initial capacitor voltage of 4.27 kV is sufficient forachieving a droop of 0.5 %. However, with real componentswith tolerances of ±10 % the worst case droop becomes0.77 % (C ′

in = 163 nF, C ′c = 550 nF, L′

c = 11 µH).One possible solution to reduce the worst case droop is

setting the initial capacitor voltage higher. At a certain point,this is not possible anymore because the minimum droop isalready reached. In that case, different bouncer circuit valueshave to be chosen (e.g a higher L′

c). In our example, thisis fortunately not necessary. By setting the initial capacitorvoltage V ′

Cc0 to 5.13 kV, the worst case droop is 0.5 %which meets the requirements. The simulated waveformsfor this bouncer are shown in fig. 11.

To show the benefit of a bouncer circuit, in tab. II alsothe component values for a modulator without bouncer anda droop of 0.5 % are given. There it can be seen, that theamount of stored energy (and the system volume) is muchhigher for the system without bouncer.

The specifications of the two-winding bouncer inductanceare given in tab. III.

-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4365'200365'400365'600365'800366'000366'200366'400366'600366'800367'000367'200

Time (μs)

Vout (V)

Exact Component Values

Worst Case Droop

Δ = 0.21%

Δ = 0.5%

Fig. 11. Simulated output pulse voltage for the parameters given in II.There curves for ideal components and for worst case droop in case ofcomponent tolerances are given.

Finally, the effect of the leakage inductance of the two-winding inductor (bouncer transformer) is investigated.With this leakage inductance, the load current must becontinuous and could not include steps (cf. fig. 5). Basedon the specifications given in tab. II and the design of thebouncer transformer in tab. III, a simulation of the circuitincluding an equivalent circuit of the bouncer transformerand the klystron has been performed, which is given in fig.12. To allow a comparison of the different waveforms, theamplitudes are normalized.

There one can see, that the leakage inductance onlyslightly influences the output pulse waveform, because itis small compared to the bouncer inductor. The leakageinductance also influences the bouncer resonance frequency.To compensate this effect, the bouncer inductance couldbe adjusted to keep the resonance frequency constant. Inthis case, this is not necessary. Additionally, the leakageinductance acts like a voltage divider, which is compensatedby adjusting the initial capacitor voltage V ′

Cc0.Fig. 12 shows that the influence of the pulse transformer is

TABLE IICOMPARISON OF THREE DIFFERENT BOUNCER CIRCUITS FOR THE

SPECIFICATIONS GIVEN IN TABLE I.No Bouncer Without Tolerances With Tolerances

Cin 9.6 mF 2.88 mF 2.88 mFC′c - 500 nF 500nFL′c - 10 µH 10 µHRl 1075 Ω 1075 Ω 1075 ΩVCin0 3 kV 3 kV 3 kVV ′Cc0 - 4.2 kV 5.13 kVI′Cc,max - 1 kA 1.2 kAECin 43 kJ 12.96 kJ 12.96 kJECc - 4.55 J 6.58 JEtotal 43 kJ 12.96 kJ 12.97 kJ

TABLE IIIPARAMETERS OF THE TWO-WINDING INDUCTOR FOR THE BOUNCER

WITH TOLERANCES

Core METGLAS AMCC 630Core Size 90x130x70 mmNumber of Primary Turns 4Number of Secondary Turns 7Air gap 8.8 mmLeakage Inductance (secondary side referred) 144 nH

very strong. The finite rise time influences the bouncer op-eration remarkably. The bouncer operates with a relativelylow current compared to the load current which producesa significantly different output waveform. In the simulatedcircuit, the droop is even lower in the real system. Thesimulation also shows, that the pulse transformer cannot beconsidered as an ideal transformer and has to be included inthe bouncer design process which will be done in a futurepaper.

-0.5 0 0.5 1 1.5 2 2.5 3 3.5 40.995

0.996

0.997

0.998

0.999

1

1.001

Time (μs)

Vout (p.u.) With Bouncer Inductor Leakage Inductance

Ideal Bouncer Inductor

With Pulse Transformer Model and Klystron Load

Fig. 12. Output voltages with leakage inductance.

VII. CONCLUSION

In this paper, a design and optimization procedure fortwo-winding inductor bouncer circuits is presented. First,the basic operation principle is described and then theinfluence of the different bouncer parameters on the out-put waveform is investigated and a new design methodincluding circuit limitations and component tolerances isproposed. For validating the design procedure, results for120 MW/370 kV pulse modulator with and without bouncercircuit are presented and the amount of required storedenergy is calculated. Furthermore, the influence of theleakage inductance of the bouncer transformer on the outputpulse is investigated. It was shown that the pulse transformerhas a large influence on the bouncer operation and thereforehas to be included in the bouncer design process.

ACKNOWLEDGMENT

The authors would like to acknowledge the support ofPPT in relation to the practical realization of the project.

References

[1] A. Oppelt et al., ”Towards a low Emittance X-ray FEL at PSI”, Proc.of the Free-Electron Laser Conference (FEL), 2007, pp. 224-227.

[2] D. Bortis, J. Biela and J. W. Kolar, ”Optimal Design of a Two-WindingInductor Bouncer Circuit”, Proc. of the IEEE International PulsedPower Conference, 2009, pp. 1390-1395.

[3] D. Bortis, J. Biela and J. W. Kolar, ”Design and Control of anActive Reset Circuit for Pulse Transformers”, IEEE Transactions onDielectrics and Electrical Insulation, vol. 16, (no. 4), pp. 940-947,2009.

[4] D. Bortis, J. Biela and J.W. Kolar, ”Active Gate Control for CurrentBalancing in parallel connected IGBT Modules in Solid State Modula-tors”, 16th IEEE International Pulsed Power Conference (PPC), 2007,pp. 1323-1326.

[5] E. Herbert, ”High Frequency Matrix Transformer”, Patent US4,845,606 [Online], July 1989, Available: http://www.eherbert.com.