Pulse current generator with fast rise time based on ......Pulse current generator with fast rise time based on transformers and single active switch for plasma drilling Oliver Keel

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Pulse current generator with fast rise time based on transformers and single active switch for plasma drilling

O. Keel, J. Biela Power Electronic Systems Laboratory, ETH Zürich

Physikstrasse 3, 8092 Zürich, Switzerland

mailto:[email protected]

Pulse current generator with fast rise timebased on transformers and single active switch

for plasma drilling

Oliver Keel and Juergen BielaLaboratory for High Power Electronics, ETH Zurich

8092 Zurich, [email protected]

Keywords”Pulse current generator”, ”Plasma drilling”

AbstractThis paper presents a new pulse generator topology based on the flyback converter and the XRAM gen-

erator concept. The presented topology has the advantage of only requiring a single active switch which

results in a simpler control and a higher robustness. Those requirements are essential for plasma drilling,

for which the pulse generator has to operate in harsh environment with a high ambient temperature and

high mechanical stresses. This paper presents the design procedure of the pulse transformer of the pro-

posed topology and results for a first design.

1 IntroductionGeothermal energy is a promising renewable energy source for continuous power generation for the base

load. To access the energy, holes need to be drilled to a depth of up to 10 km. At such depths, the ambient

temperature reaches up to 300 ◦C, which makes it possible to efficiently produce electricity [1]. However,

the cost of drilling deep holes with a mechanical grinding process grows exponentially with the depth.

Therefore, conventional drilling is typically not very cost-effective for holes deeper than 5 km [2].

To reduce the drilling cost, new drilling concepts have been proposed, including laser cutting and drilling

[3], rock spallation with a hydrothermal flame [4] or electro pulse drilling [2]. Another promising concept

is plasma drilling [5], which uses a pulsed plasma to generate fast temperature changes at the surface of

the rock to disintegrate the rock by thermal contraction. For plasma drilling, current pulses with a fast

rise time in the range of a few 100 ns and large pulse energy are required. In addition, a relatively low

constant current for a pilot arc is required in between the pulses (fig.1), so that always a small pilot arc

burns. The pilot arc is initially triggered with a high voltage igniter next to the electrode.

Due to the influence of parasitics, the pulse generator must be placed close to the load in order to achieve

fast current pulse rise times. In the considered application, this means that the generator must be installed

in the drill head, which is exposed to high ambient temperatures and pressure. To protect the pulse current

generator, it is placed inside a protection vessel and connected via a cable (a MV transmission line) to

Vin

S

T2 Tn

D2Dn

iin

iLT1

D1

Z0

+-

Module n Module n-1 Module 1

Pilot arc phase

Pulse phase

Igniterfor pilot

arc

Surface Transmission lineLength up to 10km

Protection vessel Electrodes for plasma drilling

Ae

Be

iL(t)

t2

tt3t1

Arc

Figure 1: Proposed concept of single switch current adder (SSCA)

Pulse current generator with fast rise time based on transformers and single activeswitch for plasma drilling

KEEL Oliver

EPE'19 ECCE Europe ISBN: 978-9-0758-1531-3 - IEEE catalog number: CFP19850-ART P.1Assigned jointly to the European Power Electronics and Drives Association & the Institute of Electrical and Electronics Engineers (IEEE)

a power supply with a switch at the surface. Because the conditions in the protection vessel are harsh

in terms of temperature and EMI, actively controlled switches are not suitable for integration in the

protection vessel.

Possible concepts for the pulse current generator for the considered plasma drilling application are pulse

transformers [6], meat grinders [7] and XRAM generators [8]. All those topologies have fast current rise

times and offer current multiplication. Especially the XRAM generator has the additional advantage of

being modular, which offers scalability in terms of power and current for the pulse drilling application.

In the considered application, the XRAM modules would need to fit inside the protection vessel so that

the active switches and the related control hardware would be exposed to the high ambient temperature

what decreases the reliability of the system. In order to overcome this limitation, a new concept which

does not require switches inside the protection vessel is presented in this paper (Fig. 1). The concept

is modular and utilises transformers for current adding/multiplication. The operation is controlled with

a single switch, which could be located at the surface and the new concept can inherently generate the

current for the pilot arc.

Section 2 presents the new concept and its underlying operating principle. Thereafter a model of the

transformer with its parasitics is introduced and the effects on the rise time of the pulse current is ex-

plained. The following section 3 introduces the design procedure of the transformer with a subsection

on the calculation of the parasitics. Finally in the last section 4, a possible transformer design based on

specifications for the application is presented.

2 Single switch current adder (SSCA)The proposed single switch current adder (SSCA), shown in fig. 1, requires no active switch within the

protection vessel and the power supply as well as the switch for controlling the operation can be located

at the surface and connected with a cable to the modules in the bore hole. A single module n in the

protection vessel consists of transformer Tn and diode Dn. The concept of a module is based on a flyback

converter, i.e. the transformer is used for storing energy.

The operation of the SSCA could be divided in two phases. In the pilot arc phase, i.e. in the time interval

t1 to t2, the pilot arc burns between the electrode due to the pilot current, which also is used to store

energy in the flyback transformer. In the subsequent pulse phase, i.e. in the time interval from t2 to t3,

the energy is transferred from the flyback transformer to the (pilot) arc.

During the pilot arc phase, switch S connects all the primary windings of the transformers in series

to the load and the windings of the transformers are interconnected in such a way, that the diodes Dn

are reverse biased. The charging current iin flows through the series connected primary windings and

also across the electrode, so that the converter inherently generates the required current for the pilot arc

(current path: blue doted line in fig. 1). At the end of the pilot arc phase, switch S is opened and the

transformers commutate the current to the secondary winding and forward bias diodes Dn. Consequently,

all secondary windings are connected in parallel to the load RL and the current in the flyback transformer

is added up, i.e. multiplied by the number of modules n. The commutation from a series to a parallel

connection is similar in flyback converters and/or XRAM system. At the end of the pulse phase, switch

S is closed again and the cycle starts over again.

The maximum current during the pilot arc phase is reached by the end of the interval and depends mainly

on the value of the load resistor RL, the primary winding resistance Rpri and the input voltage Vin. In the

following section, the detailed current and voltage waveform for the modules during the two phases are

presented.

2.1 Operation principle

In the SSCA primary windings of the transformer are connected in series in phase 1 and all secondary

windings are connected in parallel to the load in phase 2. This results in different input vin,n and output

vout,n voltage waveforms for each module. In contrast the primary and secondary current waveform are

the same for all modules. Fig. 2a shows the first module 1 which is connected to the electrode and fig.


KEEL Oliver


T1

D1

Module 1

vpri,1

vsec,1

isec,1

ipri,1

v in, 1

= v

pri,1

+ v

L

v out,

1 = v L

Vin

Vin/n

vin, 1(t)

tt

vout, 1(t) = vL(t)

ipri,1(t) isec,1(t)

Imax Imax

RL·Ipilot·n

Tn

Dn

Module n

vpri,n

vsec,n

isec,n

ipri,n

RL·Ipilot

v in, n

v pr

i, +

vL

Vin

vin, n(t)

t

ipri,n(t)

Imax

RL·Imax·(n-1)

t

vsec/out, n=vout, 1(t) = vL(t)isec,n(t) / vout, n(t)

v out,

n

Imax

RL·Imax·(n-2)

Vin

t1

t1

t1

t1

t2

t2

t2

t2

t3 t3

t3 t3

vD,1

vD,n

a)

b)

n

Figure 2: Ideal voltage and current waveform of module 1 and n

2b the last module n which is connected to the cable. On the left, the input voltage vin and the primary

current ipri waveforms are shown and on the right, the output vout respectively secondary voltage vsec and

the secondary current isec waveforms are presented.

In the following description of the basic current and voltage waveforms, the transmission line and para-

sitic components are neglected for the sake of simplicity and it is assumed that the SCCA is connected

to an ideal voltage source at the input.

Pilot arc phase

At the beginning of the pilot arc phase, switch S is closed at t = t1, so that all the primary windings and

the load are connected in series to the input voltage Vin. The primary current ipri in the RL circuit with

the time constant τ = n·LmRL

, increases exponentially and all the diodes Dn are reverse biased.

The input voltage vin,n at module n is equal to the input voltage Vin as shown in fig. 2b. Due to the series

connection of the primary windings, the magnetizing inductor acts as an inductive voltage divider during

the pilot phase, what defines the input and output voltages of all modules. Since the inductive voltage

drop across the magnetizing inductors Lm decays, the voltage vout across RLbecomes equal to Vin at the

end of the pilot arc phase.

Pulse phase

At the beginning of the pulse phase, switch S is opened and in case of an ideal transformer (Lσ = 0), the

primary current ipri commutes immediately to the secondary winding. Due to the parallel connection of

the secondary windings, the load current rises to:

iL =n

∑ζ=1

isec,ζ (1)

The load voltage vL as well as the secondary voltages vsec of modules increase with the rising current

through the load i.e. the arc. The induced voltages onto the primary winding add due to the series


KEEL Oliver


Tn

Dn

Module n

Rsec

Rpri L

Cstray

Lm

Tn

Dn

Module 1

Rsec

Rpri L

Cstray

Lm

iL (t) t2tImax

a)

iC,stray current module 1

iC,stray current module n

ipulse Pulse currentipilot Pilot arc current

RLoad

iL(t)

b)

iL

isec

isec(t) t2t2

i - i = iL

t2

vc,n(t) / vc,1(t)

t t t

t

vL + v +vL

n n

c)

vc,n vc,1

iL

n · ipilot

Figure 3: (a) Module with parasitic components and the current distribution before and after t = t2 (b) Voltage

waveform for Cstray at t2 (c) Pulse, pilot arc and stray capacitor current waveform and resulting load current

connection of the modules. Therefore, the maximum voltage value results for input voltage vin,n of

module n which is equal to the sum of all primary winding voltages and the load voltage.

2.2 Impact of parasitics on the pulse performance

In order to evaluate the behaviour of a non-ideal SSCA, a model of the transformer including the para-

sitics is essential. Generally, a transformer has two main parasitics which significantly impact the pulse

behaviour of the system. Those parasitics are the leakage inductance and the stray capacitance shown in

fig. 3. The magnetic behaviour of the transformer is modelled with a T-equivalent circuit assuming that

the leakage inductance is transferred to the primary. In general, the stray capacitances of the transformer

can be represented with the ”six capacitor model (6C)” presented, for example, in [10]. The capacitors

of the 6C-Model depend on the geometry of the core and the winding. In the case of the SSCA topology,

the model is simplified to one interwinding capacitor Cstray (Fig. 3a), since they have the largest effect

on the current rise time as explained in the following.

For the proposed application, the main goal is to achieve a fast current rise time of the pulse and therefore,

the current and voltage waveforms before and after the start of the pulse at t = t2 are analysed in detail

(see fig.3b/c).

Voltage vin and voltage vout across RL become equal to Vin and voltage vc is zero assuming that shortly

before t = t2, the primary winding voltages vpri decayed to zero and the current iLσ is equal Imax. At

the moment t = t2, switch S opens and the pilot arc current ipilot from the voltage source becomes zero,

shown as a blue dotted line in fig. 3a/c. Leakage current iLσ must be continuous and commutes to the

stray capacitance Cstray. The stray capacitor current iC,stray is shown as green dotted line in fig. 3a/c.

Due to the current, the stray capacitance voltage vc,n (Fig. 3b) increases and starts oscillating since the

leakage inductor and the stray capacitor form a series RLC circuit. The capacitor current iC,stray is in the

opposite direction of the pulse current ipulse shown in the second graph in fig. 3c. Therefore, the resulting


KEEL Oliver


load current iL, shown as red line on the right graph in fig. 3c, is the difference between the capacitor

current iC,stray and the pulse current ipulse. The current rise time of a single module is therefore limited

to the resonance frequency of the RLC circuit. Moreover, the stray capacitance is charged to a higher

voltage moving from module 1 close to the electrodes to module n close to the cable, because vin,n is the

sum of all vLσ,n, vLm,n and the load voltage vL which further affects the current rise time.

3 Design procedureIn the following the design procedure of the SSCA is presented, which is split into two parts. In the first

part the load model of the plasma for the circuit simulation is introduced. In the second part, the general

design procedure of the transformer is shown.

3.1 Plasma load model

The pulse waveform subdivided in two phases shown in fig. 1. For both phases, the load current iLflows through the arc plasma. Therefore, the behaviour of the pulse waveform is highly depended on the

V-I characteristic of the plasma. The V-I characteristic can be approximated with a conductance model

used for DC arc discharges in gas environments presented in [11]. In this application, the considered

gas behaves like steam. In the model the conductance G of the gas is assumed to be proportional to

the electron density ne of the plasma (2) and the constant F describes an experimental constant which

describes the relation between conductance and gas properties.

G =iv= Fne (2)

The rate of production of electrons (3) depends on the electric power subtracted by two electron loss

terms. The first loss term describes the recombination at the outer wall of the plasma and the second

term expresses the recombination losses inside the plasma. Wall losses are modelled to be proportional

to the electron density ne whereas the recombination losses depend exponentially on the electron density

ne. Each term of the rate equation has its own linear proportionality factor (A, B,C, D) to describes the

gas properties.

dne

dt= Aiv− Bne −CeDne (3)

LE=100nH

CE=10pF

**A

- - +

**

1/s

D

C

eu

**

B

A */

*/A=0.01B=2000C=200D=1.45

Ae

Be

a)

W1

W2

W3

b)

Figure 4: (a) Arc plasma model. (b) Winding arrangement W1 to W3.


KEEL Oliver


Replacing the electron density in (3) with (2) results in (4), in which the mathematical manipulation leads

to the constants A = AF , B = B, C = CF and D = D/F .

dGdt

= Ai2

G−BG−CeDG (4)

The constants are fitted with experimental data presented in [12], [13] and [14]. In these publications, a

water gap was pulsed with a high DC voltage until break down was initiated. The arc through the water

gap, heats up the water and then generates plasma from the steam. The current and the voltage values

for the breakdown were measured. Publication [13] presents arcs with currents values up to 4.5 kA. The

data extracted from the measurements in [12] show a conductance between 0.5 S and 5.8 S with a time

constant between 4.8 μs and 5.1 μs. In [14], the authors increased the applied voltage step wise from

7 kV to 13 kV while varying the external pressure between 0 and 4 MPa. Furthermore, the experiment

was performed with a coaxial electrode with a water gap of 5 mm. The resulting current waveform shows

the behaviour of an underdamped RLC circuit. The arc resistance decreased with higher pulse voltage

and increased with increasing hydrostatic pressure. The measured values were in a range from 4 S to

8 S for the arc without external applied pressure. The tested peak current value was between 15 kA and

35 kA. The authors do not specify an exact current rise time but measurements on the same setup in [13]

indicate a current rise time below 50 μs.

Based on this experimental data, the parameters A,B,C,D are fitted such that the conductance value

varies between 2.68 S and 0.57 S from phase 2 to phase 1. The highest conductance value is reached at

the end of the pulse interval after the plasma has heated up. The modelled time constant is set to the value

of 23 μs. The plasma model (Fig. 4a) is implemented in PLECS as capacitor in parallel to an inductor

and a controlled voltage source, in which the voltage source represents the voltage drop of the plasma.

The voltage value results from the differential equation for the conductance multiplied by the impressed

current. Besides the plasma load model, the SSCA requires a transformer design procedure to calculate

the design parameter to full fill the pulse specification which is shown in the following.

3.2 Transformer design procedure

The optimal selection of the core size and its core material is crucial to achieve minimal losses and the

required pulse energy Epulse. Constraints for the optimization are the available space, the pulse energy.

The current rise time value is feed into an algorithm which determines analytically the pulse energy and

total losses.

- ipri & isec - Core dimensions

Core materialdata

Store solution

Parameter sweep specification

Compute:-Losses

-Inductance-Pulse energy

Pulse energycheck

Delete solution

Normalize solution

Weighting function

Optimal core1 2 3 4 5 61

1.5

2

2.5

3

3.5

4

Epulse>EminEpulse<Emin

Extract geometrical dataand build core CAD model

Derive value of parasiticcomponents with FEM

Circuit simulation withderived parasitic components

trise [ns]

Cstr

ay [p

F]

Lle

akag

e [

]

Solution space

iL(t)

t1

tt2t0

tpulseTpulserate

trise

Ipulse=Ipilot·Mn

Epulse

Imax

ipri(t)+isec(t)

t

Imax

Imin

τRτF

Bcore(t)

Bmax

Load current waveform

Module current & flux density waveform

Figure 5: Transformer design procedure


KEEL Oliver


The total losses consist of conduction losses of the winding and core losses. As the pulse rate is low

(300 Hz), skin effect losses are only considered for the secondary winding which is conducting the high

frequency pulse. The DC resistance is calculated with the current density of 6 Amm2 . The core losses

are calculated with the iGSE method [15] which uses the extracted Steinmetz parameters from the data

sheet. Moreover, to the non-linear behaviour of the core material is modelled with a magnetization

function given by the manufacturer for estimating the correct pulse energy.

The algorithm stores all solutions which reached the minimal required pulse energy. All the solutions

are then normalized by the result with either the lowest losses, inductance or number of turns. The

goal of keeping the inductance and the turn number low is to attain a low input voltage Vin respectively

achieve low parasitic values. Those three normalized values are summed up as an weighting function

and weighted equally. The sum with the lowest value represents the optimal core size.

3.2.1 Calculation of parasitics

The values of parasitics components in the parasitic model in fig. 3 are determined with finite element

method (FEM) simulations. The parasitics depend mainly on the geometrical arrangement of the primary

and secondary winding. Therefore, three different winding topologies are evaluated. The three topologies

are presented in fig. 4b. The first winding arrangement (W1) has two round shaped single conductors

placed next to another. Thus, the single turns are on the same radial position. For the second arrangement

(W2), the primary is positioned at a different radial position than the secondary winding. The last winding

arrangement (W3) is based on a foil winding. The conductor has a rectangular shape and is as wide as

it does not touch the adjacent turn. Moreover, the primary and secondary winding are placed on top of

each other.

The design process is reduced to three main parameters which determine the position of the windings.

The first parameter is the distance to the core in radial direction Sair. The second one is the distance in

between the two windings Swin. In case the two winding are on the same layer this parameter is linked to

to the third and last parameter as a function, which is the number of turns Nturns.

The circuit model of the transformer requires the values of the stray capacitance and leakage inductance

of the windings. Therefore, two simulations of the it at i.e. electric and magnetic field were conducted.

In case of the electric field, one winding is grounded and the other one is set to a specific potential. With

the electric energy in the simulation domain the capacitance value is derived. For the leakage field both

windings are set to equal contrary current values. The leakage inductance follows analogue to the stray

capacitance with the energy in the magnetic field and the current value of the winding.

The calculation of the parasitics are performed for all combinations of core sizes and winding arrange-

ment. The resulting capacitance and inductance values are used in the parasitic transformer model to

calculate the pulse performance.

4 Resulting design parametersIn this section, results of the algorithm for the core design, the winding design and the pulse simulation

are presented. For each section of the design procedure, the design parameters and the constrains are

introduced. The solutions of each section are used as input parameter for the subsequent section. This

leads finally to a feasible implementation of the transformer.

4.1 Results of core selection algorithm

The input parameters for the core optimization are the core material properties in addition to the chosen

core geometry and current waveform. The two core geometries which fit into the protection vessel are

presented in fig. 6b. The focus is put on powder core materials since the offer a high temperature stability,

low losses and relatively soft saturation. The evaluated materials are MPP, High Flux, Kool Mu Max and

XFlux. All of them have a curie temperature higher than 460 ◦C and a relative permeability in the range

of 14 to 550.


KEEL Oliver


iL(t)

t

Imax=300A

Imin=10A

τR=1.8·103s-1

τF=6.1·105s-1

Irms, primary 280 AIrms, secondary 20 ASrms 6·106 A/m2

a)Inner diameter 77.19 mm 55.75 mmOuter diameter 134 mm 103 mmHeight 26.8 mm 17.9 mm

Core nr. 1 Core nr. 2

Pulse rise time trise <600 nsPulse duration tpulse

Pulse frequency fpulse 300 HzMaximal primary current Imax 300 APulse energy Epulse >50 J

b)

Figure 6: (a) Current waveform and winding specification (b) Core dimensions and pulse specifications

The current waveform considered for the optimization is presented in fig. 6a. The minimum pilot current

to avoid extinction of the arc is set to 10 A. Furthermore, the maximum pilot current is set to 300 A.

The current waveform shows a time constant for the rise and fall slope. Those value are derived from

the specification of the pulse frequency and pulse duration, given in table below the core geometry.

Furthermore, the design parameters are limited to the range from 6 to 16 numbers of turns, a minimum

pulse energy of 10 J and 10 to 30 cores in parallel.

The lowest losses are achieved for the High Flux material. For which the solution space contains 272

possible implementations in the case of core number 1. Specifically, the core implemented with a relative

μr of 150 is achieving the lowest losses. Fig. 7 shows the solution space for four different values of μr

in a total losses versus number of cores plot. The core material is distinguished by different symbols

whereas the number of turns is shown by a grey scale. The optimal solution is highlighted with an red

arrow. The table on the right hand side of the plot shows the detailed solution for both core sizes.

4.2 Results of parasitic components simulations with FEM

A parametric CAD model of the transformer geometry is implemented for the FEM simulation which

simplifies the parametric sweep. Furthermore, the geometry is reduced to a symmetrical element of the

toroidal transformer to reduce computation time. The critical material parameters for the evaluation are

the permittivity in which the transformer is operating and the core material. The transformer is placed

inside an oil filled chamber and therefore the relative permittivity is selected to be 2.2.

200 400 600 800 1000 1200 14006

7

8

9

10

11

12

13

14

15

16

Num

ber o

f cor

es

Total losses [W]

Num

ber o

f tur

ns

μr=60μr=125μr=147μr=160

Core nr. 1 Core nr. 2μr 125 125PLosses core 69 W 49 W PLosses winding 128 W 130 WNturns 10 12Lm 0.243 mH 0.260 mHEstored 10.01 J 10.39 JΔB 0.93 T 1.13 TBMax 0.98 T 1.2 TNCore 10 13

10

15

20

25

30

a) b)Selected solution for core nr.1

Figure 7: (a) Solution space for core nr. 1 (b) Resulting core specification for both core dimensions


KEEL Oliver


Cstray [pF] Lleakage

W3

Swin [mm]

LleakageCstray [pF]

Sair= 1mmSair= 3mm

2 3 4 5 6 7 8 9 10150

200

250

300

350

400

450

5

6

7

8

9

10

11

12

13

1 1.5 2 2.5 3 3.5 4 4.5 5300

400

500

600

700

800

900

1000

3

3.5

4

4.5

5

5.5

6

Swin [mm]

W2W1

Core nr. 2

Sair [mm]1 1.5 2 2.5 3 3.5 4

340

350

360

370

380

390

400

410

420

4.3

4.4

4.5

4.6

4.7

4.8

4.9

5LleakageCstray [pF] Core nr. 2 Core nr. 2

Figure 8: Values for the parasitics depending geometrical parameter Swin and Sair. The circles and asterisks repre-

sent the calculated values.

The parametric sweep is conducted for the range from 1 mm to 10 mm for the parameter Swin which is the

distance between the windings. Furthermore, the parameter Sair is swept from 1 mm to 3 mm. In some

cases, the geometry does not offer sufficient space in the protection vessel, and therefore, these solutions

are not considered further. For each solution, the electrostatic and magnetic energy of the whole domain

is calculated.

The results are presented in fig. 8, which shows three graphs with the stray capacitance on the left and

the leakage inductance on the right vertical axis. The top table shows the solution for core nr. 1 for which

only the winding arrangement W1 fits inside the protection vessel. This is due to the fact that core nr. 1

has a bigger diameter and therefore the winding has not enough space to fit in between the outer diameter

of the core and the inner diameter of the protection vessel. Therefore winding arrangements W2 and W3

are not feasible with core nr. 1. Therefore, the only feasible solution with core nr. 1 results in 279 pF

for Cstray and 5.52 μH for Lleakage. All winding arrangements can be implemented with core nr. 2 and the

resulting parasitics are shown in the three graphs.

Winding arrangement W3 results in the highest stray capacitance values and the lowest leakage inductance

which is expected for foil windings. The other two arrangement result in both low values for the stray

capacitance as the facing area between the winding is smaller for the round conductor and the distance

is higher. The lowest stray capacitance is attained with the core nr. 2 and winding arrangement W2.

4.3 Resulting pulse rise time

The values for the parasitics resulting from the FEM simulation are evaluated with PLECS. In a first

step, only the extreme values of Swin or Sair are simulated. By that measure, the computational time can

be reduced. The results shows that the rise time is more sensitive to the capacitance than to the leakage

inductance value. Thus, only the solution with the smallest stray capacitance for both core sizes are

simulated. Fig. I shows on the X-axis the current rise time whereas on the primary and secondary Y-axis,

the stray capacitance respectively leakage inductance is shown.

The plot shows the general trend that with a higher stray capacitance the rise time increases. Therefore,

the best result is obtained with the lowest stray capacitance value resulting for core nr. 2 and winding ar-

rangement 2. With this combination a pulse current rise time of ¡500 ns could be achieved. Furthermore,

it shows that with the winding arrangement 2 faster current rise times can be achieved as with the other

two arrangements.


KEEL Oliver


Core Winding arrangement Cstray Lleakage trise

Nr. 1 W1 279 pF 5.52 μH 559 ns

Nr. 2 W1 346 pF 4.94 μH 575 ns

Nr. 2 W2 185 pF 11.72 μH 494 ns

Nr. 2 W3 314 pF 5.91 μH 575 ns

Table I: Fastest achievable rise time for each core and winding combination

5 ConclusionThis paper proposes a new topology for generating fast current pulses, which is based on a combination

of the XRAM generator and flyback converter. The main advantage of the presented topology is the

increased robustness by lowering the number of active switches to one and the fact that the switch can be

placed at the surface. The proposed topology has a modular design and is therefore scalable. To achieve

the required fast current rise time, a detailed analysis and optimisation of the parasitic components of

the pulse transformer are required. The core material is selected with an algorithm to achieve a minimal

solution regarding losses, inductance, and numbers of turns. The calculation is performed for two dif-

ferent core geometries, which lead to similar optimal results. In a second step, the parasitic components

of three different winding arrangements are determined with a FEM simulation. The resulting parasitic

values are feed into a PLECS model to attain the current rise time. The fastest achievable current rise

time is below 500 ns for core nr. 2 and winding arrangement 2.

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KEEL Oliver


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Pulse current generator with fast rise time based on ......Pulse current generator with fast rise time based on transformers and single active switch for plasma drilling Oliver Keel