Multiple-switch pulsed power generation based on a transmission line transformer

Multiple-switch pulsed power generation

based on a transmission line transformer

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de

Technische Universiteit Eindhoven op gezag van

de Rector Magnificus, prof.dr.ir. C.J. van Duijn,

voor een commissie aangewezen door het College

voor Promoties in het openbaar te verdedigen op

dinsdag 22 januari 2008 om 16.00 uur

door

Zhen Liu

geboren te Xiang Cheng, China

Dit proefschrift is goedgekeurd door de promotoren:

prof.dr.ir. J.H. Blom

en

prof.dr. M.J. van der Wiel

Copromotor:

dr.ing. A.J.M. Pemen

This work is carried out with the financial support from the Dutch IOP-EMVT program

(Innovatiegerichte Onderzoeksprogramma’s – Electromagnetische Vermogens Techniek).

CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN

Liu, Zhen

Multiple-switch pulsed power generation based on a transmission line transformer / by

Zhen Liu. – Eindhoven : Technische Universiteit Eindhoven, 2008.

Proefschrift. – ISBN 978-90-386-1764-0

NUR 959

Trefw.: hoogspanningstechniek / hoogspanningspulsen / elektrische doorslag /

transformatorschakelingen / transmissielijnen.

Subject headings: high-voltage techniques / pulsed power supplies / spark gaps / pulse

transformers / transmission lines.

…To my parents and my wife

i Table of Contents

Summary........................................................................................................................... iii Chapter 1 Introduction..................................................................................................... 1

1.1 Background ........................................................................................................... 1 1.2 State-of-the-art of pulsed power............................................................................ 2

1.2.1 Switching devices....................................................................................... 3 1.2.2 Traditional multiple-switch pulsed power circuit....................................... 5

1.3 Objective of this dissertation................................................................................. 8 References................................................................................................................... 9

Chapter 2 Transmission line transformer based multiple-switch technology ........... 15 2.1 Principle of the multiple-switch technology ....................................................... 16 2.2 Experimental studies ........................................................................................... 20

2.2.1 Characteristics of the synchronization and the output.............................. 21 2.2.2 Other observations.................................................................................... 24

2.3 Variations for square pulse generation................................................................ 30 2.4 Summary ............................................................................................................. 32 References................................................................................................................. 32

Chapter 3 Multiple-switch Blumlein generator............................................................ 35 3.1 Introduction......................................................................................................... 36 3.2 Single-switch (traditional) Blumlein generator ................................................... 36 3.3 Novel multiple-switch Blumlein generator ......................................................... 37 3.4 Experimental studies ........................................................................................... 45

3.4.1 Experiments on a resistive load................................................................ 45 3.4.2 Experiments on a bipolar corona reactor.................................................. 48

3.5 Summary ............................................................................................................. 52 References................................................................................................................. 52

Chapter 4 Four-switch pilot setup ................................................................................. 53 4.1 Introduction......................................................................................................... 54 4.2 The four-switch pilot setup ................................................................................. 54 4.3 Experiments with resistive loads......................................................................... 56

4.3.1 Four independent loads ............................................................................ 56 4.3.2 Parallel output configuration .................................................................... 57 4.3.3 Series output configuration ...................................................................... 59 4.3.4 Analysis.................................................................................................... 60

4.4 Demonstration of the pilot setup on a corona-in-water reactor ........................... 63 4.4.1 Discharging in deionized water ................................................................ 64 4.4.2 Discharging in tap water .......................................................................... 66 4.4.3 The dye degradation ................................................................................. 68

4.5 Conclusions......................................................................................................... 69 References................................................................................................................. 69

Chapter 5 Ten-switch prototype system........................................................................ 71 5.1 Overview of the system....................................................................................... 72 5.2 Resonant charging system................................................................................... 74 5.3 Transformer......................................................................................................... 75

5.3.1 Introduction .............................................................................................. 75 5.3.2 Effects of the coupling coefficient k ........................................................ 76 5.3.3 Design and construction ........................................................................... 78

ii Table of Contents

5.3.4 Testing of the transformer ........................................................................ 82 5.4 Ten-switch system............................................................................................... 86

5.4.1 Charging inductors ................................................................................... 86 5.4.2 Spark gap switches ................................................................................... 86 5.4.3 The TLT ................................................................................................... 87 5.4.4 Integration of components into one compact unit .................................... 92 5.4.5 The load.................................................................................................... 92

5.5 Characteristics of the system............................................................................... 94 5.5.1 Repetitive operation by the LCR.............................................................. 94 5.5.2 Output characteristics............................................................................... 97 5.5.3 The energy conversion efficiency .......................................................... 102

5.6 Summary ........................................................................................................... 104 References............................................................................................................... 105

Chapter 6 Exploration of using semiconductor switches and other … .................... 107 6.1 Synchronization of multiple semiconductor switches ....................................... 108

6.1.1 Thyristors ............................................................................................... 108 6.1.2 MOSFET/IGBT...................................................................................... 113

6.2 Other multiple-switch circuit topologies........................................................... 114 6.2.1 Inductive adder....................................................................................... 114 6.2.2 Magnetically coupled multiple-switch circuits ...................................... 116

References............................................................................................................... 120 Chapter 7 Conclusions.................................................................................................. 121

7.1 Conclusions....................................................................................................... 121 7.1.1 TLT based multiple-switch circuit technology....................................... 121 7.1.2 Multiple-switch Blumlein generator....................................................... 123 7.1.3 Repetitive resonant charging system...................................................... 123

7.2 Outlook ............................................................................................................. 123 References............................................................................................................... 124

Appendix A. Coupled resonant circuit ........................................................................ 127 A.I Complete energy transfer .................................................................................. 128 A.II Effect of the coupling coefficient k on the first peak value of VH ................... 131 A.III Efficient resonant charging ............................................................................ 133

Appendix B. Repetitive resonant charging ................................................................. 135 Appendix C. Calibration of current probe ................................................................. 137 Appendix D. Schematic diagram of high-pressure spark gap switches.................... 141 Acknowledgements........................................................................................................ 143 Curriculum Vitae .......................................................................................................... 145

Summary

Repetitive pulsed power techniques have enormous potential for a wide range of

applications, such as gas and water processing and sterilization, intense short-wavelength

UV sources, high-power acoustics and nanoparticle processing. The main difficulty for

industrial applications of pulsed power technologies arises from simultaneous

requirements on power rating, energy conversion efficiency, lifetime and cost. Significant

improvements are especially possible in the field of repetitive ultra-short high-voltage and

large-current spark gap switches.

This dissertation investigates a novel multiple-switch pulsed power technology. The

basic idea is that the heavy switching duty is shared by multiple switches. The multiple

switches are interconnected via a transmission line transformer (TLT), in such a way that

all switches can be synchronized automatically and no special external synchronization

trigger circuit is required. In comparison with a single-switch circuit, the switching duty

or switching current for each switch is reduced by a factor n (where n is the number of

switches). As a result, the switch lifetime can be expected to improve significantly. It can

produce either exponential or square pulses, with various voltage and current gains and

with a high degree of freedom in choosing output impedances. The proposed multiple-

switch topology can also be applied in a Blumlein configuration.

To gain insight into the principle and characteristics of this technology, an equivalent

circuit model was developed and an experimental setup with two spark gap switches and a

two-stage TLT was constructed. It was found that the closing of the first switch will

overcharge the other switch, which subsequently forces it to close. During this process,

the discharging of capacitors is prevented due to the high secondary mode impedance of

the TLT. When the closing process is finished and all switches are closed, the energy

storage capacitors discharge simultaneously into the load(s) via the TLT. Now the TLT

behaves as a current balance transformer and the switching currents are determined by the

characteristic impedance of the TLT. In terms of the currents, the equivalent circuit has

good agreement with the experimental results. An interesting feature of this topology is

that the risetime of the output pulse can be determined by the switch that closes lastly.

This was verified by combining a fast multiple-gap switch with a conventionally triggered

spark gap switch; the output current risetime was improved by almost a factor of 2 (from

21 ns to 11 ns).

As for the Blumlein configuration, an equivalent model was also proposed. The model

was verified by experiments on a two-switch Blumlein generator with a resistive load and

a more complex load (i.e. a plasma reactor). It was observed that the synchronization

process of the multiple switches is similar to that of the multiple-switch TLT circuit and is

independent of the type of load. After all the switches have closed, the charged lines at the

switch side are shorted, and then the pulse is generated in the same way as for a traditional

(single-switch) Blumlein generator. Moreover, the experimental results fit the model.

For the generation of large pulsed power (500 MW-1 GW) with a short pulse (~50 ns)

using this technology, the input impedance of the TLT must be low. There are two

approaches to realize low input impedance, namely (i) using a TLT with multiple coaxial

cables per stage and a few switches, and (ii) using a TLT with one single coaxial cable per

stage. Both of them are investigated. A pilot setup with four spark gap switches and a

four-stage TLT (four parallel coaxial cables per stage) was developed to study the first

approach. It was evaluated with different output configurations (with independent loads, a

parallel output configuration or a series output configuration). The application of this

setup to generate a pulsed corona discharge in water was demonstrated. It was observed

that the multiple switches can be synchronized for each of the output configurations.

However, the peak output power is significantly limited by the low damping coefficient ξ

of the input loop of the TLT. To generate large pulsed power effectively, the damping

coefficient must be improved significantly.

A ten-switch prototype system was developed according to the second approach.

Compared to the four-switch pilot setup, several improvements were made: (i) the setup

was much more compact to minimize stray inductance, (ii) one coaxial cable per stage

was used instead of four parallel cables, and (iii) the number of switches was increased to

ten. With these improvements, a high damping coefficient ξ of the input loop of the TLT

and a low input impedance of the TLT were obtained. As expected, efficient large pulsed

power generation with a fast rise-time and a short pulse was realized on the ten-switch

prototype system. Ten switches can be synchronized to within about 10ns. The system

produces a pulse with a rise-time of about 10 ns and a width of about 55 ns. And it has

good reproducibility. An output power of more than 800 MW was obtained. The energy

conversion efficiency varies between 93% and 98%.

In addition, to charge the prototype system, a high-ratio pulse transformer with a

magnetic core was developed. An equivalent circuit model was proposed to evaluate the

swing of the flux density in the core. It was observed that the minimal required volume of

magnetic material to keep the core unsaturated depends on the coupling coefficient. The

transformer was developed on the basis of this observation. The core is made from 68

glued ferrite blocks. There are 17 air gaps along the flux path due to the inevitable joints

between the ferrite blocks, and the total gap distance is about 0.67 mm. The primary and

secondary windings are 16 turns and 1280 turns respectively, and the ratio actually

obtained is about 1:75.4. A coupling coefficient of 99.6% was obtained. Experimental

results are in good agreement with the model, and the glued ferrite core works well. Using

this transformer, the high-voltage capacitors can be charged to more than 70 kV from a

capacitor with an initial charging voltage of about 965 V. With 26.9 J energy transfer, the

increased flux density inside the core was about 0.23 T, which is below the usable flux

density swing (0.35 T-0.5 T). The energy transfer efficiency from the primary to the

secondary was around 92%.

Finally, the use of semiconductor switches in the multiple-switch circuits was explored.

The application of thyristors has been successfully verified on a small-scale testing setup.

A circuit topology for using MOSFET/IGBT was proposed. Also other multiple-switch

circuit topologies (i.e. multiple-switch inductive adder and magnetic-coupled multiple-

switch technique) are discussed as well.

Chapter 1 Introduction

1.1 Background

Pulsed power is a technology that accumulates energy over a relatively long period

and releases it into a load within a short time interval, thus generating high instantaneous

power. It was first developed during the Second World War for use in radar. From that

time on, the defense-related applications were one of the key driving forces behind pulsed

power technology [Lev(1992)], primarily in connection with nuclear weapons simulation,

applications of high-power microwave sources, high-power laser sources, electromagnetic

guns, etc. The pulsed power systems for these applications are typically large machines

and are operated in a single-shot mode or at a low repetition rate. The performance of the

pulsed power system is the most important issue, while the cost and lifetime are of

secondary concern [Kri(1993)].

Over the last two decades, more and more non-military applications of pulsed power

technology have been studied. More than one hundred possible applications can now be

listed [Lev(1992), Kri(1993), and Yan(2001)]. In particular, repetitive pulsed power

techniques have enormous potential in areas such as gas and water processing [Vel(2000)],

sterilization [Kim(2004)], intense short-wavelength UV sources [Kie(2006)], high-power

acoustics [Hee(2004)], nanoparticle processing [Ost(2005)], surface treatment, etc.

However, the repetitive pulsed power supply is still a barrier for large-scale industrial

applications. The technical difficulty arises from simultaneous requirements on power

rating, energy conversion efficiency, lifetime, and cost [Hee(2004)]. The investigations in

this work will contribute to realize a breakthrough in large pulsed power generation for

industrial applications.

In more specific terms, the typical ranges of parameters involved in pulsed power

technology are summarized in Table 1.1 [Pai(1995)]. It is clear that the encountered

properties have an enormous span, ranging for example from megawatt peak powers to

terawatt levels. Generally, the very high peak power levels are obtained for longer pulse

durations and at single shot or very low repetition rates. This can be seen in Figure 1.1,

where the solid line represents peak power levels versus pulse duration for state-of-the-art

pulsed power systems (situation around 2000). For pulses in the nanosecond range, typical

peak powers are much lower – far below 100 MW.

2 Chapter1

Table 1.1 Ranges of parameters involved in pulsed power technology

This nanosecond range is the regime where we want to focus our research. In summary,

our targets are: much higher peak power at much shorter pulse durations and at much

higher repetition rates, as compared to current capabilities. To be more specific, our

challenge is to reach about 1 GW of peak power within a pulse width of less than 100 ns

and at a repetition rate of >100 pps. The typical ranges focused on in our research are also

shown in Table 1.1. Figure 1.1 presents our achievement in relation to our previous

milestones (1994, 2001) [Yan(2001)].

Fig. 1.1 Visualization of the achievement as described in this thesis (TU/e 2007) as

compared to previous milestones obtained at TU/e and the state-of-the-art pulsed power

technology (as of 2000)

1.2 State-of-the-art of pulsed power

Capacitive (energy stored in a capacitor) and inductive (energy stored in an inductor)

systems are often used for the repetitive pulsed power systems with medium energy per

pulse. Though the energy density of an inductive system can be 25 times higher compared

Introduction 3

with a capacitive system, capacitive systems are more frequently adopted since they are

much easier to realize and require simpler closing switches instead of highly complex

opening switches [Pem(2003)]. The pulsed power systems discussed in this thesis utilize

capacitive energy storage.

1.2.1 Switching devices

The most critical component in repetitive pulsed power systems is the switch. It plays

an important role in the performance of a system, affecting factors such as rise-time,

efficiency, repetition rate, lifetime, etc. Systems with capacitive energy storage require

closing switches such as: (i) magnetic switches, (ii) semiconductor switches, (iii) spark

gap switches.

(1) Magnetic switches are saturable inductors that utilize the nonlinear magnetization of

magnetic material, especially the saturation. When the magnetic material used in the

switch is unsaturated, the magnetic switch has a high impedance which represents the “off

state.” When the core becomes saturated, it has a much lower (typically a factor µr lower)

impedance which is the “on state.” Magnetic switches are robust and can be used for high

repetition rates (several kHz) [Jia(2002a)]. A long lifetime can also be realized (>1010

shots) [Har(1990)]. They are usually used in combination with slower semiconductor

switches [Ber(1992), Oh(2002), Jia(2002a), Rim(2005)] or thyratrons [Oh(1997)], where

the magnetic switch is used to compress the pulse to much shorter pulse widths. Typically,

the energy conversion efficiency of magnetic switches is low (i.e. around 60-80%).

(2) Semiconductor switches used in pulsed power systems include thyristors, MOSFETs

(Metal-Oxide-Semiconductor Field-Effect Transistor), and IGBTs (Insulated Gate Bipolar

Transistor). Thyristors can hold a high voltage in excess of several kV and carry a large

current (kA). However, the switching time is slow (on the order of µs), and thyristors are

often used for microsecond pulse generation [Ren(1997), Yan(2004), Gli(2004)].

Compared with thyristors, MOSFETs and IGBTs are much faster devices, and their

switching times are typically about 20 ns and 200 ns [Hic(2001)] respectively. Generally

IGBTs are more efficient and have a larger power capacity (up to multiple kV and kA)

[And(2006)]. Many pulsed power circuits based on IGBTs are available [Gau(1998),

Gau(2001), Cas(2002), Bae(2005)]. MOSFETs are limited to around 1 kV and 100 A

[And(2006)]. So, MOSFETS are generally only used when high switching speed (~10ns)

or high repetition rate (hundreds of kHz or even MHz) [Wat(2001), Jia(2002b), Kot(2004)]

is needed. The main advantages of semiconductor switches are their long lifetime and

high repetition rate. However, the main problems are: (i) their limited power capacity and

(ii) the high cost of devices for large-scale industrial applications.

(3) Spark gap switches are widely used in pulsed power systems. In comparison with

other switches, the main advantages of spark gap switches are a high hold-off voltage,

large conducting current, high energy efficiency, low cost, as shown in Table 1.2.

4 Chapter1

Table 1.2 Comparison of different switches

The switching speed and the spark resistance of spark gap switches depend on many

factors such as voltage, current, gap distance, gas species, pressure, etc. [Kus(1985),

Sor(1977), Car(1979), Ist(2005), Vla(1972)]. When they are used in air, a typical risetime

of 20-30 ns can be realized [Liu(2005), Liu(2006a)]. Very fast switching, with switching

times on the order of several ns or less than 1 ns, can be obtained when pressured gas

[Bow(1994), Bro(1994), Byk(2005)], water [Xia(2002)], or a gas with a light molecular

weight (e.g. H2) [Kus(1985)] is used as switching medium or when multiple gaps are

adopted [Mes(2005), Liu(2006b)]. When spark gap switches are used in a

photoconductive mode, where the gap is fully ionized by a high-power femtosecond laser

instantaneously [Hen(2006), Kei(1996), Dav(2000)], an extremely fast speed (on the order

of ps) and very low jitter (<20 ps) can be obtained. When spark gap switches become fully

conductive, their spark resistance is very low (on the order of 0.1-0.2 Ohm [Kus(1985),

Hus(1998)]). With fast switching and a low spark resistance, the spark gap switch can

have a very high energy efficiency (>95%).

The repetition rate of spark gap switches depends on the recovery time of the switching

medium. For unblown spark gap switches, the repetition rate is typically less than 100 pps

(pulses per second) for most gases such as air, nitrogen, argon, oxygen, and SF6

[Mor(1991)]. When the spark gaps are flushed with a forced gas flow [Fal(1979), Yan

(2003), Win(2005)], or a water flow [Xia(2003), Xia(2004)], or are filled with pressurized

hydrogen [Mor(1991), Gro(1992)], much higher repetition rates (1-3 kHz) can be obtained.

By using pressured hydrogen (70 bar) and triggering the spark gap switch below its self-

breakdown voltage (50%), 100 µs recovery time (corresponding to 10 kHz) was

demonstrated on a two-pulse system [Mor(1991)].

As shown in Table 1.2, the main drawback of spark gap switches is their short lifetime.

This is affected by several factors such as the material of the electrodes, shape of the

electrodes, voltage and current level and duration, electrode erosion. However, the main

Introduction 5

factor for the limited lifetime is the erosion of electrodes. After a number of shots, the

erosion will reach a level at which the spark gap becomes unstable and difficult to trigger.

Solutions to increase the lifetime of a spark gap switch are to maximize the allowable

erosion volume of electrode material or to minimize the erosion rate. The first can be

realized by using electrodes with a large volume, success with which is described in

[Win(2005)]. The latter can be realized by choosing a good electrode material or by

reducing the switching duty. However, the effect of the electrode material is not so

significant that major improvements can be expected. Based on the following literature

[Dic(1993), Don(1989), Leh(1989)], the erosion rate was observed to be a nonlinear

function of the transferred charge per shot (i.e. switching current). When the transferred

charge per shot is reduced by a factor n, the erosion rate can be reduced by a factor in

excess of n2. Thus, sharing the heavy switching duty by multiple switches is an effective

way to significantly increase the lifetime of spark gap switches.

From the above discussions, one can see that the spark gap switch is superior to other

switches for efficient large pulsed power generation with a short pulse width and a fast

speed.

1.2.2 Traditional multiple-switch pulsed power circuit

For the generation of very high pulsed power ratings, multiple-switch based circuit

topologies are normally used to produce high-voltage or large-current pulse and/or their

combination. When multiple switches are used in series, large pulsed-power generation is

realized by producing a higher voltage pulse. On the other hand, when the multiple

switches are used in parallel, large pulsed power generation is realized by producing a

large current pulse. Typical conventional multiple-switch circuit topologies are listed

below.

(1) Hard stack

Load

Load

Fig. 1.2 Hard stack of multiple switches

A simple way to utilize multiple switches is to directly stack them in series or in

parallel, as shown in Figure 1.2. Within this dissertation, we call these configurations a

“hard stack.” Obviously, critical issues in a hard stack configuration are how to

synchronize the individual devices within a short time interval and how to get the voltage

6 Chapter1

or current balance among individual devices. Failure of the switches can be easily caused

by an overvoltage or overcurrent in individual devices due to poor switch timing,

especially when semiconductor switches are used. Normally, careful selection of

switching devices with similar specifications is required. Also, the use of highly-

simultaneous, sufficient drive signals or timing-adjustable trigger signals is required.

(2) Marx generator

Fig. 1.3 Schematic diagram of a Marx generator with three switches

A widely used multiple-switch topology is the Marx generator (Figure 1.3), as

proposed by Marx in 1924, for high-voltage pulse generation [Mar(1952)]. Capacitors are

initially charged in parallel and are then discharged in series via multiple spark gap

switches, thus achieving voltage multiplication. The main advantage of this generator is

that the multiple spark gap switches will be synchronized automatically. The closing of

the first switch leads to an overvoltage across the other switches that are not yet closed.

Subsequently, this overvoltage forces them to close. During the closing process of the

spark gap switches, the discharging of capacitors is prevented by the large impedance of

the charging resistors. The Marx generator is used extensively in pulsed power

applications, and many different Marx based systems have been developed, such as large

X-ray machines (e.g. the PBFA-Z at Sandia National Labs [Spi(1997)] and the MAGPIE

at Imperial College, London [Mit(1998)]), PFN (pulse-forming network) generators

[Wan(1999), Tur(1998), Mac(1996)], high repetition rate solid-state setups [Red(2005)].

(3) LC generator

Another multiple-switch topology is the classical LC generator (Figure 1.4 (a)), as

proposed by Fitch and Howell in 1964 [Fit(1964)]. Initially, the capacitors are charged to

a voltage V0, where the various capacitors have different polarities as shown in Fig. 1.4.

After charging, the switches are closed simultaneously, and after half an LC oscillation

cycle, the voltages on the capacitors with even numbers are fully reversed. The voltage on

an open output will now be NV0, where N is the number of capacitors. The advantage of

the LC generator over the Marx generator is that the number of switches is reduced by a

factor of 2 [Har(1975), Mes(2005)]. However, compared with the Marx generator, it is

difficult to synchronize all switches within a short time interval because the closing of

Introduction 7

switches does not lead to an overvoltage across the switches that are not yet closed. In

addition, oscillations take place in the various LC loops. Adding additional diodes and a

main switch S into the circuit, as shown in Fig. 1.4 (b), can reduce the oscillations and

improve the problematic synchronization of multiple switches, since the main switch S

will only be closed until the voltages on all capacitors with even numbers have been fully

reversed.

Fig. 1.4 (a) Classical LC generator, (b) diode and main switch used to prevent oscillations

(4) Inductive adder

As a fourth example of a commonly used multiple-switch topology, we discuss the

inductive adder configuration. In a classical inductive adder configuration, as shown in

Figure 1.5 (a), the secondary windings of the pulse transformers (1:1) are all connected in

series and the capacitors are discharged simultaneously into the primary sides of the pulse

transformers [Coo(2002), Coo(2005)]. The total output voltage on the secondary windings

is the sum of all the voltages on the primary windings. Using transformers with single-

turn primary and secondary windings, Coo(2005) successfully developed solid-state

modulators with a fast rise-time (10 ns) and high repetition rate (on the order of MHz). In

addition, by putting diodes in parallel with the primary windings of the transformers, as

shown in Fig. 1.5 (b), this technology can be used to develop voltage-adjustable pulsers

by turning on different numbers of switches.

8 Chapter1

Fig. 1.5 (a) Classical inductive adder, (b) voltage-adjustable topology

1.3 Objective of this dissertation

In 2001, Yan proposed a novel multiple-switch pulsed power topology [Yan(2001)],

which was first verified on a small-scale model with three spark gap switches [Yan(2003)].

The proposed topology is different from the multiple-switch circuit topologies described

above. The multiple switches are interconnected via a transmission line transformer (TLT)

in such a way that all spark gap switches close almost simultaneously. No special

synchronization trigger circuit is required. At the output side of the TLT, various

connections in series and/or in parallel can be used; it can even synchronize multiple

independent loads. It can produce either exponential or square wave pulses, with various

voltage and current gains and with a high degree of freedom in choosing output

impedances. The proposed multiple-switch topology can also be applied in a Blumlein

configuration. In comparison to a single-switch circuit, the switching duty or switching

current for each switch is reduced by a factor n (where n is the number of switches). As a

result, the switch lifetime can be expected to improve by a factor in excess of n2.

The proposed topologies are very promising for the development of high pulsed power

systems for large-scale industrial applications. For this reason, we began investigating this

technology systematically. The main objectives of this dissertation are to get a better

understanding of this technology and to realize efficient large pulsed power generation

through use of this technology. The main work will be presented in the following chapters.

In Chapter 2, a novel transmission line based multiple-switch technology is described.

To gain insight into the mechanism and the characteristics of this technology, an

equivalent circuit was introduced and experimental studies were carried out on a two-

switch experimental setup with a resistive load.

Introduction 9

In Chapter 3, another novel pulsed power circuit, namely a multiple-switch Blumlein

generator, is presented. As in chapter 2, in this chapter an equivalent circuit model was

introduced, and an experimental setup was developed and tested to gain a deep

understanding of the circuit’s mechanism and characteristics.

There are two possible approaches to generating large pulsed power levels with a short

pulse width by means of the presented multiple switch technology. These are investigated

in Chapter 4 and Chapter 5 respectively.

In Chapter 4, a four-switch pilot setup was developed for investigation of the first

approach, and was evaluated under different output configurations. The factors affecting

the output power are systematically analyzed. In addition, the application of this

technology to generate a pulsed corona discharge in water is demonstrated.

Chapter 5 describes the development of a ten-switch prototype system for investigation

of the second approach. Efficient high pulsed power generation was achieved. In addition,

to charge this system, a 50 kW high-voltage pulse transformer was developed using a

ferrite core made from many small ferrite blocks.

Chapter 6 explores the use of semiconductor switches for the proposed multiple-

switch circuits. Other multiple-switch circuit topologies, such as a multiple-switch

inductive adder and magnetic-coupled multiple-switch technique, are discussed as well.

Finally, Chapter 7 contains the conclusions of the research and the outlook for the

multiple-switch technology investigated within this dissertation.

This dissertation also contains four appendices. Appendix A presents a detailed

analysis of coupled resonant circuits; in particular, the role of the coupling coefficient k of

a transformer in a resonant circuit is discussed. Appendix B presents the analysis of a

repetitive resonant charging circuit for the case in which the low-voltage capacitor is

larger than the matching value. Appendix C describes the calibration of a single-turn

Rogowski coil, which was used in Chapter 5 of this thesis for the measurement of very

large, fast currents. Appendix D presents the mechanical sketch of the construction of

high-pressure spark gap switches used in the ten-switch system.

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10 Chapter1

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Chapter 2 Transmission line transformer based

multiple-switch technology####

This chapter discusses a novel multiple-switch technology. It is based on the

TLT (Transmission Line Transformer) and multiple switches. As a result of

the interconnection between the switches and the TLT, multiple switches

can be synchronized. Through this technology, not only the high-voltage

pulse but also the large-current pulse can be generated. To understand the

fundamental mechanism of the multiple-switch synchronization, an

equivalent circuit was introduced. The experimental studies were then

carried out to gain insight into the characteristics of this technology. It was

found that the multiple switches can be closed within a short time interval

(nanoseconds) and during this closing process the energy storage

capacitors cannot discharge. When the closing process is finished and all

switches are closed, the energy storage capacitors discharge

simultaneously into the load(s) via the TLT. The TLT behaves as a current

balance transformer, and the switching currents are determined by the

characteristic impedance of the TLT. In terms of the currents, the equivalent

circuit has good agreement with the experimental results. An interesting

feature of this topology is that the risetime of the current into the load(s) is

determined by the last switch that closes.

# Parts of this chapter have been published previously:

Z. Liu, K. Yan, A. J. M. Pemen, G. J. J. Winands, and E. J. M. Van Heesch. 2005.

Synchronization of multiple spark-gap switches by a transmission line transformer.

Review of Scientific Instruments, Vol. 76, Issue 11.

Z. Liu, K. Yan, G. J. J. Winands, A. J. M. Pemen, E. J. M. Van Heesch, and D. B.

Pawelek. 2006. Multiple-gap spark-gap. Review of Scientific Instruments, Vol. 77, Issue

07.

16 Chapter 2

2.1 Principle of the multiple-switch technology

The Transmission Line Transformer (TLT) based multiple-switch pulsed power

technology was proposed in 2001 [Yan(2001)]. By interconnecting multiple switches via a

TLT, multiple switches can be synchronized and no external synchronization trigger

circuit is needed. This topology was first verified on a small-scale model with three spark-

gap switches [Yan(2003)].

C2

C1S1

S2

+-

+-

Stage 1

Stage 2

TLT

Magnetic cores

Stage 1

C2

C1S1

S2

+-

+-Stage 2

TLT

Magnetic cores

Stage 1

C2

C1S1

S2

+-

+-

Stage 2

TLT

Magnetic

(a) with a series output connection

(c) with independent loads

(b) with a parallel output connection

Fig. 2.1 The schematic diagrams of three circuit topologies with two switches and a two-

stage TLT

Figure 2.1 presents the schematic diagrams of three circuit topologies with two spark-

gap switches S1 and S2 and a two-stage TLT. Magnetic cores are placed around the

transmission lines to increase the secondary mode impedance Zs, which is defined as the

wave impedance between two adjacent stages of the TLT seen from the input side. At the

Transmission line transformer based multiple-switch technology 17

input side of the TLT, two identical capacitors C1 and C2 are interconnected to the TLT

via two switches, and they are charged in parallel up to V0. At the output side, the TLT

can be put in series for high-voltage generation, as shown in Figure 2.1 (a), or in parallel

to produce a large current pulse, as shown in Figure 2.1 (b), or can be used to drive

independent loads, as shown in Figure 2.1 (c).

If we assume that the TLT is ideally matched at the output side and the transit time for

a pulse propagating along the outsides of the TLT is much longer than the time interval

for the synchronization of the multiple switches, an equivalent circuit for the input side of

the TLT can be derived as shown in Figure 2.2. Here each transmission line is represented

by its characteristic impedance Z0. Following the connections in Figure 2.2, it can be seen

that both stages (i.e. C1-S1-Z0 and C2-S2-Z0) are connected in series. The secondary mode

impedance is represented by Zs.

Fig. 2.2 The equivalent circuit at the input side of the TLT (I1 and I2 are the switching

currents in S1 and S2 respectively)

Because the impedance Zs is designed to be much larger than the characteristic

impedance Z0 of the TLT, a voltage V12 is generated over the impedance Zs whenever one

switch (e.g. S1) is closed and the other one is still open. Now capacitor C1 or C2 will

discharge very slowly due to the large Zs, and thus energy transfer to the loads is blocked.

The maximum value of V12 is equal to [Zs/ (Z0+Zs)] ×V0 = V12 ≈ V0, where V0 is the

charging voltage on the capacitors. Moreover, because the stray capacitance of the spark

gap switch S1 or S2 is much smaller than the capacitances of C1 or C2, the voltage across

the unclosed switch can rise from V0 up to V0+V12 ≈ 2V0. This generated overvoltage will

cause the second switch to close.

When all the switches are closed, one can derive the following equations from the

equivalent circuit shown in Figure 2.2:

−=⋅−+⋅

−=⋅−+⋅

∫

∫t

ss

t

ss

dIC

VZtIZZtI

dIC

VZtIZZtI

0

2

0

0102

0

1

0

0201

)(1

)()()(

)(1

)()()(

ττ

ττ

(2.1)

18 Chapter 2

In above equations, I1(t) and I2(t) are the currents flowing in switches S1 and S2

respectively, and C0 is the value of capacitors C1 and C2 (C1 and C2 are identical). Solving

these two equations, one can obtain the following expressions for I1(t) and I2(t):

)CZ

texp(

Z

V(t)I(t)I

000

0

21⋅

−⋅== (2.2)

It can be seen that after both switches are closed, the switching currents I1(t) and I2(t) are

identical and determined by the characteristic impedance Z0 of the TLT. And the voltage

V12 across Zs will drop to zero. Now all stages of the TLT are used in parallel equivalently.

After a short time delay (transit time of the TLT) after all the switches have been closed,

an exponential pulse will be generated over the loads at the output side. For all the circuits

in Figure 2.1, the input impedance Zin of the TLT is the same (i.e. Z0/2). The pulse

duration and the peak output power are also the same; the pulse duration is determined by

the constant Z0C0, and the peak output power is determined by charging voltage V0 and

input impedance Zin and equals V02/Zin. However, the output voltage and current are

different for the different output configurations. For the series output configuration in

Figure 2.1 (a), the peak output voltages and currents are 2V0 and V0/Z0 respectively. For

the parallel output configuration in Figure 2.1 (b), the peak output voltages and currents

are V0 and 2V0/Z0 respectively. As for the configuration in Figure 2.1 (c), the peak output

voltages and currents on each load are V0 and V0/Z0 respectively.

It is noted that for a practical circuit, although the described equivalent circuit cannot

be used to accurately derive the switching behaviors due to the limited secondary mode

impedance Zs and the finite length of the TLT, the model presents the basic principle of

the technology. No general model has been available for all kinds of situations (longer

pulses, or with mismatching loads) until now. The present model is valid for nanosecond

pulse generation, assuming the TLT is matched. For long pulse (µs-range) generation, the

transmission line acts as coupled inductors, and details for this situation are presented in

Section 6.1.1.

In principle, the circuit topologies described above can be extended for any number of

switches. As an example, Figure 2.3 shows the schematic diagrams of three-switch circuit

topologies. At the input side, three identical capacitors are interconnected to the TLT via

three switches. And at the output side, the transmission lines can be put in series, in

parallel or connected to independent loads. These three circuits, similar to the circuits in

Figure 2.1, generate the same output power but at different output voltages and currents.

Yan(2002) presented a comprehensive discussion of the different output configurations

when the number of switches is scaled up to 50.

Moreover, the equivalent circuit in Figure 2.2 can easily be extended for any n-stage

TLT. As an example, Figure 2.4 gives the equivalent circuit at the input side of the three-

switch TLT topologies as in Figure 2.3. Zs1, Zs2 and Zs3 are the impedances between

stages 1 and 3, stages 1 and 2, and stages 2 and 3 respectively. Similar to two-switch

circuits, one can analyze the three-switch circuit and derive the same results after all the

switches are closed, namely:


)CZ

texp(

Z

V(t)I(t)I(t)I

000

0

321⋅

−⋅=== (2.3)

Fig. 2.3 Circuit topologies with three switches and a three-stage TLT

20 Chapter 2

Fig. 2.4 Equivalent circuit for the input side of the three-switch circuit topologies

in Figure 2.3

However, according to the equivalent circuit in Figure 2.4, when increasing the number

of the switches, the overvoltage to close the switches that are not yet closed after the

closing of the first switch becomes less. For instance, if Zs2=Zs3 in Figure 2.4, then after

the switch S1 is closed, the maximum overvoltage added to switches S2 and S3 is about

0.5V0, which is a factor of 2 lower as compared with that in the two-switch circuits. This

may cause the closing of the second switch to fail when a large number of switches are

used. To synchronize all the switches properly, special designs may be needed to ensure

the closing of the second switch shortly after the closing of the first switch. Detailed

discussions of this issue will be presented in Section 5.4.3.

2.2 Experimental studies

The experimental setup, shown in Figure 2.5, was used to study the mechanism of the

multiple-switch technology and its characteristics. It consists of three air-core inductors

(L1, L2, L3), two high-voltage capacitors (CH1 and CH2), two spark gap switches (S1 and

S2), a two-stage TLT and a resistive load. The three inductors are used to charge the

capacitors, and they behave as a high blocking impedance during the closing process of

the switches. As for the two switches, S1 is a triggered spark gap switch and S2 is a self–

breakdown spark gap switch; the distance of their main gaps is about 12 mm. After the

high-voltage capacitors are charged, switch S1 is triggered and closes first. Now an

overvoltage will be generated over switch S2, which forces it to close almost

instantaneously. The TLT is made from 1.5 meters of coaxial cable (RG217) and the

distance between the outer conductors of the two cables is about 10 cm. The transmission

lines are connected in parallel to a 25 Ω resistive load. Magnetic cores are placed around

the cables to increase the impedance Zs. The length covered by the magnetic cores on each


cable is 1 m. The value of Zs is estimated to be about 3 kΩ, and the two-way transit time

between the outsides of the TLT is estimated to be more than 60 ns. The detailed

discussion on the effect of the magnetic material is presented in Chapter 5. The two-

switch experimental setup was able to run reliably in air up to 50 pps (pulses per second).

Fig. 2.5 Schematic diagram of the experimental setup

2.2.1 Characteristics of the synchronization and the output

Fig. 2.6 Typical waveforms of the voltages on the positive ends of the high-voltage

capacitors CH1 and CH2, where CH1=CH2=1.3 nF

22 Chapter 2

Figure 2.6 presents the typical waveforms of the voltage on the positive ends of

capacitors CH1 and CH2. They clearly show the voltage transient before, during and after

the synchronization of switches S1 and S2. Initially, the high-voltage capacitors CH1 and

CH2 were charged to a voltage of 28 kV. Spark gap S1 was triggered first. As predicted by

the model shown in Figure 2.2, the voltage on the positive end of CH2 starts to increase

after the closing of the first switch S1. And its value was 51.5 kV when the switch S2

broke down 31 ns after the first switch S1 closed. This value is equal to 92% of the

maximum theoretical value of 56 kV as predicted by the model in Figure 2.2. This

difference is simply caused by the fact that the switch S2 already broke down before the

voltage could reach the theoretical value.

Fig. 2.7 Typical waveforms of the switching currents in the switches S1 and S2,

respectively, when CH1=CH2=1.3 nF and the switching voltage was 28 kV

Figure 2.7 shows the typical waveforms of the currents flowing in switches S1 and S2

respectively. Here the switching voltage, namely the voltage on the high-voltage

capacitors when switch S1 closed, was 28 kV. From Figure 2.7, one can clearly see that

the two switches work in two distinctive phases. After switch S1 was triggered first, at

about -38.8 ns, the first phase starts. Then switch S2 closes about 30 ns after the closing of

the first switch. In the first phase, a small prepulse exists in the switching current through

S1 due to the introduction of the charging inductors and the finite value of the secondary

mode impedance Zs of the TLT. When all the switches are closed, the first phase ends.

Then the second phase starts, in which the TLT behaves as a current balance transformer,

and the switching currents are determined by the characteristic impedance of the TLT.

Now the capacitors will be discharged rapidly and simultaneously into the load via the


TLT. The peak values of the currents in S1 and S2 are 343 A and 329 A respectively,

which are less than the theoretical value of 560 A given by equation (2.1). This is the

result of the stray inductance of the connections between components and the energy

losses (e.g. spark gap switches and the TLT). The effect of the stray inductance will be

presented in Section 4.3.4.

Within the present experimental setup, Z0 and C0 are 50 Ω and 1.3 nF respectively,

thus the time constant Z0C0 is 65ns. For an exponential pulse as described by equation

(2.1), the theoretical decay time (90-10%) is equal to 2.2Z0C0, namely 143 ns. In fact, the

decay time of the measured current shown in Figure 2.7 is 141 ns, which is very close to

the theoretical value given by equation (2.1). Thus, from this point of view, one can

conclude that the experimental result is in good agreement with the model.

From the above experimental results, one can see that though the proposed model

cannot be used to derive the exact behaviors of the presented circuit, it clearly presents the

mechanism of synchronization of multiple switches. Furthermore, from Figures 2.6 and

2.7, it can be concluded that even though the two spark-gap switches close within a

relatively long period (~30 ns), the capacitors, however, can only be discharged rapidly

and simultaneously after all the switches have been closed. It is this property that makes

the circuit unique in comparison with conventional multiple-switch pulsed power circuits.

Fig. 2.8 Typical output voltage and current when the TLT was connected in parallel to a

resistive load and CH1=CH2=1.3 nF

24 Chapter 2

Figure 2.8 shows the typical output voltage and current waveforms when the setup

was operated with a charging voltage of 28.3 kV at a repetition rate of 50 pps in air. The

peak values of output voltage and current are 19 kV and 698 A, respectively. The risetime

of output voltage and current are 22 ns and 25 ns respectively. From the plots shown in

Figure 2.8, one can see that there are also small prepulses in the rising parts of both the

output voltage and the output current due to the closing process of the switches. Similar to

the case of the switching current, the small pulse in Figure 2.8 can be used as an indicator

to estimate the time interval for the closing process.

2.2.2 Other observations

(a) Factor affecting the prepulse

To evaluate the factors affecting the small prepulse in the rising part of the pulses, the

two-stage TLT was replaced with 50 Ω resistors, as shown in Figure 2.9. The other

components, such as the inductors, the switches and the high-voltage capacitors, were

kept the same as in the setup in Figure 2.5. Thus during the synchronization process, the

influence of the secondary mode impedance of the TLT is eliminated and only the

charging inductor is involved. In this situation, the only possible path for the current to

flow is as indicated by the dashed line in Figure 2.9. Figure 2.10 plots the typical

switching currents in switches S1 and S2 respectively when the two-stage TLT was

replaced by resistors. It can be seen that the small prepulse still exists. Therefore, it can be

concluded that the charging inductors can strongly contribute to the small pre-pulse.

Fig. 2.9 Two-switch experimental setup when the TLT is replaced by two 50 Ω resistors.

C1=C2=1.3 nF (the dotted line shows the path for the pre-pulse current)


Fig. 2.10 Typical switching currents when the two-stage TLT is replaced by two 50 Ω

resistors

(b) Effect of the charging voltage on the switching process

From the experiments on the TLT, it was observed that the time interval for the

closing of the switches and the overvoltage on the second switch varied with the charging

voltage. When the charging voltage V0 is lower (e.g. 23 kV) it takes longer (e.g. 60 ns) to

close the two switches in sequence, and the voltage seen by the second switch is nearly

twice the charging voltage. While when the charging voltage is higher, the time interval

for the closing of the switches is less (e.g. 10 ns and even 0), and the overvoltage seen by

the second switch is much less since it already closed before the overvoltage reaches its

peak value. Figure 2.11 gives the typical voltages on the positive ends of the capacitors

and the switching currents when the charging voltage was about 40 kV. From Figure 2.11,

it can be seen that both switches close almost simultaneously and both the overvoltage and

the small pre-pulse in the switching current have disappeared, compared to Figures 2.7

and 2.10. When the small pre-pulse disappears in the switching current, the pre-pulse is no

longer present in the output current into the load, in comparison with Figure 2.8. The

switching currents and the output current are nearly identical, as shown in Figure 2.12.

26 Chapter 2 Voltage [kV]

Current [A

]

Fig. 2.11 Typical voltages on CH1+ and CH2+ and currents in both switches (CH1+ and

CH2+ refer to the positive ends of capacitors CH1 and CH2)

Input current [A

]

Output current [A

]

Fig. 2.12 Typical switching currents and output current when no small pre-pulse occurs


(c) Sensitivity to capacitance values

In order to study the circuit’s sensitivity to the value of the main components, Figure

2.13 plots the typical switching currents when CH1=2.6 nF and CH2 =1.3 nF. As observed

with two identical capacitors, there is no problem at all concerning their synchronization.

But when both the capacitors do not have the same value, an oscillation at the end of the

pulse can be observed due to mismatched capacitors. Also the currents in the two switches

become unbalanced. For efficient pulsed power generation, the capacitors need to be as

close to identical as possible. Also, each stage of the TLT needs to be identical, including

the number of cables per stage and the length of the cables.

Fig. 2.13 Typical switching current waveforms when CH1=2.6 nF and CH2=1.3 nF

(d) Dominance of the last-closed switch

As discussed in Section 2.2.1, the switches typically close in sequence within a short

time interval. During this closing process, the channel of the switch S1 (closed first) is

heated continuously by the flowing current and hence further ionized. Therefore, the

channel of S1 will become fully conductive and have a very low resistance before the last

switch closes. Thus, performance of switch S2 (closed last), such as the collapse rate of the

channel resistance, can strongly affect the performance of the multiple-switch circuit (e.g.

the output rise-time).

28 Chapter 2

To verify the above hypothesis, an experiment was conducted in which two different

spark gap switches were used for S2: a single-gap spark gap switch and a multiple-gap

spark gap switch, as shown in Figure 2.14.

Fig. 2.14 Experimental setup in which two different switches were used for S2: a single-

gap switch and a six-gap switch

Some advantages of the multiple-gap switch over the single-gap switch are [Den(1989),

Kov(1997), Mes(2005)]: (i) substantial current cannot flow through the switch until the

last gap has closed, (ii) before the last gap closes, the gaps closed first will become fully

ionized so the last gap mainly determines its switching speed, and (iii) because the last

gap is significantly overvolted, it closes very rapidly. Figure 2.15 shows an example of the

dependence of the pulse rise-time on the number of gaps. This data was obtained at a

switching voltage of about 44 kV [Liu(2006)]. One can see that when the gap number was

increased from 2 to 6, the rise-time was improved from 13.5 ns to 6 ns.

Within the experimental setup in Figure 2.14, the single-gap spark gap switch has a

gap distance of 12.5 mm; the multiple-gap switch is a 6-gap spark gap switch and each

gap distance was 1.5 mm. The value of each high-voltage capacitor is 1 nF. At the output

side, the TLT was connected in parallel to a 24.4 Ω resistive load. In both cases, switch S1

was triggered at 32.8 kV. Figure 2.16 shows the typical output currents for both cases.

When the single-gap switch was used as S2, the peak current and the current rise-time

were 870 A and 21 ns, respectively. However, when the much faster 6-gap switch was

used for S2, the peak current and current rise-time were 993 A and 11 ns respectively,

which confirmed that the switch closed last can significantly affect the performance of the

multiple-switch circuit.


Fig. 2.15 The dependence of the rise-time on the number of gaps

Output current [A

]

Fig. 2.16 Typical output currents when two different switches were used for S2

30 Chapter 2

2.3 Variations for square pulse generation

Load

Load

Load

2Load

1

Fig. 2.17 Two-switch circuit topologies for square pulse generation using PFLs

All the previously described circuit topologies are used to produce exponential pulses.

In principle, square pulses can be generated by replacing the capacitors with PFLs (Pulse

Forming Line). Figure 2.17 shows the schematic diagrams of two-switch circuit

topologies for square pulse generation. At the left side of the TLT, two identical PFLs

(PFL1-2) are interconnected to the TLT via two switches S1-S2. Magnetic material is put

around both the PFLs and the TLT to increase the secondary mode impedance Zs. At the

output side, similar to the circuits in Figures 2.1 and 2.3, the TLT can be connected in

series or parallel, or to independent loads. Similarly, the multiple switches will be

synchronized automatically by interconnecting the PFLs to the TLT via the multiple

switches. Suppose that the PFLs have an electrical length of τ, and are charged in parallel

to an initial voltage V0. Under ideal conditions, for instance when the TLT is perfectly

matched and after all the switches are closed, a square pulse with a width of 2τ will be

generated over the load. The switching current of each individual switch is equal to


V0/2Z0. For the series output configuration in Figure 2.17 (a), the output voltage and

current are V0 and V0/2Z0 respectively. For the parallel output configuration in Figure

2.3 (b), the output voltage and current are V0/2 and V0/Z0 respectively. As for the

configuration in Figure 2.3 (c), the output voltage and current on each load are V0/2 and

V0/2Z0 respectively. The output power is, of course, the same for each configuration.

Short pulses (nanoseconds) can be easily generated when using coaxial cables as PFLs.

While, for long pulse (microseconds) generation, a PFN (Pulse Forming Network)

consisting of lumped capacitors and inductors can be used. Figure 2.18 shows the

schematic diagrams of two-switch circuit topologies when the PFL is replaced by a PFN.

Assume that each PFN consists of m stages and the values of the capacitors and the

inductors are C and L/2 respectively; then the characteristic impedance of the PFN is

(L/C)1/2

and the electrical length is m(LC)1/2

. For the ideal situation in which both the TLT

and the PFN are matched, a pulse with a width of 2m(LC)1/2

will be produced on the load

after all the switches have been closed. The pulse width can be adjusted by changing the

number of stages.

Load

Load

Load

1Load

2

Fig. 2.18 Schematic diagram of PFN based square pulse generator with two switches

32 Chapter 2

2.4 Summary

The TLT based multiple-switch pulsed power technology was discussed. By

interconnecting the energy storage components (capacitors or PFLs) to the TLT via

multiple switches, the multiple switches can be synchronized automatically and no

external synchronization trigger circuit is needed. This technology can be used to generate

either a high-voltage pulse or a large-current pulse or even to drive independent loads

simultaneously. Moreover, both exponential pulses and square pulses can be generated.

An equivalent circuit model was developed to understand the mechanism of this

technology. An experimental setup with two spark gap switches and a two-stage TLT was

constructed to gain insight into the characteristics of this multiple-switch circuit. It was

found that the closing of the first switch leads to an overvoltage over the switches that are

still open, causing them to be closed in sequence within a short time interval

(nanoseconds). During this closing process the energy storage capacitors cannot discharge.

When the closing process is finished and all switches are closed, the energy storage

capacitors discharge simultaneously in parallel into the load(s) via the TLT. The TLT

behaves as a current balance transformer, and the switching currents are determined by the

characteristic impedance of the TLT. In terms of the currents, the equivalent circuit shows

good agreement with the experimental results. To obtain efficient pulsed power generation,

identical components (capacitors and each stage of the TLT) are necessary. An interesting

feature of this topology is that the switch closed last can significantly affect the output

performance. This was verified by combining a fast multiple-gap switch with a

conventionally triggered spark gap switch. The output current risetime was improved by a

factor of almost 2 (from 21 ns to 11 ns).

References

[Den(1989)] G. J. Denison, J. A. Alexander, J. P. Corley, D. L. Johnson, K. C. Hodge, M.

M. Manzanares, G. Weber, R. A. Hamil, L. P. Schanwald, and J. J. Ramire.

Performance of the Hermes-III Laser-Triggered Gas Switches. Proc. 7th

IEEE

Pulsed Power Conference, June 11-14, 1989, pp. 579-582.

[Kov(1997)] B. M. Kovalchuk. Multiple gap spark switches. Proc. 11th IEEE Pulsed

Power Conference, 1997, pp. 59-67.

[Liu(2006)] Z. Liu, K. Yan, G. J. J. Winands, A. J. M. Pemen, E. J. M. Van Heesch, and

D. B. Pawelek. Mutliple-gap spark gap switch. Review of Scientific Instruments, 77,

073501 (2006).

[Mes(2005)] G. A. Mesyats. Pulsed Power. New York: Kluwer Academic.



[Yan(2002)] K. Yan, E. J. M. van Heesch, P. A. A. F. Wouters, A. J. M. Pemen, and S. A.

Nair. Transmission line transformers for up to 100 kW pulsed power generation.


Proc. 25th

international Power Modulator Symposium and High-Voltage Workshop,

30 June-3 July 2002, pp. 420-423.

[Yan(2003)] K. Yan, H. W. M. Smulders, P. A. A. F. Wouters, S. Kapora, S. A. Nair, E. J.

M. van Heesch, P. C. T. van der Laan, and A. J. M. Pemen. A novel circuit

topology for pulsed power generation. Journal of Electrostatics, Volume 58, Issues

3-4, June 2003, pp. 221-228.

Chapter 3 Multiple-switch Blumlein generator####

The Blumlein generator has been one of the most popular pulsed power

circuits. Traditionally, it was commutated by a single switch. One critical

issue for such a single-switch based circuit topology is related to the large

switching currents. In this chapter, a novel multiple-switch based Blumlein

generator will be presented. The Blumlein generator can be commutated by

multiple switches and the heavy switching duty can be shared identically by

multiple switches. To gain a deep understanding of this technology, an

equivalent circuit model was introduced, and an experimental setup was

developed. It was observed that the mechanism of the multiple-switch

synchronization is similar to that of the TLT based multiple-switch circuit,

namely the multiple switches are closed in sequence and after all the

switches have closed the charged PFLs discharge simultaneously and

identically. The experimental results are in good agreement with the

equivalent circuit model. Moreover, the experimental setup was successfully

used to generate the bipolar corona plasma.

# Parts of this chapter have been published previously:

Z. Liu, K. Yan, G. J. J. Winands, E. J. M. Van Heesch, and A. J. M. Pemen. 2006. Novel

multiple-switch Blumlein generator. Review of Scientific Instruments, Vol. 77, Issue 03.

36 Chapter 3

3.1 Introduction

The Blumlein generator [Blu(1941) and Blu(1945)] is commonly used for generating

square pulses. The main advantage is that the output voltage on a matched load is equal to

the charging voltage [Sim(2002)]. Conventionally, the pulse forming lines are charged in

parallel and synchronously commutated by a single switch, such as a spark gap

[Ros(2001), Dav(1991), Bor(1995), Ver(2004)]. For such a single-switch based generator,

the main problem when increasing the power is the large switching current. Multiple

switches are preferred in heavy-duty pulsed power systems. The critical issue for multiple

switches is how to synchronize them. In this chapter, a novel multiple-switch based

Blumlein generator will be presented. The charged pulse-forming lines can be

synchronously commutated by multiple switches and no external synchronization trigger

circuit is needed.

3.2 Single-switch (traditional) Blumlein generator

Figure 3.1 shows an example of a single-switch based stacked Blumleins. It consists of

four identical coaxial cables (Line1 - Line4), a spark-gap switch S and a load. Line1 and

Line2 are used in parallel, which is identical to a single line with a characteristic

impedance of 0.5Z0, where Z0 is the characteristic impedance of the cables. This is also

true for Lines 3 and 4. Initially, the four lines are charged to a voltage of V0. When switch

S is closed, EM waves will be excited inside lines 1 and 2 and the switching current is

equal to 2V0/Z0. After the transit time τ of lines 1 and 2, the excited EM wave will reach

the load. With a matched load (Z0), a square pulse with a width of τ2 will be generated,

and the output voltage and current are V0 and V0/Z0 respectively.

Fig. 3.1 Single-switch based Blumleins stacked in parallel

Multiple-switch Blumlein generator 37

Such an experimental example is given in Figure 3.2. Here the four pulse-forming

lines are 4.5-meter-long RG217 (50 Ω) cables, and the switch is a triggered spark gap.

The charging voltage is 27 kV, and the resistive load is 49.8 Ω. One can see that the

switching current is twice the output current, as described above. The switching current

would increase significantly when using a larger number of stacked Blumleins (i.e. to

increase the power) or a low characteristic impedance cable.

Fig. 3.2 Typical voltage and current waveforms for single switch Blumlein

3.3 Novel multiple-switch Blumlein generator

Figure 3.3 gives three examples of two-switch based Blumlein generators with parallel

output configurations. The circuit shown in Figure 3.3 (a) consists of four identical

coaxial cables (Line1 - Line4), two switches S1 and S2 and a load. At the left side, Line1

and Line2 are interconnected via switches S1 and S2. Magnetic cores are placed around

Line1 and Line2 to increase the secondary mode impedance. At the right side, Line1 and

Line2, and Line3 and Line4 are connected in parallel to a load. Actually, the circuit in

Figure 3.3 (a) is a two-stage Blumlein stacked in parallel and is identical to the circuit in

Figure 3.3 (b) in which a single line (Line3) with a characteristic impedance of 0.5Z0 is

used to replace Line3 and Line4. In both circuits, the load is connected to the inner

conductors of the lines, and thus the output pulse is bipolar, namely the potentials at

positions A and B are positive and negative respectively. In contrast, in the circuit shown

in Figure 3.3 (c) the load is connected to the outer conductors of the lines; the output is

unipolar, and it can be positive (when position A is grounded) or negative (when position

B is grounded).

38 Chapter 3

Fig. 3.3 Three two-switch Blumlein circuits with parallel output configurations


Fig. 3.4 Equivalent circuit models at the switch side of the circuits as shown in Fig. 3.3

during and after the synchronization

Suppose that all the lines of the circuits in Figure 3.3 are charged to an initial voltage

of V0. When switch S1 is closed first, charged Line1 will discharge via the secondary mode

impedance Zs, as shown in Figure 3.4 (a). A voltage VZs will also be generated over Zs.

This voltage VZs is equal to [Zs/(Z0+Zs)]×V0. In addition, a voltage pulse with an

amplitude of -[Z0/(Z0+Zs)]×V0 will travel towards the load along Line1. When the Zs is

designed to be much larger than the characteristic impedance Z0 of the lines, the values of

VZs and -[Z0/(Z0+Zs)]×V0 will be almost V0 and 0 respectively, which means that the

40 Chapter 3

discharging of Line1 can be neglected. Since the voltage on Line1 almost maintains a

constant value of V0, it can be treated as a DC voltage source with an amplitude of V0 or

as a capacitor with a charging voltage of V0. Moreover, Line2 cannot discharge before

switch S2 closes, so it can also be regarded as a DC voltage source. When the transit time

τs between the outer conductors of Line1 and Line2 is long enough, that is 2τs is larger than

the time interval for the synchronization, a simplified equivalent circuit at the switch side

can be derived, as shown in Figure 3.4 (b). It can be seen that the voltage across S2 can

theoretically rise from V0 up to V0+VZs ≈ 2V0 during the synchronization process. The

generated overvoltage will force switch S2 to close subsequent to the closing of S1.

After all the switches have been closed, the equivalent circuit shown in Figure 3.4 (b)

is no longer valid, since Line1 and Line2 start to discharge into each other simultaneously,

as shown in Figure 3.4(c). Now a voltage pulse will travel towards the load in both Line1

and Line2, which is contributed to by the discharging of both Line1 and Line2. Assume that

in Line1 the contributions from the discharging of Line1 and the discharging of Line2 are

represented by V11 and V12 respectively. The expressions of V11 and V12 can be written as:

⋅+

−=

⋅+

−=

0

00

0

12

0

00

0

11

//

//

//

VZZZ

ZZV

VZZZ

ZV

s

s

s (3.1)

At the switch side, the total voltage over Line1 now becomes V0+V11+V12=0, which

implies Line1 is shorted. The same result is obtained for Line2. Moreover, the voltage

across Zs is equal to V12+V21=0, which indicates that no energy flows into the Zs. The

switching currents I1 and I2 through switches S1 and S2 are identical and written as:

0

0

0

12

0

11

21Z

V

Z

V

Z

VII −=+== (3.2)

From the discussions above, it can be seen that after all the switches have closed, Line1

and Line2 are shorted at the switch side. This is similar to the situation in the traditional

Blumlein configuration, and the output pulse will be generated in the same manner as in

the single-switch circuit. Namely, after transit time τ, the excited pulse inside Line1 and

Line2 will reach the load. Ideally (i.e. with matched loads), a square pulse with a width of

2τ is generated for all the circuits in Figure 3.3. For example: the pulse forming process of

the circuits shown in Figures 3.3 (a) and (b) is shown in Table 3.1. For all the circuits in

Figure 3.3, the output voltage is same, namely V0. Their polarities, however, are different.

The potentials at positions A and B, in the circuits shown in Figures 3.3 (a) and (b), are

+V0/2 and –V0/2 respectively. For the circuit in Figure 3.3 (c), the output voltage can be

either V0 or –V0 when position A or B is grounded, respectively. It is noted that although

the above model is not exactly accurate due to the finite secondary mode impedance Zs, it

presents the fundamental principle of the synchronization of the multiple-switch Blumlein

generator.


Table 3.1 Pulse forming process of the circuits in Figures 3.3 (a) and (b)

with matched loads

Fig. 3.5 Two-switch Blumlein generators with series output configuration

42 Chapter 3

Besides the parallel output configuration, at the output side the Blumlein can also be

connected in series to obtain a high-voltage pulse. Figure 3.5 shows two circuit topologies

of two-switch Blumleins stacked in a series configuration, where Line1 and Line2 form

one Blumlein and Line3 and Line4 form the other stage. At the left side, Line1 and Line3

are interconnected via the switches S1 and S2. And at the output side, the two-stage

Blumleins are put in series. The closing process of multiple switches is exactly the same

as that of the circuits with a parallel output configuration. If all the lines are charged to V0

and the Blumleins are ideally matched, then after closing of all the switches, the switching

current per switch is V0/Z0. And after transient time τ the output pulse with 2τ duration

will be generated over the load. The output voltage and current are 2V0 and V0/2Z0

respectively. However, the polarities of the output pulses generated by the circuits in

Figures 3.5 (a) and (b) are different. For the circuit in Figure 3.5 (a), the potentials at

positions A and B are +V0 and –V0 respectively; as for the circuit in Figure 3.5 (b), the

polarity of the output pulse can be either positive or negative when position A or B is

grounded, respectively.

In principle, the circuit topologies described in Figures 3.3 and 3.5 can be extended for

any number of switches. Figures 3.6 and 3.7 show circuit topologies of the three-switch

Blumleins stacked in parallel and in series respectively.

In Figure 3.6, at the left side, lines Line1-Line3 are interconnected via the switches S1-

S3. At the output side, the lines Line1-Line3 are put in parallel. The load is connected to

the inner/outer conductors of the lines. Line4 has a characteristic impedance of Z0/3. After

the closing of all the switches, the output pulse with a duration of 2τ will be produced on a

matched load. The output voltage and current are V0 and 3V0/2Z0. The output polarities of

the circuits in Figures 3.6 (a) and (b) are positive and negative respectively. However, the

switching current per switch is V0/Z0, which is one-third of that of the single-switch

circuit.

For the circuits in Figure 3.7, actually they include 3-stage Blumleins, i.e. Line1 and

Line2, Line3 and Line4, and Line5 and Line6 form one stage Blumlein, respectively. At the

left side, Line1, Line3, and Line5 are interconnected via the switches S1-S3. And at the

output side, the three-stage Blumleins are connected in series. After all the switches are

closed, a pulse with a duration of 2τ will be produced on a matched load. And the output

voltage and current are 3V0 and V0/2Z0, respectively. The output polarities of the circuits

in Figures 3.7 (a) and (b) are positive and negative, respectively. Same to the circuits in

Figure 3.6, the switching current per switch is V0/Z0.

Moreover, the equivalent circuit model shown in Figure 3.4 can be extended for any

n-switch circuit. As an example, Figure 3.8 shows the equivalent circuit at the switch side

of the three-switch Blumlein generators shown in Figures 3.6 and 3.7 during the

synchronization process. The DC voltage sources with an amplitude of V0 represent the

charged lines Line1-Line3, and Zs1, Zs2, and Zs3 represent the secondary mode impedances

formed by Line1 and Line2, Line2 and Line3, and Line3 and Line2 respectively.


Fig. 3.6 Three-switch Blumlein generators with parallel output configurations

44 Chapter 3

Fig. 3.7 Three-switch Blumlein generators with series output configurations


Fig. 3.8 Equivalent circuit at the switch side of the three-switch Blumlein generators

shown in Figures 3.6 and 3.7 during the synchronization process

3.4 Experimental studies

To verify the novel multiple-switch Blumlein circuit topology and the proposed model,

and to gain a deep understanding of the characteristics of the multiple-switch Blumlein

circuit and its characteristics, an experimental setup with two switches was developed. It

was then evaluated for both a resistive load and a corona plasma reactor.

3.4.1 Experiments on a resistive load

The schematic diagram of the experimental setup with a resistive load is as shown in

Figure 3.3 (a). The four identical lines (Line1-Line4) are made from 4.5-meter-long

RG217 coaxial cables with a characteristic impedance Z0=50 Ω. The distance between the

outer conductors of Line1 and Line2 is about 10 cm. The length of the magnetic cores

around Line1 and Line2 is about 1 meter. The value of Zs is estimated to be about 3 kΩ,

and the two-way transit time between the outsides of Line1 and Line2 is estimated to be

more than 60 ns. A detailed discussion of the effect of the magnetic material is presented

in Chapter 5. Switch S1 is a triggered spark gap switch, while switch S2 is a self-

breakdown spark gap type. The 49.8 Ω resistive load is made from HVR disc-type

resistors.

Figure 3.9 gives typical voltage waveforms of V1 and V2, where V1 and V2 are the

voltages over switches S1 and S2 respectively. The four lines are charged to an initial

voltage of 26.8 kV. The triggered spark gap S1 is closed first. As predicted by the model

shown in Figure 3.4, the voltage on the second switch S2 starts to increase after the closing

of the first switch S1. This increment continues until the overvoltage forces switch S2 to

46 Chapter 3

breakdown 29 ns after switch S1 has been closed. The obtained voltage of 44.5 kV over S2

is lower than the maximum theoretical value of 53.6 kV given by the model, since S2

already broke down before V2 could reach the maximum value.

Figure 3.10 shows the current waveforms of Is1, Is2 and Iout, where Is1 and Is2 are the

switching currents through the switches S1 and S2, and Iout is the output current. As

predicted by the model, the two switching current pulses are almost identical and

approximately equal to the output current. The switching current is about a factor of two

lower compared with that of the single-switch Blumlein circuit shown in Figure 3.1. In

addition, the measured values of switching currents are smaller than the theoretical value

of 536 A given by (3.2) due to mismatching and energy losses. Figure 3.11 shows the

typical waveforms of the output voltage Vout and current Iout. The rise-time and width are

around 20 ns and 50 ns respectively, and the peak output voltage and current are 25.5 kV

and 510 A respectively. It can be seen that, although there is some time delay between the

closing of both switches S1 and S2, their outputs are nearly synchronous and identical in

terms of their switching currents. This unique feature is the same as that of the TLT based

multiple-switch circuits discussed in Chapter 2. In addition, in contrast to the TLT based

multiple-switch circuit shown in Figure 2.5, no charging inductors are required, thus no

small pre-pulse (see Figures 2.7 and 2.10) occurred in the rising part of the currents.

Fig. 3.9 Typical voltage waveforms of V1 and V2, where V1 and V2 are the voltages on the

inner conductors of Line1 and Line2 at the switch side in Fig. 3.3 (a)


Fig. 3.10 Typical switching currents and output current in Fig. 3.3 (a)

Voltage [kV]

Current [A

]

Fig. 3.11 Typical output voltage and current in Fig. 3.3 (a)

48 Chapter 3

To evaluate the energy conversion efficiency, the output power Pout, the output energy

Eout and the energy conversion efficiency R

η are calculated according to the following

equations:

∫∫ == dtIVdtPEoutoutoutout

(3.3)

2

05.0 VCEEE

HouttotaloutR==η (3.4)

In (3.4), Etotal and H

C refer to the energy stored in the four lines and the total capacitance

of the four lines (1.8 nF) respectively. The typical output power and energy waveforms

are shown in Figure 3.12. The output peak power and energy are 13 MW and 0.568 J,

respectively. The calculated energy efficiency R

η is 82%. The energy loss is caused by

the spark gaps and the secondary mode impedance, and the loss caused by the secondary

mode impedance is negligibly small within the present design.

Fig. 3.12 Output power and energy when the load is resistive in Fig. 3.3 (a)

3.4.2 Experiments on a bipolar corona reactor

To evaluate the multiple-switch Blumlein topology for a more complex load,

experiments were done on a bipolar corona reactor [Yan(1990)]. The schematic diagram

of the setup with a corona reactor is shown in Figure 3.13. Compared with the circuit

shown in Figure 3.3 (a), the resistive load is replaced by a plasma reactor and an inductor

L is added for charging the lines. The inductor L is designed to have a high impedance

during the pulse-forming process. The corona plasma reactor consists of two steel “saw

blade” arrays. Each array includes nine steel saw blades connected in parallel. The length

of each saw blade is 80 cm, and the distance between two arrays is about 8 mm. Details of


the reactor are shown in Figures 3.14 (a) and (b). Because the potentials on the two arrays

are positive and negative respectively during plasma generation, we call this a bipolar

plasma reactor. Figure 3.14 (c) shows a time integrated (0.5 s) photo of the generated

corona plasma.

Fig. 3.13 Schematic diagram of the two-switch Blumlein experimental setup with a

bipolar corona plasma reactor

Fig. 3.14 Reactor configuration and plasma photo

50 Chapter 3

Fig. 3.15 Typical switching currents in Fig. 3.13

Fig. 3.16 Typical voltage and current on the plasma reactor in Fig 3.13


Fig. 3.17 Typical plasma power and energy in Fig. 3.13

Figure 3.15 shows the typical waveforms of the switching currents Is1 and Is2 in

switches S1 and S2, respectively. As observed with a 49.8 Ω resistive load, the currents are

synchronized and identical. Figure 3.16 shows the typical plasma voltage and current

waveforms. The peak values of voltage and current are 29 kV and 506 A, respectively.

Figure 3.17 shows the typical waveforms of plasma power Pplasma and energy Eplasma. The

peak value of plasma power is 12 MW, and there is nearly no reflection after the first

power pulse, which means that most of the electrical energy is transferred to the plasma.

The energy conversion efficiency of plasma generation is calculated as:

2

05.0 VCdtPEE

Hplasmatotalplasmaplasma ∫==η (3.5)

where plasma

E is the energy absorbed by the corona plasma, as shown in Figure 3.17.

Within the present setup, the energy efficiency plasma

η is in the range of 73.2-76.8%,

which agrees with previous works [Yan(2001)]. For comparison of this efficiency with

that for a matched resistive load, we define the relative efficiency as:

Rplasmarelative

ηηη = (3.6)

The relative efficiency η is in the range of 89.3-93.7%, which indicates that the plasma

reactor is well matched and the energy conversion efficiency is in reasonable agreement

with that for a matched load.

52 Chapter 3

3.5 Summary

In this chapter, a novel multiple-switch based Blumlein generator was introduced and

the circuit topologies with different output configurations were discussed. To gain insight

into the mechanism and the characteristics of the multiple-switch Blumlein circuits, an

equivalent circuit was introduced and an experimental setup with two spark gap switches

was developed.

It was observed that the mechanism of the multiple-switch synchronization is quite

similar to that of the TLT based multiple-switch circuit, namely the closing of the first

switches will overcharge the switches that are not yet closed. This forces them to close

sequentially. During the closing process of the multiple switches, the discharging of the

initially charged lines is blocked by the high secondary mode impedance. After all the

switches have been closed, the charged lines at the switch side become shorted, at which

point the multiple-switch Blumlein behaves similarly to a traditional (single-switch)

Blumlein and the output pulse is generated in a similar manner as in the traditional one.

The experimental results clearly show that multiple switches can be synchronized for

either a resistive load or a plasma reactor. An efficient plasma can be generated by means

of this technology, and the switching duty can be reduced by a factor of n (the number of

switches).

References

[Blu(1941)] A. D. Blumlein. Improvements in or relating to apparatus for generating

electrical impulses. UK Patent 589,127, filed Oct. 10, 1941.

[Blu(1945)] A. D. Blumlein. Apparatus for generating electrical impulses. US Patent

2,496,979, filed Sept. 24, 1945.

[Bor(1995)] D. L. Borovina, R. K. Krause, F. Davanloo, C. B. Collins, F. J. Agee, and

L. E. Kingsley. Pulsed Power Conference. July 3-6, pp. 1394-1399.

[Dav(1991)] F. Davanloo, R. K. Krause, J. D. Bhawalkar, and C. B. Collins. Pulsed Power

Conference. June 16-19, pp. 971-974.

[Ros(2001)] J. O. Rossi, and M. Ueda. Pulsed Power Plasma Science. Volume 1, June

17-22, pp. 536-539.

[Smi(2002)] P. W. Smith. Transient electronics: pulsed circuit technology. Chichester:

Wiley.

[Ver(2004)] R. Verma, A. Shyam, S. Chaturvedi, R. Kumar, D. Lathi, et al. Proceedings

of the 26th International Power Modulator Symposium and High-Voltage

Workshop. May 23-26, pp. 526-529.

[Yan(1990)] K. Yan, R. Li, M. Cui, L. Zhou, H. Zhao, and H. Zhang. 4th

Int. Conf. on

Electrostatic Precipitation. Beijing, China, pp. 635-649.

[Yan(2001)] K. Yan. Corona plasma generation. Phd diss., Eindhoven University of


Chapter 4 Four-switch pilot setup

There are two possible approaches to generate large pulsed power using

the TLT based multiple-switch circuit topology: (i) using a TLT with

multiple parallel cables per stage and a few switches, or (ii) using a TLT

with a single cable per stage and a large number of switches. In this

chapter, a four-switch pilot setup was built for investigation of the first

approach. Resistive loads were used to evaluate it and the application of

this setup to generate a pulsed corona discharge in water was demonstrated.

The synchronization of multiple switches is performed correctly for different

output configurations (series/parallel or with independent loads) and

different loads. However, the peak output power of the setup was much

lower than the expected value. This is mainly caused by the low damping

coefficient ξ of the input loop of the TLT. To generate large pulsed power

effectively, improvements need to be made to obtain a damping coefficient

that is as high as possible as well as a low input impedance of the TLT.

54 Chapter 4

4.1 Introduction

We know from Chapter 2 that after all the switches have been closed, all stages of the

TLT are used in parallel equivalently and the output power of the multiple-switch circuit

is determined by the switching voltage Vs and the input impedance Zin of the TLT and is

theoretically equal to Vs2/Zin. Thus, for generation of a pulse with a large peak power

(500 MW-1 GW) and a short width (~50 ns), the input impedance Zin of the TLT must be

low. There are two ways to realize a low Zin: (i) using a TLT with multiple parallel cables

per stage and a few switches, or (ii) using a TLT with one single cable per stage and a

large number of switches. Both approaches have different advantages and disadvantages.

For the first approach it is easy to realize the synchronization of a few switches; however,

it is complex in mechanical construction. As for the second approach, it is easy for the

connection of a TLT with a single cable per stage; however, it becomes critical for the

synchronization of a large number of switches. This chapter presents the investigation of

the first approach.

4.2 The four-switch pilot setup

To investigate the generation of a large pulsed power using a TLT with multiple

parallel cables and a few switches, a four-switch experimental setup was developed. This

setup was also used to verify the synchronization of multiple switches for different output

configurations; (i) with independent loads, (ii) with a parallel output configuration, and (iii)

with a series output configuration. Moreover, this technology was demonstrated on a more

complex load, namely a corona-in-water reactor.

Fig. 4.1 Schematic diagram of the four-switch pilot setup

Four-switch pilot setup 55

.

Fig. 4.2 Two different output configurations

Fig. 4.3 Photos of the four-switch pilot setup

56 Chapter 4

Figure 4.1 shows the schematic diagram of the pilot setup. It includes seven charging

inductors L1-L7, four high-voltage capacitors CH1-CH4, four switches S1-S4, a 4-stage TLT

with four parallel cables per stage, and four independent loads. The inductors have a value

of 150 µH. The capacitance value of each capacitor is 3.9 nF. All of the four switches are

spark gap switches and one of them (S1) is a triggered switch, while the other three are

self-breakdown spark gap switches. The TLT is made from a 1.5-meter-long coaxial cable

of type RG217; thus each stage has a characteristic impedance Z0 of 12.5 Ω, and the input

impedance Zin of the TLT is 3.125 Ω. Magnetic cores are placed around stages 1, 2, and 4

to increase secondary mode impedances between two adjacent stages of the TLT (for

detailed information about the effect of magnetic cores, please see Section 5.4.3). At the

output side, as shown in Figure 4.1, the TLT is connected to independent loads Load1-

Load4. However, experiments were also conducted with parallel and series output

configurations, as shown in Figure 4.2. The photo of the pilot setup with independent

loads is shown in Figure 4.3.

4.3 Experiments with resistive loads

4.3.1 Four independent loads

To study the synchronization process of the four switches, an experiment was

conducted with four independent loads, as shown in Figure 4.1. The value of each

resistive load is about 12.9 Ω, while the characteristic impedance Z0 of each stage of the

TLT is 12.5 Ω; thus the output current on each load is approximately equal to that in the

corresponding switch. Therefore, the output currents can be used to monitor the switching

behaviors of the four switches. Figure 4.4 gives the typical waveforms of output currents

I1-I4, where I1-I4 refer to the currents in loads Load1-Load4 respectively. As observed on

the two-switch experimental setup described in Section 2.2, the switching process has two

distinctive phases. After switch S1 is first triggered at -57 ns, the first phase starts. During

this first phase switches S2-S4 closed at -32 ns, -15 ns and -4 ns respectively. The time lag

between the closing of two switches becomes shorter since more overvoltage occurs on

the switches that are not yet closed. The small pre-pulse of switching currents in the first

phase is caused by the charging inductors and secondary mode impedance, and almost no

energy will be transferred to the load. When all the switches are closed, the first phase

ends. Then, the second phase starts, in which the TLT behaves as a current balance

transformer and the switching currents are determined by the characteristic impedance of

the TLT. Now the capacitors will be discharged rapidly and simultaneously into the load

via the TLT. The peak values of currents I1-I4 are 980 A, 947 A, 939 A and 947 A,

respectively.


Fig. 4.4 Typical output currents through the four independent loads in Fig. 4.1

4.3.2 Parallel output configuration

Output current [kA]

Fig. 4.5 Typical output current for the parallel output configuration (Fig. 4.2 (a)) at a

switching voltage of about 27 kV

58 Chapter 4

Fig. 4.6 The calculated output power and energy for the measured current

shown in Figure 4.5

Figure 4.5 gives the typical output current when all the stages of the TLT are

connected in parallel to a load, as shown in Figure 4.2 (a). For the parallel configuration,

the output impedance of the TLT is very low (i.e. 3.125 Ω). The value of the load is about

3.25 Ω. In Figure 4.5, the peak value and the rise-time (10-90%) of the output current are

3.72 kA and 37 ns respectively. The peak value of the output current approximately equals

that of the sum of the currents I1-I4 (3.81 kA) shown in Figure 4.4. In addition, the output

power Pout and the output energy Eout were calculated as:

Loadoutout

RIP 2= (4.1)

∫= dtPEoutout

(4.2)

In the above equations, Iout and RLoad refer to the output current and the value of the

resistive load respectively. Figure 4.6 shows the calculated Pout and Eout according to the

current in Figure 4.5. The peak output power and the output energy were 45.2 MW and

4.15 J respectively.


4.3.3 Series output configuration

Fig. 4.7 Typical output current waveform for a series output configuration

with RLoad=49.8 Ω in Fig. 4.2 (b)

Fig. 4.8 The calculated output power and energy for the measurement

shown in Figure 4.7

60 Chapter 4

Experiments were also done on a series output configuration, as shown in Figure

4.2 (b). For the series configuration, the output impedance of the TLT is 50 Ω. The

resistance value of the load used in this experiment was about 49.8 Ω. Figure 4.7 shows

the typical output current at a switching voltage of about 27 kV. The peak value and the

rise-time (10-90%) of the output current are 971 A and 30 ns respectively. The output

current is roughly equal to the values of the currents shown in Figure 4.4. Based on the

measured output current, the output power Pout and the output energy Eout were calculated

using (4.1) and (4.2), and are shown in Figure 4.8. The peak output power and the output

energy were 47 MW and 4.19 J respectively.

4.3.4 Analysis

According to the experiments on resistive loads described above, the synchronization

of the four switches is performed correctly and is independent of the output configuration.

Since the present setup was operated at a switching voltage of 27 kV and has an input

impedance Zin of 3.125 Ω, the theoretical peak output power Ptheoretical given by Vs2/Zin

should be 233 MW. However, the obtained output peak power Pout is 45-47 MW, which is

much smaller than the theoretical value and is only about 20% of Ptheoretical.

Fig. 4.9 Equivalent circuits for each stage of the setup after all switches are closed


To gain insight into the reason for the low peak output power of the pilot setup,

equivalent circuits shown in Figure 4.9 were used. Figure 4.9 (a) represents one stage of

the present setup after the synchronization of all switches, where the resistance of the

switch is ignored, and Ls and ZLoad represent the effective stray inductance per stage and

the effective load per stage respectively. Representing each stage of the TLT by its

characteristic impedance Z0 at the input side and by a voltage source of 2Vin in series with

Z0 at the output side, one may derive the simplified circuit shown in Figure 4.9 (b), where

Vin and Vout are the voltage input into the transmission line and the output voltage across

the load respectively. From the simplified circuit, one can derive (4.3) and (4.4).

( )

( ) ( )0

22

2

0

0 444

ZZp

Load

Load

pLoad

GGZZ

ZZ

==≤⋅

+

⋅= λξξλ (4.3)

>

−

−−

⋅

=

<<

−

−−

⋅

= −

11

)1

tanh(

exp

1

101

)1

tan(

exp

)(

2

2

1

2

2

ξ

ξ

ξ

ξ

ξ

ξ

ξ

ξ

ξ

ξ

ξ

ξ

ξ

ξ

when

a

whene

when

a

G (4.4)

In the above equations, the coefficient λp=Pout/Ptheoretical and ξ is the damping coefficient of

the input loop of the TLT, which is equal to ( )0s0

CL2Z . From (4.3), it can be seen

that coefficient λp is a function of Z0, ZLoad and the damping coefficient ξ. When the TLT

is matched (i.e. ZLoad=Z0), λp is equal to0ZZ

pLoad =

λ and is only determined by the damping

coefficient ξ.

Figure 4.10 gives the dependence of the λp on the damping coefficient ξ when the TLT

is matched. It clearly shows that λp changes nonlinearly as a function of ξ, and the higher

the value of ξ, the larger λp becomes. Especially values of ξ from 0 to 4 have a significant

influence on the λp. Looking at the current waveforms obtained on the pilot setup, one can

see that they are apparently under-damped. And the damping coefficient ξ can be

calculated by the following equation;

+=

)(ln11

2

2

Iλ

πξ (4.5)

where λI is the absolute ratio of the first positive peak current value to the first negative

peak value. Based on the current waveforms, the damping coefficient ξ of the present

setup is approximately 0.55. According (4.3), the value of λp when ξ=0.55 is 33% for a

62 Chapter 4

matching situation. Under the assumption of no energy losses, the peak output power

should be 76 MW when ξ=0.55. This is still unacceptably low compared to the theoretical

value of 233 MW given by Vs2/Zin.

0 1 2 3 4 5 6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

The ratio λ

p| Zload=Z0

The damping coefficient ξ

ξ=0.55

λp=0.33

Fig. 4.10 Dependence of λp on the damping coefficient ξ when ZLoad=Z0

From the above discussions, one can determine that the peak output power of the

present setup is significantly limited by the low damping coefficient ξ, namely due to the

stray inductance of the input loop of the TLT. To reduce the stray inductance, the

structure must be compact. However, it is difficult to improve the compactness due to

mechanical complexity when a TLT with multiple parallel cables per stage is used. To

obtain a high damping coefficient, a TLT with a single cable per stage has the following

advantages: (i) simpler mechanical construction, (ii) each stage has a larger characteristic

impedance Z0, thus the damping coefficient ξ is higher since ξ = ( )0s0

CL2Z , (iii) a

low input impedance Zin can also be obtained when a large number of stages are used. The

development of a prototype system using a TLT with a single cable per stage will be

presented in Chapter 5.


4.4 Demonstration of the pilot setup on a corona-in-water reactor

To verify the application of the four-switch system on a more complex load,

experiments were done on a corona-in-water reactor. Pulsed corona generation in water is

an interesting application of this technology. The discharge in water creates chemical

species such as OH radicals, ozone and hydrogen peroxide (H2O2) as well as UV and

shock waves [Loc(2006), Sat(1996), Gry(2003), Gry(2001)]. It is effective for the

degradation of organic compounds (phenol, organic dye, etc.) and for sterilization

[Hay(2001), Gry(1999), Gra(2006)]. Within the present work, a corona-in-water reactor as

shown in Figure 4.11, was built and tested. Both anode and cathode are immersed into the

liquid. The anode is a 12cm long hollow brass tube with thin pins, so a very strong

electrical field can be generated near the tip of the pins. Moreover, small holes with a

diameter of 1 mm were drilled along the length of the brass tube. Thus the air can be

bubbled into the liquid via the hollow brass tube and the air bubbles are diffused along the

brass tube over the entire reactor volume. The cathode is a metal mesh cylinder, and its

diameter and length are 9 cm and 20 cm respectively. The vessel was made from Perspex,

and it holds 1.4 liters of liquid. The discharge in water was realized using the present pilot

setup with a series output configuration. Both deionized water and tap water were tested;

moreover, the degradation of dye (Methylene blue) was tested.

Fig. 4.11 Photo of the corona-in-water reactor

64 Chapter 4

4.4.1 Discharging in deionized water

Figure 4.12 shows photos of the discharge in deionized water. Figure 4.12 (a) shows

the discharge when no air bubbling was used, while Figure 4.12 (b) shows the discharge

when air bubbling was used. When no air was bubbled into the water, multiple strong

streamers were generated near the pin tips. When air bubbling was used, the streamers

were produced in air bubbles.

Fig. 4.12 Photos of the discharge in deionized water: (a) no air bubbling, (b) with air

bubbling

Figures 4.13 and 4.14 show typical waveforms of the reactor voltage and current

without and with air bubbling respectively. Some time difference can be observed

between the peaks of the current and voltage; obviously the voltage is lagging the current.

This is because the reactor behaves like a capacitor before corona inception. The

capacitance of the reactor is estimated to be 330 pF. The initial water resistance of the

reactor was 6.4 kΩ. From Figure 4.13, one can see that the peak output voltage and

current are 100 kV and 882 A, respectively. However, with air bubbling the peak output

voltage and current are 89.3 kV and 885 A respectively. Furthermore, the negative peak

current was reduced from -540 A to -367 A. The power and energy injected into the

reactor are shown in Figure 4.15, where P1 and E1 are the output power and energy

respectively in the case of no air bubbling; and P2 and E2 are the output power and energy

respectively in the case of air bubbling. The peak values of P1 and P2 are 47 MW and

51 MW, respectively; the energy values E1 and E2 are 0.77 J and 1.62 J, respectively. One

can see that by using the air bubbles much more energy can be injected into the reactor.


Fig. 4.13 Typical voltage and current when deionized water and no air bubbles were used

Fig. 4.14 Typical voltage and current when deionized water and air bubbles were used

66 Chapter 4

Fig. 4.15 Typical power and energy injected into the reactor filled with deionized water

(P1 and E1 are the power and energy in the case of no air bubbling; P2 and E2 are

the power and energy in the case of air bubbling)

4.4.2 Discharging in tap water

As was the case with deionized water, tap water was also tested under two conditions

(i.e. with and without air bubbling). The initial resistance of the reactor filled with the tap

water was 103 Ω. In the case of no air bubbling, only a very few weak streamers occurred

near the pin tips; while in the case of the air bubbling, more streamers were generated,

which seemed similar with the streamers shown in Figure 4.12 (b). In terms of the

electrical characteristics, the discharge in tap water was found to be quite different from

that in the deionized water, and the reactor acted more like a resistive load. Figure 4.16

gives the typical voltage and current for the discharge in tap water without air bubbles.

The peak output voltage and current were 62.2 kV and 984 A, respectively. In addition, it

was observed that the electrical characteristics of discharging in tap water for both cases

(i.e. no air bubbling and with air bubbling) were quite similar. The power and energy

injected into the reactor are almost the same for both situations, as shown in Figure 4.17.

This implies that, for the discharge into a liquid with a high conductivity, air bubbling

does not contribute much to the total energy injection.


Fig. 4.16 Typical voltage and current of the discharging into tap water without air bubbles

Fig. 4.17 Typical power and energy injected into the reactor filled with tap water (P1 and

E1 are the power and energy in the case of no air bubbling; P2 and E2 are the power and

energy in the case of air bubbling)

68 Chapter 4

4.4.3 The dye degradation

A volume of 1.4 liters of dye (Methylene blue) solution at an initial concentration of

10 mg/l was tested with air bubbling at a flow rate of 20 l/min. The pulsed discharge was

generated at a repetition rate of 15 pps (pulses per second). The resistance of the reactor

and the dye concentration were measured every 30 minutes. Figure 4.18 shows the

dependence of the reactor resistance and dye concentration on the treatment time. With

increasing treatment time, the resistance of the reactor decreased: it dropped particularly

dramatically within the first 30 minutes, from 2.89 kΩ to 458 Ω, and it reached a minimal

value of 130 Ω after 150 minutes. This is close to the resistance of the tap water reactor.

This indicates that the conductivity of the dye solution increases with treatment time. This

is caused by the erosion of the pin electrode and dye decomposition. It was observed that

the discharge in the dye solution is initially similar to the discharge in deionized water,

while it looked more and more like discharging in tap water with increasing treatment

time. From Figure 4.18 one also can see that the dye concentration of the dye solution

dropped from 10 mg/l to 6.22 mg/l; this occurred most rapidly during the period from 0 to

30 minutes during which it dropped by 2 mg/l. A detailed chemical analysis during the

dye degradation was reported elsewhere [Gra(2006)].

Fig. 4.18 Dependence of the solution resistance and the dye concentration

on treatment time


4.5 Conclusions

A four-switch pilot setup using a TLT with four parallel cables per stage was

developed and tested with different output configurations. Also the application of this

setup to generate a pulsed corona discharge in water was demonstrated.

The multiple switches can be synchronized for each of possible output configuration

(with independent loads, or the parallel configuration or the series configuration).

However, the obtained peak output power was lower than the theoretical value. Analysis

shows that the low output power of the pilot setup is mainly caused by the low damping

coefficient ξ of the input loop of the TLT, and to generate large pulsed power effectively,

the coefficient ξ must be as high as possible. To obtain a high damping coefficient, a TLT

with a single cable per stage has the following advantages: (i) simpler mechanical

construction; (ii) each stage has a larger characteristic impedance Z0, thus the damping

coefficient ξ is higher since ξ = ( )0s0

CL2Z . (iii) a low input impedance Zin can be

obtained as well when a large number of stages are used.

Proper operation of the setup was also realized on a more complex load (i.e. a corona-

in-water reactor). The experiments showed that the discharge in liquid is sensitive to the

conductivity of the liquid. For a liquid with a high conductivity, the reactor behaves as a

resistive load and thus more energy can be injected into the reactor; however, the air-

bubbling contributes little to the total energy injection.

References

[Hay(2001)] D. Hayashi, W. F. L. M. Hoeben, G. Dooms, E. M. van Veldhuizen, W. R.

Rutgers, and G. M. W. Kroesen. LIF diagnostic for pulsed-corona-induced

degradation of phenol in aqueous solution. J. Phys. D: Appl. Phys. 33, pp. 1484-

1486.

[Gra(2006)] L. R. Grabowski. Pulsed corona in air for water treatment.

PhD diss., Eindhoven University of Technology, ISBN 90-386-2441-7

(http://alexandria.tue.nl/extra2/200610478.pdf).

[Gry(2001)] D. R. Grymonpre, A. K. Sharma, W. C. Finney, and B. R. Locke. The role of

Fenton’s reaction in aqueous phase pulsed streamer corona reactors. Chemical

Engineering Journal, 82, pp. 189-207.

[Gry(1999)] D. R. Grymonpre, W. C. Finney, and B. R. Locke. Aqueous-phase pulsed

streamer corona reactor using suspended activated carbon particles for phenol

oxidation: Mode-data comparison. Chemical Engineering Science 54, pp. 3095-

3105.

[Gry(2003)] D. R. Grymonpre, W. C. Finney, R. J. Clark, and B. R. Locke. Suspended

activated carbon particles and ozone formation in aqueous-phase pulsed corona

discharge reactors. Ind. Eng. Chem. Res. 42, pp. 5117-5134.

70 Chapter 4

[Loc(2006)] B. R. Locke, M. Sato, P. Sunka, M. R. Hoffmann, and J. -S. Chang.

Electrohydraulic discharge and nonthermal plasma for water treatment. Ind. Eng.

Chem. Res. 45, pp. 882-905.

[Sat(1996)] M. Sato, T. Ohgiyama, and J. S. Clements. Formation of chemical species and

their effects on microorganisms using a pulsed high-voltage discharge in water.

IEEE Transactions on Industry Applications Vol. 32, No. 1, January/February

1996.

Chapter 5 Ten-switch prototype system

This chapter describes another approach to generate pulsed power by

means of the presented multiple-switch technology, namely with a large

number of switches and a TLT with one cable per stage. Based on this

approach, a prototype system with ten spark gap switches and a ten-stage

TLT was developed. It is charged by a resonant charging system.

To charge the system, a high winding ratio (1:80) transformer with a

magnetic core has been developed. One critical issue related to the

magnetic transformer is the saturation of the core. An equivalent circuit

was introduced to analyze the swing of the flux density inside the core. It

was found that for a given energy transfer per pulse, the volume of the core

must be larger than a critical value, which is dominated by the coupling

coefficient. The transformer was designed on the basis of this model. The

core was made from 68 ferrite blocks. The experimental results are in good

agreement with the values given by the model and the glued ferrite core

works well. Using this transformer, the ten-switch system can be charged to

more than 70 kV. With 26.9 J of energy conversion transfer per pulse, the

energy efficiency of the transformer was around 92%.

Compared with the four-switch setup, this ten-switch prototype consists of

ten spark gap switches and a ten-stage TLT with one cable per stage. The

ten switches are air pressurized and blown by the forced air flow. They are

installed in one single compartment. Consequently, they “see” each other’s

UV and other discharge products, which will improve the switching process.

Moreover, the high-voltage capacitors, the switches, and the TLT are

integrated into one compact structure, which will improve the pulse rise-

time. The results show that using the TLT with one cable per stage and a

large number of switches is an efficient way to generate large pulsed power.

The ten switches can be synchronized within about 10 ns. An output pulse

with a rise-time of about 10 ns and a pulse width of about 55 ns has been

realized. More than 0.8 GW of output power was obtained. The energy


72 Chapter 5

5.1 Overview of the system

Figure 5.1 shows the schematic diagram of the ten-switch prototype system. It

includes a resonant charging system and a ten-switch pulsed power unit.

The resonant charging unit was developed earlier and has been used successfully

[Yan(2001), Nai(2004), Win(2007)]. It includes a three-phase rectifier, a storage capacitor

C0, a low-voltage capacitor CL, a charging inductor L0 and three thyristors Th1-Th3, a

transformer TR, a resistor R1, and diodes D1 and D2. It can charge the high-voltage

capacitors repetitively (up to 1000 pps). The charging voltage depends on the value of

low-voltage capacitor CL and the ratio of the transformer. To charge the high-voltage

capacitors to around 70 kV, a high-ratio transformer was developed. An equivalent circuit

model was also developed for designing the transformer. Detailed information about the

design and the testing results will be presented in Section 5.3.

The ten-switch unit consists of nineteen inductors L1-19, ten high-voltage capacitors

CH1-H10, ten switches S1-10, a ten-stage TLT, and a load. The ten high-voltage capacitors

are interconnected in series to the TLT via the ten switches. The ten switches are high-

pressure spark gap switches, and the switch S1 is a triggered switch with an LCR trigger

circuit, while the others are self-breakdown switches. The layout of the ten switches was

designed to be very compact to minimize stray inductance. The TLT is made from coaxial

cable (RG218) and each line is 2 m long. Magnetic cores are placed around the coaxial

cables for the purpose of synchronization. The length of each cable that is covered by the

magnetic cores is about 1 meter. At the output side of the TLT, the transmission lines are

connected in parallel to a 5 Ω resistive load.

Compared with the four-switch pilot setup, several improvements are made: (i) the

setup was designed to be very compact to minimize stray inductance, (ii) one cable per

stage is used instead of four cables in parallel per stage; (iii) the number of switches is

increased to ten; (iv) more efficient (i.e. high-pressure) switches are used (switching

voltage can be adjusted by pressure). With these improvements, a high damping

coefficient ξ of the input loop of the TLT will be obtained, and the input impedance of the

TLT will be low as well. As discussed in Section 4.3.4, a large pulsed power with a faster

switching time and a high energy efficiency should be obtained. Efficient large pulsed

power can be realized with this approach. The ten switches can be synchronized within

about 10 ns. An output pulse with a rise-time of 10 ns and a pulse width of about 55 ns

has been realized. More than 800 MW peak output power was obtained. The energy

conversion efficiency varies between 93% and 98%. Detailed information about the ten-

switch system is presented in Section 5.4.

Ten-switch prototype system 73

Resonant charging system

Ten-switch system

TR

CL

D2

R1

L0

C0

Th2

Th3

Th1

D1

1 2 3

C L R

+ -

+ -+ -+ -

L1

L2

L3

L16

L17

L18

L19

S10

CH10

CH9S9

CH2S2

S1

CH1

Stage1

Stage2

Stage9

Stage10

Fig. 5.1 Schem

atic diagram of the ten-switch prototype

TLT

74 Chapter 5

5.2 Resonant charging system

The principle of the resonant charging unit was comprehensively discussed previously

[Yan(2001)]. Initially, the storage capacitor C0 is charged up to V0 (~535 V). The system

accomplishes one charging cycle via three steps. As an example, Figure 5.2 shows the

typical voltages on the low-voltage capacitor CL and the high-voltage capacitor CH during

one charging cycle. First, by closing thyristor Th1, capacitor CL is charged from the

storage capacitor C0 from a voltage ∆VL(i-1) to a voltage VL(i). Secondly, after the

charging of CL is finished and thyristor Th1 is switched off, by closing thyristor Th2

capacitor CH is charged from 0 to the voltage VH(i) by CL via transformer TR. Then, after

the charging of CH is finished and thyristor Th2 is switched off, CH is discharged via the

spark gap switch. Finally, with thyristor Th3, the polarity of the remaining voltage on CL

can be reversed from -∆VL(i) to ∆VL(i). The i is the charging cycle sequence number.

Figure 5.2 was obtained with the newly designed transformer within the present charging

unit in the case of CL<n2CH, where n is the ratio of the transformer (n=75.4). The values of

CL and CH are 54.4 µF and 10.37 nF, respectively. As shown in Figure 5.2, ∆VL(i-1), VL(i),

and ∆VL(i) are 93 V, 890 V, and 93 V respectively and VH(i) is equal to 54.6 kV.

Fig. 5.2 Typical voltages on CL and CH during one charging cycle for the case of CL<n

2CH,

when CL and CH are 45.4 µF and 10.37 nF respectively (switching times of thyristors

Th1-Th3 and the spark-gap switch are indicated)


Ideally, namely assuming an ideal transformer and no energy losses in the circuit, one

may derive the following expressions of VL(i), ∆VL(i), and VH(i) when the charging

system is operated properly.

≥⋅+

<⋅+

=∞→

H

2

L0

L

H

2

L

H

2

L0

H

2

H

2

L

L

CCVC

CC

CCVC

CC

)(Vlim

nwhenn

nwhenn

n

ii

(5.1)

≥⋅−

<⋅−

=∞→

HL

L

HL

HL

H

LH

Li

CnCwhenVC

CnC

CnCwhenVCn

CCn

(i)∆V2

0

2

2

02

2

lim (5.2)

≥

<⋅=

∞→

HL

HL

H

L

Hi

CnCwhennV

CnCwhenCn

CnV

(i)V2

0

2

20

2

2lim (5.3)

From the above equations, it can be seen that the values of VL(i), ∆VL(i), and VH(i) are

stabilized when the charging cycle sequence number i approaches infinity. We call this the

steady situation. Under the steady situation, the voltage VH on CH is a function of CL for a

given value of CH; when CL<n2CH, voltage VH increases linearly as the value of CL

increases; while when CL≥n2CH, voltage VH is independent of CL and remains at a

constant value (see Figure 5.7 from the experimental results). Detailed information about

the above equations for CL<n2CH was given in [Yan(2001)]. For the case of CL≥n

2CH,

please see Appendix B.

5.3 Transformer

5.3.1 Introduction

Transformers are often used in a resonant mode in pulsed power systems to step up the

charging voltage. This may be either an air-core transformer or a magnetic-core

transformer. For the air-core transformer, there is no saturation problem, and it is light-

weight and easy to construct. However, the coupling coefficient k is low (normally k<0.8)

[Lee(2005), Zha(1999)]. To obtain efficient energy transfer, the air-core transformer is

normally used in dual resonant mode (i.e. as a Tesla transformer) [Fin(1966)], and at least

one primary oscillation cycle is required to accomplish the charging process (when k=0.6)

[Den(2002)]. Moreover, the charging voltage is bipolar, which makes it difficult to use

semiconductor switches (thyristor, IGBT, and MOSFET) or magnetic switches. When a

magnetic core is used, a high coupling coefficient (k>0.99) can be obtained [Mas(1997),

Win(2007)]. By using a magnetic-core transformer, an efficient energy transfer can be

realized with only a half of the primary oscillation cycle (i.e. in single resonant mode).

76 Chapter 5

(For more information about the role of the coupling coefficient k in the resonant circuit,

please see Appendix A).

One critical issue associated with the magnetic-core transformer is the saturation of

the core. Though the coupling coefficient of a magnetic-core transformer is high, it is

always less than 1. In a resonant circuit, the unavoidable leakage inductance affects the

charging time and thus also affects the flux density in the core. The influence of the

coupling coefficient k has never been reported in literature. In this section, an equivalent

circuit is developed to evaluate effects of the coupling coefficient k on the core volume

and the magnetizing energy. Based on this model, a high-ratio magnetic transformer was

developed. Ferrite blocks were adopted to make the core. A total of 68 blocks were used,

and they were glued with epoxy resin. Along the magnetic path of the core, there are 17

air gaps due to the inevitable joints between the blocks. The transformer was tested on a

resonant charging system. It was found that the glued ferrite core works well and the

output capacity of the transformer meets the design requirement. Detailed information

about the effect of the coupling coefficient k, the design of the transformer, and the testing

results will be presented.

5.3.2 Effects of the coupling coefficient k

Figure 5.3 shows the resonant charging circuit and its equivalent circuits. The resonant

circuit, as shown in Figure 5.3 (a), includes a low-voltage capacitor CL, a stray inductor Ls

induced by connection leads, a transformer TR, a diode D, and a high voltage capacitor

CH. When stray capacitance is neglected, the transformer TR can be represented by an

ideal transformer in combination with two uncoupled inductors [Tho(1998)], as shown in

Figure 5.3 (b), where L1 and L2 are the primary and secondary inductance of transformer

TR respectively. The k is the coupling coefficient of transformer TR and

equals21

LLM (M is the mutual inductance of the transformer) and n is the ratio of the

transformer and equal to M/L1 or 12

LLk . By transferring the inductance (1-k2)L2 and

capacitor CH to the primary side of transformer TR, one can derive the equivalent circuit

shown in Figure 5.3 (c). Here the primary inductor L1 is neglected since its value is much

larger than L1(1-k2)/k

2 for a magnetic-core transformer.

Suppose that the transformer is operated linearly and under the matching condition (i.e.

CL=n2CH). Then one may derive the following equations from the model shown in Figure

5.3 (c).

πωt0)cosLL

LL(1

2

(0)V(t)V

s

sL

Pri≤≤

+

−+= ωt (5.4)

L)C(Lπ∆Ts

+= (5.5)

)1k

1(

L

L

AN2

CL)0(πVdt)(V

AN

1∆B

2

11

1L

T

0

Pr

1

−+== ∫∆

s

it (5.6)


In the above equations, VPri(t), ∆T, and ∆B are the voltage on the primary, the charging

time, and the incremental flux density inside the core respectively. L is the leakage

inductance and equal to L1(1-k2)/k

2, and C=CL/2. A and N1 are the cross-section area of

the core and the number of turns of the primary winding respectively. The inductance of

the primary winding can be written as:

l

ANL

2

1

1

µ= (5.7)

In (5.7), µ and l are the permeability of the core and the mean length of the magnetic

path respectively. Substituting (5.7) into (5.6), one may derive the relationship between

the ∆B and the volume of the core [Aℓ].

Fig. 5.3 (a) the resonant charging circuit, (b) the real transformer is represented by an

ideal transformer combined with two uncoupled inductors, (c) the simplified equivalent

circuit, where the components at the secondary side are transferred to the primary side

78 Chapter 5

1)k

1(

L

L

A

µE

2

π∆B

2

1

s −+=l

(5.8)

where, E is the energy transferred per pulse and equal to CVL2(0). From (5.8), it can be

seen that ∆B is a function of the energy transferred per pulse E, the volume of the core

[Aℓ], the ratio of Ls to L1, and the coupling coefficient k.

For proper operation, ∆B must be less than the allowable swing of the flux density ∆Bm

of the applied magnetic material. Therefore the volume of the core must be designed to

match the following condition.

critical22

m

2

2

1

s

2

m

2

][A1)k

1(

4

µEπ1)]

k

1(

L

L[

4

µEπ][A ll =−>−+≥

∆B∆B (5.9)

From the above equation, one can see that the volume of the core must be larger than a

critical volume [Aℓ]critical, which is determined by the coupling coefficient k.

In a transformer, energy is needed to support the magnetic flux inside the core during

the charging process. This energy is called magnetizing energy EM and can be estimated

as:

1)k

1(

8

Eπ]

L

L1)

k

1[(

8

EπE

2

2

1

s

2

2

M−>+−= (5.10)

From (5.10) it can be seen that the magnetizing energy EM is a function of the energy per

pulse E, the coupling coefficient k and the ratio of Ls to L1. When the stray inductance Ls

is negligible, the magnetizing energy is mainly determined by the coupling coefficient k.

For instance, if k=99.6%, then at least 0.99% of the energy transferred per pulse is used to

magnetize the core.

It is noted that the calculated values for ∆T and ∆B on the basis of the model described

above are a little larger than the actual values. The higher the coupling coefficient k, the

less the difference becomes. Especially when k>99%, the differences for ∆T and ∆B are

less than 0.5% and 1.4% respectively.

5.3.3 Design and construction

The transformer is designed for the resonant charging unit to charge the high-voltage

capacitor CH (about 10 nF) to a voltage of around 70 kV, where the low-voltage capacitor

CL is initially charged to about 1 kV. Thus the voltage transfer ratio of the transfer needs

to be at least about 1:70; in practice, the winding ratio was chosen to be 1:80. Ferrite

blocks were used to construct the core. With regard to the ferrite material, the relative

permeability, the saturation flux density, and the residual flux density are 2400, 0.5 T, and

0.15 T respectively. The dimensions of each ferrite block are 5cm×5cm×10cm. The ferrite

blocks are glued together by epoxy resin to obtain the desired core shape and dimensions.

The advantage of using discrete ferrite blocks is the flexibility in construction of various

kinds of cores (C-type or shell type) with various dimensions.


(a) Determine the volume of the core

70 cm

60 cm

Fig. 5.4 The transformer core

To estimate the critical volume of the ferrite core according to (5.9), the following

assumptions were made: (i) The stray capacitance of the transformer is assumed to be

around 0.5 nF and is added to the high-voltage capacitor CH. So CH becomes 10.5 nF; and

thus under the matching condition CL=n2CH, the transferred energy per pulse E is about

33 J. (ii) According to the specification of the ferrite material, the allowable swing of the

flux density is 0.35 T; in this design, a value of ∆Bm=0.3 T was used. (iii) The coupling

coefficient k and the relative permeability µr of the core were empirically set to be 0.996

and 1200 respectively. Under these assumptions, from (5.9), the critical volume of the

core was estimated to be 11190 cm3, which means that at least 45 ferrite blocks are

needed. Due to the stray inductance, and to ensure the proper operation of the transformer,

68 ferrite blocks were actually used. By gluing these blocks together with epoxy resin, a

shell-type core was made, as shown in Figure 5.4. The size of the core is

50cm×10cm×70cm; other dimensions are also shown in Figure 5.4. Except for the two

removable blocks on the top, all the blocks are glued together. The mean length of the

magnetic path is 1.7 m. Along the magnetic path, there exist 17 air gaps due to the

80 Chapter 5

inevitable joints between the blocks. And the initially estimated length of the 17 gaps is

between 0.5 mm and 1 mm.

(b) Select the number of turns of the primary

The number of turns of the primary winding N1 was chosen according to the

specification of the resonant charging unit. To keep the charging unit within safe margins,

the maximum primary current must be less than the current rating of thyristor Th2 in the

present resonant unit (2 kA). Based on the model shown in Figure 5.3 (c), with the

assumptions of k=0.996 and Ls=0 the peak primary current was estimated for different

numbers of turns, from 10 to 20. These estimations were made for two different total

lengths of air gaps (i.e. 1 mm and 0.5 mm respectively). The primary turn number N1=16

was chosen, since for this value the primary peak current will stay within safe margins. In

addition, other parameters (e.g. the equivalent µr, primary inductance L1) were evaluated

when N1=16, as shown in Table 5.1. One may find the transformer will be operated

properly with N1=16, provided it could be ensured that the total length of air gaps was

between 0.5 mm and 1 mm.

Table 5.1 Evaluation of the design when N1=16

(c) Construction

The 16-turn primary winding was made from copper foil with a thickness of 1 mm and

a width of 29 mm. The windings are wound on a square bobbin made from fiberglass. The

secondary winding has 1280 turns and is wound on a cone-shaped fiberglass bobbin. It

was made from copper wire with a diameter of 0.42 mm. To reduce the winding resistance,

two parallel layers were used. They were interconnected at the middle (i.e. the top layer

goes to the bottom and the bottom layer goes to the top). Both the primary and the

secondary windings are placed around the middle leg of the core. An aluminum

cylindrical screen with a 1 cm split was put between primary and the secondary to prevent

the capacitive coupling between the primary and the secondary. The secondary winding is

equipped with a round ring to control the high electric field. The two outer legs of the core

are also provided with field-control aluminum parts. The whole transformer is supported


by a wooden frame. A photo of the transformer is shown in Figure 5.5. This transformer is

immersed into transformer oil. The parameters were measured using an LCR meter and

are shown in Table 5.2. According to the primary inductance, the effective µ r and the total

length of air gaps are estimated to be 1238 and 0.665 mm respectively; they are within the

estimated ranges shown in Table 5.1. A coupling coefficient of 99.62% was obtained, and

the actual ratio n is about 1:75.4.

Fig. 5.5 Photo of the transformer

Table 5.2 Parameters of the transformer

82 Chapter 5

5.3.4 Testing of the transformer

Fig. 5.6 Schematic diagram of the testing setup

The designed transformer (TR) was tested within a setup as shown in Figure 5.6. It

consists of a resonant charging unit and a high-voltage pulser. The resonant charging unit

is the same as that shown in Figure 5.1. The high-voltage pulser includes a high-voltage

capacitor CH, a switch S, an LCR trigger circuit, and a resistive load. The switch S is a

multiple-gap spark gap switch [Liu(2006)] consisting of three 9 mm gaps. The LCR

trigger circuit consists of an inductor L, a capacitor C and a resistor R [Yan(2003)]. The

value of CH is about 10.37 nF, and the load is about 81.5 Ω.

Fig. 5.7 Dependence of the voltage VH on the value of CL when CH=10.37 nF


Experiments were conducted with values of CL varying from 41.1 µF to 67 µF, while

the value of high-voltage capacitor CH was kept the same at 10.37 nF. For these values,

the voltage VH on the high-voltage capacitor CH was measured when the test setup was

operated in a steady situation. Figure 5.7 shows the dependence of the voltage VH on the

value of low-voltage capacitor CL. It can be seen that the voltage on CH increases linearly

when increasing the value of low-voltage capacitor CL from 41.1 µF to 57.9 µF. While

upon increasing CL from 60.6 µF to 67 µF, voltage VH remains at a constant value of over

70 kV, since CL>n2CH. We can conclude that the designed transformer meets the voltage

requirement. From Figure 5.7, we also can find that the relationship between voltage VH

and the value of CL is in good agreement with equation (5.3). In addition, from Figure 5.7,

the matching value of CL (where CL=n2CH) is approximately 59 µF, which is slightly less

than the theoretical value of 60.3 µF (the stray capacitance of the transformer was taken

into account). This is due to the fact that the high-voltage capacitors used for CH are

slightly voltage dependent, and the capacitance may become slightly smaller at a high

voltage.

Fig. 5.8 Typical voltages on CL and CH during one charging cycle under steady operation

when CL=60.6 µF and CH=10.37 nF in Fig. 5.6

The experiments with the value of CL=60.6 µF (CL>n2CH) were used to evaluate the

transformer. Figure 5.8 shows the voltages on CL and CH during one charging cycle under

steady operation. The low-voltage capacitor CL was charged to 965 V from an initial

voltage of 16 V. After closing thyristor Th2, the voltage on CL dropped to 16 V again and

the high-voltage capacitor CH was charged up to 70.3 kV. Then spark gap switch S is

triggered and high-voltage capacitor CH discharges into the load. In contrast to the

situation shown in Figure 5.2, the voltage on CL does not become negative since CL>n2CH.

84 Chapter 5

Time [µs]Time [µs]

79 µs

260200180 240160 220100 120 14080

1600

800

1400

1200

600

1000

400

200

0

-200

-400

Primary voltage [V

]

800

1200

600

1000

400

200

0

-200

Primary current [A

]

Current

Voltage

Fig. 5.9 Typical voltage and current on the primary winding of the transformer

when CL=60.6 µF and CH=10.37 nF in Fig. 5.6

Fig. 5.10 Swing of the flux density ∆B inside the transformer core in Fig. 5.6


Figure 5.9 shows the typical voltage and current on the primary winding of the

transformer when CL=60.6 µF. It can be seen that the peak value of the primary current is

1.14 kA. This is about 57% of the current rating of thyristor Th2, which indicates that the

design of the transformer ensured the switch is used safely. Furthermore, according to the

current waveform shown in Figure 5.9, the charging time is about 79 µs. The leakage

inductance of the transformer L1(1-k2)/k

2 is about 17.8 µH, thus the stray inductance LS in

the present test system is approximately 2.9 µH. By integrating the primary voltage shown

in Figure 5.9, the swing of the flux density inside the core can be estimated, and the result

is shown in Figure 5.10. It can be found that when the charging is finished, the increased

flux density inside the core is 0.23 T, which means that the design of the transformer

ensured the core became unsaturated. This value is in good agreement with the theoretical

value of 0.232 T given by equation (5.6). The further increase of the flux density after the

charging has been finished is caused by the voltage oscillation between the primary and

the secondary (as shown in Fig. 5.9).

Fig. 5.11 The values of Ein and Eout when CL=60.6 µF under steady operation in Fig. 5.6

The total energy conversion efficiency η of the transformer was evaluated by the

following equation:

∫∫

==(t)dt(t)IV

(t)dt(t)IV

E

Eη

pripri

HH

in

out (5.11)

86 Chapter 5

where Ein and Eout refer to the energy input into the transformer and the energy output

from the transformer, namely the energy that flowed out of diode D2. VPri(t), VH(t), IPri(t)

and IH(t) refer to the voltage across the primary of the transformer, the voltage on CH, the

current in the transformer primary winding, and the current flowing out of the transformer

secondary winding respectively. These four parameters were measured simultaneously

when CL=60.6 µF under steady operation. The calculated values of Ein and Eout are given

in Figure 5.11. When the charging is complete, the values of Ein and Eout are 26.9 J and

24.7 J respectively, thus the energy efficiency is 91.8%. The losses are mainly caused by

the resistance of the primary and secondary windings, the secondary stray capacitance,

and the transformer core (magnetizing energy EM and eddy current). The losses caused by

them were estimated to be about 1.9%, 2.4%, 2.1%, and 1.8% respectively. One can see

that there is a slight drop in the Ein after the charging is complete. This is due to the

recovery process of thyristor Th2 after the charging is complete.

5.4 Ten-switch system

5.4.1 Charging inductors

The nineteen inductors L1-L19, shown in Figure 5.1, are used to charge the ten high-

voltage capacitors CH1-CH10 in parallel during the resonant charging process. During the

synchronization process of the ten spark gap switches they provide high impedance to

block the discharging of the high-voltage capacitors. To ensure proper synchronization,

the value L of the inductors must be:

2

∆ZL s s

T⋅>> (5.12)

where ∆Ts is the time interval for the synchronization of all switches. For instance, when

Zs=2 kΩ and ∆Ts=30 ns, the inductance should be much larger than 30 µH.

Within the present setup, rod-type air-core inductors were used. The length and the

diameter of the rods are 152 mm and 80 mm, respectively. Each inductor has 142

windings of copper wire with a thickness of 1.07 mm. Aluminum plates with round edges

were connected to the ends of the inductors to control the electric field. The inductance

value L of each inductor is 605 µH.

5.4.2 Spark gap switches

High-pressure spark gap switches (S1-S10) were used for the present system.

Compared with atmospheric-pressure spark gaps, the advantages of a high-pressure spark

gaps are: (i) smaller conductive resistance, (ii) smaller inductance, and (iii) a faster

switching time due to the shorter gap distance and higher field strength. For a uniform or

nearly uniform gap filled with air, the breakdown voltage VB is a function of the air

pressure p and the gap distance d, and can be expressed as:


pd6.53pd24.4VB

+= (5.13)

where p and d are the air pressure in bar and the gap distance in cm respectively.

Switch S1 was constructed as a triggered spark gap switch, while the other nine

switches S2-S10 are self-breakdown switches. The electrodes of each switch are made of

brass, and the diameter of each electrode is 20 mm. They were designed to have the same

breakdown voltage in accordance with equation (5.13). For the self-breakdown switches,

the gap distance is 4 mm. For the triggered switch, the distances of the trigger gap and the

gap between the trigger electrode and the cathode are 1 mm and 2.8 mm respectively.

With such gap distances, all the switches have approximately the same breakdown voltage,

as shown in Figure 5.12.

Fig. 5.12 Breakdown voltage of the ten spark gap switches (breakdown voltage is

calculated according to (5.13))

5.4.3 The TLTs

The TLT plays an important role in synchronizing the multiple switches and in

transferring the energy from the capacitors to the load. To ensure the synchronization and

to block the discharging of the high-voltage capacitors during the synchronization process,

the secondary mode impedance Zs must be much larger than the characteristic impedance

Z0 of the coaxial lines, namely:

Zs >>Z0 (5.14)

Moreover, to avoid reflections of the high-voltage pulse between the outer conductors of

the TLT, the transit time between the outer conductors of the TLT should be longer than

88 Chapter 5

0.5∆Ts, where ∆Ts is the time interval for the synchronization of the multiple switches.

Therefore, the length l of the coaxial cables covered by magnetic cores needs to be:

s

s

l∆T

2

1≥

υ (5.15)

In the above equation, υs is the velocity of the high-voltage pulse between the outer

conductors of the TLT.

From discussions in Chapter 2, the overvoltage induced by the closing of the first

switches is important for the synchronization of multiple switches. Suppose that the

number of applied switches is m and the first several switches (quantity j) have been

closed. Then, under the assumption that the secondary mode impedances between the

adjacent stages of the TLT are the same, the maximum overvoltage ∆V(m-j) over the (m-j)

switches that are not yet closed can be given by:

jm

VjV

jm−

⋅=∆ −

0

)( (5.16)

where, V0 is the initial charging voltage on the high-voltage capacitors. It can be seen that

the overvoltage ∆V(m-1) induced by the closing of the first switch to close the switches that

are not yet closed is equal to V0/(m-1). When a large number of switches are used, the

small overvoltage ∆V(m-1) may be too small to close the second switch. This will cause the

failure of the synchronization of multiple switches. Two solutions can be used to prevent

this: (i) using different magnetic cores with different µr; or (ii) putting similar magnetic

cores around specific stages of the TLT. Both these solutions will give different secondary

mode impedances and provide the second switch with a higher overvoltage. Once the first

few switches have been closed, more and more overvoltage can be added to the switches

that are not yet closed during the synchronization process. This will result in proper

synchronization.

In addition, to ensure the high secondary mode impedance, saturation of the magnetic

material must be avoided. Thus equation (5.17) must be observed:

sm

pr0

sZ

VµµB

l> (5.17)

where Bs is the saturation flux density of the magnetic material, ℓm is the mean length of

the magnetic path of the magnetic toroid, and Vp is the voltage over the secondary mode

impedance Zs.

The model shown in Figure 5.13 can be used to evaluate the secondary mode

impedance of the TLT and the wave velocity between the outer conductors of the TLT; D

is the distance between the magnetic cores, D0 is the diameter of the outer conductor of

the cable, D1 and D2 are the inner and outer diameters of the magnetic toroid respectively.

Suppose that the current is distributed uniformly around the outer conductor. Then, the

secondary mode impedance and wave velocity can be written as:


0

0

20

10

2

2

r

0

0

2sD

D2D]ln

D)D2(D

D)D2(Dln

D

D1)[ln(µ

D

D2Dln120Z

+

−+

−++−+

+= (5.18)

0

0

20

10

2

2

r

0

0

1sD

D2D]ln

D)D2(D

D)D2(Dln

D

D1)[ln(µ

2

1

D

D2Dln120Z

+

−+

−++−+

+= (5.19)

0

01-

20

10

2

2

r

0

0

02sD

D2Dln]

D)D2(D

D)D2(Dln

D

D1)[ln(µ

D

D2Dln

+

−+

−++−+

+= υυ (5.20)

0

01-

20

10

2

2

r

0

0

01sD

D2Dln]

D)D2(D

D)D2(Dln

D

D1)[ln(µ

2

1

D

D2Dln

+

−+

−++−+

+= υυ (5.21)

In the equations shown above, Z2s and υ2s are the secondary mode impedance and the

wave velocity when magnetic cores are placed around both coaxial cables. Similarly, Z1s

and υ1s are for the situation when only one coaxial cable is covered with magnetic cores.

µ r is the relative permeability of the magnetic material. υ0 is the wave velocity in air. The

same model was used by Win(2007) to evaluate a two-stage TLT, and it was observed that

the model agrees well with experimental results.

D2

D1

D0

D1

D0

D2

D

Fig. 5.13 Schematic diagram of two parallel coaxial cables covered

with magnetic material

Within the present system, the same magnetic cores were used. Figure 5.14 gives an

overview of the input side of the TLT and the specific coaxial cables covered with

magnetic cores. Magnetic cores are not put around the cables of stages nos. 3, 6 and 8.

The secondary mode impedances between two adjacent stages covered or not covered by

magnetic cores are different. Thus the overvoltage induced by the closing of the first

switch will be nonuniformly added to the switches that are not yet closed (e.g. the

overvoltage added to switch S2 is larger than that over switch S3). The switch with more

overvoltage will close shortly after the closing of switch S1. Once the second switch has

been closed, the synchronization can be accomplished properly.

90 Chapter 5

Fig. 5.14 Configuration of the magnetic cores around the coaxial cables of the TLT

in Fig. 5.1

The magnetic material used within the present system is metglass MP4510. Its relative

permeability µr is 245. The values of D0, D1 and D2 are 18.3 mm, 19.6 mm, and 48.4 mm

respectively. Calculated values of the secondary mode impedance and the wave velocity

versus distance D are shown in Figures 5.15 and 5.16 respectively. It can be seen that a

secondary mode impedance Zs>2 kΩ can be obtained. Upon increasing the value of D

from 10 cm to 100 cm, the ratio of Z2s to Z1s is 1.4. For a value of D less than 100 cm, the

values of υ2s and υ1s are less than 4.47×107 m/s and 6.25×10

7 m/s respectively. If the

length covered by magnetic material is 100 cm, the two-way transit times corresponding

to υ2s and υ1s are 45 ns and 32 ns respectively. In addition, the values of Bs and ℓm of

metgalss MP4510 are 1.56 T and 10.55 cm respectively. It can be kept far below the

saturation, for instance, when Zs =2 kΩ and Vp=40 kV the flux density inside the toroid is

only 0.058 T.


Fig. 5.15 Calculated secondary mode impedance Z1s and Z2s versus D based on equations

(5.18) and (5.19)

Fig. 5.16 Calculated wave velocity υ1s and υ2s versus D based on equations (5.20) and

(5.21)

92 Chapter 5

5.4.4 Integration of components into one compact unit

To obtain a fast rise-time, the structure must be as compact as possible. Within the

present work, the ten switches S1-S10, the ten high-voltage capacitors CH1-CH10, and the

TLT connections are integrated into one compact structure, as shown in Figure 5.17 (for

the mechanical sketch, see Appendix D). The ten switches are installed in one single

compartment. Consequently, they “see” each other’s UV and other discharge products,

which will improve the switching process. The ten switches are put into two arrays, with

five switches per array. A compressed air flow can be used to flush the spark gap switches

for the high-voltage and high-repetition-rate operation. This unit is able to hold a pressure

up to 10 bar.

Fig. 5.17 3-D overview of the compact structure at the switch side of the TLT in Fig. 5.1

(Nos. 1, 3, 5, 7, and 9 indicate the stage numbers of the TLT)

5.4.5 The load

At the output side of the TLT, all the coaxial cables are connected in parallel, thus the

output impedance is low (i.e. 5 Ω). Due to the low output impedance, the stray inductance

of the connections to the load must be as low as possible for good matching between the


TLT and the load. For instance, if the stray inductance is 20 nH, then effective impedance

corresponding to a 10 ns pulse is about 4.4 Ω, which is very close to the resistance of the

load. To obtain a small stray inductance, the load is constructed coaxially, as shown in

Figure 5.18. The load is made from five 1 Ω hard disc resistors. A single-turn Rogowski

coil (shown in Figure 5.18) is integrated into the load construction for the current

measurements. Additionally, air can be flushed through the structure to cool the load.

Fig. 5.18 Overview of the load construction (the construction also contains a single-turn

Rogowski coil for current measurement)

Figure 5.19 gives a total overview of the constructed 10-switch pulsed power system,

and pictures of the switch compartment and the output configuration of the TLT.

94 Chapter 5

Fig. 5.19 Total overview of the ten-switch pulsed power system in Fig. 5.1

5.5 Characteristics of the system

5.5.1 Repetitive operation by the LCR

As shown in Figure 5.1, the present system was operated repetitively by means of an

LCR trigger circuit [Yan(2003)]. This circuit automatically triggers the first spark gap

switch S1. It consists of an inductor L, a capacitor C and a resistor R. It is designed to have


R>>2(L/C)1/2

and CH>>C. During the charging of the high-voltage capacitors, the voltage

VH(t) on the high-voltage capacitors and the voltage VT(t) on the trigger electrode can be

expressed as:

≥

≤≤−=

πω

πωω

twhenV

twhentV

tVH

max

max 0)]cos(1[2)( (5.22)

≥∆−

−⋅+−+

≤≤+−−+

=

πωτγ

π

γ

γ

πωωωγτ

γγ

γ

twhenTtV

twhentttV

tVT

]exp[]1)[exp(12

0)]sin()cos()exp([12

)(

2

2

max

2

max

(5.23)

where Vmax is the voltage on the high-voltage capacitor when the charging is finished, ω is

the charging frequency of the resonant charging circuit, ∆T is the charging time and is

equal to π/ω, τ is the time constant of the LCR trigger circuit and equal to RC, and the

coefficient γ is equal to ωτ. Within the present work, the values of C and R are 323 pF and

429 kΩ respectively.

Fig. 5.20 Typical waveforms of VH and VT when CL=37 µF and CH=10.69 nF

Figure 5.20 gives the typical waveforms of VH(t) and VT(t) during one pulse cycle

when CL=37 µF and CH=10.69 nF.. It can be seen that during the charging process the

voltages VH and VT increase simultaneously. After the charging has been finished, voltage

96 Chapter 5

VH almost remains constant, while the voltage VT on the trigger electrode decreases

exponentially because capacitor C will be further charged by CH via the LCR circuit.

Consequently, the voltage across the trigger gap (between the anode and the trigger

electrode), increases exponentially until the trigger gap breaks down at 42 µs after the

charging has been finished. Now an overvoltage will appear over the gap between the

trigger electrode and the cathode, which subsequently causes the switch to close.

The switching behavior of the triggered switch can be divided into pre-firing and

normal switching. In the case of pre-firing, the switch closes before the charging is

finished, while in the case of normal switching, the switch closes after the charging is

finished. Figure 5.21 gives the averaged value of VH from 128 shots and the value of VH

from one single shot, where the system was operated at a repetition rate of 20 pps and the

input and output pressure of the switch compartment were 4.25 bar and 1.8 bar

respectively. It can be seen that no pre-fire occurred and the switch was operated within

the normal switching region. In Figure 5.21 it can be seen that the time delay and the

jittering of the triggered switch were 61-131 µs and 106 µs respectively.

Fig. 5.21 The averaged value of VH from 128 shots and the value of VH from one single

shot in Fig. 5.1

The present system was operated reliably at different repetition rates from 20 pps to

240 pps when CL=37 µF. Figure 5.22 shows the averaged charging voltage at different

repetition rates. It can be seen that the average charging voltages at different repetition

rates are almost the same, which indicates that the spark gap switches operated within the


normal switching region. Moreover, one may find that the average charging voltage

decreases slightly as the repetition rate is increased. This is due to a small drop in the

voltage on the storage capacitor C0 (see Fig. 5.1) at the high repetition rate.

Fig. 5.22 The charging voltages at different repetition rates when CL=37 µF in Fig. 5.1

5.5.2 Output characteristics

Figure 5.23 shows typical waveforms of output voltage and current when the setup

was operated at a repetition rate of 20 pps. For the ten-switch compartment, the input and

output pressure were 3.4 bar and 2.4 bar respectively. The low-voltage capacitor CL has a

value of 37 µF and the high-voltage capacitors were charged up to 43.8 kV under steady

operation. The voltage on the high-voltage capacitors when the switches closed was

42.8 kV. The peak values of the output voltage and current are 48.4 kV and 6.46 kA

respectively. The rise-times (10-90%) of the output voltage and current are 11.0 ns and

12.2 ns respectively. Compared with the four-switch pilot setup, no bipolar oscillation

occurred in the output pulse and the rise-time of the output pulse is much faster.

98 Chapter 5

Fig. 5.23 Typical output voltage and current when CL=37 µF in Fig. 5.1 (the rise-time of

the output voltage and current are 11 ns and 12.2 ns respectively)

Fig. 5.24 Typical output power and energy when CL=37 µF in Fig. 5.1 (the peak output

power and the output energy are 312 MW and 9.31 J respectively)


From Figure 5.23, one can see that a small step with a duration of about 10.4 ns occurs

within the rising part of the output pulse (see magnified view in Figure 5.23). This, in fact,

implies that the ten spark gap switches are closed in sequence within about 10 ns.

Moreover, it was observed that the output pulse forms are exponential. For an exponential

pulse, the 10-90% decay time is ideally equal to 2.2τ. From the discussions in Section 2.1,

after all switches have closed, the ten high-voltage capacitors will discharge in parallel

into the TLT. The total capacitance of the high-voltage capacitors and the input

impedance of the TLT are 10.7 nF and 5 Ω respectively. Thus, the theoretical 2.2τ is equal

to 117.7 ns. The actual 10-90% decay time of the ten-switch system is about 121 ns, and is

in good agreement with the theoretical value.

Figure 5.24 shows the output power and energy for the measurement shown in Figure

5.23. The peak output power and the output energy are 312 MW and 9.31 J, respectively.

The voltage on the high-voltage capacitors when the switches closed was 42.8 kV.

Therefore, ideally (i.e. no energy loss and the TLT with a perfectly matched load), the

theoretical value of the peak output power should be 366 MW. The ratio of the

experimental value to the theoretical one is about 85%, which is much larger than that of

the four-switch pilot setup (20%) (see Section 4.3.4).

To evaluate the reproducibility of the present system, Figure 5.25 gives the

comparison of the averaged waveforms of the output current (averaged over 101 shots)

and a single shot record when CL=37 µF and the setup was operated at 50 pps. One can

see that both signals are in good agreement, which means that the ten-switch system has

good reproducibility. However, when the repetition rate was increased to 150 pps, it was

observed that a difference between the two signals occurred. Possibly the cooling of the

load is insufficient to cool it and keep its resistance stable at a high repetition rate.

Consequently, the current will change slightly during operation.

The peak output power is proportional to the square of the switching voltage.

Experiments were carried out with different values of CL, varying from 24 µF to 58.2 µF.

Figure 5.26 gives the peak output power at different switching voltages. The theoretical

value of the peak output power is also given in Figure 5.26, which is calculated under the

assumption that the TLT is perfectly matched and the energy loss can be neglected.

Apparently, due to energy losses and the reflection, the experimental values are always

less than those calculated ones. From experimental results, it can be seen that the peak

output power increases as the switching voltage increases. More than 800 MW peak

output power was obtained when CL=58.2 µF.

Figure 5.27 gives the typical output voltage and current when CL=58.2 µF and at a

switching voltage of 69.7 kV. The peak values of the output voltage and current are

76.8 kV and 10.95 kA respectively. The output power and the output energy for the

measurement in Figure 5.27 are shown in Figure 5.28. The peak output power and the

output energy are 810 MW and 24.1 J, respectively.

100 Chapter 5

Fig. 5.25 Comparison of the averaged waveforms of the output current and a single shot

record when CL=37 µF in Fig. 5.1

Fig. 5.26 Peak output power at different switching voltages in Fig. 5.1


Time [ns]10050 200150 300 3502500-50-100

80

20

60

0

40

12

6

10

4

8

2

0

Output voltage

Output current

Fig. 5.27 Typical output voltage and current at a switching voltage of 69.7 kV (their peak

values and rise-times are 76.8 kV and 10.95 kA, and 10 ns and 11 ns respectively)

Fig. 5.28 The typical output power and energy at the switching voltage of 69.7 kV (the

peak output power and the output energy are 810 MW and 24.1 J respectively)

102 Chapter 5

5.5.3 The energy conversion efficiency

The energy conversion efficiency η of the ten-switch pulsed power system was

calculated according to the following equation.

∫∫

==dttItV

dttItV

E

E

HH

outputoutput

ingch

load

)()(

)()(

arg

η (5.24)

where, Eload and Echarging are the energy obtained in the load and the total energy used to

charge the system, respectively. They are calculated by integrating the corresponding

product of the voltage and the current. Within the present setup, the energy conversion

efficiency varied between 93% and 98%.

The main energy losses are caused by the LCR trigger circuit, the spark gap switches,

the resistance of the inner conductors of the TLT, and the secondary mode impedance of

the TLT.

The losses in the LCR trigger circuit are caused by the resistor R and the capacitor C.

The resistor R dissipates energy during and after the charging period until the spark gap

switches close; the capacitor C absorbs energy during these processes, and the energy

stored in C will be dissipated by the triggered switch S1 after it has been triggered. The

relative contribution to the losses by these factors can be calculated with the following

equations:

ingch

TH

ingch

C

CE

tVtVC

E

Et

arg

2

arg

2/)]()([)(

−==η (5.25)

ingch

T

ingch

R

RE

RdttV

E

Et

arg

2

arg

/)()(

∫==η (5.26)

RC

ingch

RC

ingch

LCR

LCRE

EE

E

Et ηηη +=

+==

argarg

)( (5.27)

In above equations, ηC, ηR, and ηLCR are the loss ratios for the resistor R, the capacitor C,

and the LCR trigger circuit respectively. EC, ER, and Echarging refer to the energy absorbed

by C, the energy dissipated by R, and the energy used to charge the ten-switch unit

respectively.

Figure 5.29 shows the calculated values of ηC, ηR, and ηLCR when CL=37 µF (charging

time ∆T=68 us). It can be observed that the LCR loss ratio is a function of time. When

t=∆T, namely the moment when the charging is finished, the values of ηC|t=∆T, ηR|t=∆T, and

ηLCR|t=∆T are 0.14%, 0.8% and 0.94% respectively. After a much longer time (t→∞), the

values of ηC|t→∞, ηR|t→∞, and ηLCR|t→∞ are 2.86%, 2.54% and 5.40% respectively.

Apparently, if the switches work in the normal switching region (i.e. they are closed at

t≥∆T), the minimal loss caused by the LCR will be less than 1% and the maximum loss

can be up to 5.40%.


C

Fig. 5.29 The calculated ηC, ηR, and ηLCR when CL=37 µF (∆T=68 µs) in Fig. 5.1

Fig. 5.30 The typical experimental values of EC, ER and ELCR when CL=37 µF in Fig. 5.1

104 Chapter 5

Figure 5.30 shows typical waveforms for EC, ER, and ELCR when CL=37 µF and the

setup was operated steadily. The charging time ∆T and the charging energy Echarging were

about 68 µs and 10.17 J respectively. It can be seen that, when the charging is finished, EC,

ER and ELCR are 0.022 J, 0.066 J and 0.088 J respectively. Thus the corresponding values

of ηC, ηR, and ηLCR are 0.22%, 0.65% and 0.87% respectively. From Figure 5.30, one can

also see that after the charging has been finished and before the switches have been closed,

the energy EC and ER increase continuously because capacitor C is further charged by the

high-voltage capacitors, and when the switches closed 66 µs after the charging finished

(i.e. at the moment t=1.97∆T), EC, ER and ELCR were 0.096 J, 0.167 J and 0.263 J

respectively; and thus ηC, ηR and ηLCR were about 0.94%, 1.64% and 2.59% respectively

and the theoretical value of ηLCR is 2.67%.

The losses caused by other factors, namely the spark gap switches, the core of the TLT,

and the secondary mode impedance Zs of the TLT, were estimated using η- ηLCR. It was

observed that when CL=37 µF and the switches worked within the normal region, the

losses caused by other factors accounted for roughly 3.4% of the total charging energy.

5.6 Summary

Using the presented multiple-switch pulsed power technology, efficient high pulsed

power generation with a fast rise-time and a short pulse width has been realized. The

system operated correctly at repetition rates up to 300 pps. The ten spark gap switches

were properly synchronized.

A high ratio transformer was developed for charging the system. An equivalent circuit

model was introduced to analyze the influence of the coupling coefficient on the swing of

the flux density of the core and the magnetizing energy. The transformer was designed on

the basis of this model. The core is made from 68 ferrite blocks. Along the flux path there

are 17 air gaps, and the total gap distance is about 0.67 mm. The primary and secondary

windings are 16 turns and 1280 turns respectively, and the transformer ratio actually

obtained is 1:75.4. The coupling coefficient of 99.62% was obtained. The transformer was

tested on the resonant charging system. The experimental results show that the model can

provide a good guideline for designing a resonant magnetic transformer and that the glued

ferrite core works well. Using this transformer, the high-voltage capacitors can be charged

to more than 70 kV repetitively (potentially up to 1000 pps). With 26.9 J of energy

transfer, the increased flux density inside the core was 0.23 T, which is below the usable

flux density swing (0.35 T-0.5 T). The energy transfer efficiency from the primary to the

secondary was approximately 92%.

The ten-switch unit consists of ten high-voltage capacitors, ten high-pressure spark

gap switches, and a ten-stage TLT. All these components are integrated into a compact

structure. Magnetic cores were placed around specific coaxial cables of the TLT for proper

synchronization of the multiple switches. The results showed that using a TLT with one


cable per stage and more switches (compared to the four-switch pilot setup) is an efficient

way to achieve high pulsed power generation using the presented multiple-switch

technology. Ten switches can be synchronized within about 10 ns. This system is able to

produce a pulse with a rise-time of about 10 ns and a width of about 55 ns. It has good

reproducibility. An output power of more than 800 MW was realized. The energy


References

[Den(2002)] M. Denicolai. Optimal performance for Tesla transformer. Review of

Scientific Instruments Vol. 73, No. 9, September 2002, pp. 3332-3336.

[Fin(1966)] D. Finkelsten, P. Goldberg, and J. Shuchatowitz. High-voltage impulse

system. Review of Scientific Instruments Vol. 37, No. 2, February 1966, pp.159-

162.

[Lee(2005)] J. Lee, C. H. Kim, J. H. Kuk, J. K. Kim, and J. W. Ahn. Design of a compact

epoxy molded pulsed transformer. Proceedings of 15th IEEE International Pulsed

Power Conference June 2005, pp. 477-480.

[Liu(2006)] Z. Liu, K. Yan, G. J. J. Winands, E. J. M. Van Heesch, and A. J. M. Pemen.

Multiple-gap spark-gap. Review of Scientific Instruments Vol.77, Issue 7, 2006.

[Mas(1997)] K. Masugata, H. Saitoh, H. Maekawa, K. Shibata, and M. Shigeta.

Development of high voltage step-up transformer as a substitute for a Marx

generator. Rev. Sci. Instrum. Vol. 68, No. 5, May 1997, pp. 2214-2220.

[Nai(2004)] S. A. Nair. Corona plasma for tar removal. PhD diss., Eindhoven University

of Technology 2001, ISBN-90-386-2666-5.

[Tho(1998)] R. E. Thoms, and A. J. Rosa. The analysis and design of linear circuits.

ISBN-0-13-535379-7, 1998, pp. 485-487.

[Win(2007)] G. J. J. Winands. Efficient streamer plasma generation. PhD diss., Eindhoven

University of Technology, 2004, ISBN-978-90-386-1040-5.

[Yan(2003)] K. Yan, E. J. M. van Heesch, S. A. Nair, and A. J. M. Pemen. A triggered

spark-gap switch for high-repetition rate high-voltage pulse generation. Journal of

Electrostatics 57 (2003), pp. 29-33.


Technology, 2001, ISBN-90-386-1870-0.

[Zha(1999)] J. Zhang, J. Dickens, M. Giesselmann, J. Kim, E. Kristiansen, J. Mankowski,

D. Garcia, and M. Kristiansen. The design of a compact pulse transformer.

Proceedings of 12th IEEE International Pulsed Power Conference, June 1999, pp.

704-707.

Chapter 6 Exploration of using semiconductor

switches and other circuit topologies

In this chapter, exploration of utilizing semiconductor switches in the TLT

based multiple-switch circuit is presented. The application of thyristors has

been verified on a small-scale testing setup. Through use of a BOD (Break

Over Diode), the transient overvoltage is no longer problematic. And the

multiple-switch technology provides an excellent current balance among

individual devices. A circuit topology for using MOSFET/IGBT is also

proposed. In addition, other multiple-switch circuit topologies (i.e.

multiple-switch inductive adder and magnetically coupled multiple switches)

are presented and analyzed.

108 Chapter 6

6.1 Synchronization of multiple semiconductor switches

As discussed previously, one characteristic of the multiple-switch technology is that

the closing of the first switches leads to an overvoltage over the switches that are not yet

closed. This is very helpful to the synchronization process when spark gap switches are

used. However, when semiconductor switches (thyristor, MOSFET/IGBT) are used, the

transient overvoltage can easily damage them. Precautions are needed to protect

semiconductor switches against transient overvoltages.

6.1.1 Thyristors

Load

Fig. 6.1 Schematic diagram of the testing setup with three thyristors

The synchronization of multiple thyristors has been verified on a small-scale testing

setup with three thyristors, as shown in Figure 6.1. Three identical capacitors C1-C3 are

charged in parallel via resistors R1-R6, and interconnected to a three-stage TLT via three

thyristors Th1-Th3. The transmission lines Line1-Line3 are made from coaxial cables

(Z0=50 Ω) wound on ferrite toroids. And they are connected in parallel to a resistive load

at the output side. Thyristor Th1 is manually triggered by closing switch S. The other two

thyristors Th2 and Th3 are used as self triggering switches (like spark gap switches) by

putting a break-over diode (BOD) in series with a resistor RT between their anodes and

gates [Law(1988)]. BOD is a gateless thyristor. It is designed to break down and conduct

at a specific voltage in excess of several kVs and is used in protection applications. When

the transient overvoltage across Th2 and Th3 exceeds the BOD breakover voltage (which

is chosen below the voltage rating of thyristors), the BOD becomes conductive and

provides a trigger current, which turns on the thyristor. The value of this trigger current is

limited by the resistor RT, in series with the BOD. Once the thyristor is turned on, the

Exploration of using semiconductor switches and other… 109

parallel-connected RC snubber will provide the holding current to keep it conductive until

all thyristors are closed. Three diodes D1-D3 are used to complete the energy transfer from

the capacitors to the load when oscillation occurs. Within the present testing circuit, two

diacs stacked in series were used as BODs, with a clipping voltage of about 90-100 V. C1-

C3 have values of about 1.88 µF; RT is 5 kΩ; R and C are 1 kΩ and 2 nF respectively; the

resistance value of the load is about 1.25 Ω; and the charging resistors R1-R6 are about

7 kΩ.

Figure 6.2 shows the typical voltages over the thyristors (Th2 and Th3) and the

switching current in Th1. They clearly show the working process of the thyristors before,

during and after the synchronization. Initially, the capacitors are charged to 60 V.

Thyristor Th1 was closed first by closing switch S manually. As expected, the closing of

the first Th1 leads to an overvoltage across thyristors Th2 and Th3, which forces the two

BODs to conduct and turn on Th2 and Th3 sequentially within a time interval of 5 µs. The

voltage over Th3 when it closed was 100 V, which is below the maximum value of 180 V,

since the BOD already broke down before the maximum value has been reached. During

the closing process, the switching current in Th1, as shown in Figure 6.2, was very small

due to the large inductance formed by the coaxial cables, which prevents the discharging

of the capacitors. After all thyristors have been closed, the cables behave like a current

balance transformer and the switching current increases and the capacitors discharge into

the load rapidly and simultaneously.

Fig. 6.2 Typical voltages over thyristors Th2 and Th3 and the switching current in Th1

before, during and after the synchronization process in Fig. 6.1

110 Chapter 6

Fig. 6.3 Typical switching currents in thyristors Th1-Th3, respectively in Fig. 6.1 (they are

shifted from each other for the clarity; actually they are simultaneous and identical)

Fig. 6.4 Relationship between the switching current and the output current in Fig 6.1 (they

are shifted from each other for the clarity; actually they are simultaneous)


Figure 6.3 shows the switching currents in all thyristors Th1-Th3. Note that the three

curves are shifted in time for clarity; actually they overlap (see small plot within the

figure). As can be seen, the time needed for all switches to close is about 5 µs, however,

the switching currents are simultaneous and identical. Figure 6.4 gives the relationship

between the switching current and the output current. Note that, again, both curves are

shifted in time. It can be seen that they are simultaneous, and the output current is three

times the switching current, as expected.

It can be seen that by using BODs, overvoltage is no longer a problem for using

thyristors in the multiple-switch circuit. Moreover, an excellent current balance can be

realized. Today, optical triggered thyristors with integrated BODs are available [Sch(1996)

and Prz(2003)]. It is believed that by using the multiple-switch technology, pulses on the

order of microseconds can be generated that meet various voltage and current

requirements, e.g. the large-current (in excess of several hundreds kAs) pulse for

electrohydraulic spark plasma [Yan (2004)].

Fig. 6.5 Equivalent circuit of the three-switch circuit in Fig. 6.1 for µs-pulse generation

Although the characteristics of the circuit shown in Figure 6.1 are similar to those of

the spark gap switch based topologies discussed in Chapter 2, the equivalent circuit

presented in Section 2.1 is no longer valid. This is because for the relatively long pulse

duration, the lines act as coupled inductors, as shown in Figure 6.5. The circuit model

shown in Figure 6.5 can be used to gain insight into the three-switch circuit shown in

Figure 6.1. Here, three stages of the TLT are represented by three identical 1:1

transformers K1-K3 respectively, and the winding inductance and the mutual inductance

are L and M respectively. From the circuit model shown in Figure 6.5, one can derive the

following equations for different situations: (i) switch S1 is closed and S2-S3 are open; (ii)

switches S1-S2 are closed and S3 is open; and (iii) all switches S1-S3 are closed.

112 Chapter 6

(i) Switch S1 is closed and switches S2-S3 are open

+

−+−==

+=

sLZ

ksLZsVsVsV

ZsL

sVsI

C

SS

C

/2

3/)1(2/1

2

)(3)()(

2

)()(

32

1

(6.1)

(ii) Switches S1-S2 are closed and switch S3 is open

+−

−+−=

+−==

sLZk

ksLZsVsV

ZLks

sVsIsI

CS

C

/2)2(

3/)1(2/21)(3)(

2)2(

)()()(

3

21

(6.2)

(iii) All three switches S1-S3 are closed

=

+−===

)(3)(

3)1(2

)()()()(

1

321

sIsI

ZLks

sVsIsIsI

Load

C

(6.3)

In the above equations, Z is the load impedance; k is the coupling coefficient of the

transformers; VC(s) is the Laplace form of the voltage on the capacitors; I1(s), I2(s), I3(s),

and ILoad(s) are the Laplace forms of the currents in switches S1-S3 and in the load

respectively; VS2(s) and VS3(s) are the Laplace forms of voltages on switches S2 and S3

respectively. Under the assumption that k≈1, from (6.1-3) one can conclude that: (i) when

the first switch S1 is closed and the other two switches S2-S3 are open, the current in S1

will be negligible (as shown in Figure 6.2) when ωL>>Z; the closing of the first switch S1

will lead to an overvoltage over the other switches (S2-S3) that are open (as shown in

Figure 6.2), and the theoretical voltages on S2-S3 could by up to about 1.5 times the

charging voltage; (ii) when two switches S1-S2 have been closed and while switch S3 is

open, the switching current in S1-S2 can be still kept very small (as shown in Figures 6.2-

6.4) provided that ωL>>Z; and the voltage on S3 will continue to increase (as shown in

Figure 6.2), theoretically it can be up to about 3 times the charging voltage; (iii) after all

three switches have been closed, the currents in S1-S3 are identical (as shown in Figure 6.3)

and determined by the leakage inductance and the load; and the current in the load is equal

to three times the current in each switch, as shown in Figure 6.4; and the discharging of

each capacitor can be represented by an equivalent circuit model shown in Figure 6.6,

where the capacitor discharges into the load with a value of 3Z via an inductance 2(1-k)L.

Fig. 6.6 Equivalent circuit model for each capacitor after all switches are closed


The three-switch circuit topology shown in Figure 6.5 can be extended to any number

of switches (m). After all m switches have been closed, the current in each switch and the

current in the load can be expressed as (according to (6.3)):

mjwhere

smIsI

mZLks

sVsI

Load

C

j...2,1

)()(

)1(2

)()(

1

=

=

+−=

(6.4)

6.1.2 MOSFET/IGBT

C H5

CH8

C H10

Fig. 6.7 Schematic diagram of the circuit using MOSFET/IGBT

A circuit topology using multiple MOSFETs/IGBTs is shown in Figure 6.7. Diodes

are connected between the cathodes of the switches and the negative ends of the

capacitors. The closing of the first switches will cause the diodes of the switches that are

not yet closed to become forward biased and thus conducting. Consequently, the current

will flow via the diodes and the voltage blocked by these switches equals the charging

voltage. However, when the switches are closed the corresponding diodes become

reversed biased and open, and the discharging of the capacitors starts. So, one can see that

by using diodes the overvoltage will never occur over individual MOSFET/IGBTs during

114 Chapter 6

the closing process. However, it is noted that the driving circuits must be synchronized,

and isolated gate circuits are required (e.g. optical trigger), since all the switches are at

different potentials during the closing process.

6.2 Other multiple-switch circuit topologies

6.2.1 Inductive adder

Fig. 6.8 Circuit topologies of three-switch inductive adders


The basic idea of the previously described multiple-switch circuits can be also applied

for the conventional inductive adder circuit (see Section 1.2.2), thus leading to new

multiple-switch inductive adders, as shown in Figure 6.8. Capacitors C1-C3 are

interconnected to the primary windings of transformers K1-K3 via the switches S1-S3. At

the secondary sides, the secondary windings can be put in series to obtain high voltage as

shown in Figure 6.8 (a), or in parallel to produce large current as shown in Figure 6.8 (b).

Fig. 6.9 Simulated results for the circuit in Figure 6.8 (a) (C1=C2=C3=1 µF; the load

resistance is 20 Ω; primary and secondary inductances of all transformers are 1 mH,

and the coupling coefficient is 1; stray inductance at the primary side is 1 µH per stage;

the time delay between two switches is 3 µs)

In principle, the characteristics of the circuits shown in Figure 6.8 are similar to those

of the TLT based multiple-switch circuit topologies. Figure 6.9 gives an example of the

simulated results of the circuit in Fig. 6.9 (a). Here the values of the capacitors C1-C3 are

1 µF; the resistance of the load is 20 Ω; the primary and secondary inductances of all

transformers are 1 mH, and the coupling coefficient is 1; the stray inductance caused by

the connection loop at the primary side is 1 µH per stage; the time delay between two

switches is 3 µs. As expected, the closing of the first switch leads to an overvoltage over

the switches that are not yet closed; during the closing process the discharging of the

capacitors is prevented due to the interconnection. After all three switches have been

closed, the capacitors discharge simultaneously to the load via the pulse transformers. The

voltage on the load is equal to three times that on the primary sides of the transformers.

116 Chapter 6

6.2.2 Magnetically coupled multiple-switch circuits

Fig. 6.10 Topologies of the magnetically coupled three-switch circuits

Figure 6.10 shows topologies of magnetically coupled three-switch circuits. Three

identical transformers are used to synchronize multiple switches and to ensure the balance

of currents among the multiple switches. The primary windings are connected in series

with the three switches S1-S3; the three secondary windings are interconnected in series

with each other. The circuit topology can be used to drive independent loads, as shown in

Figure 6.10 (a), or to drive a single load, as shown in Figure 6.10 (b). The basic principle

of the synchronization of multiple switches is similar to that of the previously described

circuits, namely the closing of the first switches leads to an overvoltage over the switches

that are not yet closed and forces them to be closed subsequently. After all the switches

have ignited, the energy will be transferred into the load(s) via the three switches

simultaneously and identically. [Pem(2007)] gives a comprehensive discussion about the

characteristics of the topology for driving multiple plasma torches (similar to the situation

in Figure 6.10 (a)).


Suppose that the primary and secondary inductances and the coupling coefficient of

the transformers are L1 and L2, and k respectively. Then, one can derive the following

equations for the circuit in Figure 6.10 (a) under different situations: (i) switch S1 is closed

and switches S2-S3 are open; (ii) switches S1-S2 are closed and switch S3 is open; and (iii)

all switches S1-S3 are closed.

(i) Switch S1 is closed and switches S2-S3 are open

+−+==

+−=

11

2

2

1

2

1

1

)3(1)()()(

)3/1(

)()(

32 sLZk

ksVsVsV

ZksL

sVsI

SS

(6.5)

(ii) Switches S1-S2 are closed and switch S3 is open

( )( ) ( )( )( )

( )( ) ( )( )( )

( )

++−+−

+++=

++−+−

+=

++−+−

+=

2

1

2

21121

22

121

2

3

2

1

2

21121

22

1

11

2

2

1

2

21121

22

1

12

1

/3/))(3()23(

/)(21)()(

//3/13/21

/1)()(

//3/13/21

/1)()(

LsZZsLZZkk

sLZZksVsV

LsZZsLZZkksL

sLZsVsI

LsZZsLZZkksL

sLZsVsI

S

(6.6)

(iii) All three switches S1-S3 are closed

( ) ( )

( ) ( )

( ) ( )

( )

++=

+

++

−+

++

−+−

+

++

=

+

++

−+

++

−+−

+

++

=

+

++

−+

++

−+−

+

++

=

)()()(3

1)(

31

3

21)1(

1)(

)(

31

3

21)1(

1)(

)(

31

3

21)1(

1)(

)(

321

2

1

sec

3

1

3

321

22

133221

2

1

321

2

2

1

2

1

2

21

1

21

3

3

1

3

321

22

133221

2

1

321

2

2

1

2

1

2

31

1

31

2

3

1

3

321

22

133221

2

1

321

2

2

1

2

1

2

32

1

32

1

1

1

1

sIsIsIL

LksI

Ls

ZZZ

Ls

ZZZZZZk

sL

ZZZkksL

Ls

ZZ

sL

ZZsV

sI

Ls

ZZZ

Ls

ZZZZZZk

sL

ZZZkksL

Ls

ZZ

sL

ZZsV

sI

Ls

ZZZ

Ls

ZZZZZZk

sL

ZZZkksL

Ls

ZZ

sL

ZZsV

sI

(6.7)

118 Chapter 6

Fig. 6.11 Typical switching currents in Fig. 6.10 (a) under the condition of ωL1>>Z1,

ωL1>>Z2 and ωL1>>Z3 (this figure is reproduced from [Pem(2007)])

Fig. 6.12 Typical switching currents in Fig. 6.10 (a) when the condition of ωL1>>Z1,

ωL1>>Z2 and ωL1>> Z3 failed (this figure is reproduced from [Pem(2007)])


In the equations (6.5-7), Z1, Z2 and Z3 are the impedance of each load respectively; V(s)

is the Laplace form of the voltage source; I1(s), I2(s), I3(s), and Isec(s) are the Laplace

forms of the currents in switches S1-S3 and in the secondary windings of the transformers

respectively; VS2(s) and VS3(s) are the Laplace forms of the voltages on switches S2 and S3

respectively. Under the assumption that k≈1, from (6.5-7) one can conclude that: (i) when

the first switch S1 is closed and the other two switches S2-S3 are open, the current in S1

will be negligible if ωL1>>Z1; the closing of the first switch S1 leads to an overvoltage

over the other switches (S2-S3) that are open, and the theoretical voltages on S2-S3 could

be up to about 1.5 V(s); (ii) when two switches S1-S2 have been closed and while the

switch S3 is open, the switching current in S1-S2 can be still kept very small provided that

ωL1>>Z1 and ωL1>>Z2; and the voltage on S3 can theoretically be up to about 3 V(s); (iii)

after all three switches have been closed, the currents in S1-S3 are almost identical when

the conditions of ωL1>>Z1, ωL1>>Z2 and ωL1>>Z3 are matched.

Figures 6.11 and 6.12 give examples of the typical switching currents when three

independent plasma torches were used [Pem(2007)]. As shown in Figure 6.10, when the

conditions of ωL1>>Z1, ωL1>>Z2 and ωL1>>Z3 are met, the currents are almost identical

despite the fact that the impedance of the three plasma torches will probably not be the

same. However, when the impedances of the torches become relatively high and this

condition failed, a current imbalance occurred, as shown in Figure 6.11.

When the three loads have an identical impedance (i.e. Z1=Z2=Z3=Z) the current in

each switch will be always the same, and from (6.7) one can derive:

ZLks

sVsIsIsI

+−===

1

2321)1(

)()()()( (6.8)

From the above equation, one can represent the discharging of each switch by the circuit

shown in Figure 6.13.

Fig. 6.13 Equivalent circuit for each switch of the circuit in Figure 6.2.3 (a) after

the synchronization under the condition Z1=Z2=Z3=Z

With regard to the circuit topology in Figure 6.10 (b), the characteristics are similar to

those of the circuit in Figure 6.10 (a). When the impedances of the three switches are

much smaller than the impedance ωL1, the currents in the three switches will be almost

the same. Especially when the impedances of the three switches are negligible, the

currents in the three switches can be expressed as:

120 Chapter 6

ZLks

sVsIsIsI

3)1(

)()()()(

1

2321+−

=== (6.9)

References

[Law(1988)] H. M. Lawatsch, and J. Vitins. Protection of thyristors against overvoltage

with Breakover Diodes. IEEE Transactions on Industry Applications Vol. 24, No.

3, May/June 1988.

[Pem(2007)] A. J. M. Pemen, F. J. C. M. Beckers, L. J. H. van Raay, Z. Liu, E. J. M. van

Heesch, and P. P. M. Blom. Electrical characteristics of a multiple pusled plasma

torch. Proceedings of IEEE Pulsed Power and Plasma Science Conference June

2007.

[Prz(2003)] J. Przybilla, R. Keller, U. Kellner, C. Schneider, H. -J. Schulze, F. -J.

Niedernostheide, and T. Peppel. Direct light-triggered solid-state switches for

pulsed power applications. Proceedings of 14th IEEE Pulsed Power Conference

June 2003, Vol. 1, pp. 150-154.

[Sch(1996)] H. –J. Schulze, M. Ruff, and B. Baur. Light triggered 8 kV thyristors with a

new type of integrated breakover diode. Proceedings of 8th International

Symposium of Power Semiconductor Devices and ICs May 1996, pp. 197-200.



Oxid. Technol. Vol. 7, No. 2, 2004.

Chapter 7 Conclusions

7.1 Conclusions

The main aim of the investigation is to gain insight into the mechanisms and

characteristics of a new multiple-switch pulsed power technology and to realize efficient

(>90%) generation of large pulsed power (500 MW-1 GW) with a short pulse width (~50

ns) and a fast rise-time (~10 ns) using this technology. Based on the investigations, the

following conclusions can be drawn.

7.1.1 TLT based multiple-switch circuit technology

(a) By interconnecting multiple spark gap switches via a transmission line transformer

(TLT), multiple spark gap switches can be synchronized automatically. The

synchronization process is quite unique, and typically has two distinctive phases. Once

one of multiple spark gap switches is triggered, the first phase starts. The synchronization

process is as follows: the closing of the first switch(s) leads to an overvoltage over the

switches that are not yet closed. This overvoltage forces them to close sequentially within

a nanosecond time scale (typically 10-50 ns). During the first phase, the energy storage

components (e.g. capacitors or PFLs) can hardly discharge. When all the switches have

been closed, the first phase ends and the second phase starts. And now all stages of the

TLT are used in parallel equivalently, and the capacitors discharge simultaneously and

identically into the load(s) via the TLT.

(b) The secondary mode impedances Zs of the TLT play an important role in the

synchronization of multiple spark gap switches. It must be much larger than the

characteristic impedance Z0 of each stage of the TLT (i.e. Zs>>Z0), to guarantee a high

overvoltage over the switches that are not yet closed and to prevent the leak of the energy

storage capacitors during the synchronization process.

When a large number of spark gap switches, the overvoltage induced by the closing of

the first switch can be too small for a fast and proper closing of the second switch. To

ensure proper synchronization in this case, a higher secondary mode impedance can be

used for specific stages of the TLT. In this way, a higher overvoltage will be provided to

the second switch, causing it to close more easily. This can be realized by using magnetic

cores around specific stages of the TLT, as successfully applied in the ten-switch system.

122 Chapter 7

(c) The synchronization of multiple spark gap switches does not depend on the

different configurations that can be realized at the output side of the TLT. The output of

the TLT can be connected to a load in a series configuration (to obtain a high voltage

pulse), or in a parallel configuration (to obtain a large current). The outputs can also be

connected to multiple independent loads. Moreover, the synchronization is independent of

the type of the load. This was confirmed by experiments on matched resistive loads and

on a more complex non-matched load, namely a corona plasma reactor.

(d) An interesting feature of the analyzed topology is that the rise-time of the output

pulse is mainly determined by the last switch that will close. This implies that only one of

the multiple switches has to be optimized for very fast switching (e.g. by applying a

multiple-gap spark gap switch), provided that the order of switching of the switches can

be controlled (e.g. by using varying values for the secondary mode impedances).

(e) The peak output power of the multiple-switch circuit is a nonlinear function of the

damping coefficient (i.e. stray inductance) of the input connection loop of the TLT. The

higher the damping coefficient, the larger the peak output power becomes. The low output

power of the four-switch pilot setup (using a TLT with four parallel coaxial cables per

stage) is mainly caused by the low damping coefficient of the input loop of the TLT.

(f) Compared with using a TLT with multiple parallel coaxial cables per stage (and

thus a relatively low characteristic impedance per stage, as for the four-switch system),

using a TLT with one single coaxial cable per stage is more effective in generating large

pulsed power, due to the following advantages: (i) it is easier to realize compact

connections; (ii) each stage has a larger characteristic impedance Z0, thus the damping

coefficient ξ is higher; (iii) a low input impedance Zin can also be obtained when a large

number of stages are used.

(g) Through use of the present multiple-switch technology, an efficient repetitive large

pulsed power generation with a short pulse and a fast rise-time has been achieved on a

ten-switch prototype system. This prototype consists of ten high-voltage capacitors, ten

high-pressure spark gap switches, and a ten-stage TLT with a single coaxial cable per

stage. Experiments show that the ten switches can be synchronized within about 10 ns.

This system is able to produce a pulse with a rise-time of about 10 ns and a width of about

55 ns. It has a good reproducibility. More than 800 MW output power was realized. The

energy conversion efficiency of more than 90% has been obtained.

(h) Not only spark gap switches but also semiconductor switches can be applied for

the multiple-switch circuits analyzed in this dissertation. Either short pulses (ns, by using

spark gaps or MOSFET switches) or longer pulses (µs, by using thyristors) can be

generated this way. Precautions must be taken to limit the overvoltages on the

semiconductor switches, for instance by applying break-over diodes across the

semiconductor switches.

Conclusions 123

7.1.2 Multiple-switch Blumlein generator

The synchronization of multiple switches was also successfully applied for the widely

used Blumlein configuration. Using this circuit, square pulses can be generated over a

matched load with an amplitude that is equal to the charging voltage of the lines. The

characteristics of the synchronization of the multiple switches in a Blumlein configuration

are the same to those of the TLT based multiple-switch circuit. This has been successfully

used to generate an efficient corona plasma. In addition, the investigated multiple-switch

Blumlein circuit is highly flexible in allowing the choice of different output configurations

and polarity of the output pulse (positive, negative or bipolar).

7.1.3 Repetitive resonant charging system

(a) When the low-voltage capacitor CL of the resonant capacitor charging circuit has a

value lower than the matching value of n2CH, the charging voltage on the high-voltage

capacitor CH can be linearly tuned by adjusting the value of CL (here n is the

transformation ratio of the pulse transformer). For the situation that CL≥ n2CH, the high-

voltage capacitor CH will be charged to a constant value, which does not depend on CL.

(b) When a magnetic core transformer is used in a resonant charging circuit, the

energy conversion efficiency from the low-voltage capacitor CL to the high-voltage

capacitor CH can be as high as 99%. The required minimal volume of magnetic material to

keep the core unsaturated (for a given energy per pulse) is determined by the coupling

coefficient of the transformer, and is independent of the number of turns of the primary

winding.

(c) We successfully applied a pulse transformer with a magnetic core that was

constructed from many small ferrite blocks, glued together with epoxy resin. This allows a

high degree of freedom in core size and shape. The multiple air gaps that are present due

to the gluing of the blocks could be kept very small. Doing so, a high coupling coefficient

of over 99.6% could be obtained.

7.2 Outlook

By using this technology, an efficient pulsed power source has been realized with

specifications that are far beyond the state-of-the-art. Very high peak power has been

obtained within a nanosecond time scale, and at high repetition rates. The low output

impedance of the ten-switch system provides very large output currents. Multiple switches

are successfully used, which share the heavy switching duty and are synchronized within

nanoseconds. Based on literature [Dic(1993), Don(1989), Leh(1989)], the erosion rate was

observed to be a nonlinear function of the transferred charge per shot (i.e. switching

current). When the transferred charge per shot is reduced by a factor n, the erosion rate

can be reduced by a factor over n2. Thus, the lifetimes of the discribed multiple-switch

124 Chapter 7

systems are expected to be extended to over n2 times, compared with a single-switch

system with the same switching duty.

In terms of the characteristics of the technology, it can be used in many applications

such as large-scale plasma generation [Win(2007)], plasma generation with a high volume

density of streamers or for the generation of EUV (Extreme UV, typically 13.5 nm

wavelength) [Kie(2006)]. Particularly the ten-switch system as described in this

dissertation is very suitable for these applications, as well as for other applications, due to

its capacity for delivering a large current. An example is the generation of very large

currents (several hundreds of kA) in electrohydraulic discharges for high-resolution

seismic imaging or water treatment [Yan(2004), Sat(2006)]. It can also be used for a

plasma reactor with a large capacitance [Yan(2001)] due to its capacity for a low output

impedance. Of course, it can also be used for loads with a higher impedance (e.g.

broadband EM-sources) since this technology allows a high degree of freedom in

choosing different output impedances.

From an industrial application point of view, the system can be made more cost-

effective. Within the present prototype system, the spark gaps were flushed with a

pressurized air flow for operation at higher repetition rates. Replacing the present spark

gap switches with multiple gap switches filled with a gas with a light molecular weight

(e.g. H2), no expensive compression and flushing system is required, and the system will

become cheaper, while fast switching, a high repetition rate and a high energy conversion

efficiency can be obtained as well.

References

[Dic(1993)] J. C. Dickens, T. G. Engel, and M. Kristiansen. Electrode performance of a

three electrode triggered high energy spark gap switch. 9th

IEEE International

Pulsed Power Conference 21-23 June, 1993, pp. 471-474.

[Don(1989)] State-of-the-art insulator and electrode materials for use in high current high

energy switching. IEEE Transactions on Magnetics Vol. 25, Issue 1, pp. 138-141.

[Kie(2006)] E. R. Kieft, Transient behavior of EUV emitting discharge plasmas a study by

optical methods. PhD diss., Eindhoven University of Technology (available at

http://alexandria.tue.nl/extra2/200512577.pdf).

[Leh(1989)]F. M. Lehr, and M. Kristiansen. Electrode erosion from high current moving

arcs. IEEE Transactions on Plasma Science Vol. 17, No. 5, October 1989.

[Sat(2006)] B. R. Locke, M. Sato, P. Sunka, M. R. Hoffmann, and J. -S. Chang.

Electrohydraulic Discharge and Nonthermal Plasma for Water Treatment. Ind. Eng.

Chem. Res. 2006, 45, pp. 882-905.

[Win(2007)] G. J. J. Winands. Efficient streamer plasma generation. PhD diss., Eindhoven

University of Technology. 2007, ISBN-978-90-386-1040-5.


Technology, 2001 (available at http://alexandria.tue.nl/extra2/200142096.pdf).

Conclusions 125



Oxid. Technol. Vol. 7, No. 2, 2004, pp. 116-122.

Appendix A. Coupled resonant circuit

Fig. A.1 Coupled resonant circuit

A coupled resonant circuit, as shown in Figure A.1, is frequently used in pulsed power

systems to increase the charging voltage. Initially, the low-voltage capacitor CL is charged

to a voltage of V0. By closing switch S, the high-voltage capacitor CH will be charged by

CL via the transformer TR. From the circuit in Fig. A.1, one can derive the following

equations:

=++

=++

∫

∫

0)(1

)()(

)(1

)()(

0

2221

0

0

1211

t

H

t

L

dttIC

tIdt

dLtI

dt

dM

VdttIC

tIdt

dMtI

dt

dL

(A.1)

where L1, L2 and M are the primary, secondary, and mutual inductance of the transformer

Tr. The Laplace expressions of the above equations can be written as:

=++

=++

0)()1

()(

)()()1

(

221

0

211

sIsC

sLssMI

s

VssMIsI

sCsL

H

L (A.2)

From (A.2), one can derive:

−⋅⋅+−

=

+−

+⋅

−⋅

−=

)]sin()sin([4)1(

)(

)()(

1

)1()(

2211

1

2

22

0

2

2

2

2

2

2

2

1

2

2

1

2

1

2

22

21

0

2

ttL

L

TkT

VkCtI

sskLL

kVsI

H ωωωω

ω

ω

ω

ω

ωω (A.3)

128 Appendix A

where)1(2

4)1()1(1,

2

22

2

2

2

2

1k

TkTT

CLH

−

+−+⋅=

mωω ,

L

H

CL

CLT

1

2= and

21LL

Mk = . And then

the voltage VH(t) on CH can be calculated as:

)]cos()[cos(4)1(

)(1

)(12

1

2

22

0

0

2tt

L

L

TkT

kVdttI

CtV

t

H

Hωω −⋅⋅

+−== ∫ (A.4)

A.I Complete energy transfer∗

The voltage VH on CH has the maximum value when the following conditions are

matched.

=

±=

1)cos(

1)cos(

1

2

mt

t

ω

ω, namely

...3,2,1,0,)12(

1

2=

=

++=nmwhere

mt

nmt

πω

πω (A.5)

From the equation above, one can derive the following equations:

++=

+

−−=

⋅+−

±=

2

2

1

2

22

0

max

)12

(

)1(

)1)((

4)1(

2)(

m

nm

T

TTk

L

L

TkT

kVtV

H

α

α

αα (A.6)

For the complete energy transfer, the energy stored in CH when VH reaches its maximum

peak value should be equal to the initial energy stored in CL, i.e.

2

0

1

2

22

2

0

2

2

max 2

1

4)1(

2])([

2

1VC

L

L

TkT

VCktVC

L

H

HH⋅=⋅

+−= (A.7)

From (A.7), one can obtain T=1, namely

HL

CLCL21

= (A.8)

Under the situation of L1CL=L2CH, the voltages VL(t) and VH(t) can be expressed as:

−−

+=

−+

+−=

)]1

cos()1

[cos(2

)(

)]1

cos()1

[cos(2

)(

0

0

k

t

k

t

C

CVtV

k

t

k

tVtV

H

L

H

L

ωω

ωω

(A.9)

∗M. Denicolai. Optimal performance for Tesla transformers. Review of Scientific

Instruments Vol. 73, No. 9, September 2002, pp. 3332-3336.

Coupled resonant circuit 129

where ω=1/(L1CL)1/2

=1/(L2CH)1/2

. With specific values of the coupling coefficient k, the

complete energy transfer will be realized. And k is determined by

1

1

+

−=

α

αk (A.10)

The voltage on CH, when the complete energy transfer is finished, will be

1

2

00)(

L

LV

C

CVtV

H

L

MaxH== (A.11)

From the discussion above, it can be seen that completely transferring energy from CL

to CH requires both L1CL=L2CH and specific values of k. The specific values of k are

determined by the numbers m and n. Different m and n will give different values of k;

therefore, there are a lot of usable values of k. As an example, Table A.1 gives some

specific values of k for complete energy transfer.

Table A.1 some specific values of k for complete energy transfer

Fig. A.2 (a) k=0.117 when m=8 and n=0; complete energy transfer is realized after 4.5

primary oscillations

130 Appendix A

Fig. A.2 Typical examples of complete energy transfer in Fig. A.1 when L1CL=L2CH; and

L1=2 mH, L2=200 mH, CL=1 µF, CH=10 nF, and V0=1 kV; VH(t)|max=10 kV

Moreover, the number of primary oscillation cycles required for complete energy

transfer is dependent on k, namely m and n. And it is equal to (m+2n+1)/2. For instance,

when k=0.117, 0.6 and 0.969, the numbers of primary oscillation cycles required for

complete energy transfer are 4.5, 1, and 4 respectively, as shown in Figure A.2. It is noted

that when k=0.6 (m=1 and n=0), only one primary oscillation cycle is needed for complete

transfer. And it is the minimal one. This is why k=0.6 is normally adopted for air-core

Tesla transformers.


A.II Effect of the coupling coefficient k on the first peak value of VH

From Figure A.2, one can see that the first peak value of VH varies with the coupling

coefficient k. To further evaluate the effect of k, the first peak value of VH was

numerically calculated according to (A.9) at different values of k, under the condition of

L1CL=L2CH. And the values of ωt, efficiency η, and VL at the moment when VH reaches

its first peak value were calculated as well. All the calculated results are shown in Table

A.2 and plotted in Figures A.3 and A.4. Here the efficiency η is defined as the energy

absorbed by CH to the energy stored in CL initially.

Table A.2 Numerical calculations at different values of k under L1CL=L2CH (in Fig. A.1)

132 Appendix A

Fig. A.3 Effect of k on the values of VL and VH in Fig. A.1 at the moment

VH reaches its first peak value

Fig. A.4 Effect of k on the conversion efficiency η in Fig. A.1 at the moment

VH reaches its first peak value

Figures A.3 and A.4 clearly show that the voltage VH and the efficiency η increase as

k increases. The higher the coupling coefficient k, the higher the first peak value of VH

and the efficiency η. When k is close to 1, almost all the energy stored in CL can be

transferred to CH at the moment when VH reaches it first peak value.


A.III Efficient resonant charging

Fig. A.5 Resonant charging circuit with a magnetic-core transformer

Figure A.5 shows the resonant charging circuit used in this dissertation, where a diode

D is used on the secondary side. In this way, the voltage on CH when the charging finishes

is the fist peak value of VH in the circuit in Fig. A.1. From the above discussions, one can

conclude that for efficient energy transfer using the circuit in Figure A.5, the coupling

coefficient k needs to be as high as possible. When a magnetic-core transformer is used,

the coupling coefficient k of over 0.996 could be obtained. Thus, the feasible energy

conversion efficiency of the circuit in Figure A.5 could be up to about 99%. In addition,

by means of the circuit in Figure A.5, the voltage on CH is unipolar, which makes it easy

to use semiconductor or magnetic switches. With regard to how to design a magnetic

transformer for such a resonant circuit, please see Section 5.3.

Appendix B. Repetitive resonant charging

Fig. B.1 (a) Main circuit of the resonant charging system; (b) Equivalent circuit model,

where CH is transferred into the primary side of TR and C’=n2CH

Figure B.1 shows the main circuit of the resonant charging system used within this

dissertation and its equivalent circuit. Initially, the storage capacitor C0 (C0>>CL) is

charged up to a voltage of V0, and it remains constant. The circuit accomplishes one

charging cycle through four steps as described in Section 5.2. As discussed in Section

5.3.2, by representing the transformer TR as an ideal transformer with a ratio of n and two

uncoupled inductors and transferring the component on the secondary side of TR to the

primary side, one can derive the equivalent circuit as shown in Figure B.1 (b). Here n is

equal to k(L2/L1)1/2

; L1 and L2 are the primary and the secondary inductance of the TR

respectively; k is the coupling coefficient of the TR; and C’=n2CH.

Assuming the coupling coefficient is large enough (e.g.>0.996), L1 will be much

larger than the inductance L1(1-k2)/k

2 and most of the energy (>99%) stored in CL will be

136 Appendix B

transferred into C’ and only a very tiny part (<1%) will be absorbed by L1 during one

charging cycle. Ignoring L1 and energy losses during the charging cycle, one can derive

the following expressions for the situation of CL≥C’=n2CH under the assumption that the

voltage on CH is completely discharged before each charging cycle starts.

)1('

'2)(

0

0

0

0

0 −⋅+

−⋅

+

−−⋅

+= jV

CC

CC

CC

CCV

CC

CjV L

L

L

L

L

L

L (B.1)

)('

')( jV

CC

CCjV L

L

L

L ⋅+

−=∆ (B.2)

)('

2)(' jV

CC

CjV L

L

L

C ⋅+

⋅= (B.3)

)()('

jVnjVCH

⋅= (B.4)

In the above equations, j refers to the charging cycle sequence number; VL(j) is the

voltage on CL when the charging from C0 to CL is finished during charging cycle j; ∆VL(j)

and VC’(j) are the voltages on the CL and on the C’ when charging from CL to C’ is

complete; VH(j) is the obtained voltage on CH during charging cycle j. Since C0>>CL, (B.1)

can be approximately expressed as:

)1('

'2)( 0 −⋅

+

−−≈ jV

CC

CCVjV L

L

L

L

...2(2(2000

+⋅+⋅+= VVV εε

...1(2 32

0++++⋅= εεεV (B.5)

In the above equation,32

32

CC

CC

+

−−=ε , and 1<ε . When the charging cycle sequence

j→∞, one may have:

00

'

1

12)(lim V

C

CCVjV

L

L

Lj

⋅+

=−

⋅=∞→ ε

(B.6)

According to (B.2-4), one can derive the following equations:

0

')(

'

'lim)(lim V

C

CCjV

CC

CCjV

L

L

L

L

L

jL

j⋅

−=⋅

+

−=∆

∞→∞→ (B.7)

0' 2)('

2lim)(lim VjV

CC

CjV L

L

L

jC

j=⋅

+

⋅=

∞→∞→ (B.8)

0'

2)(lim)(lim nVjVnjVC

jH

j=⋅=

∞→∞→ (B.9)

From the above equations, one can see that the voltages on CL and CH will become

stabilized. Actually, after 3-5 shots they already approach the steady values.

Appendix C. Calibration of current probe

Fig. C.1 (a) Schematic diagram of the current probe; (b) equivalent circuit; (c) simplified

circuit model, where the transmission line T is represented by a resistor Z and by a voltage

source 2V in series with a resistor Z at both sides respectively

Figure C.1 shows the current probe used on the ten-switch prototype system. It is

based on a Rogowski coil and an integrator. The Rogowski coil is connected to an

integrator via a transmission line T, which is terminated with a resistor R1. The integrator

is composed of a resistor Ri and a coaxial capacitor Ci and connected directly to the

oscilloscope with an 1 MΩ input impedance. Figure C.1 (b) shows the equivalent circuit

of the current probe where M is the mutual inductance between the current I and the coil

and L represents the self inductance of the coil. Representing the transmission line T by a

resistor Z at the left side of T and by a voltage source 2V in series with a resistor Z at the

right side of T, one can derive the simplified circuit model as shown in Figure C.1 (c),

where Z and V are the characteristic impedance of T and the voltage across T at the left

side respectively.

138 Appendix C

From the simplified circuit shown in Fig. C.1 (c), one can derive the following

expression:

ZRZ

LCRwhendtV

k

dt

dVkkVI iiout

out

out ≈>>⋅+⋅⋅+= ∫ 1

2

1 &τ

τ (C.1)

In the above equation, k≈RiCi/M, τ1≈L/Z and τ2≈RiCi. There are three terms at the right

side of (C.1). The first term represents the ideal system; the second term is a correction

factor for the high frequency; the third term is a correction factor for low frequency. To

obtain the actual current, first the obtained signal Vout must be corrected by (C.2); then, by

multiplying by the corrected Vcorrected and the coefficient k, one can derive the actual

current I, as expressed by (C.3).

∫⋅+⋅+= dtVdt

dVVV out

out

outcorrected

2

1

1

ττ (C.2)

corrected

VkI ⋅= (C.3)

Fig. C.2 Calibration of the current probe; current I was measured with a Pearson probe

(model 6600), Vout is the actual signal obtained by the designed probe,

Vcorrected is corrected signal according to (C.2)

Within the designed current probe, a single Rogowski coil, as shown in Figure 5.18,

was adopted. Its self inductance L and mutual inductance M are estimated to be about

0.5 nH. Thus the second term in (C.2) was ignored when the signal Vout was corrected.

The calibration of the designed current probe was carried out on a small pulse generator.

Calibration of current probe 139

The pulse is generated by discharging a 1.3 nF capacitor into a 40 Ω resistive load. The

current I of the pulse was measured with a Pearson current probe (model 6600, bandwidth

120 MHz), and it has a rise-time of 9 ns. The Vout was corrected with τ2=4 µs. Figure C.2

shows typical results of I, Vout and Vcorrected. From the plots shown in Figure C.2, it can be

seen that the tail of the actual signal Vout is negative and does not fit with the current I;

however, after the correction, the signal Vcorrected is in perfect agreement with the current I.

Based on the reference current I and the corrected signal Vcorrected, the coefficient k was

determined according to (C.3), and its average value is about 5475 A/V. Its statistic

deviation, mean error, and maximum error are 37.68 A/V, 0.69%, and 1.76% respectively.

Appendix D. Schematic diagram of high-pressure

spark gap switches

Acknowledgements

First of all, I would like to express my sincere gratitude to Dr. A.J.M. Pemen, my thesis

co-promotor. His constant support and supervision has played a significant role in the

completion of the work. Without his guide and efforts, it is impossible to have the

dissertation in the present form. I also wish to express my sincere thanks to Prof. J.H.

Blom, my first promotor, for his solid support, interest, and valuable remarks.

I am deeply grateful to Prof. K. Yan, who was closely involved in the present work in the

first two and half years. The present work has greatly benefited from his deep insight into

the subject, extensive knowledge and experience, and advices. My sincere thanks to Dr.

E.J.M. van Heesch for inspiring talks and encouragements, which always helped me to

have a deeper understanding of problems I met during the project.

I do very appreciate my second promotor Prof. M.J. van der Wiel, and core committee

members Prof. A.J.A. Vandenput and Prof. J.A. Ferriera, for spending their valuable time

reading the manuscript of the thesis. The present dissertation has greatly benefited from

their valuable remarks and corrections.

I am very indebted to Mr. Ad van Iersel, one of the best engineers in our group. Without

his special talent contribution, it is impossible to convert ideas into practical systems such

as the pulse transformer and the ten-switch system, which are indeed essential for

completing the work. I would also like to express my sincere gratitude to Mr. R.T.W.J.

van Hoppe, for his great help with the calibration of the current probe, installation of the

pulse counter, and experiments carried out on the ten-switch system. My sincere thanks

also go to Dr. L.R. Grabowski for his help with measuring the concentration of the dye

solution. I would also like to thank Dr. E.M. van Veldhuizen and Mr. A.H.F.M. Baede for

sharing their knowledge and experiences on light measurement.

Throughout the project, I have benefited a lot from my colleagues within EPS group. I

would like to thank all of them. In particular I would like to tank Dr. G.J.J. Winands, Dr.

P.A.A.F. Wouters, Ms. D.B. Pawelek, Mrs. L. Cuijpers, Mr. H.M. van der Zanden, Mr.

Huub Bonn÷, and Mr. Arie van Staalduinen for sharing their knowledge and experiences,

common research and assistances.

Curriculum Vitae

Zhen Liu was born on June 06, 1978, in Xiang Cheng, China. In 2000, he completed his

bachelor study at the Department of Electronic Science from Xi’an Jiaotong Univeristy,

China. In 2003, he received his master degree at the Electrical Department from Tsinghua

University, China. His master thesis was awarded as one of the best master theses by

Tsinghua University in 2004. Since November 2003, he started his Ph.D project in the

EPS (Electrical Power Systems) group, TU/e (Technische Universiteit Eindhoven), the

Netherlands. The subject is to develop an efficient large pulsed power supply using a

transmission line transformer based multiple-switch technology.

Multiple-switch pulsed power generation based on a transmission line transformer

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