 Figure 1. Tesla Coil basic schematic diagram |
1. GENERAL
2. BACKGROUND
2.1. Nikola Tesla
2.2. The Tesla Coil
2.3. Applications
2.3.1. Testing of insulating materials
2.3.2. Generation of high-voltage
pulses
2.3.3. Research on lightning discharges
3. TESLA COIL TOPOLOGIES
AND VARIATIONS
3.1. Theory of operation
3.2. Alternative coupling schemes
3.2.1. 3-coils, inductive coupling
3.2.2. 3-coils, series feed
3.3. Static vs. rotary spark gap
3.4. AC vs. DC power supply
3.5. Effect of increased pulse rate
3.6. Pulsed vs. continuous wave
3.7. Tesla Coil physical dimensions
5. DESIGN SOLUTIONS
5.1. Power supply topologies
5.1.1. Conventional stabilized DC power
supply
5.1.2. DC power supply employing a
high-voltage switch element
5.1.3. High-frequency converter
5.2. Power supply selection
6. REFERENCES
The project Thor was started at the High Voltage Institute of HUT (Helsinki University of Technology) on January 1999. Dr. Martti Aro is in charge of project supervision and Marco Denicolai of project development and implementation. Within this project a Tesla resonance transformer is analyzed, designed and built for study and research.
This paper describes the design criteria that led to the selection of the Tesla transformer topology and size, the power supply topology and the spark gap type.
Nikola Tesla was born in Smijlan, Croatia in
1856. He attended the Technical University of Graz, Austria, and
the University of Prague (1879-1880). His first employment was in
a government telegraph engineering office in Budapest, where he
made his first invention, the loudspeaker. In 1882 Tesla went to
work in Paris for the Continental Edison Company, and constructed
his first induction motor.
Tesla moved to America in 1884: in May 1885, George Westinghouse,
head of the Westinghouse Electric Company in Pittsburgh, bought
the patent rights to Tesla's polyphase system of
alternating-current dynamos, transformers, and motors. In 1887
Tesla established his own laboratory in New York City, where he
performed countless experiments included work on a carbon button
lamp, on the power of electrical resonance, and on various types
of lighting.
Tesla also invented fluorescent lights and a new type of steam
turbine, and he became increasingly intrigued with the wireless
transmission of power. A controversy between alternating current
and direct current advocates raged in 1880s and 1890s, featuring
Tesla and Edison as leaders in the rival camps.
In Colorado Springs, where he stayed from May 1899 until early
1900, Tesla made what he regarded as his most important discovery
- terrestrial stationary waves. By this discovery he proved that
the earth could be used as a conductor and would be as responsive
as a tuning fork to electrical vibrations of a certain pitch. He
also lighted 200 lamps without wires from a distance of 25 miles
and artificial lightning with arcs measuring 135 feet.
Tesla had a way of intuitively sensing hidden scientific secrets
and employing his inventive talent, but was quite impractical in
financial matters. Returned to New York in 1900, because of a
lack of funds, his ideas kept remaining in his notebooks, which
are still today examined by engineers for unexploited clues. He
died in 1943, the holder of more than 100 patents.
Among Tesla's inventions, the resonance
transformer occupies a place of its own. Originally named
"Apparatus for transmitting electrical energy" by its
inventor, it was intended for transferring electrical energy
without wires to lamps and possibly other devices. The Tesla
resonance transformer is nowadays better known as Tesla Coil or
simply resonance transformer. In the rest of this paper the Tesla
Coil will be referred to as TC.
A TC is an electrical device capable of developing high
potentials ranging from a few hundreds of kilovolts up to several
megavolts: the voltage produced is not DC but AC, being the
voltage frequency typically 50 - 400 kHz. TCs are typically
operated in pulsed mode, with pulse widths varying from some
nanoseconds up to several hundreds of microseconds according to
the particular application.
In its simpler configuration, a TC is composed by two air-cored
coils, the primary and the secondary. While in conventional
metal-core transformers (50 - 60 Hz) the primary and secondary
voltage ratio is directly related to the windings number of turns
ratio, the output voltage of a TC it is related to primary and
secondary inductance ratio.
TCs have been object of interest during all this century from
different groups of people
in the first half of this century industry have manufactured small-sized TCs to generate high-voltage for a number of classical applications (X-ray generators, electrocution and coagulation for veterinary purposes, etc.). Nowadays the TCs used in most of these applications have been replaced by conventional technology using discrete electronic components.
Research groups have replicated Tesla's original TC designs and produced new ones, according to the increasing number of materials becoming available (plastics and isolators in general). Many attempts have been made to complete the rudimental measurements Nikola Tesla originally performed and provide a robust and proven mathematical model covering all operational principles of TCs.
The spectacular breakouts produced by TCs, that remind very much downsized natural lightning, has attracted the film industry from its very beginning. TCs are still today manufactured and used to produce special effects in movies and theatre shows.
TCs have fascinated a number of hobbyists all around the world that have engaged in building low-cost, small- and medium-sized TCs in their garages. These individuals have given an enormous contribute in demolishing and replacing existing theories about TC operational principles.
Nowadays, applications for Tesla Coils fall within the following categories.
Insulation materials used in high-voltage
switched-mode power supplies are exposed to both high frequencies
and high voltages. Traditional tests performed with high DC
voltages might not reveal the true ageing effects occurring
during rated operation: successful experiments have been
conducted using high-frequence, high-voltage power sources
[Har98].
Cored transformers are not preferred for generating high test
voltages at high frequencies, since the must employ ferrite
instead of iron and therefore are quite costly for the power
required by these applications. Furthermore, the reactive power
needed by the capacitive load of the sample under test has to
pass also through the transformer and be supplied to it
Ferrite-cored resonance transformers have small dimensions but a
comparatively high stray capacitance that is in the order of the
sample capacitance: the ferrite core also produces high flux
non-linear effects that result in unacceptable harmonics.
The Tesla Coil avoids non-linear effects because it is air-cored:
as the size of its coils is bigger, the distance between its
windings can be bigger as well so that the stray capacitance
becomes smaller. Options are available to increase the test
voltage level and to modify the voltage frequency.
Although it is difficult to control the generated wave-shapes,
the damped high frequency oscillations of Tesla Coils are
somewhat similar to typical transient disturbances found in power
systems (e.g. caused by switching operations or by arcing to
ground). Therefore TCs can be used as a supplement to the Marx
generator for insulator testing [Phu91] and synthetic testing of
circuit breakers [Dam87].
Sources of short high-voltage pulses with high
repetition rate are considered to be of interest for a number of
problems: for instance, they can be used to generate ultra-wide
electromagnetic radiation to measure objects to a high precision
or powerful microwave pulses with 3-cm wavelength [Gub97].
Numerous papers have been published with particular emphasis on
the use of a TC in relativistic electron beam generators [Hof75,
Mat82]: its main advantages over the Marx generator are high
repetition rates of operation and low cost because of the lower
number of capacitors used.
Tesla Coil use is also reported in a series of compact and
portable devices to drive cold-cathode e-beam tubes and X-ray
tubes [Mes95]: applications include express spectral analysis of
minerals and jewels, as well as rapid radiography on-field.
Recent research on natural lightning has been
motivated by the desire to prevent spectacular accidents, such as
occurred in 1969 during the launch of Apollo 12 [God70] and in
1987 during the launch of Atlas-Centaur 67 [Bus87].
While cloud-to-ground lightning has been studied more
extensively, cloud-to-cloud and cloud-to-air discharges still
need to be understood more thoroughly as they occur less
frequently and therefore are more difficult to be investigated
[Uma87]. Field observations of lightning can reveal directly
little of the physics of the phenomenon: the propagation process
and the leader velocity are best studied by scaling of laboratory
sparks [Les77, Les81]. In pre-war work Allibone and Meek had
succeeded to demonstrate the existence of a laboratory analogue
to the lightning stepped leader discovered by Schonland in 1933
[Wat96].
As well as direct physical models of lightning, laboratory
generated sparks can also aid interpretation and extension of the
standard geometrical and electrogeometric models. For example,
although the rolling-sphere concept was developed from the known
stepped-leader process, the important choice of sphere radius is
at present an arbitrary 60 m.
A Tesla Coil can be built using only a few basic components. A transformer generates a high voltage (typically 5 - 30 kV) from the mains that charges the primary capacitor C through the primary coil LP. LP is composed by a few turns (5 - 20) of heavy copper wire having a very low resistance.
Figure 1. Tesla Coil basic schematic diagram |
When C is sufficiently charged, the potential
difference between the spark gap electrodes becomes sufficient
for the gap to fire and allow current to pass through. While the
gap is conducting, C is connected in parallel to LP through the
gap and gets discharged into it. C and LP form a parallel
resonant circuit with a resonance frequency defined by their
capacitance and inductance values.
The magnetic field generated by LP is partly induced into the
secondary coil LS. LS is composed by about 1000 turns of thin
copper wire and its top lead is connected to a spherical or
toroidal terminal with a capacitance of typically 15 - 30 pF. LS
and its top terminal form a series resonant circuit: if its
resonance frequency is near to the one of the primary circuit, an
extremely high potential is developed at the top terminal.
As the secondary can easily reach potentials ranging from 100 kV
to several MV, the electric field generated is usually sufficient
to breakdown the surrounding air dielectric releasing a leader
discharge. Once the capacitor C gets completely discharged, the
spark gap stops conducting and the same process already described
repeats again.
 Figure 2. Inductively coupled primary and secondary circuits in a TC |
The operation of a TC is regulated by the
mathematical laws describing two air-cored, inductively coupled
resonant circuits [Ter43, Smy50]. The first circuit is formed by
the primary capacitor and primary coil connected in series
through the spark gap, while the second circuit is constituted by
the secondary coil in series with the top terminal acting as a
capacitance connected to ground (Fig. 2).
As the spark gap closes, the energy stored in the primary
capacitor feeds the primary circuit that oscillates to its
resonance frequency: part of this energy is coupled into the
secondary that, in turn, oscillates to its resonance frequency
too. The amplitude of the resultant oscillation is a maximum when
these are in phase: this produces the phenomenon of beats like
that observed in water and sound waves (see the example in Fig.
3).
The energy transfers back and forth from one circuit to the other
with this beat frequency until it is entirely dissipated in
resistive and RF losses: at this time the current in the primary
circuit is minimum and the spark gap opens.
 Figure 3. Top terminal voltage for a single spark gap pulse |
The voltage ratio of the resulting transformer is not dependent on the turn ratio between primary and secondary coils but is instead directly proportional to the square root of the ratio of secondary and primary inductance. The coupling coefficient between the two coils is also quite different from the usual values of 0.9 - 1 used in traditional iron-core transformers: typical values range from 0.1 to 0.6.
In the basic 2-coil TC presented in Fig.1 the energy from the primary circuit is inductively coupled to the secondary and potential at the secondary builds-up by resonant charging. A series of different solutions for transferring the primary circuit energy have been investigated by Nikola Tesla himself and replicated during the years with success by experimenters.
This connection scheme is known among hobbyists
as "magnifier" and employs what Nikola Tesla named as
the "extra coil". The basic idea (see Fig. 4) is to
move the most of the traditional secondary coil far away from the
magnetic field generated by the primary: the secondary is reduced
to a few turns tightly coupled to the primary (coupling
coefficient used is about 0.6).
The voltage rise-up in the reduced secondary is now governed by
the turn ratio, as in a usual transformer: the top of the
secondary is used to series feed the "extra coil",
where the voltage built is still due to resonant charging.
Several TCs have got their top terminal potential limited by its
distance from the primary or the floor they are placed on:
leaders develop easily as the breakdown threshold is lower than
the maximum potential achievable. The benefit of this TC
configuration is that the top terminal (together with the extra
coil) can be elevated far from any grounded point thus avoiding
any breakout to ground.
Anyway, the assembly is made more difficult by the need to
provide high inductive coupling between primary and secondary
while still keeping a good isolation between the two of them. The
tight coupling requires a rugged and fast rotary spark gap to
avoid dissipating all the energy in losses during transfers
between primary and secondary circuits.
 |
 |
 |
| Figure 4. From left to right, basic TC, 3-coil inductively coupled TC and 3-coil series feed TC | ||
This connection scheme differs from the previous as the primary coil is connected in series and also inductively coupled to the secondary: primary and secondary therefore implement an autotransformer that series feeds the extra coil. Primary and secondary don't need anymore to be isolated but the requirements for the spark gap are still quite strict.
The simplest solution for the spark gap is a
static couple of electrodes separated by a suitable dielectric
(usually a dry gas mixture including SF6, Nitrogen, etc.).
Breakout occurs when a voltage threshold is exceeded and the arc
self-extinguish when the current passing through the gap
decreases below a certain value.
Commercial spark gaps usually employ also a trigger electrode to
provide an initial ionization of the dielectric and facilitate
breakout between the two main electrodes: this way it is possible
to control the exact breakout rate, as required by radars,
lasers, etc. Strict constraints are placed on the triggering
pulse rise time, duration and amplitude, usually required to be
100% of the switched voltage.
The high current flowing in the primary circuit of a typical
middle-sized TC is capable of quickly warming-up these static
spark gaps: water or other kind of cooling is thus required.
Using a series of multiple static gaps results in an even heat
distribution and can partly reduce this problem: the spread
between the minimum and maximum triggering voltage is anyway
worsened by the connection.
For an optimal Tesla Coil performance the gap is also required to
stop conducting without re-igniting: the ionized dielectric gas
mixture must be renewed after each pulse, maintaining a suitable
pressure inside the gap. Vacuum or sealed static spark gaps are
not suitable for TC use because they require a recovery time of
several milliseconds between pulses.
Commercial static spark gaps are expensive to purchase and also
to operate: their construction with conventional amateur
techniques is almost impossible. In practice, simple two or
multiple electrode spark gaps with air dielectric are viable for
small-sized TCs where switched power doesn't exceed 2 kW: ionized
air is removed from the gap by using compressed air or vacuum
suction.
Rotary spark gaps represent a solution to several of the above
mentioned problems: being engineered in different configurations,
they basically consist of a set of stationary electrodes and a
set of rotating ones. When a rotating electrode comes in
proximity of the static ones the dielectric width is at a minimum
and breakout occurs.
Rotary spark gaps can be easily manufactured by using brushless
motors or DC motors when a variable pulse rate is required.
Static electrodes are cooled by providing them with proper heat
sinks, while moving electrodes usually don't get even sensibly
warm. By using fast rotating speeds there is no need of removing
ionized dielectric and high pulse rates can be easily achieved.
The basic TC described in Fig. 1 employs an AC
power supply: the rate of the pulses generated by the spark gap
closures is related to its triggering voltage. If this voltage is
slightly lower than the supplied peak voltage, the pulse rate is
equal to the AC supply frequency (50 or 60 Hz) as there is only
one pulse for each cycle.
A decrease in the spark gap triggering voltage allows for a
higher pulse rate but the TC operation gets much more
complicated. Note that when the spark gap is closed the power
supply is effectively short-circuited: at spark gap opening the
primary capacitor charging voltage depends on several factors
the power supply current capabilities
the instantaneous voltage value available from the mains (i.e. the temporal "phase "of the previous pulse)
the spark gap triggering voltage, together with its intrinsic level of randomness.
The net result is a functional mode where
performance optimization is made problematic. If the power used
is higher than a few kilowatts, the use of rotary spark gaps
becomes mandatory adding one more factor to the three listed
above: namely, the phase relation between the AC supply voltage
and the presentation of the gap electrodes.
On the other hand, the use of a rotary spark gap provides also a
mechanism to control the TC performance better than with a static
one. This can be achieved in several ways
the pulse rate dictated by the rotating spark gap is sensibly higher than the AC supply frequency (e.g. 400 - 700 Hz). This way the phase relation between gap and supply voltage becomes unimportant, as the pulses are on average uniformly distributed.
The rotary spark gap employs a synchronous motor fed from the same AC voltage used for the power supply. Gap and supply are thus in phase and a pulse rate equal to an integer multiple of the supply frequency can be achieved. The phase angle can be precisely set for the pulses to be distributed in an optimal area of the supply voltage semi-wave cycle.
The power supply is replaced by an alternator driven by the same motor used for the spark gap [Gla48]. The system can be designed so that the generated AC voltage frequency is exactly equal to the gap pulse rate: because the alternator and gap rotors are mounted on the same motor shaft, a constant phase angle between them is ensured.
While the above solutions allow for reaching a
stable and optimal performance point, the resulting amplitude of
each single pulse is still not a constant: measurements of the
coil parameters are very difficult as each pulse should be
analyzed as a unique entity.
A great simplification is introduced by using a stabilized DC
power supply together with a rotary spark gap. The pulse rate is
uniquely dictated by the gap pulse rate, provided that the power
supply is capable of providing enough current to charge the
primary capacitor between pulses. All pulses have the same
amplitude, as the capacitor gets always charged to the same
voltage: spark gap phase and rotating speed do not need anymore
to be precisely controlled.
In the resulting scenario parameter measurement is facilitated,
although a higher complexity is required for the design of a DC
power supply.
Pulse rates practically achievable with rotary or
static spark gaps (below 1 kHz) don't affect the potential
developed in the secondary circuit, as the energy of one pulse is
completely dissipated before the following pulse. Even if higher
pulse rates could be realized, a constructive potential build-up
at the secondary would require the oscillations generated by each
pulse to be perfectly in phase with each other.
If the TC is allowed to breakout with leaders discharging into
air, increased pulse rate results in longer leaders extending
over the typical distance expected to be achieved for the
secondary potential developed. This effect is only partly
understood and probably relates to the air dielectric ionization
hysteresis: the mechanism employed is similar to the one
regulating natural lightning.
If instead the TC breaks-out to a grounded target, increased
pulse rate produces a brighter streamer, as the energy per time
unit employed is directly proportional to the pulse repetition
rate.
All Tesla Coils described in the previous
chapters use a spark gap to discharge a capacitor into the
primary coil and thus generate oscillations in the primary
circuit: a natural extension of this principle is having the
primary coil directly driven by a power oscillator. In this case
the potential developed at the secondary is no more a series of
high voltage pulses but instead a continuous AC voltage, that can
be used for a wider range of applications.
As the pulsed TC is fed with a high power pulse derived from a
capacitor discharge, the continuous TC is fed by a continuous
oscillation with sensibly smaller instant power. Oscillators
operating in Class A, B or C can be used, with different
performance [Cor87].
With Class A and B oscillators the efficiency achieved is low:
the maximum voltage rise at the secondary is obtained when the
primary equivalent impedance is equal to the secondary equivalent
impedance. In this condition the power delivered to the secondary
is maximum and equal to 50% of the total power. The coupling
required to match the impedance of the two circuits is usually
very loose, well under 0.1: with increasing coupling the
secondary voltage drops down because the coupled primary
resistance reduces the secondary Q value.
With Class C oscillators a higher efficiency can be reached
(about 80%): the primary circuit impedance rises between the
current pulses and the secondary Q keeps high values. This means
that a higher value of coupling can be used (typically 0.2),
reducing losses and increasing efficiency. A higher coupling
coefficient, in turn, produces the beat envelope typical of
air-core inductively coupled circuits: this beat can be removed
by tuning secondary and primary to slightly different
frequencies.
TC oscillators usually employ triode or tetrode vacuum tubes, for
the high voltage and relatively high currents required: solid
state devices like IGBTs and FETs don't provide the same power
switching capabilities but can be run in Class D with an
efficiency figure of about 90%.
Oscillator driven TCs allow to generate a continuous AC voltage
instead of the pulsed AC obtained with spark gap driven TCs:
anyway, they are much more sensible to losses, loading in the
secondary circuit and capacitive proximity effects. For the same
power supply and coil configuration, they don't allow to generate
peak potentials as high as with the pulsed-mode operation. More,
from a visual point of view, leaders into air generated by
oscillator driven TCs are not so spectacular as the
lightning-like breakouts generated in pulsed-mode.
The performance of a Tesla Coil, intended as the peak potential developed at the secondary top terminal, is also influenced by a number of factors partly related to its physical dimensions
inductance of primary and secondary coils. Potential developed is directly proportional to the square root of the secondary and primary coils inductance ratio.
Resistive losses in the primary coil.
Resistive losses in the secondary coil.
Capacitive losses in the secondary coil. Coils with lower height to width ratio exhibit a lower self-capacitance.
Distance between top terminal and primary coil. Usually the grounded point nearer to the top terminal is the primary coil. A taller secondary allows for the top terminal to sustain higher potentials before arcing to the primary.
Top terminal size. The minimum radium of curvature of the top terminal influences directly its breakout threshold voltage.
The geometry of the secondary coil is a
compromise between the above factors and is partly driven also by
empirical evidence. In general, bigger TCs imply a smaller
voltage transformation ratio: on the other hand, they are capable
of handling a higher top terminal potential and therefore
suitable to produce a higher voltage.
Practical experience suggests that the power required for a
satisfactory performance of a TC is not linearly proportional to
the height of its secondary coil but the dependency is instead at
least quadratic.
The principle of operation of the Tesla Coil is
only partly understood: a series of models have been developed
during the years, including a resonance cavity model, a 1/4
wavelength dipole model and a mutually coupled inductance model.
The justifications are often unsatisfactory or empirical and some
of these theories have been turned down by experimental results.
A reference that encompasses all the parts of a TC, following the
energy transformations from the power supply to the breakout into
free air is missing. Most of printed material concentrates on
practical construction phases or just scraps the surface of the
underlying theory.
The main goal of this project is to make some light on the
principle of operation of the Tesla Coil, confirming or refining
one of the existing models. A TC has to be built for a case
study, offering enough flexibility for testing different
operational modes and parameter values.
The power supply must be capable of charging the primary
capacitor to a variable but exact and repeatable output voltage.
The achievable pulse rate must extend over the 400 Hz typically
found in today's TC designs and reach at least 800 Hz. Nikola
Tesla used a pulse rate of over 2400 Hz in his own experiments,
together with an average power of about 15 kVA [Tes78, Hul93].
Apart from the main purpose, the framework and some of the
components built for this project can be used for subsequent
research on related topics. For instance, one of the less
investigated aspects of TCs is the dynamics of the breakouts
developed from its top terminal and their relationship to the
other operational parameters. It is well known from practical
experimentation that rising the pulse rate into the TC primary
circuit can increase leaders' length. Obtained breakouts are
noticeably longer than what the voltage developed at the
secondary would allow.
Different coupling schemes can be tested taking advantage of the
same power supply, while little modifications in the primary and
secondary coils coupling and replacement of the primary coil
drive circuit allow functionality in either pulsed or continuous
mode.
The output of a TC is a combination of three effects
an electromagnetic field and an electrostatic field both generated by the secondary top terminal
electrical breakouts into free air
electrical breakouts to solid grounded points.
The above three effects are usually all present
in every TC run, randomly mixed with each other: the mechanisms
employed by them are all different and concur to make TC modeling
a difficult task. By using different setups it is possible to
isolate these three energy transfer forms, having one of them
predominant among the others and thus simplifying the modeling
process.
A large toroidal top terminal is used to increase the breakout
threshold voltage, thus preventing leader formation and allowing
to precisely measure the electromagnetic field generated. When
using a suitable grounded spherical terminal in proximity of the
toroid, it is possible to ensure a controlled breakout to ground
with almost no leaders into air. If breakouts into air have to be
investigated, an artificial protuberance on the toroid surface
has the effect to offer a preferential point for leader formation
and concentration. Therefore a set of toroids of different size
is required, each of them allowing for a different operational
mode.
As seen in the previous chapters, continuous wave TCs are
extremely sensible to losses, capacitive proximity effects and
loading of the top terminal: they also don't allow to reach
potentials as high as in pulsed mode. The Tesla Coil object of
this project is thus chosen to work in pulsed mode, using a spark
gap.
3-coil TCs require a high-speed, high-performance rotary spark
gap and for inductive feed also proper isolation between primary
and secondary. They imply an increased engineering difficulty and
are much more complex to be modeled for including three resonant
circuits. The coupling scheme chosen for this project is
therefore the basic 2-coil, for its simplicity.
Because of the high price of commercial spark gaps, a rotary
spark gap is going to be built using an off-the-shelf DC motor
together with a proper speed control unit. The choice of the
2-coil configuration relaxes the constraints on the breakout time
duration that otherwise would have required a high electrode
rotational speed.
To be immune from unwanted side effects and, at the same time,
allow to display all phenomena involved with sufficient
magnitude, a middle-sized Tesla Coil is planned, with a secondary
height of about 1.5 meters. A TC of this size should be
relatively insensible to field distortion and capacitive
proximity effects caused by probing sensors and other objects
nearby the secondary coil.
Repeatability of pulses in the primary circuit is
essential: the primary capacitor must always get charged to a
stable, predefined potential without fluctuations due to the
pulses phase or repetition rate. This way, measurements can be
concentrated only on tracking and modeling the variance of
parameters object of study without unnecessary complications.
This requirement, together with the high desired pulse rate of
800 Hz, put a special emphasis on the selection of the power
supply design. The constraints to be satisfied can be specified
as follows
the primary capacitor must get charged before each pulse to an exact, known value.
This charging voltage must be variable, in order to obtain a range of different operating conditions.
Maximum desired charging voltage is about 20 kV.
Maximum desired pulse rate is 800 Hz.
Estimated maximum power required is about 20 kW (for a primary capacitor of 0.1 µF).
Direct AC feed is not feasible for the reasons seen in the previous chapter, while a number of different DC solutions can be examined for feasibility.
A stabilized DC power supply employing a full-bridge rectifier is modeled in Fig. 5. V1, V2 and V3 represent the secondary of a 10 kV three-phase distribution transformer. L1, L2 and L3 are three current limiting inductors equivalent to the actual ones inserted in series with the transformer primary phases. Capacitor C1 provides charge storage sufficient for pulse rates up to 800 Hz, with a maximum voltage decrease of less than 2 %. L4 has got the function of limiting the current drained from C1 during the time the spark gap conducts, as well as charging the primary capacitor C2 through diode D7.
 Figure 5. MicroSim model of a conventional DC power supply |
 Figure 6. MicroSim simulation results for the conventional power supply |
The presence of L4 and D7 realizes a resonant charging scheme that allows voltage developed on C2 to rise up to about 30 kV. Fig. 6 is the result of a simulation run at a pulse rate of 800 Hz: as L1, L2 and L3 limit the power consumed to about 20 kVA, the available power supply voltage on C1 assumes a value of about 10 kV at regime condition. Regulation of pulse energy (i.e. C2 charging voltage) is performed by a 30 A three-phase variac (not shown) feeding the transformer primary. In spite of the simplicity of this approach, the following shortcomings must be considered
the 30 A three-phase variac, together with L1, L2, L3 and L4 constitute a set of bulky components requiring a lot of space and possibly also custom manufacture.
C1 is an expensive, heavy and large component.
The final charging voltage on C2 is partly affected also by the time the spark gap remains closed: this is a parameter that can be hardly controlled.
With the conventional stabilized DC power supply
seen in the previous section, the primary capacitor got charged
to a potential related to the supply output voltage. The
capacitor charging voltage was varied by changing the power
supply output voltage through a variac connected on the mains
side.
A different approach is to keep the power supply voltage constant
and to charge the primary capacitor through a high-voltage
switch: the switch has to be opened when the capacitor reaches
the desired voltage (Fig. 7).
 Figure 7. Power supply employing a high-voltage switch |
As the switch opening/closing frequency is at
least equal to the maximum pulse rate (800 Hz), it cannot be
inserted on the primary side of a conventional transformer
because it would introduce high-frequency components in the
original 50 Hz sinewave. This would, in turn, generate high
losses and heat the transformer core.
Inserting the switch element on the secondary (high voltage) side
means that a hold-off voltage of at least 15 kV is required, with
an estimated maximum current of about 10 A. Solid state devices
currently available on the market (thyristor, triac, BJT, MOSFET,
GTO, IGBT, MTO) have no problem to switch currents of several
thousands of Amperes but are limited to a maximum operating
voltage of 9 kV. The only possible solution is thus to connected
several under-rated devices in series in order to increase their
hold-off voltage.
Traditionally, the series operation of high-voltage devices has
been challenging in two respects [Pal95]
switching control signals have to be level shifted across a high voltage barrier still ensuring a very low stray capacitance to ground, due to the high dv/dt encountered. This problem is widely known and it is usually solved with magnetic or optical methods.
A reasonable voltage sharing must be ensured in the transient and steady state, so that some devices are not over-voltaged. Uneven voltage distribution is due to each device exhibiting slightly different characteristics.
Recent literature about operation of series connected devices with increased blocking voltage is mostly devoted to the solution of the voltage sharing problem. Several viable strategy are presented
utilization of snubbers to slow down all the devices to the speed of the slowest device [Che96, Pod91, Oka97].
Master-slave approaches were the devices are sequentially turned on and off [Bur96, Gui93].
Active control of the device voltage or current with a local feedback loop influencing the device control signal [Bru98, Ger96, Pal95, Pal96, Pal97, Pal98].
Overdrive of the device control signal in order to eliminate differences due to parameter spread [Ber96].
Uniform voltage sharing still remains a difficult
task to be accomplished: all the proposed methods are more or
less in the experimental stage and there is no ready and
established solution ready for the industry.
Devices such as BJTs (Bipolar Junction Transistors) and
thyristors require complicated and very inefficient methods of
driving due to their low gain and minority carrier device
characteristics. In addition, thyristors become difficult to
control due to loss of gate control during turn-off and required
additional forced-commutation circuitry [Mit95]. Power MOSFET
(Metal-Oxide Semiconductor Field Effect Transistors) devices can
be driven with low power voltage pulses but in high-voltage
applications exhibit increased RDS(on) resulting in lower
efficiency due to the increased conduction losses [Tak95].
The IGBT (Insulated-Gate Bipolar Transistor) combines the low
conduction loss of a BJT with the switching speed of a power
MOSFET and, at operating frequencies between 1 and 50 kHz, offers
an attractive solution over traditional BJTs, MOSFETs and
thyristors. GTOs (Gate Turn-Off thyristors) and MTOs (MOS
Turn-Off thyristors) are instead limited to switching frequencies
below 500 Hz [Ber96].
The two approaches previously seen rely on a more
or less stabilized DC high-voltage to be generated from a
conventional 50 Hz transformer through rectification: a
high-frequency converter focuses on charging the primary
capacitor with high voltage pulses.
One circuit topology that may be utilized is the series-resonant
converter [Lip91, Nel90, Nel92]. In this circuit (see Fig. 8) the
switches and resonant components L and C are connected to the low
voltage side of the transformer: only the rectifiers on the
transformer secondary must have high voltage ratings. By closing
in proper order the switches in pairs, pulses of alternate
polarity are applied to the transformer: using a high turn ratio,
high voltage pulses are generated at the secondary, increasing
the capacitor charge.
 Figure 8. Power supply employing a high-frequency converter |
The leakage inductance of the transformer may be
utilized as the resonance inductor L. The switching frequency may
be held constant at a value such as one-half of the circuit
resonant frequency: alternatively the switching frequency may be
started at a low value and then increased to approximately the
resonance value during the charge cycle. When the desired
capacitor voltage is reached, a command is sent to turn off all
switches.
One characteristic of this circuit which makes it attractive for
capacitor charging is its ability to operate under short circuit
conditions, such as that represented by the capacitor at charging
start. Operation at high switching frequencies can reduce the
size and weight of the transformer. Regulation can be improved by
the utilization of control techniques like pulse-width modulation
or constant on-time control.
Solid state devices for the switches can be selected according to
the same considerations reported in the previous section: in this
case there is no need for series connection of several devices as
the required voltage and current ratings are widely supported.
Integrated circuits are readily available for driving the
switching devices (e.g. IR2110 from International Rectifier) and
also for regulating switching frequency and duty-cycle (e.g.
UC3860 from Unitrode Integrated Circuits) [Lip91]. The input Vin
voltage can be derived by rectifying and filtering the 230 V
mains or the three-phase 400 V lines for increased power demand.
Compromises must be made when designing the transformer to
operate under both high-frequency and high-voltage conditions.
High frequency requires a small, high-permeability core (e.g.
ferrite), tight windings and close proximity between primary and
secondary. High-voltage design instead requires a minimum
separation between individual turns and between primary and
secondary windings, to avoid dielectric breakdown.
The conventional stabilized power supply has been
modeled in detail but requires a lot of bulky components. A 20 kW
variac, a 1.5 H 30 kV inductor plus a triple limiting inductor
demand for a lot of space: regulation of the primary capacitor
charging voltage still cannot guarantee repeatability.
A power supply employing a high-voltage switch element demands
for a particular effort in designing and optimizing a voltage
sharing strategy: ready-made solutions are not currently
available. Devices to be connected in series with blocking
voltages greater than 3 kV are available only for currents of
several hundreds of amperes: they are large and expensive,
require special mounting mechanics and are definitively wasted
for an application using at most 10 A of current.
The high-frequency converter is a solution often reported in the
literature for capacitor charging: all components are readily
available on the consumer market, besides the transformer that
must be custom-wound. Schematics can be easily derived from
existing low-power designs, as the topology remains the same: the
high-voltage secondary affects only in a very small part the
overall design and the ratings of a few components.
By choosing this solution there is no need of big current
limiting inductors, variacs or heavy and life-dangerous filtering
capacitors. The primary capacitor charging voltage can be easily
regulated from a low potential point minimizing losses and
without danger of electrical shock. A block diagram of the
selected power supply is presented in Fig. 9.
 Figure 9. Selected power supply employing a high-frequency converter |
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