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

3.1. 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


5.1. 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



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.


2.1. Nikola Tesla

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.

2.2. The Tesla Coil

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

2.3. Applications

Nowadays, applications for Tesla Coils fall within the following categories.

2.3.1. Testing of insulating materials

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].

2.3.2. Generation of high-voltage pulses

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.

2.3.3. Research on lightning discharges

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

3.1. Theory of operation

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.

3.2. Alternative coupling schemes

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.

3.2.1. 3-coils, inductive coupling

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

3.2.2. 3-coils, series feed

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.

3.3. Static vs. rotary spark gap

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.

3.4. AC vs. DC power supply

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 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

  1. 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.

  2. 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.

  3. 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.

3.5. Effect of increased pulse rate

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.

3.6. Pulsed vs. continuous wave

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.

3.7. Tesla Coil physical dimensions

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

  1. inductance of primary and secondary coils. Potential developed is directly proportional to the square root of the secondary and primary coils inductance ratio.

  2. Resistive losses in the primary coil.

  3. Resistive losses in the secondary coil.

  4. Capacitive losses in the secondary coil. Coils with lower height to width ratio exhibit a lower self-capacitance.

  5. 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.

  6. 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

  1. an electromagnetic field and an electrostatic field both generated by the secondary top terminal

  2. electrical breakouts into free air

  3. 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.

5.1. Power supply topologies

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

  1. the primary capacitor must get charged before each pulse to an exact, known value.

  2. This charging voltage must be variable, in order to obtain a range of different operating conditions.

  3. Maximum desired charging voltage is about 20 kV.

  4. Maximum desired pulse rate is 800 Hz.

  5. Estimated maximum power required is about 20 kW (for a primary capacitor of 0.1 F).

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.

5.1.1. Conventional stabilized DC power supply

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

5.1.2. DC power supply employing a high-voltage switch element

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]

  1. 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.

  2. 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

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].

5.1.3. High-frequency converter

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.

5.2. Power supply selection

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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