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Tesla coil theoretical model and experimental verification

J. Voitkans (Researcher, RTU), A. Voitkans (Researcher, LU)

Abstract – In this paper a theoretical model of a coil ending. This construction allows to slightly increase output operation is proposed. is described as a long line with . scattered parameters in a single-wired format, where the line voltage is measured against electrically neutral space. By using a principle of equivalence of one-wired and two-wired schemes it is C C shown that equivalent two-wired scheme can be found for a single-wired scheme and the already known theory of long lines can be successfully applied to a Tesla coil. A new method of multiple reflections is developed to characterize a signal in a long line. Formulas for calculation of voltage in a Tesla coil by coordinate and calculation of are proposed. Theoretical calculations are verified experimentally.

Resonance frequencies of a Tesla coil are measured and voltage L2 L2 standing wave characteristics are obtained for different output capacities in a single-wired mode. Wave resistance and phase coefficient of a Tesla coil is obtained. Experimental measurements show good compliance with proposed theory. Formulas obtained in this paper are also usable for a regular two-wired long line with scattered parameters. e(t) L1 e(t) Keywords – Tesla coil, single-wire scheme, long line, resonance frequencies. L1

Introduction Tesla is a device which is used for obtaining a b . It is invented by genial Serbian scientist Nikola Figure 1: Tesla transformer Tesla. Importance of his works in science and technology is hard to overestimate. Many of N. Tesla’s discoveries so There are other Tesla transformer construction variations predated their time, that only now we can fully assess their where is winded in cone or like flat spiral. Transformer size essence, but some of them are still waiting for their time, for may vary from few centimetres to few tens of meters. Output example, wireless transfer of energy in great distances. voltage may be from few tens to millions of . In Currently Tesla transformer operating principles are not experiments in Colorado Springs N. Tesla gained voltage of sufficiently explained, model of operation that would describe approximately 50 million volts. Electrical voltage spatial physical processes in Tesla coil is not created. It is very distribution by a length of coil coordinate is shown in difficult to design Tesla coil and predict its necessary Figure 2. properties and parameters. Tesla transformer design is shown in Figure 1 (a). It consists of primary winding with small number of winds which is operated by generator . Operating currents of this winding can be relatively big; it is winded with increased diameter wire because of that. Secondary winding (Tesla coil) consists of much more winds which are winded with small diameter wire usually in one layer. Upper ending of the winding is connected to load, in this case spatial capacity (conducting sphere, hemisphere, ellipsoid, it may also be a load with two connectors). Tesla coil lower ending is connected ether to or generator casing. In Figure 1 (b) Tesla variant is shown. In this variant upper ending is connected with lower Figure 2: Voltage U distribution by coil length

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In Figure 2 can be observed that voltage by Tesla coil Cv Cv length coordinate is gradually increasing with a maximum in Cs Cs its output. General transformer output voltage is proportional to ratio of secondary and primary winding number of winds. Tesla transformer output voltage does not correspond to this regularity, it is many times higher. To get high voltage in output it is necessary to tune it to some particular Cs Cs which is called working or resonance frequency. Anomalous Cv Cv voltage increase in output could be explained by occurring of series in secondary winding because this Figure 4: Tesla coil winding scheme resonance is characterized by voltage increase on reactive elements times comparing with input voltage, where is In Tesla coil theory processes occurring in Tesla coil can be contour goodness [1]. Nevertheless attempts to describe described knowing its inductivity by length unit and processes occurring in Tesla transformer in bounds of the winding slef-capacity by length unit , resonance frequencies voltage resonance theory have not yielded results [2], [3]. can be calculated, phase coefficient , characteristic In this work Tesla coil theoretical model is given and impedance can be determined. comparison of theoretically acquired parameters with Co(F/m) Co(F/m) Cizo(F) experimental measurements is performed. Lo(H/m) Csl(F) Tesla coil theoretical model e(t) In the proposed theoretical model it is assumed that Tesla Co(F/m) Co(F/m) Co(F/m) transformer high voltage winding is operating in a long line with distributed parameters mode with multiple reflections Figure 5: Tesla coil model electrical scheme from coil endings. Direct and reflected voltage and current waves are forming which mutually summing create different Tesla coil model electrical scheme (Figure 5) consists of standing wave sights by corresponding resonance frequencies. sinusoidal electrical voltage generator , where one end is In this work Tesla transformer secondary coil operation is connected with ground or other big spatial capacity. Its output described as long line in single wire electrical system format voltage is and frequency . To the output of a generator [4], [5], [6], where circuit currency is measured against beginning of a Tesla coil winding with a length and diameter infinitely distant sphere (i.e. against neutral surrounding is connected. Other end of the winding is connected to a space). In free space positioned electric wire of which spatial load capacity which together with the coil idle secondary winding consists equivalent scheme is shown in running capacity (Figure 5) is forming combined output Figure 3. capacity . Any electrically conductive body with self- C capacity can be a load capacity. Spherical body has Lv self-capacity , where sphere radius. It is possible to measure a self-capacity of a conductive body [8]. Lv Lv Main characteristics of Tesla winding are inductivity by C C length unit (H/m) and capacity by length unit (F/m). Figure 3: Single wire equivalent scheme Virtual ground of single-wire scheme In scheme (Figure 3) is straight wire inductivity by Any single-wired electrical scheme can be substituted by an length unit (several microhenries on meter), is wire self- equivalent two-wired scheme where as a common connection capacity (capacity against infinitely distant sphere) by length serves virtual ground. Its theoretical description and unit (approximately 5pF/m). and values are dependant experimental verification is shown in work [7]. Existence of from length and diameter of wire. Tesla coil that is winded virtual ground is discovered theoretically by describing one- from such a wire is shown in Figure 4. In this case , wired schemes with Kirchhoff equations, where electrical because there are several winds in length unit, and capacity and electrical potential of a conductive body is because additional inter-wind capacity is introduced. is determined against infinitely distant sphere. Illustration of dependant from by the side positioned wind distance and virtual ground is shown in Figure 6.a. diameter. In Figure 6.a. a spherical two layer condenser is shown As we are viewing Tesla coil as single-wire long line with where one electrode is in free space placed spherical distributed parameters, by applying alternating input voltage, electrically conductive body with diameter , which is voltage and current travelling wave is introduced with centrically encased by spherical hollow electrode with multiple reflections from winding ends. At certain frequencies inner radius . Electrical capacity of such two layer condenser with different wave lengths resonance occurs. is

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distance to VZ boundary for coil is smaller than for

sphere because the diameter of the coil is smaller than the diameter of the sphere. Virtual ground is connected with a If radius tends toward infinity, which corresponds to casing of the generator , because displacement currents infinitely remote sphere, as defined in electro-physics, with which are generated by single-wire scheme capacities connect zero electrical potential , then sphere with radius to it. gains capacity Physically free, neutral space with a zero electrical potential , (2) serves as a virtual ground. Displacement currents created by which is also called self-capacity of a conductive body self-capacity of bodies which are proportional to a speed of towards infinitely remote sphere. Electrical potential of a change of and capacity value flow in it. body is determined against a zero potential of this sphere, in electrical resistance for displacement currents is close to this case zero. It is ensured by huge cross-section area of a virtual . electric wire. Joule – Lance losses of are close to zero, too. φ0=0 r2 Tesla transformer equivalent two-wire scheme As one-wire connection electrical scheme (Figure 5) is r1 completely equivalent to two-wire scheme (Figure 7) and it C corresponds to traditional long line, a known theoretical description of long line with distributed parameters can be applied to one-wire system [9]. V Z Lo Lo Lo Lo

a Ri Co Co Co Ciz0 Csl e(t) V Z Virtuālā zeme r 0 l x L rL C e(t) C Figure 7: Tesla coil equivalent two-wire scheme and frame of reference

φ0=0 Zero point of coordinate (Tesla coil beginning), direction of change and length of line (Tesla coil ending) is shown in b Figure 7. Figure 6: Conductive body To simplify calculations, capacity , as shown in Figure and its virtual ground (VZ) 7, which is created by last winds of the coil and output, and

load capacity are unified into one output capacity . Nevertheless, current understanding of infinitely remote These capacities are connected in parallel, due to that sphere in electro-physics create problems for its practical use . because it is difficult to understand how electrical Long line is considered homogenous and without losses. It lines could be completed as it is required by principle of is assumed that loss resistance by length unit and loss continuity of after passing infinite distance if conductivity by length unit . In the first approximation electrical field propagates with limited speed (speed of light). it may be done because Tesla coil goodness is large: . Is it possible to change something in our understanding of infinitely remote sphere? Answer is in formula (1). It turns out Direct and reflected voltage wave in Tesla coil that conductive body acquires a value close to its self- When describing physical processes in Tesla coil (Figure 5) capacity if radius of outer sphere gets only several tens and its equivalent scheme (Figure 7) it is assumed that of times bigger than . Five per cent boundary is achieved multiple voltage and current wave reflections are occurring. In when , but one per cent difference of from self- addition to that coil ending matches idle running mode with a capacity value is when . It can be concluded that nature of capacitive load and beginning matches short circuit infinitely remote sphere is close to conductive body and it because generator is connected to ground and its inner would be more understandable to call it a virtual ground resistance is close to zero. (Figure 6). Generator is a source of sinusoidal voltage with a For a complex configuration body like generator frequency and amplitude . (Figure 6.b.) series connection with coil and capacity area , (3) of virtual ground is dependant from linear dimensions of where . each separate components. As we can see in Figure 6.b.,

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It is assumed that is an ideal source of voltage, in this zero. Wave resistance value has a small significance, case inner resistance because for Tesla coil . either. Hence at the coordinate a wave reflected in a Generator output voltage (3) in the long line induces direct direct direction is in an opposite phase with the falling wave running-wave which is describable by two-argument function . (12) , (4) where – phase coefficient. Tesla coil amplitude-frequency characteristic Direct voltage running-wave propagates in axis direction Tesla coil is a resonance system with a high goodness . until reaches the end of line Coefficient shows how many times output voltage is bigger . (5) than input voltage Phase offset angle value and sign is determined by a . load. In case of capacitive load is negative and in case of To make a determination of an amplitude-frequency inductive load is positive. While idle running, when characteristic of a Tesla coil easier it is assumed that a voltage , , too. wave propagates in a line without losses, it is reflected times Under influence of an unbalanced load wave is without changing amplitude and then immediately disappears. reflected and propagates in a direction of generator moving the In a result output voltage will be increased times which same distance as the direct wave which is dependent on conforms to the reality. When a goodness of a coil would and . Changing coordinate has to be counted off the end of change the resonance frequencies should also change slightly, the line, due to that has to be substituted by . As a but this approximation does not anticipate it. It should be result we get a reflected wave considered a shortcoming of this method. To get a Tesla coil amplitude-frequency characteristic it is (6) Reflected voltage wave at the beginning of the coil desirable to transition from two argument function to a single where is argument function. It is possible to get rid of the time dimension by transferring direct (4) and reflected (6) wave (7) At this point wave is reflected again in the direction of the functions to the complex plane: direct wave due to short circuit. Let’s label it . ; (13)

(14) Calculation of Tesla coil load influence This transformation allows writing direct and reflected Angle that characterizes an influence of a load to a signals in a complex form as shown in the expressions (13) Tesla coil can be calculated using the complex reflection and (14). coefficient at the end of the line. Direct wave in line

.

Direct wave at the end of a line together with an influence of a load where complex direct voltage at the output of a line; . Reflected wave at the end of a line , using (11) complex reflected wave at the output of a line;

. characteristic impedance; Reflected wave in a line complex output impedance.

Inserting into expression (8) the value of output impedance . Reflected wave at the beginning of a line we get .

It is reflected from the beginning of a line again as shown in

Module of reflection coefficient is (12) and becomes a reflected direct wave

. . Reflected direct wave at a current coordinate of a line Its phase can be expressed using sinus or tangents . from but preference is given to function due to a Similarly further direct and reflected waves can be found fact that this function also respects a position of this angle in a quadrant , ,

,

and using (8) it can be expressed , and so on times. If the last reflected wave in a line is . (11)

There is a short circuit at the beginning of a line, . due to that. At this point there is no significance to a value of It is beneficial to choose goodness of a coil equal with input capacity because it is shunted by short-circuit which is where is a natural number starting with 1, because in this created by an inner resistance of a generator which is close to case an analytical function of sum of different waves can be

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easily found. As an example a summary voltage in a coil with where

which corresponds to is shown.

(15) In Figure 8 an example of amplitude-frequency Inserting into expression (15) corresponding direct and characteristic with values , , reflected waves and summing them by pairs, after , , is shown. simplification, an expression is obtained

Multiplier corresponds to the time function . (17) It can be observed that cosine (17) argument is not anymore dependant from coordinate . That means that a standing wave has formed in a line, but the rest part of the expression (16) Figure 8: Tesla coil amplitude-frequency characteristic

In Figure 8 it can be observed that at increasing frequency shows an amplitude of the standing wave in a dependence resonance output voltage decreases, it happens due to from coordinate . increasing phase shift which is caused by output Expression (16) in a general way for different values of capacity . At frequencies between base micro goodness can be written resonances with small amplitude are being formed, these can be considered as a background voltage in a coil.

Determination of Tesla coil resonance frequencies

Differentiating voltage amplitude multiplier in the at a condition that , where is a natural number expression (19) by variable and equalizing this derivative starting with 1 with zero it frequencies of voltage maximum in a line can be . calculated. To avoid influence of micro maximums it is Using (19) voltage for a line with other can be advisable to use the multiplier of the four wave variation written. For example, if then goodness of a coil (21) of the expression (19) is , and an expression is obtained: by substituting with line end coordinate .

Deriving by variable and equalizing it with zero, an expression is obtained

It is not allowed to use goodness of a coil in , formula (19) because in this case and it is not a , (24) natural number. where . If is inserted in the expression (19) and it is Inserting into (24) expression and solving it simplified, a four wave summary voltage which against , resonance frequencies are obtained corresponds to goodness is obtained:

(21) For example, for a quarter wave resonance : is the smallest allowed value that is usable in formula (19). There is no upper limit for the natural number .

Inserting into the equation (18) , phase coefficient For wave resonance and its angular frequency is , substituting angle by the formula (10), taking and applying module to , an expression for the Tesla coil amplitude-frequency characteristic at the end of a line when is obtained. Similarly resonance angular frequencies for other waves can be found.

Tesla coil standing wave calculation

, (22)

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To acquire standing wave sight amplitude multiplier of the If the closest to a load minimum coordinate and number expression (19), which is dependant from coordinate , can be of whole half waves in a coil are known value can be used and maximum voltage in a line can be normalized. As a calculated by equalling the expression (28) with zero: result normalized voltage is obtained, it is necessary to take . module of it: Physically corresponding solution of this equation is . (28) . (29) Using the expression (28) and normalizing it to the length By substitution of and into the unit a voltage distribution in a homogenous line without equation (29) it can be obtained losses can be obtained. Value of the phase coefficient has to be such that a corresponding wave resonance would set in a Tesla coil. Standing wave sight for a quarter wave resonance which is usable both with capacitive and inductive loads in a is shown in Figure 2. case when is natural number: number of full half waves in Tesla coil.

If , the equation (30) gives at that

corresponds to idle-load of a long line. If , idle-load

mode corresponds to coordinate . Formula (30) is not

applicable to quarter wave resonance because it gives

undetermined state ( and ). For this resonance has to be determined by other means. a Determination of load induced phase shift for quarter wave resonance To determine angle in a quarter wave resonance it is necessary to know angle frequency of this resonance, three quarters resonance frequency and its . Determining from the expression (9) and writing it for two first resonances an equation system is obtained

b

Figure 9: Voltage distribution in Tesla coil for and

wave resonances

which is solved against unknowns and . As a result In Figure 9 voltage distribution examples for (Figure product of output capacity and wave resistance

9.a) and (Figure 9.b) wave resonances by coordinate are shown. Output of the coil is loaded by electrically conductive and load induced phase shift for quarter wave resonance sphere with a diameter and self-capacity . Output idle-load capacity which is created by are obtained. last windings of the coil and coil output terminal is approximately . Summary output capacity If approximated angle may be calculated easier. As . resistance of capacitive output is inversely proportional to In idle load mode when maximal voltage of a line frequency , knowing voltage shift angle is equal for both all half waves, and output quarter introduced by coil output reactivity at one frequency it can be wave . If there is a reactive load at the output of a proportionally calculated for other frequency, therefore coil, .

In a case of a capacitive load voltage minimum point coordinate moves closer to the load and output quarter Equation (34) gives a result which is approximately by 5% wave gets shorter, i.e. gets smaller than , but in a case of different comparing with the formula (33). inductive load coordinate moves away from the load and Knowing quarter wave resonance , its wave length output quarter wave gets longer than . can be calculated which is not obtainable from standing wave

sight. In order to do it, it is necessary to find at what coordinate voltage reaches maximum, equation (28) Determination of load induced angle if standing wave distribution is known has to be derived by , substituted by and

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, and equalized with zero. Expressing quarter wave diameter and connected to resonance wave length from the obtained equation we get: coil output. Self-capacities of these spheres are and . Length of connection wire is

approximately 5 cm. Formula (35) shows that in case of a negative quarter During experiments different resonance frequencies are wave is bigger than a coil length . measured and standing wave characteristics for each of them are registered. Results of the measurements are shown in Tesla coil as a long line experimental research Table 1. Voltage knot point coordinates are labelled by , Experimental scheme for Tesla coil research is shown in where n – resonance sequence number, m – knot sequence Figure 10. In a one layer winded as one-wired connection number starting from the closest to the load. Tesla coil is attached to a voltage generator Γ-112A output Resonances also occur at higher frequencies but their (Figure 5). Diameter of the coil is , length voltage level is low and it is difficult to perform qualitative , diameter of enamelled wire including isolation measurements. , number of winds . From the measurement results it can be observed that under Tesla coil inductivity if measured with influence of load capacity resonance frequencies slightly bridge E7-8 at a frequency is . That decrease and voltage knot points move closer to the end of a means . line. Using standing wave knot coordinates it is possible to very L if the line is homogenous by comparing number of half waves C of one standing wave sight with the maximum number of half

waves. When load is not connected for a resonance number 0 x l of whole half waves in a coil and their lengths are show E(t) in Table 1. Figure , 10: Scheme of experiment

,

In experiments when load capacity is required different . diameter metallic balls or cylindrical bars that are attached to Comparing different half wave lengths in different Tesla coil output with approximately long wire are used. In coil regions it can be observed that they are different. That measurements without load connection output wire remains means phase coefficient and characteristic impedance are and together with the last wind form an idle-load output dependant from coordinate of a long line. It can be concluded capacity of the coil. that the basic parameters of the line and are also Electrical field intensity distribution near Tesla coil is changing. At the ends of a coil half wave lengths increase, registered ether with neon lamp by observing intensity of its glow or by voltage induced in oscilloscope probe which has therefore , , decrease. at the centre of a high input resistance. coil is homogenous; therefore inductivity by length unit is Measurements are performed both when load is not the highest. By getting closer to the ends of a coil magnetic connected, and with electrically conductive spheres with field starts to scatter and is decreasing. Table 1 Sphere D Wave type

0 Frequency 1.635 4.525 7.036 9.266 0 ( )

Knot point – 67.5 72.5 coordinates 34 46.5 ( ) 24.5 39.4 Frequency 1.473 4.156 6.633 8.836 2.19 ( )

Knot point – 73.5 77.5 coordinates( ) 36.6 49.5 26.3 65 Frequency 1.362 3.977 6.478 8.717 3.62 ( )

Knot point – 76.5 78.5 coordinates 38 50.5 ( ) 26.5

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In Figure 11 experimentally determined resonance It must be admitted that coordinates for higher resonances frequency placement of a Tesla coil is shown. Amplitude is and are located close to the end of the coil, therefore given in relative units because it is a problem to exactly their determination is associated with high measurement error. measure voltage in a line and its ends without changing its Measurement offset in bounds of one centimetre causes value. It is a problem because there is no such voltmeter that change of value by more than 10 degrees. would have input capacity equal with 0. Experiments show By knowing average resonance wave lengths , using that Tesla coil working conditions are being influenced even formula respective average phase coefficients by connection of 1 capacity. Output voltage value can be can be calculated: indirectly estimated by a length of electric spark at the output ; of a coil. ; ; . Knowing average phase coefficients , product

for each resonance can be calculated:

;

;

;

. Average capacity by length unit :

Figure 11: Experimental Tesla coil resonance frequencies ;

;

By comparing experimental AFR (Figure 11) with a ; theoretical (Figure 8) it can be observed that they are close and . are matching each other. A resonance network forms in a Average characteristic impedance : Tesla coil. Theoretical distances between resonances ; should be equal (Figure 8), but experimental ; measures indicate that by increasing frequency distance ; slightly decreases (Figure 11). It may be due to a fact that real . line is not homogenous, and losses of electromagnetic energy By viewing obtained data it can be noticed that average while frequency is rising are increasing because radiated wave capacity by length unit by rising frequency is increasing by length is closing to the dimensions of a coil. By approximately 35% and is decreasing by approximately increasing of the losses resonance frequency decreases, 20%, although these values should be constant. It might be therefore decreases . explained with inhomogeneity of the line. Using the closest to an output of a coil voltage minimum To obtain idle-load output capacity and local coordinate for different resonances characteristic impedance in reflection zone it is necessary

to obtain together with idle-load resonance frequencies and ( , average wave length and angle output angles the same parameters for a known load values for different resonances with not connected output capacity . Obtained results have to be processed using capacity can be determined. formula (32) and equation system for idle-load and loaded for a wave cases have to be solved. resonance;

for a wave resonance;

for a wave resonance. By solving equation (36) characteristic impedance at the By using formula (30) angle is obtained: reflection zone

for a wave resonance;

for a wave resonance; and idle-load output capacity are obtained

for a wave resonance.

By knowing and using formulas (33) and (35) quarter By inserting into the equations (37) and (38) respective wave resonance parameters can be calculated (from Table 1) and (formula (30)) values following results and . are obtained:

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1. From resonance 7. Obtained mathematical single wire line results can also be applied to a traditional two wire long line. 1.1. For sphere, 8. In Tesla coil parameters , , and are , dependant from length coordinate . , . 9. It is better to calculate Tesla coil base parameters 1.2. For sphere from lower resonances due to lower measurement , errors. , .

2. From resonance

2.1. For sphere References

, 1. Dūmiņš I., Tabaks K., Briedis J. u. c. Elektrotehnikas teorētiskie pamati. Stacionāri procesi lineārās ķēdēs, I. Dūmiņa , . 2.2. For sphere redakcija. Rīga: Zvaigzne ABC, 1999. 301 lpp. 2. Mitch Tilbury, The Ultimate Tesla Coil Design and , Construction Guide (McGraw-Hill, 2008). , . http://issuu.com/theresistance/docs/-np--the-ultimate-tesla-coil- Differences between calculated results and , which desig_20101219_062111 are obtained for both resonances, can be observed. 3. Marco Denicolai, Tesla Transformer for Experimentation and resonance data should be considered more correct because of Research. http://www.saunalahti.fi/dncmrc1/lthesis.pdf increasing measurement errors for higher order waves. 4. J. Voitkāns, J. Greivulis. Elektriskās enerģijas pārvadīšanas iespējas pa vienvada līniju. II Pasaules latviešu zinātnieku kongress. Tēžu krājums, Rīga, 2001, 263 lpp. Conclusions 5. J. Voitkāns, J. Greivulis. Vienvada elektropārvades līnijas 1. Tesla coil can be considered a one-wire electrical eksperimentālās iekārtas tehniskie raksturojumi. Zinātniskā system. konference „Elektroenerģētika tehnoloģijas”. Tēžu krājums, 2. Tesla coil is a long line with distributed parameters Kauņa, 2003. that as a common wire has a virtual ground. 6. J. Voitkans, J. Greivulis, A. Locmelis. Single wire transmission line of electrical energy. EPE – PEMC scientific conference, 3. At particular frequencies electrical resonances with Riga, 2004. different spatial configurations form in a coil. 7. J. Voitkāns, J. Greivulis, A. Voitkāns. Single Wire and 4. Resonance processes in a Tesla coil can be Respective Double Wire Scheme Equivalence Principle. 7th theoretically described using traditional theory of a International Scientific Conference „Engineering for Rural long line. development”, Jelgava, 2008. 5. Existence of resonance networks in Tesla coils is 8. J. Voitkāns, S. Voitkāns, A. Voitkāns. LV patents Nr. 13785 approved experimentally. „Elektriski vadoša ķermeņa paškapacitātes mērītājs”, „Patenti 6. Obtained experimental results comply with un preču zīmes”, 2008. Nr.10. theoretically calculated values. 9. I. Dūmiņš Elektrotehnikas teorētiskie pamati. Pārejas procesi, garās līnijas, nelineārās ķēdes., Zvaigzne ABC, Rīgā, 2006. 10. J. Voitkāns, A. Voitkāns, I. Osmanis. „Investigations on 16. G.L.Johnson. Solid State Tesla Coil.2001. Electrical Fields and Current Flow Through Electrode http://hotstreamer.deanostoybox.com/TeslaCoils/OtherP System Within Electrode”. 8th International Scientific apers/GaryJohnson/tcchap1.pdf Conference „Engineering for Rural development”, Jelgava, 17. G.F.Haller, E.T.Cunningham. The Tesla High 2009. Frequency Coil. New York, 1910. 11. J. Voitkāns, J. Greivulis. LV patents Nr. 13432 „Sinusoidāla sprieguma pārvades vienvada līnija”. „Patenti Janis Voitkans, graduated from Riga Polytechnical Institute in un preču zīmes”, 2006. Nr. 6. 1976 as radioengineer. He received Dr.Sc.ing. in electrical 12. J. Voitkans, J. Greivulis. Loading aspects of a single engineering from Riga Technical University, Riga, Latvia, in in wire electric energy transmission line. International 2007. Research interests are connected with electro physics and scientific conference „Advanced Technologies for Energy . Production and Effective Utilization”. Jelgava, 2004. He is presently a Senior Researcher in the Institute of Industrial 13. J. Voitkāns, J. Greivulis. LV patents Nr. 12932 Electronics and Electrical Engineering, Riga Technical University „Vienvada regulējamā elektropārvades līnija”. „Patenti un Address: Āzenes 12, Riga, Latvia; preču zīmes”, 2002. Nr. 12. e-mail: [email protected] 14. J. Voitkāns, J. Greivulis. LV patents Nr. 13031 „Simetrizēta vienvada elektropārvades līnija”. „Patenti un Arnis Voitkans, received B.Sc and M.Sc in physics from the preču zīmes”, 2003. Nr. 7. University of Latvia, Riga, Latvia in 2003 and 2006, respectively. 15. B.B. Anderson. The Clasic Tesla Coil, 2000. Currently works as a leading systems analyst in IT department of http://www.tb3.com/tesla/tcoperation.pdf the University of Latvia. Address: Aspazijas boulevard 5, Riga, Latvia; e-mail: [email protected]