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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 Tesla coil
operation is proposed. Tesla coil 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
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 resonance frequencies are
proposed. Theoretical calculations are verified experimentally.
Resonance frequencies of a Tesla coil are measured and voltage
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.
ending. This construction allows to slightly increase output
voltage.
C
L2
e(t)
L2
L1
e(t)
Keywords – Tesla coil, single-wire scheme, long line, resonance
frequencies.
Introduction
Tesla transformer is a device which is used for obtaining
high voltage. It is invented by genial Serbian scientist Nikola
Tesla. Importance of his works in science and technology is
hard to overestimate. Many of N. Tesla’s discoveries so
predated their time, that only now we can fully assess their
essence, but some of them are still waiting for their time, for
example, wireless transfer of energy in great distances.
Currently Tesla transformer operating principles are not
sufficiently explained, model of operation that would describe
physical processes in Tesla coil is not created. It is very
difficult to design Tesla coil and predict its necessary
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 ground or generator casing.
In Figure 1 (b) Tesla autotransformer variant is shown. In
this variant
upper ending is connected with
lower
C
L1
a
b
Figure 1: Tesla transformer
There are other Tesla transformer construction variations
where is winded in cone or like flat spiral. Transformer size
may vary from few centimetres to few tens of meters. Output
voltage may be from few tens to millions of volts. In
experiments in Colorado Springs N. Tesla gained voltage of
approximately 50 million volts. Electrical voltage spatial
distribution by a length of coil coordinate is shown in
Figure 2.
Figure 2: Voltage U distribution by coil length
12
In Figure 2 can be observed that voltage by Tesla coil
length coordinate is gradually increasing with a maximum in
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 frequency
which is called working or resonance frequency. Anomalous
voltage increase in output could be explained by occurring of
series electrical resonance in secondary winding because this
resonance is characterized by voltage increase on reactive
elements times comparing with input voltage, where is
contour goodness [1]. Nevertheless attempts to describe
processes occurring in Tesla transformer in bounds of the
voltage resonance theory have not yielded results [2], [3].
In this work Tesla coil theoretical model is given and
comparison of theoretically acquired parameters with
experimental measurements is performed.
Tesla coil theoretical model
In the proposed theoretical model it is assumed that Tesla
transformer high voltage winding is operating in a long line
with distributed parameters mode with multiple reflections
from coil endings. Direct and reflected voltage and current
waves are forming which mutually summing create different
standing wave sights by corresponding resonance frequencies.
In this work Tesla transformer secondary coil operation is
described as long line in single wire electrical system format
[4], [5], [6], where circuit currency is measured against
infinitely distant sphere (i.e. against neutral surrounding
space). In free space positioned electric wire of which
secondary winding consists equivalent scheme is shown in
Figure 3.
C
Lv
Lv
Lv
C
C
Figure 3: Single wire equivalent scheme
In scheme (Figure 3)
is straight wire inductivity by
length unit (several microhenries on meter),
is wire selfcapacity (capacity against infinitely distant sphere) by length
unit (approximately 5pF/m).
and
values are dependant
from length and diameter of wire. Tesla coil that is winded
from such a wire is shown in Figure 4. In this case
,
because there are several winds in length unit, and
because additional inter-wind capacity is introduced.
is
dependant from by the side positioned wind distance and
diameter.
As we are viewing Tesla coil as single-wire long line with
distributed parameters, by applying alternating input voltage,
voltage and current travelling wave is introduced with
multiple reflections from winding ends. At certain frequencies
with different wave lengths resonance occurs.
Cv
Cv
Cs
Cs
Cs
Cs
Cv
Cv
Figure 4: Tesla coil winding scheme
In Tesla coil theory processes occurring in Tesla coil can be
described knowing its inductivity by length unit
and
winding slef-capacity by length unit , resonance frequencies
can be calculated, phase coefficient
, characteristic
impedance
can be determined.
Co(F/m)
Co(F/m)
Cizo(F)
Lo(H/m)
Csl(F)
e(t)
Co(F/m)
Co(F/m)
Co(F/m)
Figure 5: Tesla coil model electrical scheme
Tesla coil model electrical scheme (Figure 5) consists of
sinusoidal electrical voltage generator
, where one end is
connected with ground or other big spatial capacity. Its output
voltage is and frequency . To the output of a generator
beginning of a Tesla coil winding with a length and diameter
is connected. Other end of the winding is connected to a
spatial load capacity
which together with the coil idle
running capacity
(Figure 5) is forming combined output
capacity
. Any electrically conductive body with selfcapacity
can be a load capacity. Spherical body has
self-capacity
, where
sphere radius. It is
possible to measure a self-capacity of a conductive body [8].
Main characteristics of Tesla winding are inductivity by
length unit
(H/m) and capacity by length unit
(F/m).
Virtual ground of single-wire scheme
Any single-wired electrical scheme can be substituted by an
equivalent two-wired scheme where as a common connection
serves virtual ground. Its theoretical description and
experimental verification is shown in work [7]. Existence of
virtual ground is discovered theoretically by describing onewired schemes with Kirchhoff equations, where electrical
capacity and electrical potential of a conductive body is
determined against infinitely distant sphere. Illustration of
virtual ground is shown in Figure 6.a.
In Figure 6.a. a spherical two layer condenser is shown
where one electrode is in free space placed spherical
electrically conductive body with diameter
, which is
centrically encased by spherical hollow electrode
with
inner radius . Electrical capacity of such two layer condenser
is
13
If radius
tends toward infinity, which corresponds to
infinitely remote sphere, as defined in electro-physics, with
zero electrical potential
, then sphere with radius
gains capacity
,
(2)
which is also called self-capacity
of a conductive body
towards infinitely remote sphere. Electrical potential
of a
body is determined against a zero potential of this sphere, in
this case
.
r2
φ0=0
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
casing of the generator
, because displacement currents
which are generated by single-wire scheme capacities connect
to it.
Physically free, neutral space with a zero electrical potential
serves as a virtual ground. Displacement currents created by
self-capacity of bodies which are proportional to a speed of
change of electric field and capacity value flow in it.
electrical resistance for displacement currents is close to
zero. It is ensured by huge cross-section area of a virtual
electric wire. Joule – Lance losses of
are close to zero,
too.
Tesla transformer equivalent two-wire scheme
As one-wire connection electrical scheme (Figure 5) is
completely equivalent to two-wire scheme (Figure 7) and it
corresponds to traditional long line, a known theoretical
description of long line with distributed parameters can be
applied to one-wire system [9].
r1
C
VZ
Lo
Ri
a
Lo
Co
Lo
Co
Virtuālā zeme
e(t)
L
Co
Ciz0
Csl
e(t)
VZ
rL
Lo
rC
C
φ0=0
b
Figure 6: Conductive body
and its virtual ground (VZ)
Nevertheless, current understanding of infinitely remote
sphere in electro-physics create problems for its practical use
because it is difficult to understand how electrical force field
lines could be completed as it is required by principle of
continuity of electric current after passing infinite distance if
electrical field propagates with limited speed (speed of light).
Is it possible to change something in our understanding of
infinitely remote sphere? Answer is in formula (1). It turns out
that conductive body acquires a value close to its selfcapacity
if radius of outer sphere gets only several tens
of times bigger than . Five per cent boundary is achieved
when
, but one per cent difference of
from selfcapacity value is when
. It can be concluded that
infinitely remote sphere is close to conductive body and it
would be more understandable to call it a virtual ground
(Figure 6).
For a complex configuration body like generator
(Figure 6.b.) series connection with coil and capacity area
of virtual ground
is dependant from linear dimensions of
each separate components. As we can see in Figure 6.b.,
0
l
x
Figure 7: Tesla coil equivalent two-wire scheme and frame
of reference
Zero point of coordinate (Tesla coil beginning), direction
of change and length of line (Tesla coil ending) is shown in
Figure 7.
To simplify calculations, capacity
, as shown in Figure
7, which is created by last winds of the coil and output, and
load capacity
are unified into one output capacity
.
These capacities are connected in parallel, due to that
.
Long line is considered homogenous and without losses. It
is assumed that loss resistance by length unit
and loss
conductivity by length unit
. In the first approximation
it may be done because Tesla coil goodness is large:
.
Direct and reflected voltage wave in Tesla coil
When describing physical processes in Tesla coil (Figure 5)
and its equivalent scheme (Figure 7) it is assumed that
multiple voltage and current wave reflections are occurring. In
addition to that coil ending matches idle running mode with a
nature of capacitive load and beginning matches short circuit
because generator
is connected to ground and its inner
resistance is close to zero.
Generator
is a source of sinusoidal voltage with a
frequency and amplitude
.
,
(3)
where
.
14
It is assumed that
is an ideal source of voltage, in this
case inner resistance
because for Tesla coil
.
Generator output voltage (3) in the long line induces direct
running-wave which is describable by two-argument function
,
(4)
where
– phase coefficient.
Direct voltage running-wave propagates in axis direction
until reaches the end of line
.
(5)
Phase offset angle
value and sign is determined by a
load. In case of capacitive load
is negative and in case of
inductive load
is positive. While idle running, when
,
, too.
Under influence of an unbalanced load
wave is
reflected and propagates in a direction of generator moving the
same distance as the direct wave which is dependent on
and . Changing coordinate has to be counted off the end of
the line, due to that
has to be substituted by
. As a
result we get a reflected wave
(6)
Reflected voltage wave at the beginning of the coil
where
is
(7)
At this point wave is reflected again in the direction of the
direct wave due to short circuit. Let’s label it
.
Calculation of Tesla coil load influence
Angle
that characterizes an influence of a load to a
Tesla coil can be calculated using the complex reflection
coefficient at the end of the line.
where
line;
complex direct voltage at the output of a
complex reflected wave at the output of a line;
characteristic impedance;
complex output impedance.
Inserting into expression (8) the value of output impedance
we get
Module of reflection coefficient is
.
Its phase
can be expressed using sinus or tangents
from but preference is given to
function due to a
fact that this function also respects a position of this angle in a
quadrant
and using (8) it can be expressed
.
(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
input capacity because it is shunted by short-circuit which is
created by an inner resistance of a generator which is close to
zero. Wave resistance
value has a small significance,
either. Hence at the
coordinate a wave reflected in a
direct direction is in an opposite phase with the falling wave
.
(12)
Tesla coil amplitude-frequency characteristic
Tesla coil is a resonance system with a high goodness .
Coefficient shows how many times output voltage is bigger
than input voltage
.
To make a determination of an amplitude-frequency
characteristic of a Tesla coil easier it is assumed that a voltage
wave propagates in a line without losses, it is reflected times
without changing amplitude and then immediately disappears.
In a result output voltage will be increased times which
conforms to the reality. When a goodness of a coil would
change the resonance frequencies should also change slightly,
but this approximation does not anticipate it. It should be
considered a shortcoming of this method.
To get a Tesla coil amplitude-frequency characteristic it is
desirable to transition from two argument function to a single
argument function. It is possible to get rid of the time
dimension by transferring direct (4) and reflected (6) wave
functions to the complex plane:
;
(13)
(14)
This transformation allows writing direct and reflected
signals in a complex form as shown in the expressions (13)
and (14).
Direct wave in line
.
Direct wave at the end of a line
together with an
influence of a load
.
Reflected wave at the end of a line
, using (11)
.
Reflected wave in a line
.
Reflected wave at the beginning of a line
.
It is reflected from the beginning of a line again as shown in
(12) and becomes a reflected direct wave
.
Reflected direct wave at a current coordinate of a line
.
Similarly further direct and reflected waves can be found
,
,
,
, and so on times.
If
the last reflected wave in a line is
.
It is beneficial to choose goodness of a coil equal with
where is a natural number starting with 1, because in this
case an analytical function of sum of different waves can be
15
easily found. As an example a summary voltage in a coil with
which corresponds to
is shown.
(15)
Inserting into expression (15) corresponding direct and
reflected waves and summing them by pairs, after
simplification, an expression is obtained
where
In Figure
characteristic
8
,
an
example of
with values
,
amplitude-frequency
,
,
is shown.
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
shows an amplitude of the standing wave in a dependence
from coordinate .
Expression (16) in a general way for different values of
goodness can be written
at a condition that
, where is a natural number
starting with 1
.
Using (19) voltage for a line with other
can be
written. For example, if
then goodness of a coil
is
, and 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
natural number.
If
is inserted in the expression (19) and it is
simplified, a four wave summary voltage
which
corresponds to goodness
is obtained:
(21)
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
, 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.
In Figure 8 it can be observed that at increasing frequency
resonance output voltage decreases, it happens due to
increasing phase shift
which is caused by output
capacity
. At frequencies between base resonances micro
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
expression (19) by variable and equalizing this derivative
with zero it frequencies of voltage maximum in a line can be
calculated. To avoid influence of micro maximums it is
advisable to use the multiplier of the four wave variation
(21) of the expression (19)
by substituting with line end coordinate
Deriving by variable
and equalizing it
expression is obtained
,
,
where
.
Inserting into (24) expression
against , resonance frequencies are obtained
.
with zero, an
(24)
and solving it
For example, for a quarter wave resonance
For
wave resonance
and its angular frequency is
Similarly resonance angular frequencies for other waves
can be found.
Tesla coil standing wave calculation
, (22)
:
16
To acquire standing wave sight amplitude multiplier of the
expression (19), which is dependant from coordinate , can be
used and maximum voltage in a line can be normalized. As a
result normalized voltage is obtained, it is necessary to take
module of it:
.
(28)
Using the expression (28) and normalizing it to the length
unit a voltage distribution in a homogenous line without
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
is shown in Figure 2.
If the closest to a load minimum coordinate and number
of whole half waves in a coil are known
value can be
calculated by equalling the expression (28) with zero:
.
Physically corresponding solution of this equation is
.
(29)
By substitution of
and
into the
equation (29) it can be obtained
which is usable both with capacitive and inductive loads in a
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
wave resonances
In Figure 9 voltage distribution examples for
and
(Figure
9.a) and
(Figure 9.b) wave resonances by coordinate are
shown. Output of the coil is loaded by electrically conductive
sphere with a diameter
and self-capacity
. Output idle-load capacity which is created by
last windings of the coil and coil output terminal is
approximately
. Summary output capacity
.
In idle load mode when
maximal voltage of a line
is equal for both all half waves, and output quarter
wave
. If there is a reactive load at the output of a
coil,
.
In a case of a capacitive load voltage minimum point
coordinate
moves closer to the load and output quarter
wave gets shorter, i.e. gets smaller than , but in a case of
inductive load coordinate
moves away from the load and
output quarter wave gets longer than .
Determination of load induced angle
wave distribution is known
if standing
which is solved against unknowns
and
product of output capacity and wave resistance
. As a result
and load induced phase shift for quarter wave resonance
are obtained.
If approximated angle
may be calculated easier. As
resistance of capacitive output is inversely proportional to
frequency
, knowing voltage shift angle
introduced by coil output reactivity at one frequency it can be
proportionally calculated for other frequency, therefore
Equation (34) gives a result which is approximately by 5%
different comparing with the formula (33).
Knowing quarter wave resonance
, its wave length
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)
has to be derived by , substituted by
and
17
, and equalized with zero. Expressing quarter wave
resonance wave length from the obtained equation we get:
Formula (35) shows that in case of a negative
wave
is bigger than a coil length .
quarter
Tesla coil as a long line experimental research
Experimental scheme for Tesla coil research is shown in
Figure 10. In a one layer winded as one-wired connection
Tesla coil is attached to a voltage generator Γ-112A output
(Figure 5). Diameter of the coil is
, length
, diameter of enamelled wire including isolation
, number of winds
.
Tesla coil inductivity if measured with alternating current
bridge E7-8 at a frequency
is
. That
means
.
L
C
l
x
0
E(t)
Figure
10: Scheme of experiment
diameter
and
connected to
coil output. Self-capacities of these spheres are
and
. Length of connection wire is
approximately 5 cm.
During experiments different resonance frequencies are
measured
and standing wave characteristics for each of
them are registered. Results of the measurements are shown in
Table 1. Voltage knot point coordinates are labelled by
,
where n – resonance sequence number, m – knot sequence
number starting from the closest to the load.
Resonances also occur at higher frequencies but their
voltage level is low and it is difficult to perform qualitative
measurements.
From the measurement results it can be observed that under
influence of load capacity
resonance frequencies slightly
decrease and voltage knot points move closer to the end of a
line.
Using standing wave knot coordinates it is possible to very
if the line is homogenous by comparing number of half waves
of one standing wave sight with the maximum number of half
waves. When load is not connected for a
resonance number
of whole half waves in a coil
in Table 1.
,
and their lengths are show
,
In experiments when load capacity
is required different
diameter metallic balls or cylindrical bars that are attached to
coil output with approximately
long wire are used. In
measurements without load connection output wire remains
and together with the last wind form an idle-load output
capacity
of the coil.
Electrical field intensity distribution near Tesla coil is
registered ether with neon lamp by observing intensity of its
glow or by voltage induced in oscilloscope probe which has
high input resistance.
Measurements are performed both when load is not
connected, and with electrically conductive spheres with
.
Comparing different half wave lengths in different Tesla
coil regions it can be observed that they are different. That
means phase coefficient and characteristic impedance
are
dependant from coordinate of a long line. It can be concluded
that the basic parameters of the line
and
are also
changing. At the ends of a coil half wave lengths increase,
therefore , , decrease. Magnetic field at the centre of a
coil is homogenous; therefore inductivity by length unit is
the highest. By getting closer to the ends of a coil magnetic
field
starts
to
scatter
and
is
decreasing.
Table 1
Sphere D
0
0
39.4
2.19
65
3.62
Wave type
Frequency
(
)
Knot
point
coordinates
( )
Frequency
(
)
Knot
point
coordinates( )
Frequency
(
)
Knot
point
coordinates
( )
1.635
4.525
–
1.473
4.156
–
9.266
67.5
34
72.5
46.5
24.5
8.836
6.633
73.5
36.6
1.362
–
7.036
3.977
6.478
76.5
38
77.5
49.5
26.3
8.717
78.5
50.5
26.5
18
In Figure 11 experimentally determined resonance
frequency placement of a Tesla coil is shown. Amplitude is
given in relative units because it is a problem to exactly
measure voltage in a line and its ends without changing its
value. It is a problem because there is no such voltmeter that
would have input capacity
equal with 0. Experiments show
that Tesla coil working conditions are being influenced even
by connection of 1 capacity. Output voltage value can be
indirectly estimated by a length of electric spark at the output
of a coil.
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
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
while frequency is rising are increasing because radiated wave
length
is closing to the dimensions of a coil. By
increasing of the losses resonance frequency decreases,
therefore decreases .
Using the closest to an output of a coil voltage minimum
coordinate for different resonances
(
, average wave length
and angle
values for different resonances with not connected output
capacity
can be determined.
for a
wave
resonance;
for
a
wave
for
a
wave
It must be admitted that coordinates for higher resonances
and
are located close to the end of the coil, therefore
their determination is associated with high measurement error.
Measurement offset in bounds of one centimetre causes
change of
value by more than 10 degrees.
By knowing average resonance wave lengths
, using
formula
respective average phase coefficients
can be calculated:
;
;
;
.
Knowing average phase coefficients
, product
for each resonance can be calculated:
;
;
;
.
Average capacity by length unit
:
;
;
;
.
Average characteristic impedance
:
;
;
;
.
By viewing obtained data it can be noticed that average
capacity by length unit
by rising frequency is increasing by
approximately 35% and
is decreasing by approximately
20%, although these values should be constant. It might be
explained with inhomogeneity of the line.
To obtain idle-load output capacity
and local
characteristic impedance in reflection zone
it is necessary
to obtain together with idle-load resonance frequencies and
output angles
the same parameters for a known load
capacity
. Obtained results have to be processed using
formula (32) and equation system for idle-load and loaded
cases have to be solved.
resonance;
resonance.
By using formula (30) angle is obtained:
for a
wave resonance;
for a
wave resonance;
for a
wave resonance.
By knowing
and using formulas (33) and (35) quarter
wave resonance parameters can be calculated
and
.
By solving equation (36) characteristic impedance at the
reflection zone
and idle-load output capacity are obtained
By inserting into the equations (37) and (38) respective
(from Table 1) and
(formula (30)) values following results
are obtained:
19
1.
From
resonance
1.1. For
sphere,
,
,
.
sphere
,
,
.
2. From
resonance
2.1. For
sphere
,
,
.
2.2. For
sphere
,
,
.
Differences between calculated results
and
, which
are obtained for both resonances, can be observed.
resonance data should be considered more correct because of
increasing measurement errors for higher order waves.
1.2. For
1.
2.
3.
4.
5.
6.
Conclusions
Tesla coil can be considered a one-wire electrical
system.
Tesla coil is a long line with distributed parameters
that as a common wire has a virtual ground.
At particular frequencies electrical resonances with
different spatial configurations form in a coil.
Resonance processes in a Tesla coil can be
theoretically described using traditional theory of a
long line.
Existence of resonance networks in Tesla coils is
approved experimentally.
Obtained experimental results comply with
theoretically calculated values.
10. J. Voitkāns, A. Voitkāns, I. Osmanis. „Investigations on
Electrical Fields and Current Flow Through Electrode
System Within Electrode”. 8th International Scientific
Conference „Engineering for Rural development”, Jelgava,
2009.
11. J. Voitkāns, J. Greivulis. LV patents Nr. 13432
„Sinusoidāla sprieguma pārvades vienvada līnija”. „Patenti
un preču zīmes”, 2006. Nr. 6.
12. J. Voitkans, J. Greivulis. Loading aspects of a single
wire electric energy transmission line. International
scientific conference „Advanced Technologies for Energy
Production and Effective Utilization”. Jelgava, 2004.
13. J. Voitkāns, J. Greivulis. LV patents Nr. 12932
„Vienvada regulējamā elektropārvades līnija”. „Patenti un
preču zīmes”, 2002. Nr. 12.
14. J. Voitkāns, J. Greivulis. LV patents Nr. 13031
„Simetrizēta vienvada elektropārvades līnija”. „Patenti un
preču zīmes”, 2003. Nr. 7.
15. B.B. Anderson. The Clasic Tesla Coil, 2000.
http://www.tb3.com/tesla/tcoperation.pdf
7.
8.
9.
Obtained mathematical single wire line results can
also be applied to a traditional two wire long line.
In Tesla coil parameters
,
,
and
are
dependant from length coordinate .
It is better to calculate Tesla coil base parameters
from lower resonances due to lower measurement
errors.
References
1. Dūmiņš I., Tabaks K., Briedis J. u. c. Elektrotehnikas
teorētiskie pamati. Stacionāri procesi lineārās ķēdēs, I. Dūmiņa
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-coildesig_20101219_062111
3. Marco Denicolai, Tesla Transformer for Experimentation and
Research.
http://www.saunalahti.fi/dncmrc1/lthesis.pdf
4. J. Voitkāns, J. Greivulis. Elektriskās enerģijas pārvadīšanas
iespējas pa vienvada līniju. II Pasaules latviešu zinātnieku
kongress. Tēžu krājums, Rīga, 2001, 263 lpp.
5. J. Voitkāns, J. Greivulis. Vienvada elektropārvades līnijas
eksperimentālās iekārtas tehniskie raksturojumi. Zinātniskā
konference „Elektroenerģētika tehnoloģijas”. Tēžu krājums,
Kauņa, 2003.
6. J. Voitkans, J. Greivulis, A. Locmelis. Single wire transmission
line of electrical energy. EPE – PEMC scientific conference,
Riga, 2004.
7. J. Voitkāns, J. Greivulis, A. Voitkāns. Single Wire and
Respective Double Wire Scheme Equivalence Principle. 7th
International Scientific Conference „Engineering for Rural
development”, Jelgava, 2008.
8. J. Voitkāns, S. Voitkāns, A. Voitkāns. LV patents Nr. 13785
„Elektriski vadoša ķermeņa paškapacitātes mērītājs”, „Patenti
un preču zīmes”, 2008. Nr.10.
9. I. Dūmiņš Elektrotehnikas teorētiskie pamati. Pārejas procesi,
garās līnijas, nelineārās ķēdes., Zvaigzne ABC, Rīgā, 2006.
16. G.L.Johnson.
Solid
State
Tesla
Coil.2001.
http://hotstreamer.deanostoybox.com/TeslaCoils/OtherP
apers/GaryJohnson/tcchap1.pdf
17. G.F.Haller, E.T.Cunningham. The Tesla High
Frequency Coil. New York, 1910.
Janis Voitkans, graduated from Riga Polytechnical Institute in
1976 as radioengineer. He received Dr.Sc.ing. in electrical
engineering from Riga Technical University, Riga, Latvia, in in
2007. Research interests are connected with electro physics and
power electronics.
He is presently a Senior Researcher in the Institute of Industrial
Electronics and Electrical Engineering, Riga Technical University
Address: Āzenes 12, Riga, Latvia;
e-mail: [email protected]
Arnis Voitkans, received B.Sc and M.Sc in physics from the
University of Latvia, Riga, Latvia in 2003 and 2006, respectively.
Currently works as a leading systems analyst in IT department of
the University of Latvia.
Address: Aspazijas boulevard 5, Riga, Latvia;
e-mail: [email protected]