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Tesla Coil
High Frequency Resonant
Transformers and Wireless
Transmission of Power
• Tesla coils are named after their
creator Nikola Tesla.
• Born in 1856, he developed
numerous concepts including the
fundamentals of wireless
technology, and much of the
alternating current power systems
used today. His most important
invention though, is of course the
Tesla coil.
• He built numerous Tesla Coils
including one so large he thought he
was going to send free power to
everyone around the world with it.
Primary Circuit
The primary circuit
consists of:
• The high voltage
transformer
• The spark gap
• The tank capacitors
• The primary inductor
•The capacitors, primary inductor, and spark gap will form an LC circuit
How the Primary Circuit Works
• First, current enters the transformer from the mains (wall outlet)
• The current outputted by the transformer charges the capacitor bank
• When the capacitors are charged, the voltage across them is so low that
almost all of the voltage from the transformer ends up on the
electrodes of the spark gap
• At this point spark gap becomes conductive, forming a short circuit
• This creates the LC circuit. Current sloshes back and forth from one
side of the capacitors to the other in an attempt to neutralize, at radio
frequency. To do this it must travel across the spark gap and the
primary inductor
• Energy is eventually lost to the secondary coil and heat and the spark
gap ceases to be conductive
• At this point, the cycle starts over
Secondary Circuit
•The secondary circuit consists of just the secondary coil, the toroid topload,
and the ground.
•The secondary coil is an inductor which forms a transformer together with
the primary inductor
•The current oscillating at radio frequency through the primary creates a
rapidly changing magnetic flux in the secondary coil
•This induces an EMF and a current in the secondary coil
•The charge accumulates on the toroid, which is directly connected to the
secondary coil
•The bottom of the secondary coil is connected to ground in order for the
secondary circuit to have capacitance relative to the ground
Power Source
•For the high voltage power
source needed by the primary
circuit we used a neon sign
transformer
• The neon sign transformer
steps up the voltage of the
mains AC to 12kV and
outputs 60 milliamps of
alternating current
Peak Voltage vs. RMS Voltage
• It is important to note that the 12kV transformer
actually has a much higher peak voltage
• Since the voltage it puts out is AC, it is actually
a sine function that alternates between +6000
and –6000 volts
• However, these values are RMS, or RootMean-Square
• This means they are essentially an average; the
12kV is the area under the curve
• At the peak of the wave, the voltage is actually
√2 ∙ RMS
• Therefore, our transformer has a peak voltage
output of √2 ∙ 12000 or nearly 17kV
Capacitors
• The first thing we had to do
was find our target
capacitance.
• Ideally, the capacitors should
charge in the time the
transformer takes to put out its
peak voltage, which is ¼ its
period
• We therefore solve the system
of equations Q=CV=tI
• Here, t is the amount of time
the current flows, which we
want to be ¼ the period T of
the voltage function
•Therefore, Q=CV=(T/4)I
•Solving for the capacitance C, we get C=TI/(4V)
•T is the period of the AC which is 1/60 since it operates at 60 Hertz, and we shall use
the RMS voltage of 12kV
More on Capacitors
• We use the RMS value because it will yield a slightly larger capacitance, which
is generally preferable
• Substituting into the equation, C=(1/60 s)(.06A)/(4∙12000V)=20.8 nF
• In addition to achieving this capacitance, our capacitors had to withstand 17kV
with the current oscillating at radio frequency. Since capacitors are not rated for
that kind of use, we had to get capacitors rated for about twice that much
voltage
• We ended up buying 30 2kV 150 nF capacitors. We had two strings of 15 in
series, in which the voltages add to 30kV and the capacitance drops to 10 nF
according to the formula Ceq=1/(1/C1+1/C2+…+1/Cn)
• The two strings of series capacitors were then hooked up in parallel, in which
the capacitances add to 20 nF and the voltage capability remains at 30 kV
• There are also 1.5MΩ resistors across the capacitors. This is because each
capacitor has a little internal resistance, and if it is not the same for all
capacitors, they could get an unequal voltage distribution. The huge resistors
prevent this from happening by making the internal resistances insignificant
Spark Gap
•The spark gap serves the purpose of
creating a short circuit when the
capacitors charge, forming an LC
circuit
•It can be thought of as an open
switch which closes when the circuit
reaches a certain voltage
•The voltage difference from the
transformer accumulates on the
diodes and makes the air between
them conductive
•The breakdown of air for this
design is roughly 10kV per cm
•Our spark gap consists of two steel
bolts facing each other in an ABS Tfitting. There are two fans blowing
air through the tube to quench and
cool the gap
Primary Inductor
•The primary inductor is commonly called
simply the primary
•Its purpose is to create a rapidly
changing magnetic field in the center in
order to induce a huge EMF and a small
current in the secondary coil
•Since the primary is a part of the LC
circuit, the current is constantly
oscillating through it, thus creating the
changing magnetic field
•The frequency of oscillation in the LC
circuit is very important as we shall see,
and is given by the equation
ƒ=1/[2π√(LC)] where L is the inductance
of the primary and C is the capacitance of
the capacitors
•In our case, ƒ=290kHz, which is radio
frequency but well below the AM band
Our Primary consists of about seven
turns of 1/8 inch copper tubing.
Self Inductance of the Primary
• The formula for the
inductance of a spiral coil is
difficult to derive, therefore
we shall not do it here
• However, the formula is
L=(NR)²/(8R+11W) where N
is the number of turns, R is
the average radius of the coil
in inches, W is the width of
the coil in inches, and L is the
inductance in microhenrys
Resonance, Impedance and Reactance
• Before proceeding to the secondary coil, it is important to have a basic
understanding of resonance, impedance, and reactance
• Resonance is a form of constructive wave interference. That is, waves collide at
exactly the right time as to reinforce each other
• A good analogy is that of holding a slinky by the ends and pushing down on it in
the middle every time it’s on the way down. The slinky will begin to stretch more
and more because you are inputting energy at the exact right moment each time
• Impedance is similar to resistance, except it accounts for possible phase offsets
in the current
• It has an imaginary component for this phase offset. Impedance Z is given by
Z=R+jX, where R is the resistance
• X is the imaginary component of impedance, which is called reactance. There
are two kinds of reactance: inductive and capacitive. Inductive reactance has to
do with the fact that inductors resist changes in current. Therefore the inductive
reactance XL is proportional to the frequency and is given by XL=2πƒL.
Capacitive reactance has to do with the fact that while electrons cannot pass
through a capacitor, AC current effectively does, so the capacitive reactance XC
is proportional to 1/ƒ and is given by XC=1/(2πƒC)
Secondary Coil
•The secondary coil/inductor,
generally called simply the secondary,
gets an induced EMF and current due
to the changing magnetic flux at its
location
•Unlike most transformers, this
secondary has air inside of it instead
of iron. This is because instead of
stepping up the voltage with the iron
core, it uses the high frequency of
oscillation and resonance.
• For this reason the Tesla coil’s
proper name is a high frequency
resonant transformer.
Our secondary consists of almost
exactly 1000 turns of 24 gauge magnet
wire, hand-wound around 3.5”
diameter ABS pipe
Self Inductance of the Secondary
•The equation for the inductance of a helical coil
is much like that of the spiral coil
•It is not the formula for an ideal solenoid because
it is not quite ideal. It isn’t infinitely long and does
not have an infinite turn density
•It is given by L=(NR)²/(9R+10H) where L is the
inductance in microhenrys, N is the number of
turns, R is the radius of the coil in inches, and H is
the height of the coil in inches
Capacitance in the Secondary
•The secondary coil and toroid form capacitance relative to the
ground, since the bottom of the secondary is grounded
•The secondary has self-capacitance according to the equation
C=.29L+.41R+1.94√(R³/L) where C is the self-capacitance in
picofarads, L is the length of the secondary coil in inches, and R is
the radius of the coil in inches
•The toroid has capacitance equal to C=1.4(1.2781-D2/D1)√[πD2(D1D2)], where C is in picofarads, D1 is the outer diameter of the toroid
in inches and D2 is the diameter of a cross-section of the toroid in
inches
•This capacitance is necessary for the charge to arc towards
grounded objects and to create streamers
Resonance in the Secondary
• In order to function properly, the secondary has to have the same
resonant frequency as the primary circuit.
• This is so that the electromagnetic waves emitted creating the EMF
will reinforce each other instead of canceling out.
• Everything has a natural resonant frequency. For example when you
hit a pitch that coincides with the natural resonant frequency of a wine
glass, it shatters.
• The natural resonant frequency of a coil for electromagnetic purposes
occurs when its inductive reactance has equal magnitude to its
capacitive reactance. Setting the equations equal, we get
XC=1/(2πƒC)= XL=2πƒL.
• Solving this for ƒ, we get ƒ=1/[2π√(LC)].
• Note that the formula itself is the same as the formula for the
frequency of oscillation in the primary circuit. This was not derived for
us when we learned about LC circuits, but it is for the same reasons.
Streamers
The Tesla coil puts beautiful
branching arcs of electricity
just out into the air. It is able
to do this because of the
rapidly shifting charges inside
the secondary, which are
capable of actually pushing
charge out into the air, and
pulling it back in again at
radio frequency.