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[TCML] Capacitor dielectric examples and Tesla coil equations
I came across this file that answers many questions that a lot of beginners have, in a nice user friendly and plain text format. Enjoy!
My favorite part of this, that I have seen other tutorials sometimes skip, is that werever there is a letter or non-numeric value in an equation, it tells you what that variable represents right next to it! In my experience, when that type of information is missing from an introduction to a formula, I am left wondering what a certain variable means - and end up asking what, based on the tone of the replies, come across as a 'you should already know that' question - because so much documentation is aimed at people who already have exposure to some form of electrical engineering or these types of calculations, and not everyone coiling these days does, even if they are capable of contructing and using a TC safely. Especially high school students (with adult supervision of course) who are seeking to learn about this wonderful invention and this is their first exposure to inductance, capacitance and the like.
Hooray for useful documentation! And thanks to those who have been providing complete answers like these all along.
(view in a Courier or Courier New font for best redability - where each character is the same width)
---------------------------------
Brian Hall
=======================================================================
INFORMATION FOR BUILDING CAPACITORS: Comments
|
Puncture Voltage |
Material Dielectric strength per Mil |
"K" (0.001 inch) |
| | |
-----------------------------------------------------------------------
Miscellaneous
-------------
Vacuum 1.0
Paper, bond 3.0 200
Paper, Royal Grey 3.0 200
Paper, telephone, treated 2.5 - 4 200 - 250 *
Paper, Parafin Coated 2 -3.5
Paper, Kraft 2.2
Oil, Castor 4.67
Oil, Mineral, Squibb 2.7 200
Oil, Mineral 2.2
Oil, Transformer 2.1 - 2.5 75 *
Rubber 3.0
Rubber, Hard 3.0 160 - 500 *
Rubber, Vulcanized 3.2 - 3.9 1
Fibre 5.0 - 7.5 150 - 180
Fibre, Red 5.0
Mica 4.5 - 8.0 3800 - 5600
Mica, Ruby 5.4 3800 - 5600
Quartz 3.8 - 5.0 1000
Quartz (Fused) 4.2 150 - 200 *
Shellac 2.5 - 4.0 200 - 400
Spar Varnish 4.8 - 5.5
Steatite, low loss 5.8 150 - 315
Steatites (Magnesium silicate,etc) 5.5 - 7.5 200 - 300
Cambric (Varnished) 4.0 2
Alsimag 196 5.7
Gutta Percha 4.0 3
Amber 3.0 - 7.0 4
Resin 2.48 - 2.57
Enamel 5.1 450
Mycalex 7.4 250
Silicone RTV 3.6 550
Wood 2.0 - 5.2
Wax (Parafin) 2.1 - 2.5 250 - 450 *
Beeswax 2.9 - 3.0
Slate 7.0 5
Barium titanate(25 C) 1200
Bariam titanate 6000
Titanium dioxide 125
Cellulose acetate 3.3 - 3.9 250 - 600
Casein, Moulded 6.4 6
Polytetraflourethylene 2.0 A
Aluminum oxide 8.7
Tantalum pentoxide 22
Glass
-----
Glass 4.8 - 10 300
Plate Glass 6.8 - 8.4
Pyrex Glass 4.8 - 10 335
Window Glass 7.6 - 7.8 200 - 250
Ceramics
--------
Cordierite ceramics 5.0 - 5.5 100
Magnesium titanate ceramic 12 - 18 150
Porcelain 5.1 - 7.5 40 - 280
Titanium dioxide ceramic 70 - 90 100
Titanium-zirconium dioxide ceramic 40 - 60 150
Plastics
--------
Bakelite 4.4 - 5.8 300
Bakelite, Mica filled 4.7 325 - 375
Epoxy Circuit Board 5.2 700
Formica 4.6 - 4.9 450 7
Nylon (lowest values of 3 types) 3.2 407
PVC (rigid type) 2.95 725
Plexiglass 2.8 450 - 990
Polyethylene 2.2 - 2.3 450 - 1200
Polycarbonate (Lexan) 2.96 400
Polyethylene Terphthalate (Mylar) 3.0 - 3.1 7500
Polystyrene 2.5 - 2.6 500 - 700
Teflon 2.1 1000 - 2000
Gases
--------
Air (dry air at 1 atm) 1.0006 30 - 70
Air (20 atm, 19 deg. C) 1.0108 500 *
Carbon dioxide ( 1 atm, 0 deg. C) 1.000985 36 *
Carbon dioxide (20 atm, 15 deg. C) 1.020
Hydrogen (1 atm,0 deg.C) 1.000264 26.1 *
Liquids
--------
Amonia (liquid) 22
Benzene 2.28
Carbon tetrachloride 2.24 8
Chlorinated diphenyl 6.5 9
Ethyl Alcohol (O C) 28.4
Ethyl alchohol (20 deg.C) 25.8
Methyl alchohol 33.1
Water (distilled) 80 - 81
LEGEND:
* = Measured in Kilovolts per centimeter. All others are Volts per
mil (.001 inch) unless otherwise stated.
1 = Vulcanized means it has been melted, or heated in some way.
2 = Cambric is a finely woven white linen or cotton fabric.
3 = Gutta Percha is a rubbery substance made from the latex of tropical
trees and is used in insulation, waterproofing, and dentist use it
in thin sheets sometimes when working on teeth.
4 = Amber is a hard, translucent, yellow, orange, or brownish yellow
fossil resin, used in making ornamental objects like jewelry.
5 = Slate is a fine grained metamorphic rock that splits into thin
smooth faced layers. Black Boards for writting are made of this.
Also used as roofing material in some areas.
6 = Casein is a white, tasteless, oderless milk and cheese protein used
in the manufacture of plastics, glues, paints, and food. The word
'moulded' means it has been shaped by a mold.
7 = Formica is a trademark for any of various high-pressure laminated
plastic sheets of melamine and phenolic materials used for chemical
and heat-resistant surfaces.
8 = Carbon tetrachloride is a very toxic substance. It has also been
shown to cause cancer in lab animals. It is banned in most labs. It
is a liquid that was used as a strong solvent.
9 = Chlorinated diphenyl is a liquid dielectric that is used to
impregnate Kraft paper in small A.C. capacitors. This is a PCB
and may cause cancer, handle carefully.
A = Polytetraflourethylene films retain good properties even at
200 degrees Celsius (200 C).
atm = atmospheres (pressure of air at sea level is 1 atm).
deg.C = degrees Celsius.
Warning - Some liquids and gases listed may be explosive
under the right conditions. Many solids can
catch fire and burn. Use CAUTION and GOOD COMMON SENSE.
Note: Some books gave very different values for each substance so I
have given you the highest and lowest values reported. The values
will depend on the purity of the substance your using. If you
know your substance is very pure then use the higher value
reported. If you know your substance is contaminated or of poor
quality then use the lower values reported. If you have unknown
purity then use the average of the values given.
=======================================================================
EXPLAINATION OF EQUATIONS:
Here are some real handy equations. They are very simple and easy to
use.
x = Multiply by
/ = divide by ( may also use line seperating terms above and below
line as in standard mathematics).
( ) = Terms in parentheses should be calculated first as in standard
algebraic equations.
pi = 3.141592654. The circumferance of a circle divided by it's
diameter will always give you this constant.
2
Z = means the term "Z" multiplied by itself one time,"Z x Z".
Note: In some cases I do not use the symbol "x" but instead simply
put the terms close together, example: "LC" instead of "L x C".
This is standard for algebraic equations and means "multiply by".
=======================================================================
MATH FOR TESLA COILS
1. Determine your neon sign transformer (or other transformer's)
Impedence:
E
Z = ---
I
Z = Impedence
E = volts
I = current in Amps
Note: divide milliamps by 1000 to get Amps. 30 milliamps = .030 Amps.
The Impedence of the primary capacitor should match the Impedence of the
transformer at 60 Hz (60 Hz is the AC cycle rate of common household
wall sockets, at least in America).
2. To match Impedence and determine capacitor value:
1
C = -------------------
2 x pi x Z x .00006
C = capacitance in microfarads needed for primary capacitor.
Z = Impedence from equation one (Transformer Impedence)
pi = 3.141592654
Note: The .00006 is the 60 Hz AC, if you live outside the US then
substitute your cycle rate.
Next you need to find the Reactance of the primary capacitor at the
frequency you have choosen. Many times the frequency is decided by the
length of wire used on the secondary coil. See below for equations that
determine frequency by length of wire used on secondary.
When we find the Reactance , we can then find your needed Inductance
for the Primary coil.
3. To determine Reactance of capacitor:
1
X(C) = ---------------
2 x pi x C x F
X(C) = capacitor Reactance
C = Capacitor value in microfarads, from equation 2)
F = Frequency in Mhz (megahertz)
pi = 3.141592654
Note: To convert kilohertz to megahertz simply divide by 1000.
190 Khz = .190 Mhz
4. To determine the Inductance needed for Primary coil:
Set X(L) = X(C)
X(L)
L = ------------
2 x pi x F
L = Inductance in microhenries needed for Primary Coil.
To get millihenries divide the answer by 1000.
X(L) = Reactance from equation 3, same as X(C).
F = frequency in Megahertz. Divide Khz by 1000 to get Mhz.
pi = 3.141592654
Now you know the values for your capacitor and primary coil. These
values will give you the best ringing for your circuit (ie. more bang
for your buck)! Use the equations below to finnish the project.
Note: Many people don't go to the trouble to work these equations out.
They simply slap the parts together and then try to tune. If you work
the equations out first you will save lots of time in tuning, you will
at least be in the right ball park! Also, just because you worked it
out on paper that doesn't mean it will work the first time you plug it
in. Trial and error is a large part of the Tesla Coil hobby!
=======================================================================
CAPACITORS IN PARALLEL:
| |
|__C1__|
| |
|__C2__|
| |
|__C3__|
| |
Capacitance = C1 + C2 + C3, etc...
Maximum voltage rating will be equal to the voltage rating of the
lowest voltage capacitor of the group.
=======================================================================
CAPACITORS IN SERIES:
| |
|__C1__C2__C3__|
| |
| |
1 1 1
Capacitance = 1 / --- + --- + ---, etc...
C1 C2 C3
The total capacitance of several capacitors in series will always be
LESS than that of the smallest capacitor.
Total voltage rating increases with number of capacitors in series.
Simply add the voltage ratings together.
When capacitors are placed in series to increase voltage rating they
should have the same capacitance and voltage rating else voltages will
divide unevenly, most likely causing failure.
=======================================================================
EQUATION 1: PLATE TYPE CAPACITORS
Capacitance (in picofarads) = (0.224 KA / d) (N-1)
0.224 x Dielectric Strength x Area of plate
C = ----------------------------------------- x (Number of plates - 1)
distance between plates in inches
Note: to convert picofarads to microfarads divide by 1000000.
=======================================================================
EQUATION 2: LEYDEN JAR or SALT WATER TYPE CAPACITORS (jar/bottle type)
2
C = .0884 k ( pi r + 2 pi r l )
------------------------------
1,000,000 t
C = Capacitance in microfarads
k = dielectric strength
r = jar radius in centimeters
l = height of the jar portion used (in centimeters)
t = thickness of the jar wall in centimeters
pi = 3.141592654
2
r = r x r (radius squared)
=======================================================================
EQUATION 3: FREQUENCY OF A CIRCUIT
1
f = --------------------
__________
2 pi / L C
f = frequency in cycles per second
L = circuit inductance in henries
C = circuit capacitance in farads
pi = 3.141592654
_________
The symbol " / " means the square root
For a result "f" in Khz: enter "C" in microfarads, "L" in microhenries
and multiply result by 1000.
=======================================================================
EQUATION 4: INDUCTANCE OF A FLAT PANCAKE COIL
Picture a 1 inch flat ribbon that is about 30 feet long. Now, roll
that ribbon into a spiral that has all its sides about 1/2 inch apart.
Most common material is Aluminum Roof Flashing. Use plastic bolts to
hold sections of strips together if you have short pieces of ribbon.
This makes a good mechanical connection (you can't solder aluminum).
center axis
|
| | | | | | | | | | | <---cross section
| of flat spiral
|---A----| |---W---| coil.
|
2 2
a x n
L = ---------------
8 a + 11w
L = inductance in microhenries.
a = average radius in inches as measured from the central axis to
the middle of the winding.
n = number of turns in the winding.
w = width of the coil in inches.
Note: Make sure you measure "a" from center axis - the very middle
of your secondary sitting inside of your primary.
=======================================================================
EQUATION 5: NUMBER OF TURNS FOR A HELICAL PRIMARY
_________________________
/
N = / L [( 9 x R) + (10 x H)]
/ --------------------------
/ 2
\/ R
N = Number of turns needed.
L = inductance in microhenries desired.
R = radius (inches).
H = height (inches).
_________
The symbol " / " means the square root, in this case of whole
equation.
=======================================================================
EQUATION 6: LENGTH OF WIRE NEEDED FOR DESIRED FREQUENCY OF COIL
300,000
L = ------- / 4 x (3 / .9144)
f
f = frequency, in Khz, that is desired for coil.
L = length of wire needed, in feet, for desired frequency.
/ = divided by.
Note - 300,000 is the speed of light in Kilometers per second. the
term "3/.9144" is a conversion factor to turn meters to feet.
You don't have to understand this. Just thought I would tell
those who were wondering.
=======================================================================
EQUATION 7: FRQUENCY OF COIL
300,000
f = ------------------------------
T x W x pi x (.9144 / 36) x 4
f = frequency of coil in Khz
T = number of turns on coil
W = width of the coil in inches
pi = 3.141592654
=======================================================================
EQUATION 8: CAPACITANCE OF A SPHERE IN SPACE
R
C = -------
9
9 x 10
C = capacitance in Farads
R = radius in meters
9
9x10 = 9,000,000,000
6
Note: To convert Farads to microfarads simply multiply by 10 or in
other words by 1,000,000.
=======================================================================
EQUATION 9: CAPACITANCE OF A SPHERE SUSPENDED IN A DIELECTRIC
K x R
C = ---------
9
9 x 10
C = capacitance in Farads
R = radius in meters
K = dielectric constant
6
Note: To convert Farads to microfarads simply multiply by 10 or in
other words by 1,000,000.
=======================================================================
EQUATION 10: CAPACITANCE OF A TOROID
___________________
/ 2
C =(1+ (0.2781 - d2/d1)) x 2.8 x / 2 pi (d1-d2)(d2/2)
/ -------------------
\/ 4 pi
C = capacitance in picofarads (+- 5% )
d1 = outside diameter of toroid in inches
d2 = diameter of cross section (cord) of toroid in inches
Equation courtesy of Bert Pool
=======================================================================
TESLA COIL SCHEMATIC --------
| | TC
--------
O
O
SG SC FCC PC SG P-COIL O S-COIL
O---------------OOOOO---------> <----- O O
NST O | | | | O O
O | | | | O O
-----O||O * --- --- |--->O O
O||O O O
-----O||O * --- --- O O
110 | O | | | O O
Volts | O | | | O O
| O---------------OOOOO---------------------| |
| |
| |
Gnd Gnd
NST = Neon Sign Transformer, 110 volts primary, 15,000 volt secondary
at 30-60 miliamps.
SG = Safty Gap. A spark gap to insure your transformer doesn't get fried.
SC = Safty Capacitor. 300-500 picofarad rated at 50 KV.
FCC = Ferrite Core Choke. This prevents real high voltages from coming
back towards your transformer. It also seperates the capacitors.
PC = Primary Capacitor. Normally .01-.02 microfarads rated 50 KV.
SG = Spark Gap.
P-COIL = Primary Coil.
S-Coil = Secondary Coil.
TC = Terminal Capacitor. The big ball or coffee can on top.
Gnd = Ground.
Note: This is one of several possible schematics. It's just the one I
happen to use.
=======================================================================
Bibliography:
Books:
-------
Theory and Applications of Electricity and Magnetism, Charles A.
Culver, 1947, McGraw Hill Book Company, Inc.
Concept In Physics, Third edition, Frankln Miller Jr., Thomas J.
Dillon, Malcom K. Smith, 1980, Harcourt Brace Jovanovich, Inc.
Tesla Coil Secrets, R.A. Ford, 1985, Lindsay Publications Inc.
Tesla Coil, George Trinkaus, 1989, High voltage Press @Lindsay
Publications.
High frequency Apparatus, Thomas Stanley Curtis, 1916, Lindsay
Publications.
Allied Electronics Data Handbook, 1970
Tesla Coil Design Manual, J.H. Couture, 1992
Radio Amateur's Handbook, 1972
Elements of Physics, 1964
Articles:
----------
Popular Electronics, Make Your Own High Voltage Capacitors,
Anthony charlton.
=======================================================================
WARNING:
Only people who are experienced with High Voltage devices should
attempt to build Tesla Coils. They can be very deadly if you don't
know what your doing. Remember, if they find you on the floor
turning blue and frothing at the mouth - THERE IS NO SECOND CHANCE!
A FEW Safety Tips:
1. Don't ever touch the machine when it is pluged in.
2. Use a safe methode to short out the primary capacitor after the
machine has been run.
3. Don't ever get close to a running Tesla coil, the Primary can
shoot hot white arcs at you that will kill you instantly!
4. Always have a small fire extinguisher close by.
5. Always use kickback preventer circuits so you don't send
15,000 volts back through the wall!
6. Pets, children, and irresponsible adults should be kept away from
your machine intirely!!!
7. Read many books on Tesla Coils and other High Voltage devices
and learn as much as you can about High Voltage Safety!
=======================================================================
Special thanks to Mr. Pool who caught some glaring errors in the second
draft and who contributed with an equation of his own.
I wrote this file because I felt there was a need for some real
information for those of us who actually build Tesla Coils, as opposed
to those who just talk of building them (Grin). I will be adding to this
file from time to time, so watch for updates. I hope it helps you out!
P.S. Let us not forget the words of Tesla, "Let the future tell the
truth and evaluate each one according to his work and accomplishments.
The present is theirs, the future, for which I really worked, is mine".
======================= END OF FILE ===================================
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