archive:science:math
=======================================================================
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 microfarads) = (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
======================================================================= 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 5: 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 6: 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 7: 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 8: 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 9: 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 =======================================================================
EQUATION 10: POWER FACTOR CORRECTION FOR NEON SIGN TRANSFORMERS
Neons typically have an efficiency of about 50%, in that they
draw twice as much power as they put out. This problem can be
resolved with the use of power factor correction (pfc) capaci-
tance across the line. The pfc capacitors used are the same as
for capacitor starting motors. The voltage rating should be at
least twice the line current used, and I like a 4x voltage margin
for long life. The formula used to determine ballpark pfc is as
follows:
9
10^
C = Corrected kVA ------ 2
2(pi)fe^
This should read C = Corrected kVA times (10 to the ninth power)
over, (2 pi times f times e squared)
C = required capacitance in microfarads f = frequency of applied voltage e = applied voltage
CORRECTED KVA is determined by dividing the volt*amps (watts) output of the neon sign xfrmr by 1000
Equation courtesy of Richard Quick =====================================================================
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!
8. Review the FIDO text files compiled by Richard T. Quick II
======================================================================= Special thanks to Bert 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!
Jerry Gore, Member of Tesla Coil Builders Association (TCBA),
International Tesla Coil Society, and the North Dallas
Texas Tesla Coil Association.
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".
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