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RE: [TCML] Capacitor dielectric examples and Tesla coil equations
Looks like the formatting didn't come across in the email. The file can be correctly viewed from my website
http://www.figmentcode.com/tesla/TESLA-EQ.TXT
----------------------------------
Brian Hall
> From: brianh4242@xxxxxxxxxxx
> To: tesla@xxxxxxxxxx
> Date: Tue, 1 Dec 2009 19:37:03 -0500
> Subject: [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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