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Re: [TCML] Capacitor dielectric examples and Tesla coil equations
And one more thing to look out for. In that list it gives the dielectric
constant as "dielectric strength" see:
http://en.wikipedia.org/wiki/Dielectric_strength and
http://en.wikipedia.org/wiki/Relative_static_permittivity (dielectric constant)
and as John pointed out, does not give any indication of how "lossy" the
materials are at high frequency, or "loss tangent":
http://en.wikipedia.org/wiki/Loss_tangent
So just looking at that list, you might get the impression that Mylar is a great
dielectric. At TC frequencies it heats up rapidly, so not very good at all.
On Tuesday 01 December 2009 07:58:51 pm DC Cox wrote:
> If you design a coil with this math, precisely matching the cap value with
> xmfr impedance, keep in mind you will blow your nst rapidly due to resonant
> rise problems. You have to go approx 1.3 to 1.4 X cap size to prevent this
> unwanted resonance. Most list members know this, but just a warning to
> beginners --- beware.
>
> Dr. Resonance
>
> On Tue, Dec 1, 2009 at 5:37 PM, Brian Hall <brianh4242@xxxxxxxxxxx> wrote:
> > 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
> > ===================================
> >
> >
> > _________________________________________________________________
> > Chat with Messenger straight from your Hotmail inbox.
> >
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>
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