This document will describe the equipment and calculations for constructing a medium size Tesla Coil (TC) for the CMU Science Fair in August 2001.  The following diagram shows the complete TC circuit diagram broken down into modules for workgroup assignments.

Description for each module:

• Module 1 – Main power system to supply high voltage to the primary circuit.  The main component is the 15kV@30mA neon sign transformer (NST).  The MOVs are used for protection from back emf due to the reactive charge from the primary circuits.  A RFI filter (wired in backwards) is recommended to reduce RF noise in the AC mains power system.  The variac is not necessary but recommended in order to do initial tests of the power systems at low voltage.  The power factor correction capacitor (PFC) is used to optimize the transformer power transfer and minimize the load on the input power line.  A DPST switch should be used to disconnect both sides of the AC power for safety reasons.
  
  

• Module 2 – Static spark gap and safety gap.  This is the power switch to transfer the capacitor energy into the primary coil (inductor).  The safety gap is used to protect the NST and the primary capacitor from over voltage due to resonant rise from the primary circuit.  Resonant rise can produce up to 3 times the voltage of the NST output.  It should be adjusted with the primary cap and inductor disconnected from the circuit and the spacing set so that it just stops an arc from forming.  For this transformer the peak voltage out (non resonant) is 1.414 x 15kV = 21,210 V.  Spark distance is ~31kV/cm so the spacing should be ~ 21,210/31,000 = 6.8mm (7mm would be a good estimate).  The spacing (total) of the spark gap should be set to fire at the peak voltage of the NST.  This allows maximum charge of the capacitor at discharge time.  So from above it should be ~6.8mm or less.  If the spacing is too wide the safety gap would fire.  If there is no safety gap then the NST and the capacitor could be over stressed and be damaged.
  
  

• Module 3 – Primary capacitor.  This capacitor is used to store the energy from the NST and then rapidly transfer it to the primary coil (inductor) by the spark gap (switch).  Calculations for determining the size of the cap will be discussed later.  Key requirements in choosing a capacitor are, high voltage rating, low loss dielectric at high frequencies (RF), high current pulse capability and temperature handling.  There are three main techniques for making a capacitor to satisfy these requirements. 
  

1. Constructing a plate capacitor with layers of polyvinyl sheet plastic and aluminum foil and immerse in a high voltage oil.  Disadvantage - TIME CONSUMING!
2. Bottle capacitors – this can be something like a beer bottle(s) with aluminum foil wrapped around it on the outside, filled with concentrated salt water and immersed in a tank filled with salt water.  The advantage is that it is simple and cheap to build.  The main disadvantage is it is a poor dielectric and large losses will occur. 
3. MMC (Multi Mini Capacitors).  This is the popular method now.  It allows you to use inexpensive high voltage pulse capacitors instead of one very expensive pulse capacitor.  They are put in series and parallel until the necessary voltage and capacitance is achieved.
   
   

• Module 4 – Primary coil (inductor) - This combined with the primary capacitor forms the first resonance circuit of the TC.  It is generally built using air conditioning copper coils but other wire types can be used.  The key factors is that it needs a large surface area due to the high frequency involved (at high frequency skin effect occurs and most of the power is on the surface of the conductor and very little flows through the center core).  This is why a hollow tube is more cost effective and efficient (large surface area).
  
  

• Module 5 – Secondary coil (inductor) – This, combined with module 6 (top load), forms the 2^nd resonant circuit.  Both the primary and the secondary systems have to be designed to be resonant at the same frequency for optimum energy transfer.  The steps for calculating this will be discussed later.  This coil consists of many turns (800-1500) of a single layer thin wire as opposed to the 10-15 turns of the primary.  The TC does not behave the same as a conventional transformer.  First, energy transfer is not magnet/inductive as in an iron core transformer but is based on electromagnetic fields coupled from the primary to the secondary, which are air core resonant transformers.  This means lower losses due to magnetic/inductive coupling and higher operating frequencies.  In a conventional transformer the power-in/power-out is proportional to the number of primary windings and secondary windings.  In a TC it is related to the coupling factor (k) between the primary and secondary.  The higher the k factor the more efficient the energy transfer between the coils and the more power output you will get.  However, it is necessary to compromise on this.  Too tight of a coupling (a high k factor) will produce too much power in the secondary and cause ‘racing arcs'.  That is the secondary windings will begin to break down and potentially burn the coil up.  The primary coil should be placed at exactly the bottom winding of the secondary coil.  Increasing and decreasing coupling is done by moving the primary up and down relative to this position.  As such the primary or secondary should be designed to allow for adjustment to tune the energy transfer.
  
  

• Module 6 – Top load (toroid capacitor) – This supplies the capacitive load on the secondary and the 2^nd component to establish the secondary resonance frequency.  The toroid shape is optimum due to more surface area and better control of the field and streamer breakout.

Tesla Coil Calculations:

Two main techniques are used to design a TC.  One is designing the secondary system first then the primary (top down).  The second is to design from the high voltage supply to the secondary (bottom up).  The first choice is based on designing a coil with a specific output or streamer length desired.  However this is a problem if you do not have access to component resources.  In other words, you may end up with a design that requires a specific size transformer that is difficult to get.  The 2^nd method is used when you already have an NST (such as in our case).  This makes the design straightforward to do.

 NST specifications:  E=15kV I=30mA  (450VA) (220VAC f=50Hz)

Step 1:  Module 1 & Module 2 – Determining the primary capacitor.  I will not go into LTR (larger then resonance systems) in our design since we are using a static spark gap and not a synchronous spark gap.  We will be charging at the NST/Capacitor resonance frequency of 50Hz.

• Determine impedance (Z) of the NST:  Z = E / I = 15000V / . 03A = 500kohms
• Determine capacitive reactance:  C = 1 / 2pfZ = 1 / 2*p*50*500000 = .006366mF or 6.366nF

Step 2:  We will skip the primary coil design at this time because the size of the secondary coil form is already known and we will base the resonance frequency of the primary on the secondary.  Secondary coil calculations: 

Coil form parameters:  Outer diameter = 11.0cm, coil length = 52.8cm.  This is based on an aspect ratio of 4.8:1 (coil length/outer diameter).  This aspect ratio is empirical and based on other coil designs for optimum sizing.  Wire AWG (gauge) = 24 (.02246 inches or .57054mm).  Turns/inch = 1 / .02246 ~= 44.4444  or   (1 / .057054 cm = 17.52725 turns/cm)

• L = pDAH / 100      = (p*11.0*17.52725*52.8) / 100 = 319.3553 Meters 24AWG wire (1047.479 feet).
• T = AH  = 17.52725*52.8 = 924 turns

L = length of wire in meters
D = outer diameter of coil form (cm)
H = height of coil in cm
A = number of turns per cm
T = total number of turns

  Step 3:  Calculate secondary coil inductance and self-capacitance based on step 2 values.

L = (NR)^{^2} / (9R + 10H)  =  (924*2.165354)^{^2} / (9*2.165354 + 10 * 20.7874) = 17602.5uH = 17.6025mH 

L = inductance of coil in microhenrys (mH)
N = number of turns = 924
R = radius of coil in inches = (110mm/25.4) / 2 = 2.165354”
H = height of coil in inches = (528mm/25.4) = 20.7874"
C (self capacitance) = 0.29H + 0.41R + 1.94 * sqr(R³/H)  =  8.27194pF

Step 4:  Calculate ¼l frequency:  (1 / (wire length/(186000 * 5280)) / 4) = 234.391kHz

Wire length from previous equation = 319.3553 * 3.27997933 ft/m = 1047.48 ft
Use this ¼ wavelength frequency to determine top load capacitance required.

Capacitive Reactance for resonance:

            C = 1 / (4p²F²L) = 26.19281pF

            L = 17.6025mH from previous calculation

            F = 234.391kHz  from previous equation

            Top Load Capacitance needed = 26.19281pF – 8.27194pF = 17.92pF

Toroid size for ~17.92pf Outside diameter (major) – d1=406mm            Diameter (minor) -  d2=127mm (5 inches)

Step 5: Calculate Primary coil inductance required:

            L = 1 / (4p^{^2}F^²C) = 72.423mH

            F = 234.391kHz (secondary ¼ wave resonance frequency)

            C = .006366mF (primary capacitor)

Primary coil physical specifications:

• Copper tube diameter – 6.3mm
• Number of turns – 16
• Spacing between turns – 8 mm
• Spacing between secondary and primary – 25 mm
• Inner diameter of coil – 160 mm
• overall diameter ~60 cm
• maximum inductance @15 turns = 79.5895uH
• tap between turn 14 and 15 to obtain 72.423mH

Parts List:

• Module 1: 
  
  1)     15kV @30mA Neon sign transformer.
  2)     DPST power switch
  3)     Fuse and holder
  4)     3 240VAC MOVs for transient protection
  5)     EMI/RFI filter
  6)     Power cord and plug
  7)     Variac (optional)
  8)     High voltage hookup wire (10-14 AWG)
  9)     29.6 uF 220VAC PFC capacitor (power factor correction)

• Module 2:
  
  1)     Tungsten rods for main spark gap (adjustable)
  2)     Copper rod and balls for safety gap (adjustable)
  3)     Plexiglas housing for spark gaps
  4)   Fan or blower to cool/quench arc

• Module 3:
  
  1)     16 .1uF @1500VDC pulse capacitors
  2)     16 10Mohms ½ watt equipotential divider resistors
  3)     Printed circuit board

• Module 4: 
  
  1)     ~21 Meters 6.3mm diameter air conditioning copper tubing
  2)     Nylon standoffs for mounting coil windings
  3)     Base board (wood, Plexiglas, etc.) to mount the primary and secondary coils
  4)     High voltage hookup wire (10-14 AWG).

• Module 5: 
  
  1)     PVC pipe 110mm diameter, 600mm high
  2)     Polyurethane varnish/lacquer and fine paint brush
  3)     400 meters 24AWG enameled magnet wire
  4)     Plexiglas end caps for coil form
  5)     Standoff to mount toroid
  6)     Miscellaneous mounting hardware

• Module 6:
  
  1)     Toroid ~406mm” OD, 127mm Minor diameter
  2)     Cut and shape green foam from florist shop or corrugated aluminum tube
  3)     Aluminum  tape to cover the form
  4)     Wood or Plexiglas center piece covered with aluminum foil/tape