RE: Effective Resistance

["John H. Couture" <couturejh-at-worldnet.att-dot-net> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

All -

In Tesla coil design the effective resistance (Reff) and the Q factor are
unknowns and must be found indirectly. The (Reff) is related to the Q factor
by the equation
    Reff = 6.283 * Fres * L/Q

The Reff is not the same as the AC Resistance (Rac). I have never seen these
two resistances calculated for a particular TC where all of the parameters
were shown so I am using  as an example the JHCTES Ver 3.1 program default
coil. If you have downloaded this program you can obtain the necessary coil
parameters by changing only one input parameter. That parameter is the
secondary terminal which should be changed to zero then press calculate.
That will give you the necessary resonant frequency (Fres) and other
parameters needed below.

The AC resistance (Rac)  of the secondary coil wiring is found by the method
shown in the Tesla Coil Design Manual. For Fres = 270 KHZ the equation is
   Rac = Rdc * Mft * y factor
   Rdc = 26.7 ohms/Mft    Mft = 1000 ft (1571 ft)
   y factor = 1.25 from TCD Manual Fig 8 page 9-4

   Rac = 26.7 * 1.57 * 1.25 = 52.4 ohms

   Q factor = Fres/BW
   BW = Bandwidth = 6 KHZ (from scope)
   Q factor = 270/6 = 45

   Reff = 6.283 * Fres * Lcoil/Q factor
   Reff = 6.283 * 270000 * .0354/45 = 133.45 ohms

The 133.45 ohms agrees closely with the graph Fig 7 in the TCD Manual. In
this example the Reff is 2.55 times the Rac.

Many Radio books including Terman and Henney show several ways to find the Q
factors and the Effective resistances of radio tuned circuits. However,
these methods can also be used for Tesla coils. You may want to make these
tests with your coil(s) to see how they compare when using the above
calculations as a guide.

Please post your results on the List so others can learn how to design Tesla
coils..

John Couture

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