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RE: Effective Resistance



Hi John,
         Thanks for the elaboration. Perhaps I can help 
simplify this even further:

On 18 Aug 00, at 13:57, Tesla list wrote:

> Original poster: "John H. Couture" <couturejh-at-worldnet.att-dot-net> 
> 
> 
> Malcolm -
> 
> The "y factor" came from a graph in McGraw Hill's Standard Handbook for
> Electrical Engineers. I used a similar graph in the Tesla Coil Design Manual
> as Fig 8. This graph has been found to agree with other methods of
> determining the AC resistance (Rac) at a certain frequency. Refer also to
> the Bureau of Standards Circular No. 74.
> 
> Note that there was an error in my calcs for the effective resistance
> (Reff). The 133.45 ohms should be 1334.5 ohms.
> 
> There has been much confusion regarding AC resistance for Tesla coil
> circuits. Coilers use the words AC resistance, effective series resistance,
> equivalent series resistance, apparent series resistance, ESR, etc. without
> indicating exactly what they mean. Some electrical text books do not help
> much in clarifying the situation.
> 
> >From my research I have found that there are basically two categories for
> calculating AC resistance for Tesla coils.
> 
> 1. AC Series Resistance (Rac) - Where only the resistive effects are
> considered that are due to DC resistance and to "skin effect" because other
> effects are negligible. These circuits include conductors for simple single
> phase AC circuits. This is a relatively easy solution. The equation is
>    Rac = Rdc * Mft * y factor
> where the y factor is obtained from a graph and makes the adjustment for the
> "skin effect" at different frequencies.

I'd suggest that the ONLY figure of interest is the effective 
resistance (ESR) of the circuit (any circuit) at the frequency 
of interest. It doesn't care which factors contribute: it is 
simply the resistance you will measure at the frequency of 
interest. Rdc is simply the minimum resistance the circuit can 
possibly attain under any condition - in particular when the 
frequency is zero Hz. Rac as defined above would appear to be 
a particular case of ESR, i.e. non-coiled or well spaced wire.
Not generally useful IMHO.

Regards,
Malcolm

> 2. Effective Series Resistance (Reff) - Where the DC Resistance, "skin
> effect", and the other resistive effects due to eddy currents, dielectric
> losses, etc. are involved. These circuits include tuned RCL circuits such as
> in Tesla coils. These calculations are more complex than for the "Rac
> circuits". The equation that coilers use most is
>     Reff = 6.283 * Fr * L/Q
> The Reff varies in a more complex manner for different frequencies compared
> to the Rac calculations. The Reff and Q factor are both unknowns so the Q
> factor is estimated and then verified by tests when the coil is built.
> Another equation is
>      Reff = 2 * F * L * Log Dec
> The Log Dec can be found by the method (scope) I show in the Tesla Coil
> Notebook. Finding the Log Dec by this test can give you Reff, Q factor,
> damping factor, and other important Tesla coil parameters.
> 
> I believe that referring to the AC resistances as above will avoid the
> confusion that can arise when discussing Tesla coil circuitry.
> 
> John Couture
> 
> ----------------------------
> 
> -----Original Message-----
> From: Tesla list [mailto:tesla-at-pupman-dot-com]
> Sent: Wednesday, August 16, 2000 6:15 PM
> To: tesla-at-pupman-dot-com
> Subject: RE: Effective Resistance
> 
> 
> Original poster: "Malcolm Watts" <M.J.Watts-at-massey.ac.nz>
> 
> An intriguing post:
> 
> On 16 Aug 00, at 8:02, Tesla list wrote:
> 
> > Original poster: "John H. Couture" <couturejh-at-worldnet.att-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
> 
> How was that "y factor" arrived at?
> 
> >    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.
> 
> Do they show the Rac of which you speak? (Bet = no).
> 
> Reff IS the AC resistance (or ESR).
> 
> What possible good does it do introducing yet another factor
> which isn't even used?
> 
> Regards,
> Malcolm
> 
> > Please post your results on the List so others can learn how to design
> Tesla
> > coils..
> >
> > John Couture
> 
> 
>