[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

RE: Effective Resistance




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.

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