Re: PFC Question

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>

Hi Ed,

I believe the answer is volts per turn and area of the core.  An 
ungapped toroid doesn't in of its self result in saturation, its when 
the volts per turn (constant line freq) gets too high for the core 
area.  When used a a ballast and with sufficient turns, the 
inductance is too high and the current is too low but it doesn't 
saturate until one reduces the number of turns to get the inductance 
down and the current up.  The gap allows a lower inductance with 
sufficient number of turns to prevent saturation.

With normal variac use and with the setting at max output (140V out 
with 120 volts in lets say), you will probably have about twenty 
turns between the tapped input and the output (~1 volt per turn).  Of 
course any given design could trade off the volts per turn and the 
core area.  If the current rating is not violated, there should be 
sufficient margin from saturation.  Here is the derivation from a 
program I wrote for ballasting that may help with the theory 
(assuming I did it correctly)

Gerry R.


/***********************************************************************************
*
* toroid_ballast.c
*
* This program is useful for designing a toroid ballast for limiting 
current when
* using a non current limiting power source for Tesla 
Coils.  Examples of such power
* sources include PIGs, PTs, and MOTs.  Given user supplied input line voltage,
* limiting current, and line frequency, the program computes the 
required ballast
* inductance. The user is then asked for toroid physical parameters, 
GAP size, and
* material properties to compute the number of turns required, the 
volts per turn,
* and the resulting flux density for the design.
*
* METHODOLOGY:
*
*     Reqired L = [line_voltage/limiting_current] / [2*pi*line_freq] (1)
*
* Using Maxwell's equation:
*
*     integral{H.dl} = N*I
*
* and the boundary continuity equation Bcore = Bgap, (B=uH implies 
Hgap = ur*Hcore)
* the following equation results:
*
*     H = N*I/[pi*D + (ur-1)G]
*
*     where H = Magnetic field intensity in the core (amps per inch)
*           N = Number of turns
*           I = Ballast limiting current (amps)
*           D = Diameter of the toroid at the center of the core (inches)
*               (average of inside and outside diameters)
*          ur = Relative magnetic permeability of the core
*           G = Gap distance (inches)
*
* H is then used to compute the flux density B in the core:
*
*     B = ur*uo*N*I/[pi*D + (ur-1)*G] (2)
*
*     where B = Magnetic flux density (B) in Gauss
*          uo = Magnetic permeability of free space
*
* Since inductance (L) is given by:
*
*     L = N*total_flux/I  and total_flux = B*A
*     L = N*B*A/I
*
*     where A = Cross sectional area of the toroid core
*
* Therefore:
*
*     B = L*I/[N*A] (3)
*
* By combining (2) and (3) and solving for N:
*
*     N = sqrt{L*[pi*D + (ur-1)*G] / [A*ur*uo]}

NOTE: after combining (2) and (3), you can solve for whatever is the 
unknown.  In my case the inductance was a given and I needed to know 
how many turns were needed to get it.

*
*
*
* by Gerry Reynolds
*
* Revision 1.0  October 28, 2005
*
***********************************************************************************/

> Original poster: Ed Phillips <evp@xxxxxxxxxxx>
> >
>    I have never understood why saturation isn't a factor in using 
> an ungapped variac in series with a load.  When the brush is set to 
> full voltage position the series reactance would be equal to the 
> magnetizing reactance and would be quite high.  Since the core is 
> sized for the nominal operating voltage at any brush setting much 
> less than 100% that I would expect to see saturation currents 
> becoming significant.  An easy check on the leakage impedance would 
> be to short the two ends of the winding and run say about 1 amp 
> (100 watt bulb in series across 120V line) and measure the voltage 
> drop between the brush and the shorted ends for different brush 
> positions.  Why don't you do that and publish the results 
> here?  Only a few minutes work.
>
> Ed