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

Re: AC Resistance (formerly Spice Simulation Pictures)



Tesla List wrote:
<SNIP>
> 
> >From couturejh-at-worldnet.att-dot-netTue Oct 29 22:49:50 1996
> Date: Tue, 29 Oct 1996 19:34:48 +0000
> From: "John H. Couture" <couturejh-at-worldnet.att-dot-net>
> To: tesla-at-pupman-dot-com
> Subject: Re: Spice simulation pictures
> 
<SNIP>

>   Barry $ Bert -
> 
> Have you found the Rac for any of your coils?
> 
> I have a graph in one of my books that shows the effective resistance vs
> wattage for a typical Tesla coil. It is based on a Q factor graph in
> Terman's book and other information. This information was used to
> back-figure the Rac.
> 
> The graph can then be used to estimate Rac at the design stage before a coil
> is built. However, I have not had been able to verify this graph because I
> have not found coilers who make these tests and calculations.
> 
> Jack C.

Jack,

Secondary Parameters:
Diameter:                10.25 inches
Coil active Length:      31 inches
Wire Gauge:              #21 AWG Double Formvar
Wire (Cu) diameter:      0.0285 inches      
Wire (Cu) diameter:      0.072 cm
Fo with Toroid:          91 kHz
DC Resistance:           34.1 Ohms
Inductance:              73,455 uH
ZL at Fo                 42,000 Ohms
Est Turns:               995 (97% close-wound)
Est Turn:Turn Spacing:   0.0312 inches
 
1. Measured/calculated Value of Rac:
My estimate for Rac was done by backfiguring from the time constant of
the decaying exponential secondary voltage captured on a storage scope.
You could also base-excite the secondary/toroid from a low impedance
variable-frequency source, measure frequencies at the 0.707 points,
calculate Q, and then back-figure Rac. 

Conditions: gaps reduced for no corona breakout, gaps quenched at
end of 1st beat, "single shot" mode, with a pickup plate 7' from
secondary and connected to a storage scope.

The time for the output waveform to to go from the peak voltage to 5% of
peak was about 2 milliseconds. This equates to 3 time-constants (3*Tau)
for the exponential envelope, so Tau = 670 uSec. But, Tau  = 2L/Rtotal,
where Rtotal = Rac + Rground. I estimated my RF ground resistance to be
about 15 ohms based on low-voltage AC (6.3 VAC) current measurements
from the dedicated RF ground to AC (line) ground. Solving for Rac:

      Rac =  (2L/Tau) - Rground = 110 - 15 Ohms
      Rac =  95 Ohms

2. Purely calculated method for a close-wound coil (from Frederick
Terman, Radio Engineers' Handbook, 1943, McGraw-Hill, pp.77-80):     
   
      Rac/Rdc = aH + (bu1 + eu2)G[(d/c)^2]
 
Variables H, a, b, e, u1, u2, and G are all derived from the coil's
parameters, operating frequency, and a number of look-up tables. Term aH
is the skin effect  contribution, and the remaining term is from
proximity effect. Solving for the above conditions yields the following:
    
      Rac/Rdc = 1.263  +  1.160 =  2.423 (combined effect)
               (skin)   (Proximity)
 
      Rac = 2.423*34.1 = 82.6 Ohms

Considering my measurement errors (especially in estimating Tau and
ground
resistance), the two values are in reasonably close agreement. BTW, the
first method is _much_ simpler than several calculations and
interpolations from multiple tables!   

Given the above parameters, what does your graph predict for Rac?

Safe computin' to ya, Jack!

-- Bert --