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Re: Reactance
Tesla List wrote:
>
> Subscriber: Rodney.Davies-at-anu.edu.au Sat Feb 1 21:56:48 1997
> Date: Sun, 2 Feb 1997 04:18:04 +1100 (EST)
> From: Rodney Graham Davies <Rodney.Davies-at-anu.edu.au>
> To: tesla-at-pupman-dot-com
> Subject: Reactance
>
> Hi All,
>
> After reading through some extremely helpful documentation here on the
> list, I've found some formulas and concepts I've been looking for...
> Thank you too all contributing! Much appreciated and helpful!
>
> Ok, well, I'm just trying to make sure I've got a firm grasp on tuning
> and the primary LC circuit.
> As I understand, the inductive reactance in the primary has to be
> cancelled out by the capacitive reactance of the capacitors.
> Now I've got the formulas for calculating the I.R. of the primary, and
> the capacitors -
>
> X = 1/(2*Pi*F*L) for inductive reactance, where
> X is on ohms
> F is in Hz
> L is in Henries
Not quite... This should instead be:
X = 2*Pi*F*L (i.e., X should increase with increasing F or L)
>
> X = 1/2(2*Pi*F*C) for capacitive reactance, where
> X is on ohms
> F is in Hz
> L is in Henries
Not quite... This should read
____1____
X = (2*Pi*F*C) (i.e. X should decrease with increasing F or C)
>
> Am I doing alright so far?
>
> Ok, now, if the inductance of the primary coil is known, and the value of
> the capacitor(s) is known, how do you get these formulas to work out as
> to find the resonant frequency of the known series LC circuit?
>
> Ok, Scenario -
>
> Capacitors - 0.1uF -at- 50KVDC (Pulse type)
> Primary "Flat Pancake Archimedes" -
> - 5 turns 3/8" Cu Pipe
> - spacing 1" from turn-to-turn
>
> |<--------- 5.75" ------->|
> _ _ _ _ _
> -(_)---(_)---(_)---(_)---(_)- <-------primary coil
> | | |<-1"->|
> ^---- 3/8"
>
> - Outside Diameter 26.5"
> - Inside Diameter 7.5"
> - Width = 5.75"
>
Did you mean instead an inside RADIUS of 7.5", and an inside diameter of
15" perhaps? This would be the case if your outside diameter was,
indeed, 26.5". The average radius would then be 7.5+(5.75/2) = 10.375"
> Anyway, using the formula -
>
> L = R^2 * N^2 / (8*R + W)
>
> where, L = uH
> R = average radius
> N = # of turns
>
> I get a calculation of 18.40 uH. I think I did it right.
This result looks Good to me!
>
> Ok, now we know L for the primary.
> Next, calculate L-Reactance -
>
> XL = 1/( 2*Pi*50*18.40*10^(-6) )
> where F = 50 Hz (Australian Frequency)
>
> = 696.5 Ohms
>
> * * * * * * * * * * * * * * * * * * * * *
>
> This is probably where I'm stuffing up as F should be the frequency at
> which the C-Reactance cancels the L-Reactance...???
>
> Should I be working backwards from the known self-resontant frequency of
> the secondary-coil and plug that value into the equation to work out what
> sort of capacitors I need for this particular primary and secondary coil?
> (Using the C&L Reactance equations)
>
> Self-resontant frequency for my secondary (with toroid) is about 140 khz.
>
Your suspicion is correct - the F you use here should be the resonant
frequency of the secondary AND the toroid. Using the corrected equation
for inductive reactance:
Xl = 2*Pi*F*L
Xl = 6.28*140000*0.0000184 = 16.3 Ohms (inductive)
The capacitance necessary for the same reactance is:
Xc = 1/(2*Pi*F*C) = 16.3 Ohms (capacitive)
Solving for C:
C = 1/(2*Pi*F*Xc) = 1/(6.28*140000*16.3) = 0.07 uF
As a check, we solve for F (for a low resistance primary) using the
above values of L and C (in Henries and Farads):
F ~ 1/SQRT(LC)
= 1 /(2*Pi*SQRT(18.4e-6*.07e-6)
= 1/(6.28*SQRT(1.29e-12))
= 1/(6.28*1.13e-6)
= 140.2 kHz
> I may seem a little academic trying to calculate everything, but I've
> found that by doing this during design helps to give me an idea on how to
> build the coil.
A few quick calculations to design the coil to be in the ballpark can
save a LOT of grief later, and copper tubing and HV capacitors aren't
free if you've made a seat of the pants "guess" that's wrong.
> Yeah, sometimes the calculated values are out from actual
> measured values, but most of the time the margin of error is around 5-10%.
>
> Basically, the way I follow things is try to think of how many volts you> want, and build a secondary close to size. Playing the guessing game
> here, but from passed experiences it's not so much of a guess anymore.
> Ok, from there, then measure the resontant freq.
>
> Next, design a primary coil, and try and get a near match of capacitors
> simultaneously. This is where the nice hairy equations and math comes in.
Sounds like an excellent approach, and one that most experienced coilers
follow. After building enough coils, I suppose one could get a real
"feel" for what would work properly together... but a simple set of
spreadsheet equations (like Ed Sonderman's nice Excel design tool) can
save hours of work and many $ for inexperienced coilers!
>
> Ok, concepts here -
> 1) Minimize reactance in the primary.
> 2) Find capacitor value to do so. (For series LC circuit)
> 3) Hope to buggery the value of the frequency is that of the secondary.
>
> Am I doing alright again?
>
> Well, even if the values come close, the primary is tunable, but one
> hopes the values are close to begin with.
>
> Does anyone use similar approaches to strict coil design?
>
> My main idea behind all of this is that I extremely interested in the
> mathematical/physics work behind the design of TC's.
> I hope I have my concepts around the right way...
>
> Oh well, we'll wait and see then!
>
> Suggestions, flames, formulas, ideas, concepts, designs, whatever are all
> welcome!
>
> Thanks for your help guys!
>
> Catchya later!
>
> Rodney
>
> -- 'what is the average air-speed of an electron?'
> 'Erm, European or African electron?'
> 'what?! I don't know that....<crash, bang> Whaaaaaa! ... <thud!>'
No flames today, Rodney... your approach should work just fine once you
shake the bugs out of the equations. Check out Ed Sonderman's
spreadsheet on the funet site - you'll like it! Good luck on your coil!
-- Bert H. --