Designing a multilayer coil

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Inductance of a multilayer coil of rectangular cross section can be computed by below formula when optimizing maximum distributed capacitance and distributed inductance  to intensify Inductance Field Strength  to function as a voltage multiplier in switch-off conditions , as illustrated in (710) of ~. Figure (7-10) as to VIC
Coil Assembly (580) of Figure (6-1) and, is expressed:


Where,
(L) is the inductance in microhenries
(N) is the number of turns
(A) is the mean radius in inches
(B) is the length of the coil in inches
(C) is the depth of the coil in inches


what i find interesting is that this formula does not have a variable for the relative permeability of core material.. which in turn means this formula is for a air core inductor


here is the formula from wiki

Multilayer air-core coil formula

• L = inductance (µH)
• r = mean radius of coil (in)
• l = physical length of coil winding (in)
• N = number of turns
• d = depth of coil (outer radius minus inner radius) (in)

so why would stan give a formula for air core inductor? while it seems that he implies that they are wound on a core?   

he refers that vic 6-1 is an example for the multilayer coil.. 6-1 has a laminate steel core...

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Thats why i always used air core of ferrite saturable cores... AIr core have higher Q factor as don't have losses on the core. Is like a vacuum capacitor...
The wire must carry the current well


WIth 30 meters of hand made litz like wire having maybe 10 strands of 0,8mm wire and a set of capacitors i could sustain kw resonance you can see it working on youtube in my channel power videos. Inside as a former i used some antenna ferrite small pieces. The tank was loaded having water in both ways and didoes in series, otherwise the voltage would be very much higher. I actually succeed in destructing those self healing capacitors and have not found similar ones since than.


I would suggest to anyone dealing with this to make hand made capacitors using copper foil and polipropielene PP film. You will get the highest Q possible as you will have small ohmic losses cause of the series resistance being small. I would suggest ,1mm copper foil thickness maybe 10 or 20 cm wide and many meters long. the thickness of the PP film depend on the voltage limit you want. I will be an expensive but efficient device. Worth for resonance, google polipropilene resonance. http://www.alibaba.com/showroom/mkph-high-voltage-resonance-capacitor.html

[Hidden]

Inductance of a multilayer coil of rectangular cross section can be computed by below formula when optimizing maximum distributed capacitance and distributed inductance  to intensify Inductance Field Strength  to function as a voltage multiplier in switch-off conditions , as illustrated in (710) of ~. Figure (7-10) as to VIC
Coil Assembly (580) of Figure (6-1) and, is expressed:


Where,
(L) is the inductance in microhenries
(N) is the number of turns
(A) is the mean radius in inches
(B) is the length of the coil in inches
(C) is the depth of the coil in inches


what i find interesting is that this formula does not have a variable for the relative permeability of core material.. which in turn means this formula is for a air core inductor


here is the formula from wiki

Multilayer air-core coil formula

• L = inductance (µH)
• r = mean radius of coil (in)
• l = physical length of coil winding (in)
• N = number of turns
• d = depth of coil (outer radius minus inner radius) (in)

so why would stan give a formula for air core inductor? while it seems that he implies that they are wound on a core?   

he refers that vic 6-1 is an example for the multilayer coil.. 6-1 has a laminate steel core...

As you probably know the two formulas are the same. They are just represented by different variables for the representation. Now my understanding is the formulas that is used is based off on the Wheeler's formulas. The Wheeler's Formulas already have the air of permeability already built into it.  The k factor (relative permeability or the core factor) is based on the ratio against the permeability of vacuum which is 1. It is also noted that air is slightly higher than 1.  Since the permeability is close to 1 all that is needed is to multiply the formula by the k factor.

Permeabilty of the material is not the same as relative permeablity. Permeablity of the material which is air is already in the Wheeler's formula. So to do this you need to divide the answer of inductance by the permeability of air then multiply it by the permeabiltiy of the core. Now since air is at 1 then a easier method would be just use the K factor on the Wheeler's Formula.

The Wikipedia sites help. Here is some
http://en.wikipedia.org/wiki/Permeability_%28electromagnetism%29

The goal is to find permeability of the material. This is represented by u = u_r x u_o
This can be obtained  (Permeability of the material = relative permeability (k factor) x Permeability of the vacuum.)

The SI formulas are different because they do not compare other core factors with the vacuum or air. You just need u_r and u_o to find u.  Hope this made sense.

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As   you probably know the two formulas are the same. They are just   represented by different variables for the representation. Now my   understanding is the formulas that is used is based off on the Wheeler's   formulas. The Wheeler's Formulas already have the air of permeability   already built into it.  The k factor (relative permeability or the core   factor) is based on the ratio against the permeability of vacuum which   is 1. It is also noted that air is slightly higher than 1.  Since the   permeability is close to 1 all that is needed is to multiply the formula   by the k factor.

Permeabilty of the material is not the same as   relative permeablity. Permeablity of the material which is air is   already in the Wheeler's formula. So to do this you need to divide the   answer of inductance by the permeability of air then multiply it by the   permeabiltiy of the core. Now since air is at 1 then a easier method   would be just use the K factor on the Wheeler's Formula.

The Wikipedia sites help. Here is some
http://en.wikipedia.org/wiki/Permeability_%28electromagnetism%29

The goal is to find permeability of the material. This is represented by u = u_r x u_o
This can be obtained  (Permeability of the material = relative permeability (k factor) x Permeability of the vacuum.)

The SI formulas are different because they do not compare other core factors with the vacuum or air. You just need u_r and u_o to find u.  Hope this made sense.
                            

Yes i realized they were the same with different letters for representation.

So what i think your saying is that this multilayer air coil formula is a wheeler' s formula and is preset for the permeability of air.. 

also that in order to find the inductance value of this style of coil all you need to do is multiply the inductance value determined by the multilayer air coil formula by the relative permeability which is the cores K factor value..


since air core values are based on air which is 1 we know that any higher permeability introduced into a core you just have to multiply it by the inductance value provided by the relative permeability also know as k factor of a core?

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Yes!

Correct the Relative permeability (u_r) is the same thing as the k Factor.

The reason is because the permeability of air is already in the formula.  Wheeler formulas were calculated though experimentation which lead to the derivative of the formula. The SI unit formulas need the permeability of free space and the k factor to find the relative permeability of the material used. 

I just want to let you know on the internet there is a formula for metric units that what based of the Wheeler formulas. This is not a SI formula. Honestly I would use the Wheelers formulas to find inductance.. Have you downloaded the Water Fuel Cell Sheet? I made this excel sheet that has the inductance formulas on it plus all kinds of formulas. Alot of work was put behind it.

http://www.ionizationx.com/index.php/topic,1506.0.html