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Old 03-30-2012, 05:53 PM
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madhatter madhatter is offline
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Garrett, great post. Coax line though is bit more complex and involves the rotation of j or k in Erics notes. there is also the consideration of the coil too as it's usually considered a complex form or looped transmission line but simplified reduction will loose the true nature of what's going on.

I posted this in the yahoo groups and will share it here for others.
I'm developing a physical theory for capacitance to surface area between objects. I need to modify a couple equations to get the terms in there proper places. take two cylinders of radius r and r' with a given axial distance of d, I now need to put a hyperbolic curve between both tangent points that is based on induction frequency and a function of skin depth which is frequency dependent, there is also the permittivity constant k and resistivity of the cylinder to factor which is also frequency dependent too, and if that isn't enough there is still the variable of the axial distance d and that all needs to be a function of cosine of the angular frequency and needs to bring in the counter-space of rotation to plane shifting.

As much as a all-in-one equation would be great I get the feeling it may be easier to piece it out and integrate.

I'll try and explain a bit further here on the dielectric to capacitance. In Erics notes there is an equation for reactance it's a modified phase velocity equation and makes complete sense as it fits the theory I have been working on too, to cut my time short I've been going back over Erics work and he has the framework for this worked out nicely but still lacks useable engineering equations because this is completely new ground to cover and will rely on counter-space algebra. Ok so the basic outline is this, the dielectric in counter-space is time invariant, reactance is a time variant gateway to what would be best described as an open/close of counter-space this is achieved through rotation in counter-space where it translates to plane shifting in vector space. if we took a cross section look two parallel cylinders so that it would be a diagram of two circles on the same axis separated by a distance, the area of capacitance would vary over time based on the frequency of the wave, this makes the capacitance a time variant function which is why AC is not blocked by a capacitor, however this also introduces another topology, the axial linear direction. the capacitance area is a function of the wave form as it moves along the wire, now if we loop the wire the wave shift between turns will be a function of the loop radius and pitch, at the point where the wave loops upon itself and is out phase by 180* it will resonate, it becomes immediately obvious that the radius is dependent upon the frequency and will have various numerical answers, the radius also needs to account for inductance as well. For any given frequency the inductance and capacitance need to match to cancel and this is the resonance. by being able to accurately calculate these quantities we can engineer any frequency quickly.

There is a number of variables that may be circular and I want to avoid that. In the above it also highlights the DC nature of resonance as the capacitance wave phase area is no longer shifting along the wire but resonating as a standing wave, the value of the capacitance is based on the distance between the surfaces and from this theory it shows that as the distance increases the amplitude of resonance will fall off and there will be a change to the resonant point as this also effects the induction. a straight line transmission also exhibits this as well but if the distance to a nearby plane or surface is too large the value will be too small to factor. Steinmetz also points out in Chapter 2 of theory and calculation of alternating currents. from page 330
"The difference is due to the distributed character of L and C
in the transmission line and the resultant phase displacement
between the elements of the line, which causes the inductance
and capacity of the line elements, in their effect on the frequency,
not to add but to combine to a resultant, which is the projection
of the elements of a quadrant, on the diameter, or - 2/pi times the
sum, just as, for instance, the resultant m.m.f. of a distributed
armature winding of n turns of i amperes is not ni but - (2/pi)ni."
In looking at work of Steinmetz and Tesla connections start to form. the bulk of Steinmetz equations all deal with transmission line and power supply, however they are full of gems and insights that can be adapted and used to duplicate and expand further on Tesla's work. Eric's engineering of the dimensions for the coils at first brush had me scratching my head, but not one to take things at face value and wanting to always understand the why I dug further into research and reference texts and this light went on and the above theory was roughed out. close approximation isn't really going to work for longitudinal dielectricty, it needs to be fine tuned and balanced just right due to the numerous variables. electro-magnetic really is crude. a tuned distributed circuit with all terms is harmony.