Originally posted by lamare
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It's the mathematical models that are showing this, this is why the inter-winding capacitance and inductance are key and critical to proper tuning. at each point of the dot scalar field between windings there is a reciprocal gate/door and this is where the magic happens. Steinmetz covers this briefly in one of his books as a chain of condensers, reading thru and noting the equations one can see he was also referring to coils, the rare time he's not dealing with transmission lines. I do wish he had more to say, I get the feeling it was a round about way of publishing work he was to keep quiet about.
There is also the frequency factor which is ignored other than skin effect and even then it's misunderstood, get to that in a moment, if you notice in coil calculations for mutual inductance and capacitance between windings there is a simplification to sheet and field and this completely ignores the true relations of what is occurring. voltage potential between windings is far greater then the terminal ends and harmonics from the frequency and wave phase angle due to pitch and dia can be catastrophic to the coil, either very high losses or dielectric 'breakdown' which is exceedingly high potentials that become destructive.
it's that phenomenon that is exploited and controlled. Skin effect and resistance to the conjugate wave is frequency dependent and not entirely logarithmic but seems to have two curves. if the depth of the wire is too close to the skin depth for that frequency the induced thermal gradient will destroy the conductor, other than a weight penalty a solid vs hollow wire for HF is the same. Now I not touching on the surface area or circumference that factors into inductance and capacitance.
taking a simple example to highlight the parameters, two cylinders that are axial to each other and separated by a distance. the dia of each cylinder needs to be calculated for a given frequency and current and the distance between them. these ratios will effect the inductance and capacitance impedance which will effect the resonant point, a change in the spacing between cylinders will change the capacitance to greater extent then the inductance, whereas a change in the cylinder dia will effect the inductance greater then the capacitance. both of which will effect the resonant point and phase angle of the current to voltage. a greater change to phase angle in the coil diameter, this parameter also effects the inductance and capacitance in about that order of magnitude. adding to the mix is weather there is a ground termination, open end or return end on the terminal as each has its own effect.
It becomes clear that in transmission lines of two wires there is a massive amount of calculations needed to get the desired results with AC frequencies. a coil is so much more complex in terms of geometry and how the field of a dot scalar product is calculated. I'm not sure how many of those parameters hold true when the line is looped into coil or if there is a translation.
The math is difficult because the math in the first place is an imaginary construct of a net physical phenomenon. There simply has been no real civilian movement in the area of research and applied mathematics to this area, yes a few have pushed forward and made insights and some gains, I think though that most people don't comprehend the enormity of work that still needs to be done, mathematical models need inventing to produce testable theories and avoid blind research. Tesla experimented a lot, however unlike Edison Tesla understood the need for a mathematical approach to research. Steinmetz welded a pen and intellect that thankfully put down volumes of work that applied engineering can start from, Kennelly utilized Steinmetz work greatly in his applied calculations as did many others each to there own extent.
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