The classic way to greatly reduce the self-capacitance of a deep and wide multi-turn thick coil is to partition the winding into multiple adjacent deep but narrow coils connected in series. The adjacent narrow coils are magnetically coupled the same as when they were one wide coil, but the capacitance of the individual narrow coils is both reduced and in series. The reduction in overall capacitance can be quite dramatic. This method or approach has been around for about a century, as have banked windings.
For example, take a dual-winding ferrite pot core bobbin https://www.norwe.eu/products/en/006/E01.
The coil windings in each section of the bobbin have the same winding depth, but about one half the total winding width. The self-capacitance of each of the two section windings is maybe one half that of what we would have if we used a single-section bobbin https://www.norwe.eu/products/en/006/D01.
Because the two sections are adjacent, the magnetic flux threads the individual wire turns the same as before, so we get the full N^2 effect on self-inductance of the total winding turns N. But the electric fields are different, and each section has about half the self-capacitance of the one-section full-width coil, and because these individual self-capacitances are in series, the total overall self capacitance is about one quarter of that of the full width winding.
Because self-resonant frequency varies as the square root of the product of inductance and capacitance, the resonant frequency of the two-section coil will be double that of the one-section coil.
If one uses three sections, the resonant frequency will be tripled, in theory at least. The limiting factor is the loss of coil windings due to the physical bulk of the separators between the sections.
For example, take a dual-winding ferrite pot core bobbin https://www.norwe.eu/products/en/006/E01.
The coil windings in each section of the bobbin have the same winding depth, but about one half the total winding width. The self-capacitance of each of the two section windings is maybe one half that of what we would have if we used a single-section bobbin https://www.norwe.eu/products/en/006/D01.
Because the two sections are adjacent, the magnetic flux threads the individual wire turns the same as before, so we get the full N^2 effect on self-inductance of the total winding turns N. But the electric fields are different, and each section has about half the self-capacitance of the one-section full-width coil, and because these individual self-capacitances are in series, the total overall self capacitance is about one quarter of that of the full width winding.
Because self-resonant frequency varies as the square root of the product of inductance and capacitance, the resonant frequency of the two-section coil will be double that of the one-section coil.
If one uses three sections, the resonant frequency will be tripled, in theory at least. The limiting factor is the loss of coil windings due to the physical bulk of the separators between the sections.
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