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Hi All,
The attached pdf is useful for calculating or at least seeing the trends in interturn capacitance with different coil pitches, and with different coil formers, which is useful I think. It is based on experiments. He notes that the coil pitch is important-- hence the basket weave coils that ION has mentioned here an in relation to Hendershot. Also, the permittivity of the coil former is included in the formula. But most important is wire length relative to frequency of operation, because this determines whether the coil can be seen as a lumped element, or must be seen as a helical wave:
"We can however use it to deduce the circumstances under which the lumped-component theory breaks down. The situation is that, at very low frequencies, the superposition of an axial slow wave and a wave following the helix results in a helical phase velocity several times the speed of light. In this region however, the transmission-line equation asymptotes to the approximation Tanθ = θ , and the relationship between R 0 and v p is fixed from purely magnetic considerations. At intermediate frequencies, v p decreases smoothly in such a manner as to cause a reasonable match between the transmission-line model and the lumped component model. As the SRF is approached however, the scattering cross-section of the coil increases dramatically and the helix propagation mode comes to dominate the superposition."
If I understand this correctly, the phase velocity at low frequencies is irrelevant in the Cook case, since it probably naturally self oscillates at high frequency. No matter how much C you get rid of, some will remain, and there will be an LCL self-resonance through the whole device. But near self resonance, the two coils will also be transmission lines with nodes. Given the large bulk inductance and the large interwinding capacitance, the resonance should be in the low Mhz, just as a guess.
Running at high frequencies with less capacitance seems better, from an energy storage standpoint-- the less C, the less energy is stored in C and kept out of induction-- but also in the view that there is an evanescent field around the two induction coils. This is not a transverse wave but a near field induction directly between the core, that at resonance leads to near 100% magnetic energy transfer between them.
This near field or evanescent wave located around two solenoid coils in parallel is now used in Witricity, an ultra efficient wireless power system, that can transfer 40-60% of the power between the source and portable coil, even across a big room. The system works because the magnetic energy transfer is adiabatic-- the near-field magnetic field does not radiate, so no energy is lost from the field, and whatever does not travel to the other core, is returned to the first core in resonance. In order for this to happen, the frequency must be high enough so that the resonators can operate efficiently, while low enough so that the field does not radiate. The natural self oscillation of these large cores would be low enough for this effect to manifest. Wikipedia:
"Resonant inductive coupling: This means the area within about 1 wavelength (λ) of the antenna. In this region the oscillating electric and magnetic fields are separate[6] and power can be transferred via electric fields by capacitive coupling (electrostatic induction) between metal electrodes, or via magnetic fields by inductive coupling (electromagnetic induction) between coils of wire.These fields are not radiative, meaning the energy stays within a short distance of the transmitter".
A case can be made that there is strong direct magnetic energy transfer between the Cook coils, and not only that, that this takes place in a different time frame from the electrical self resonance. The magnetic energy transfer in an evanescent field has been thought by some to take place at more than C, in the case where the coils are closer than 1/4 wavelength... so the ends of the two cores would have almost simultaneous magnetic field strengths and polarities, while the electrical potentials would have to be somewhat different than that.
orthofield
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Author
Topic: Daniel McFarland Cook Generator (Read 236974 times)
