fractal_transformer

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+ | ====== Fractal transformer ====== | ||

+ | |< 100% >| | ||

+ | | // | ||

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+ | **Fractal transformer**[(Zhu> | ||

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+ | There are many fractal curves and figures which can be used as the basis for defining the shape of the windings: Hilbert curve, von Koch curve, Peano curve, etc.[(Stojanovic> | ||

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+ | Fractal technology can be useful for miniature [[coreless]] transformers for high-frequency electronics. For instance, a fractal transformer can be implemented as a single layer of conducting tracks deposited on a [[non-conducting material|non-conducting]] and [[non-magnetic material]].[(Zhu)] [[On-chip transformer|On-chip transformers]] operating at GHz frequencies (e.g. up to 60 GHz) can be implemented with this technology. | ||

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+ | {{page> | ||

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+ | <box 40% left #f0f0f0> | ||

+ | One-layer [[planar]] fractal [[micro-transformer]] with [[air core]] with windings following the Hilbert curve[(Zhu)] | ||

+ | [[file/ | ||

+ | {{page> | ||

+ | </ | ||

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+ | <box 45% left #f0f0f0> | ||

+ | Two-layer fractal transformer with windings following the Koch curve[(Stojanovic)] | ||

+ | [[file/ | ||

+ | //< | ||

+ | </ | ||

+ | |||

+ | <box 45% left #f0f0f0> | ||

+ | Two-layer fractal transformer with windings following the Peano curve[(Stojanovic)] | ||

+ | [[file/ | ||

+ | //< | ||

+ | </ | ||

+ | |||

+ | <box 40% left #f0f0f0> | ||

+ | [[Q-factor]] and [[inductance]] of fractal transformer (Koch curve) as a function of frequency and strip width[(Stojanovic)] | ||

+ | [[file/ | ||

+ | //< | ||

+ | </ | ||

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+ | ===== Construction of fractal transformers ===== | ||

+ | From theoretical viewpoint, the length of a fractal curve can be increased by incrementing the number of steps (or the order of the curve). The curve can be thus infinitely long even though it is bounded by a finite area. | ||

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+ | The infinite length is not achievable for fractal transformers (or other devices like [[fractal inductor|fractal inductors]] and [[fractal antenna|fractal antennas]]) due to the minimum width of the meandering conductor, as defined by the manufacturing process (e.g. width of the deposited track or thickness of the wire). | ||

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+ | For instance, Stojanovic et al.[(Stojanovic)] modelled tracks deposited with [[aluminium]], | ||

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+ | The [[coupling coefficient]] can be up to 0.9, which is satisfactory for coreless transformers. The parasitic primary-to-secondary capacitance can be reduced by slight offset of the positions of the windings against each other. This also improves the [[Q-factor]] and [[self-resonance frequency]]. | ||

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+ | [[Electromagnetic simulation|Electromagnetic simulations]] of such fractal transformers show that fractal layouts can give comparable or better performance than the more traditional transformers with [[spiral winding|spiral windings]].[(Stojanovic)] The simulations are confirmed by other researchers experimentally, | ||

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+ | ===== See also ===== | ||

+ | *[[fractal inductor]] | ||

+ | *[[fractal antenna]] | ||

+ | *[[list of transformer types]] | ||

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+ | ===== References ===== | ||

+ | ~~REFNOTES~~ | ||

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+ | {{tag> |