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fractal_transformer [2019/06/03 18:29]
fractal_transformer [2020/07/08 23:15] (current)
stan_zurek
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 +====== Fractal transformer ======
  
 +|< 100% >|
 +| //[[user/Stan Zurek]], Fractal transformer, [[http://Encyclopedia-Magnetica.com|Encyclopedia-Magnetica.com]], {accessed @YEAR@-@MONTH@-@DAY@}// |
 +
 +**Fractal transformer**[(Zhu>Yong Zhu , Fahimullah Khan, Junwei Lu, Dzung Viet Dao, A planar fractal micro-transformer with air core and hilbert curve, Microsystem Technologies, Vol. 21 (8), 2015, DOI 10.1007/s00542-014-2253-1, p. 1691)] - a type of [[transformer]] whose [[winding|windings]] are arranged in a fractal pattern.
 +
 +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>[[http://dx.doi.org/10.1155/2008/134805|Goran Stojanović, Milan Radovanović, Vasa Radonić, A New Fractal-Based Design of Stacked Integrated Transformers, Active and Passive Electronic Components, Vol. 2008, 2008, Article ID 134805]])]
 +
 +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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 +<box 40% left #f0f0f0>
 +One-layer [[planar]] fractal [[micro-transformer]] with [[air core]] with windings following the Hilbert curve[(Zhu)]
 +[[file/fractal_transformer_magnetica.png|{{fractal_transformer_magnetica.png}}]]
 +{{page>insert/by_SZ}}
 +</box>
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 +<box 45% left #f0f0f0>
 +Two-layer fractal transformer with windings following the Koch curve[(Stojanovic)]
 +[[file/koch_planar_transformer_-_stojanowic_et_al.png|{{koch_planar_transformer_-_stojanowic_et_al.png}}]]
 +//<sup>by G. Stojanović, M. Radovanović, V. Radonić, [[http://creativecommons.org/licenses/by/3.0/|CC-BY-3.0]] </sup>//
 +</box>
 +
 +<box 45% left #f0f0f0>
 +Two-layer fractal transformer with windings following the Peano curve[(Stojanovic)]
 +[[file/peano_fractal_transformer_-_stojanovic_et_al.png|{{peano_fractal_transformer_-_stojanovic_et_al.png}}]]
 +//<sup>by G. Stojanović, M. Radovanović, V. Radonić, [[http://creativecommons.org/licenses/by/3.0/|CC-BY-3.0]] </sup>//
 +</box>
 +
 +<box 40% left #f0f0f0>
 +[[Q-factor]] and [[inductance]] of fractal transformer (Koch curve) as a function of frequency and strip width[(Stojanovic)]
 +[[file/q-factor_and_l_for_koch_planar_transformer_-_stojanovic_et_al.png|{{q-factor_and_l_for_koch_planar_transformer_-_stojanovic_et_al.png}}]]
 +//<sup>by G. Stojanović, M. Radovanović, V. Radonić, [[http://creativecommons.org/licenses/by/3.0/|CC-BY-3.0]] </sup>//
 +</box>
 +
 +===== 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. 
 +
 +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). 
 +
 +For instance, Stojanovic et al.[(Stojanovic)] modelled tracks deposited with [[aluminium]], with 1 μm thickness and 6-10 μm width, on a 500 μm thick substrate. The modelled transformers had 1:1 [[turn ratio]] and were "stacked" so that the primary and the secondary windings were on separate layers. It is also possible to build a 1:1 fractal transformer with the primary and secondary windings on a single layer, which is less expensive from the production view point.[(Zhu)]
 +
 +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]].
 +
 +[[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, also showing that fractal transformers exhibit better performance than spiral transformers.[(Zhu)]
 +
 +===== See also =====
 +  *[[fractal inductor]]
 +  *[[fractal antenna]]
 +  *[[list of transformer types]]
 +
 +===== References =====
 +~~REFNOTES~~
 +
 +{{tag>Fractal_transformers Counter}}

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