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. 2018 Aug 28;9:3481. doi: 10.1038/s41467-018-05585-8

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — Self-decoupling a two-loop array. a Schematic of a pair of self-decoupled coils. b Electromagnetic simulation model of a pair of self-decoupled coils. The magnetic and electric coupling are balanced by tuning the C_mode capacitors, while adjusting the X_arm impedances to maintain coil tuning, and the C_match capacitors to maintain a coil input impedance of 50 Ohms. c Calculated magnetic and electric coupling coefficients (K_m and K_e) versus C_mode. d Simulated vector current distributions of magnetic coupling-dominated coils. e Simulated vector current distributions of electric coupling-dominated coils. In both cases, Coil 1 is excited with 1 Watt and its current flows clockwise along its conductors. f The coils’ transmission coefficient (|S₂₁|) versus C_mode. Coupling is minimized and the coils are self-decoupled for C_mode = 0.44 pF. g Simulated current distributions of the self-decoupled coils with Coil 1 excited. h Simulated current distributions of the self-decoupled coils with Coil 2 excited. In both cases, the residual currents due to coupling in the passive coils are negligible. i Simulated scattering parameters versus frequency for the self-decoupled coils