233 lines
12 KiB
TeX
233 lines
12 KiB
TeX
\documentclass[conference,compsoc]{IEEEtran}
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\newcommand{\todo}[1]{\textbf{TODO}\footnote{#1}}
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\begin{document}
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\date{}
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\title{Wireless Power Transfer with a Twist:
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Achieving Rotation-Invariant Coupling using Multi-Layer PCB Inductors}
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\maketitle
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\begin{abstract}
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% FIXME
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\end{abstract}
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\section{Introduction}
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Inductive wireless power transfer (WPT) is a widely used technology supported by a large corpus of research literature.
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% FIXME cite
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While working on a novel application of Inductive wireless power transfer in a Inertial Hardware Security Module (IHSM)
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as proposed by Götte and Scheuermann, % FIXME cite
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we found ourselves presented with an unusual set of constraints around inductive wireless power transfer through a
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rotating joint using a PCB inductor that does not yet seem to be addressed adequately in the existing literature on
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inductive wireless power transfer.
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Our application poses the challenge of transferring power between a stationary and a rotating part. To reduce
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manufacturing cost of both parts, and to reduce weight, and thereby inertia as well as susceptibility to vibration in
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the rotating part, we decided to use inductors that are directly patterned onto the IHSM's printed circuit boards.
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The primary constraint that results from this choice is a highly constrained turn count that is limited by the PCB
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manufacturing processes' pattern resolution and by ohmic heating.
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We found that the limited turn count of PCB inductors results in a \emph{slightly} asymmetric field, which means that
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the coupling coefficient of two such inductors oscillates at one oscillation per revolution when the inductors are
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rotated on-axis, even if both inductors are perfectly coaxially aligned.
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In other inductive wireless power transfer systems, this oscillation is mitigated by one of several factors: First, for
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this effect to matter in the first place, the two coils have to be rotating with respect to one another. In ferrite or
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iron-cored inductors, the core shapes the magnetic field and evens out any such imperfection. In wire-wound inductors,
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the (much) higher turn count and circular aspect ratio of the wires reduces this effect to almost nothing. Finally, the
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output ripple caused by this oscillation can be filtered through a voltage regulator or by using a large decoupling
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capacitor on the secondary side.
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While there exist a number of prior works focusing on efficient power transfer between two coils whose position relative
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to one another cannot be precisely controlled as is the case in wireless phone charging systems, it is generally assumed
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that the two coils remain (almost) stationary with respect to one another throughout the charging process. % FIXME cite
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There exists a small body of work on inductive power transfer through rotating joints, % FIXME cite
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but here the focus lies on higher power budgets than our application requires, which often requires ferrite or iron-core
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inductors.
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Our application is unique in that it requires power transfer through a joint that is constantly rotating at high speed,
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while we simultaneously want to avoid heavy components on the (rotating) receiver side. (Liquid) electrolytic capacitors
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cannot be used due to the large centrifugal acceleration that the rotating part experiences, and other heavy components
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such as large ceramic or polymer electrolytic capacitors or ferrite-core power inductors are inadvisable since they will
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exert large stresses onto the assembly due to the same centrifugal acceleration, and any imbalance caused by tolerances
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in the placement of heavy components will quickly cause a strong vibration.
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\subsection{Twisted inductors}
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Applying a principle inspired by rectangular or octagonal RFIC inductor design as well as by the polygonal basket-woven
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air coils used in early radio set, we propose a novel way of laying out circular PCB inductors that twists the
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inductor's windings around one another using a ring of vias each on the inside and outside of the inductor's windings.
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Applying some math, we show that we can layout a twisted inductor for any number of twists that is co-prime to the
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inductor's turn count.
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We observe that in high-frequency applications, a moderate number of twists increases the spacing between the beginning
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and end of the inductor's conductor, where the majority of the inductor's AC current flows. This decreases the parasitic
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capacitance of the inductor and raises its self-resonant frequency, raising its maximum possible operating frequency and
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improving its efficiency at lower operating frequencies. This is the same effect that is exploited in basket-woven
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air core inductors that were commonly used in old radio sets.
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% FIXME citation on this, citation on basket weaving -> It's hard to find reliable references on that.
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\section{Related Work}
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\subsection{Inductive Wireless Power Transfer in Practice}
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Inductive WPT has been proposed in a large number of scenarios, each of which comese with a set of
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unique constraints. When WPT is used to charge an electric toothbrush, the implementation cost of the system is
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critical, while efficiency and total power output are of little concern. Mechanically, in an electric toothbrush's
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charging system, the position and spacing of the transmitter and receiver coils can easily be controlled down to
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millimeter precision.
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In contrast to this, wireless smartphone charging is a much more demanding application. Here, the total cost of the
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system is only secondary, but the receiver's form factor is critical, and total power output as well as efficiency
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become major objectives. At the same time, in wireless smartphone charging, position tolerances are very coarse, and the
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two coils in the charging base and in the phone may be positioned more than a centimeter off-axis, with a gap of several
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millimeters and potentially not even in parallel planes.
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Power transfer across large distances is even more of a concern in implantable medical devices. Where a wireless phone
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charger must be able to bridge distances of a few millimeters, an implantable medical device might be situated
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underneath several centimeter of tissue and bones. At the same time, cost is of (almost) no concern in this medical
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application, which enables the use of complex manufacturing techniques, customized electronic components and exotic
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materials.
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While all of the aforementioned applications transfer somewhere between a few hundred milliwatts and several watts of
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power, at the other end of the spectrum there is a large body of research suggesting the use of inductive wireless power
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transfer for the charging of electric vehicles (EVs). In this application, the wireless power transfer system replaces
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the conventional wired charging connector, which improves the systems' user experience given the strong force required
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to seat or unseat these rather large connectors, as well as the heft of the required water-cooled cables. In this
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application, size is of (almost) no concern, but at several kilowatt up to dozens or even a hundred kilowatt, the
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transferred power is enormous and consequentially efficiency becomes of utmost importance. When charging an EV at a
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rate of 30 kW, an efficiency improvement of just $0.1\%$ corresponds to a reduction in power dissipation of 30 W.
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Besides the monetary cost of the power lost this way, each small improvement enables a reduction in size of heat sinks
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and other cooling components, which directly translates to a decrease in cost.
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\subsection{Twisted Inductors in RFIC Design}
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\subsection{Basket-Woven Air Coils}
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\subsection{Air-Core Inductors for Inductive Power Transfer}
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\subsection{Ferrite or Iron-Core Inductors for Inductive Power Transfer}
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\section{Twisted Inductor Design}
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We can approach twisted inductors by construction. Let us first consider a simple, planar, circular spiral coil with a
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fixed pitch. We will ignore trace width for now, and consider the trace a thin wire. We will assume the inductor's ports
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are both located on the positive $x$-Axis. We can rotate it so its first port aligns with the $x$-Axis. To
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minimize the loop area of the inductor's connections, inductors are usually designed with both ports close to one
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another, so we can also assume its second port aligns with the $x$-Axis.
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The trace trajectory of a standard planar spiral inductor can be parameterized in polar coordinates $r, \phi$ based on
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an Archimedean spiral: \todo{For the lulz, cite Archimedes here}
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\begin{equation}
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r &= a\cdot\phi
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\label{eqn_arch_spi_basic}
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\end{equation}
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An Archimedean spiral defined this way always starts at the origin, and it continues to infinity. Let us re-parameterize
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this spiral to a curve parameter $t$ with range $\left[0,1\right]$.
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inductor has a defined inner radius $r_0$ and outer radius $r_1$, and a
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fixed turn count $n$. Let us further re-parameterize the spiral to a curve parameter $t$ with range $\left\[0,
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1\right\]$. Taking into account that the input ports of a spiral inductor are usually placed on the outside of the
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spiral, we define the inductor's first port to lie at $\left\(\phi, r\right\)=\left\(0, r_1\right\)$, and we define that
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this corresponds to $t=0$. The resulting parametrization is:
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\begin{align}
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r &= r_1 - \frac{t}{n} \cdot \left\(r_1 - r_0\right\) \\
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\phi &= 2\pi \cdot n \cdot t
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\label{eqn_simple_spiral_ind}
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\end{align}
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For integer $n$, the spiral's second port will lie at $\left\(\phi, r\right\)=\left\(0, r_0\right\)$, however, other
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values of $n$ are possible, which will rotate the second port around the coordinate origin.
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%Let us further flip the radial coordinate axis such that the spiral's outer end is at $\phi=0$
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%because spiral inductors usually have their input ports at the outside. By normalizing the coordinate axes substituting
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%$\phi' = \frac{1}{2\pi}\phi$ and $r' = \left\(r - r_0\right\) \cdot \frac{1}{r_1 - r_0}$:
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\subsection{From Spiral to Twisted Inductor}
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\subsubsection{Ohmic Resistance}
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\subsubsection{Inductance}
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\subsection{CAD Integration}
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\section{FEM Simulation}
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To validate our analytical approximations, we performed a series of FEM simulations in both Elmer FEM and Simulia CST.
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For a number of inductor layouts, we performed simulations to determine ohmic resistance, inductance, and parasitic
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capacitance. For a subset of these layout variants we additionally performed simulations to determine the coupling
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factor between a pair of identical inductors at a number of different distances and rotations.
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\paragraph{Ohmic Resistance}
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Determining ohmic resistance by FEM is reasonably easy. In Elmer FEM, we can use the built-in joint static current and
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joule heating solver to determine the ohmic resistance at a given current.
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\paragraph{Inductance}
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We let Elmer determine inductance by first using its coil solver to determine the volumetric current density in our mesh
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given a test current, then applying its magnetodynamics solver to solve the electromagnetic field. Elmer provides
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routines to derive the total magnetic field energy $U_\text{mag}$ from an EM field solution. Since we have only our
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inductor under test inside the simulation volume, with test current $I_\text{test}$, we can then derive the inductor's
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inductance according to the well-known relation\todo{Find decent source}:
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\begin{equation}
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L = \frac{2\cdot U_\text{mag}}{I_\text{test}^2}
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\end{equation}
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\paragraph{Parasitic Capacitance and Self-Resonant Frequency}
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Determining parasitic capacitance is more complex.
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\subsection{Coupling}
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\section{Experimental Validation}
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\subsection{Inductance and Parasitic Capacitance}
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\subsection{Self-Resonant Frequency}
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\subsection{Coupling}
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\section{Conclusion}
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\section*{Availability}
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This is version \texttt{\input{version.tex}\unskip} of this paper, generated on \today.
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% The git repository with the
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% LaTeX source for this paper as well as our data analysis and demo code can be found at:
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% \center{\url{https://git.jaseg.de/nice-coils.git}}
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\printbibliography[heading=bibintoc]
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\end{document}
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