Improve related work on rotating WPT
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1 changed files with 52 additions and 45 deletions
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@ -102,7 +102,7 @@ constraints that does not seem to be addressed adequately in the existing litera
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Inertial Hardware Security Modules are a hardware security primitive that discourages tampering with a payload such as a
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single-board computer by rotating a tamper-sensing enclosure around the payload. The tamper-sensing enclosure
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continuously monitors itself for tampering using sensors such as tamper-sensing meshes\cite{TamperResistance2020a} and
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continuously monitors itself for tampering using sensors such as tamper-sensing meshes~\cite{TamperResistance2020a} and
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accelerometers. When the tamper-sensing enclosure signals a tamper alarm to the payload, the payload immediately
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destroys all sensitive data to prevent the attacker from gaining access to it. In principle, an IHSM is similar to an
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ATM that responds to attempts at opening its vault by dispensing dye over the bank notes within, rendering them
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@ -130,21 +130,28 @@ capacitor on the secondary side if the application can accomodate such component
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While there exist a corpus of prior work 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 as well as in proposed
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WPT electric vehicle chargers\cite{liWirelessPowerTransfer2015,mouEnergyEfficientAdaptiveDesign2017},
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WPT electric vehicle chargers~\cite{liWirelessPowerTransfer2015,mouEnergyEfficientAdaptiveDesign2017},
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it is generally assumed that the two coils remain quasi-stationary with respect to one another.
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There exists a small body of work on inductive power transfer through rotating
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joints\cite{
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There exists a body of work on inductive power transfer through rotating joints but here the focus often lies on higher
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power budgets than our application requires, which in practice requires more space and a ferrite or laminated iron
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core~\cite{
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fanSimultaneousWirelessPower2024,
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xiaRotaryWirelessPower2024,
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songRotationLightweightWirelessPower2019,
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wangCoaxialNestedCouplersBased2020,
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}.
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Often, these rotating joint WPT systems use coaxial structures, but segmented approaches exist, too~\cite{
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wangNovelRotatingWireless2024,
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yanFreeRotationWirelessPower2023,
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wangCoaxialNestedCouplersBased2020},
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but here the focus usually lies on higher power budgets than our application requires, which in practice requires more
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space and a ferrite or laminated iron core. Therefore, this paper bridges the gap between existing literature on
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low-power planar WPT inductor design and high-power WPT through rotating joints.
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% FIXME refer to wangNovelRotatingWireless2024,yanFreeRotationWirelessPower2023,liWirelessPowerTransfer2021 as segmented approaches. our system performs better
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xiaRotaryWirelessPower2024,
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liWirelessPowerTransfer2021,
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}.
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In lower-power applications, segmented approaches are more common. A key challenge in segmented approaches is the
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reduction of secondary-side ripple induced when the segments' alignment changes throught one revolution~\cite{
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zhangWirelessSensorPower2024,
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}, which usually requires additional secondary-side circuitry. This paper introduces a planar coil topology for WPT
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through a rotating joint using a single planar PCB coil on both the transmitting and the receiving side that improves
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rotation ripple at low turn counts.
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\subsection{Twisted inductors}
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@ -185,7 +192,7 @@ Our contributions in this paper include:
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\subsection{Inductive WPT in Practice}
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Inductive WPT has been proposed in a large number of
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scenarios\cite{zhangWirelessPowerTransfer2019,mouWirelessPowerTransfer2015}, each of which comes with a set of unique
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scenarios~\cite{zhangWirelessPowerTransfer2019,mouWirelessPowerTransfer2015}, each of which comes with a set of unique
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constraints. When WPT is used to charge an electric toothbrush, the implementation cost of the system is critical, while
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efficiency and total power output are of little concern. Mechanically, in an electric toothbrush's charging system, the
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position and spacing of the transmitter and receiver coils can easily be controlled down to millimeter precision.
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@ -197,7 +204,7 @@ two coils in the charging base and in the phone may be positioned more than a ce
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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
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devices\cite{mooreApplicationsWirelessPower2019}. Where a wireless phone charger must be able to bridge distances of a
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devices~\cite{mooreApplicationsWirelessPower2019}. Where a wireless phone charger must be able to bridge distances of a
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few millimeters, an implantable medical device might be situated underneath several centimeter of tissue and bones. At
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the same time, cost is of (almost) no concern in this medical application, which enables the use of complex
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manufacturing techniques, customized electronic components and exotic materials.
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@ -205,7 +212,7 @@ manufacturing techniques, customized electronic components and exotic 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
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(EVs)\cite{liWirelessPowerTransfer2015,mouEnergyEfficientAdaptiveDesign2017}. In this application, the wireless power
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(EVs)~\cite{liWirelessPowerTransfer2015,mouEnergyEfficientAdaptiveDesign2017}. In this application, the wireless power
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transfer system usually replaces the conventional wired charging connector, which improves the systems' user experience
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given the strong force required to seat or unseat these rather large connectors, as well as the heft of the required
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water-cooled cables. In this application, size is of little concern, but at charging rates up to tens of kilowatt,
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@ -218,16 +225,16 @@ efficiency becomes critical.
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\subsection{Core materials in WPT}
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Across application areas, air-core inductors are often used for WPT since in most applications, an air gap of several
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millimeters or more is expected\cite{curranModelingCharacterizationPCB2015}. Especially in low-power application such as
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mobile device charging, the size and weight of ferrites is an obstacle to their use, and at lower power levels losses
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millimeters or more is expected~\cite{curranModelingCharacterizationPCB2015}. Especially in low-power application such
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as mobile device charging, the size and weight of ferrites is an obstacle to their use, and at lower power levels losses
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are less of a concern.
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A common way to use ferrites in WPT applications is by magnetically shielding the inductor's back side with a ferrite
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plate such that the field does not extend beyond the coil's back side, thereby increasing the intended mutual inductance
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while simultaneously reducing eddy current losses when the WPT coils are placed near metal
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objects\cite{batraEffectFerriteAddition2015,leeSimpleWirelessPower2017,muehlmannMutualCouplingModeling2012}. Similar to
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objects~\cite{batraEffectFerriteAddition2015,leeSimpleWirelessPower2017,muehlmannMutualCouplingModeling2012}. Similar to
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how the trace layouts of planar WPT coils are optimized to improve power transfer efficiency, the layout of ferrite
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components has been proposed for optimization\cite{batraEffectFerriteAddition2015}.
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components has been proposed for optimization~\cite{batraEffectFerriteAddition2015}.
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\subsection{PCB inductor design for wireless power transfer}
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@ -235,7 +242,7 @@ Today, air-core inductors are the standard solution in inductive WPT links. Sinc
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several millimeters between the sending and receiving assemblies is expected, adding a ferrite core does not result in a
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large improvement in coupling. Instead, the impact of this misalignment is reduced by maximizing the area of the
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air-core inductors used, or by tiling multiple
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inductors\cite{curranModelingCharacterizationPCB2015,wangNovelRotatingWireless2024,zhangDynamicWirelessPower2025}.
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inductors~\cite{curranModelingCharacterizationPCB2015,wangNovelRotatingWireless2024,zhangDynamicWirelessPower2025}.
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WPT inductors tend to be mostly planar coils with only a few layers, so implementing them in a PCB process seems
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natural. Using a PCB for the inductor has the potential to reduce implementation cost since PCBs are cheap, and they can
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@ -246,36 +253,36 @@ compared to its dielectric substrate\footnote{common values are \qtyrange{15}{30
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\qtyrange{600}{1600}{\micro\meter} substrate thickness} PCB inductors tend to have poor DC resistance, albeit the thin
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copper layer decreases skin effect losses compared to a solid, round conductors of the same cross-sectional area.
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However, PCBs can still not approach the performance of litz wire used in high-frequency WPT coils, which commonly use
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wire diameters in the range of tens of micrometer\cite{zhaoDesignOptimizationLitzWire2023}.
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wire diameters in the range of tens of micrometer~\cite{zhaoDesignOptimizationLitzWire2023}.
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\textcite{lopeFrequencyDependentResistancePlanar2014} and \textcite{nomotoSplittingConductorsCoils2024} propose a
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mitigation that aims to emulate a litz wire's structure in large, high-current PCB inductors, but their mitigation is
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heavily limited by the structure size achievable in common PCB manufacturing
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processes\cite{nguyenReviewComparisonSolid2020}.
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processes~\cite{nguyenReviewComparisonSolid2020}.
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A further factor that limits the high-frequency performance of PCB inductors is distributed capacitance. Not only does a
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large air coil exhibit more parasitic capacitance than an equivalent, smaller ferrite-core inductor simply due to its
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size, when implemented in a PCB process a large fraction of the electrical fields responsible for this capacitance pass
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through the PCB's substrate, not air. The relative permittivity $\epsilon_r$ of common PCB substrates typically lies in
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the range of $4$ to $5$ \cite{mumbyDielectricPropertiesFR41989}, which increases the distributed capacitance compared to
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the range of $4$ to $5$~\cite{mumbyDielectricPropertiesFR41989}, which increases the distributed capacitance compared to
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a pure air-core inductor by approximately that same factor.
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\subsection{Planar Inductors in RFIC Design}
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Beyond WPT, planar inductors are commonly used in radio frequency integrated circuits (RFICs). In RFIC design, the major
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challenges are area optimization and precisely predicting the inductor's characteristics during the design phase. Common
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optimizations include applying a variable trace pitch\cite{lopez-villegasImprovementQualityFactor2000} and variable trace
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width\cite{hsuAnalyticalDesignAlgorithm2008}.
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optimizations include applying a variable trace pitch~\cite{lopez-villegasImprovementQualityFactor2000} and variable
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trace width~\cite{hsuAnalyticalDesignAlgorithm2008}.
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In RFICs, inductors are commonly designed as \emph{balanced} inductors with a grounded central node. Such designs
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interleave two counter-wound planar spiral inductors on the same layer with the help of some jumper connections on a
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second layer\cite{daneshDifferentiallyDrivenSymmetric2002,martinMultiturnTwistedInductor2016}. The use of such designs
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second layer~\cite{daneshDifferentiallyDrivenSymmetric2002,martinMultiturnTwistedInductor2016}. The use of such designs
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in RFIC design is mainly focused on their electrical symmetry, so that the two input ports can be fed with a fully
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differential signal, with the inductor loading both driver outputs equally across the inductor's frequency range.
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Setting the inversion count to $k=1$ in our proposed scheme yields the counterwound scheme that is commonly used for
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two-layer planar
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inductors\cite{lopeFirstSelfresonantFrequency2021,sproHighVoltageInsulationDesign2021,leePrintedSpiralWinding2011}, and
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which has been used to stack planar coils for more than a century\cite{flemingPrinciplesElectricWave1910}.
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inductors~\cite{lopeFirstSelfresonantFrequency2021,sproHighVoltageInsulationDesign2021,leePrintedSpiralWinding2011}, and
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which has been used to stack planar coils for more than a century~\cite{flemingPrinciplesElectricWave1910}.
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% Note: They note that the main point behind the design is electrical symmetry of the two ports to make driving the
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% thing differentially cleaner. We should adopt this observation for our inductors, which likewise are electrically
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@ -284,22 +291,22 @@ which has been used to stack planar coils for more than a century\cite{flemingPr
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\subsection{A Brief Historical Diversion on Basket-Woven Air Coils}
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Since the early days of radio engineering, the parasitic capacitance of inductors has been a point of
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concern\cite{nesperHandbuchDrahtlosenTelegraphie1921,flemingPrinciplesElectricWave1910}. Going back to the early days of
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wireless telegraphy after the turn of the twentieth century, coils with high inductance were needed for the construction
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of both transmitters and receivers, but the ferrites that would later permit their compact construction were still being
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developed. The ferromagnetic core material of choice back then was laminated iron, which was only useful at low
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frequencies due to eddy current losses. As a result, the inductors in radio circuits of the era were often constructed
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as air-core coils. While air-core inductors are immune to core saturation, the poor magnetic permeability of air
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necessitates a large number of wide turns of wire to reach useful inductance values, which for reasons of practicality
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or leakage inductance often could not be wound as a single layer cylindrical coil. This could be resolved by winding an
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inductor with many turns on multiple layers, which improves compactness and leakage inductance, but this in turn gives
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rise to increased distributed capacitance as now turns with a large voltage differential are layered right on top of
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each other.
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concern~\cite{nesperHandbuchDrahtlosenTelegraphie1921,flemingPrinciplesElectricWave1910}. Going back to the early days
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of wireless telegraphy after the turn of the twentieth century, coils with high inductance were needed for the
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construction of both transmitters and receivers, but the ferrites that would later permit their compact construction
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were still being developed. The ferromagnetic core material of choice back then was laminated iron, which was only
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useful at low frequencies due to eddy current losses. As a result, the inductors in radio circuits of the era were often
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constructed as air-core coils. While air-core inductors are immune to core saturation, the poor magnetic permeability of
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air necessitates a large number of wide turns of wire to reach useful inductance values, which for reasons of
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practicality or leakage inductance often could not be wound as a single layer cylindrical coil. This could be resolved
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by winding an inductor with many turns on multiple layers, which improves compactness and leakage inductance, but this
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in turn gives rise to increased distributed capacitance as now turns with a large voltage differential are layered right
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on top of each other.
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Before the invention of ferrites, a number of ways were devised to decrease distributed capacitance in multilayer
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inductors. These methods can be divided into two general categories: Optimizing the connecting order of turns to
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minimize the voltage differential between adjacent turns---a technique that is still used to this
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day\cite{lopeFirstSelfresonantFrequency2021}, and optimizing the winding schema to increase the separation between
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day~\cite{lopeFirstSelfresonantFrequency2021}, and optimizing the winding schema to increase the separation between
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turns. The main technique in the first category concerns winding the turns of a cylindrical multilayer inductor not
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layer by layer, but instead layering them diagonally, effectively connecting adjacent turns in a diagonal zigzag
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pattern. Then as now, wound inductors applying this technique were not feasible to manufacture reliably by machine, but
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@ -344,7 +351,7 @@ Both construction techniques apply similar principles to those leading to the im
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twisted inductors that we describe in this paper.\footnote{Interestingly, the winding schemes of both honeycomb and
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basket-woven coils are also governed by the same coprimality condition between the number of turns and the number of
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inversions within each turn that we describe for our twisted inductors below, although we could not find an example in
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historic literature where this condition was explicitly stated \cite{eppenAnforderungenEinzelteileRundfunkempfanger1927,
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historic literature where this condition was explicitly stated~\cite{eppenAnforderungenEinzelteileRundfunkempfanger1927,
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kleinSpulenUndSchwingungskreise1941, wiggeRundfunktechnischesHandbuch1930, querfurthCoilWindingDescription1954}.}
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\section{Twisted Inductor Design}
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@ -543,16 +550,16 @@ case.
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To allow for easy design with twisted inductors and to speed up the laboratory prototyping we performed for this paper,
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we created a tool that generates arbitrary twisted inductor layouts, and that is able to output these layouts as PCB
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footprint files for the open source KiCad EDA CAD tool\cite{KiCadEDA}. We integrated the ESR and inductance
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footprint files for the open source KiCad EDA CAD tool~\cite{KiCadEDA}. We integrated the ESR and inductance
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approximations as derived above with our tool, so that it provides immediate design feedback when generating inductors.
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In order to minimize ESR and maximize PCB area utilization, we made the tool automatically calculate the largest
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possible trace width when given a minimum clearance specification.
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To handle outputting PCB geometry in a format that can be read from KiCad, we utilized the open source EDA file format
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library \emph{gerbonara}\cite{GerbonaraToolsHandle}. To support the FEM simulations that are described in the next
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library \emph{gerbonara}~\cite{GerbonaraToolsHandle}. To support the FEM simulations that are described in the next
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section below, our tool contains functionality to map gerbonara's geometry representation into that of
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gmsh\cite{geuzaineGmsh3DFinite2009}, the FEM mesher that we chose to interface with Elmer
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FEM\cite{ruokolainenElmerCSCElmerfemElmer2023}.
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gmsh~\cite{geuzaineGmsh3DFinite2009}, the FEM mesher that we chose to interface with Elmer
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FEM~\cite{ruokolainenElmerCSCElmerfemElmer2023}.
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Our inductor design tool is available in this paper's supplementary material as well as at the git repository linked at
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the end of this paper.
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@ -580,7 +587,7 @@ We let Elmer determine inductance by first using its coil solver to determine th
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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\cite{meeekerFiniteElementMethod2015}:
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inductance according to the well-known relation~\cite{meeekerFiniteElementMethod2015}:
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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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@ -619,7 +626,7 @@ inductors almost perfectly matches that of simple two-layer inductors.
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Finally, while not particularly relevant for our application, we decided to evaluate the high-frequency performance of
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twisted inductors. It is well-known that self-resonant frequency decreases when going from a single-layer spiral
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inductor to a two-layer spiral inductor while keeping inductance and dimensions
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constant\cite{zhangImprovedCompensationMethod2025}. Our measurements show this effect, with it being more pronounced
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constant~\cite{zhangImprovedCompensationMethod2025}. Our measurements show this effect, with it being more pronounced
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with higher turn count. Intuitively, this makes sense if we consider the mechanism of inductor self-resonance. The
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primary contributor to self resonance, particularly in higher turn count inductors, is capacitive coupling between the
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inductor's windings. In a single-layer spiral inductor, this effect gets partially mitigated since the strongest
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