diff --git a/paper/paper.tex b/paper/paper.tex index b4e8387..437f641 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -102,7 +102,7 @@ constraints that does not seem to be addressed adequately in the existing litera Inertial Hardware Security Modules are a hardware security primitive that discourages tampering with a payload such as a single-board computer by rotating a tamper-sensing enclosure around the payload. The tamper-sensing enclosure -continuously monitors itself for tampering using sensors such as tamper-sensing meshes\cite{TamperResistance2020a} and +continuously monitors itself for tampering using sensors such as tamper-sensing meshes~\cite{TamperResistance2020a} and accelerometers. When the tamper-sensing enclosure signals a tamper alarm to the payload, the payload immediately destroys all sensitive data to prevent the attacker from gaining access to it. In principle, an IHSM is similar to an ATM that responds to attempts at opening its vault by dispensing dye over the bank notes within, rendering them @@ -130,21 +130,28 @@ capacitor on the secondary side if the application can accomodate such component While there exist a corpus of prior work focusing on efficient power transfer between two coils whose position relative to one another cannot be precisely controlled as is the case in wireless phone charging systems as well as in proposed -WPT electric vehicle chargers\cite{liWirelessPowerTransfer2015,mouEnergyEfficientAdaptiveDesign2017}, +WPT electric vehicle chargers~\cite{liWirelessPowerTransfer2015,mouEnergyEfficientAdaptiveDesign2017}, it is generally assumed that the two coils remain quasi-stationary with respect to one another. -There exists a small body of work on inductive power transfer through rotating -joints\cite{ +There exists a body of work on inductive power transfer through rotating joints but here the focus often lies on higher +power budgets than our application requires, which in practice requires more space and a ferrite or laminated iron +core~\cite{ fanSimultaneousWirelessPower2024, - xiaRotaryWirelessPower2024, songRotationLightweightWirelessPower2019, + wangCoaxialNestedCouplersBased2020, + }. +Often, these rotating joint WPT systems use coaxial structures, but segmented approaches exist, too~\cite{ wangNovelRotatingWireless2024, yanFreeRotationWirelessPower2023, - wangCoaxialNestedCouplersBased2020}, -but here the focus usually lies on higher power budgets than our application requires, which in practice requires more -space and a ferrite or laminated iron core. Therefore, this paper bridges the gap between existing literature on -low-power planar WPT inductor design and high-power WPT through rotating joints. -% FIXME refer to wangNovelRotatingWireless2024,yanFreeRotationWirelessPower2023,liWirelessPowerTransfer2021 as segmented approaches. our system performs better + xiaRotaryWirelessPower2024, + liWirelessPowerTransfer2021, +}. +In lower-power applications, segmented approaches are more common. A key challenge in segmented approaches is the +reduction of secondary-side ripple induced when the segments' alignment changes throught one revolution~\cite{ + zhangWirelessSensorPower2024, +}, which usually requires additional secondary-side circuitry. This paper introduces a planar coil topology for WPT +through a rotating joint using a single planar PCB coil on both the transmitting and the receiving side that improves +rotation ripple at low turn counts. \subsection{Twisted inductors} @@ -185,7 +192,7 @@ Our contributions in this paper include: \subsection{Inductive WPT in Practice} Inductive WPT has been proposed in a large number of -scenarios\cite{zhangWirelessPowerTransfer2019,mouWirelessPowerTransfer2015}, each of which comes with a set of unique +scenarios~\cite{zhangWirelessPowerTransfer2019,mouWirelessPowerTransfer2015}, each of which comes with a set of unique constraints. When WPT is used to charge an electric toothbrush, the implementation cost of the system is critical, while efficiency and total power output are of little concern. Mechanically, in an electric toothbrush's charging system, the position and spacing of the transmitter and receiver coils can easily be controlled down to millimeter precision. @@ -197,7 +204,7 @@ two coils in the charging base and in the phone may be positioned more than a ce millimeters and potentially not even in parallel planes. Power transfer across large distances is even more of a concern in implantable medical -devices\cite{mooreApplicationsWirelessPower2019}. Where a wireless phone charger must be able to bridge distances of a +devices~\cite{mooreApplicationsWirelessPower2019}. Where a wireless phone charger must be able to bridge distances of a few millimeters, an implantable medical device might be situated underneath several centimeter of tissue and bones. At the same time, cost is of (almost) no concern in this medical application, which enables the use of complex manufacturing techniques, customized electronic components and exotic materials. @@ -205,7 +212,7 @@ manufacturing techniques, customized electronic components and exotic materials. While all of the aforementioned applications transfer somewhere between a few hundred milliwatts and several watts of power, at the other end of the spectrum there is a large body of research suggesting the use of inductive wireless power transfer for the charging of electric vehicles -(EVs)\cite{liWirelessPowerTransfer2015,mouEnergyEfficientAdaptiveDesign2017}. In this application, the wireless power +(EVs)~\cite{liWirelessPowerTransfer2015,mouEnergyEfficientAdaptiveDesign2017}. In this application, the wireless power transfer system usually replaces the conventional wired charging connector, which improves the systems' user experience given the strong force required to seat or unseat these rather large connectors, as well as the heft of the required water-cooled cables. In this application, size is of little concern, but at charging rates up to tens of kilowatt, @@ -218,16 +225,16 @@ efficiency becomes critical. \subsection{Core materials in WPT} Across application areas, air-core inductors are often used for WPT since in most applications, an air gap of several -millimeters or more is expected\cite{curranModelingCharacterizationPCB2015}. Especially in low-power application such as -mobile device charging, the size and weight of ferrites is an obstacle to their use, and at lower power levels losses +millimeters or more is expected~\cite{curranModelingCharacterizationPCB2015}. Especially in low-power application such +as mobile device charging, the size and weight of ferrites is an obstacle to their use, and at lower power levels losses are less of a concern. A common way to use ferrites in WPT applications is by magnetically shielding the inductor's back side with a ferrite plate such that the field does not extend beyond the coil's back side, thereby increasing the intended mutual inductance while simultaneously reducing eddy current losses when the WPT coils are placed near metal -objects\cite{batraEffectFerriteAddition2015,leeSimpleWirelessPower2017,muehlmannMutualCouplingModeling2012}. Similar to +objects~\cite{batraEffectFerriteAddition2015,leeSimpleWirelessPower2017,muehlmannMutualCouplingModeling2012}. Similar to how the trace layouts of planar WPT coils are optimized to improve power transfer efficiency, the layout of ferrite -components has been proposed for optimization\cite{batraEffectFerriteAddition2015}. +components has been proposed for optimization~\cite{batraEffectFerriteAddition2015}. \subsection{PCB inductor design for wireless power transfer} @@ -235,7 +242,7 @@ Today, air-core inductors are the standard solution in inductive WPT links. Sinc several millimeters between the sending and receiving assemblies is expected, adding a ferrite core does not result in a large improvement in coupling. Instead, the impact of this misalignment is reduced by maximizing the area of the air-core inductors used, or by tiling multiple -inductors\cite{curranModelingCharacterizationPCB2015,wangNovelRotatingWireless2024,zhangDynamicWirelessPower2025}. +inductors~\cite{curranModelingCharacterizationPCB2015,wangNovelRotatingWireless2024,zhangDynamicWirelessPower2025}. WPT inductors tend to be mostly planar coils with only a few layers, so implementing them in a PCB process seems natural. Using a PCB for the inductor has the potential to reduce implementation cost since PCBs are cheap, and they can @@ -246,36 +253,36 @@ compared to its dielectric substrate\footnote{common values are \qtyrange{15}{30 \qtyrange{600}{1600}{\micro\meter} substrate thickness} PCB inductors tend to have poor DC resistance, albeit the thin copper layer decreases skin effect losses compared to a solid, round conductors of the same cross-sectional area. However, PCBs can still not approach the performance of litz wire used in high-frequency WPT coils, which commonly use -wire diameters in the range of tens of micrometer\cite{zhaoDesignOptimizationLitzWire2023}. +wire diameters in the range of tens of micrometer~\cite{zhaoDesignOptimizationLitzWire2023}. \textcite{lopeFrequencyDependentResistancePlanar2014} and \textcite{nomotoSplittingConductorsCoils2024} propose a mitigation that aims to emulate a litz wire's structure in large, high-current PCB inductors, but their mitigation is heavily limited by the structure size achievable in common PCB manufacturing -processes\cite{nguyenReviewComparisonSolid2020}. +processes~\cite{nguyenReviewComparisonSolid2020}. A further factor that limits the high-frequency performance of PCB inductors is distributed capacitance. Not only does a large air coil exhibit more parasitic capacitance than an equivalent, smaller ferrite-core inductor simply due to its size, when implemented in a PCB process a large fraction of the electrical fields responsible for this capacitance pass through the PCB's substrate, not air. The relative permittivity $\epsilon_r$ of common PCB substrates typically lies in -the range of $4$ to $5$ \cite{mumbyDielectricPropertiesFR41989}, which increases the distributed capacitance compared to +the range of $4$ to $5$~\cite{mumbyDielectricPropertiesFR41989}, which increases the distributed capacitance compared to a pure air-core inductor by approximately that same factor. \subsection{Planar Inductors in RFIC Design} Beyond WPT, planar inductors are commonly used in radio frequency integrated circuits (RFICs). In RFIC design, the major challenges are area optimization and precisely predicting the inductor's characteristics during the design phase. Common -optimizations include applying a variable trace pitch\cite{lopez-villegasImprovementQualityFactor2000} and variable trace -width\cite{hsuAnalyticalDesignAlgorithm2008}. +optimizations include applying a variable trace pitch~\cite{lopez-villegasImprovementQualityFactor2000} and variable +trace width~\cite{hsuAnalyticalDesignAlgorithm2008}. In RFICs, inductors are commonly designed as \emph{balanced} inductors with a grounded central node. Such designs interleave two counter-wound planar spiral inductors on the same layer with the help of some jumper connections on a -second layer\cite{daneshDifferentiallyDrivenSymmetric2002,martinMultiturnTwistedInductor2016}. The use of such designs +second layer~\cite{daneshDifferentiallyDrivenSymmetric2002,martinMultiturnTwistedInductor2016}. The use of such designs in RFIC design is mainly focused on their electrical symmetry, so that the two input ports can be fed with a fully differential signal, with the inductor loading both driver outputs equally across the inductor's frequency range. Setting the inversion count to $k=1$ in our proposed scheme yields the counterwound scheme that is commonly used for two-layer planar -inductors\cite{lopeFirstSelfresonantFrequency2021,sproHighVoltageInsulationDesign2021,leePrintedSpiralWinding2011}, and -which has been used to stack planar coils for more than a century\cite{flemingPrinciplesElectricWave1910}. +inductors~\cite{lopeFirstSelfresonantFrequency2021,sproHighVoltageInsulationDesign2021,leePrintedSpiralWinding2011}, and +which has been used to stack planar coils for more than a century~\cite{flemingPrinciplesElectricWave1910}. % Note: They note that the main point behind the design is electrical symmetry of the two ports to make driving the % thing differentially cleaner. We should adopt this observation for our inductors, which likewise are electrically @@ -284,22 +291,22 @@ which has been used to stack planar coils for more than a century\cite{flemingPr \subsection{A Brief Historical Diversion on Basket-Woven Air Coils} Since the early days of radio engineering, the parasitic capacitance of inductors has been a point of -concern\cite{nesperHandbuchDrahtlosenTelegraphie1921,flemingPrinciplesElectricWave1910}. Going back to the early days of -wireless telegraphy after the turn of the twentieth century, coils with high inductance were needed for the construction -of both transmitters and receivers, but the ferrites that would later permit their compact construction were still being -developed. The ferromagnetic core material of choice back then was laminated iron, which was only useful at low -frequencies due to eddy current losses. As a result, the inductors in radio circuits of the era were often constructed -as air-core coils. While air-core inductors are immune to core saturation, the poor magnetic permeability of air -necessitates a large number of wide turns of wire to reach useful inductance values, which for reasons of practicality -or leakage inductance often could not be wound as a single layer cylindrical coil. This could be resolved by winding an -inductor with many turns on multiple layers, which improves compactness and leakage inductance, but this in turn gives -rise to increased distributed capacitance as now turns with a large voltage differential are layered right on top of -each other. +concern~\cite{nesperHandbuchDrahtlosenTelegraphie1921,flemingPrinciplesElectricWave1910}. Going back to the early days +of wireless telegraphy after the turn of the twentieth century, coils with high inductance were needed for the +construction of both transmitters and receivers, but the ferrites that would later permit their compact construction +were still being developed. The ferromagnetic core material of choice back then was laminated iron, which was only +useful at low frequencies due to eddy current losses. As a result, the inductors in radio circuits of the era were often +constructed as air-core coils. While air-core inductors are immune to core saturation, the poor magnetic permeability of +air necessitates a large number of wide turns of wire to reach useful inductance values, which for reasons of +practicality or leakage inductance often could not be wound as a single layer cylindrical coil. This could be resolved +by winding an inductor with many turns on multiple layers, which improves compactness and leakage inductance, but this +in turn gives rise to increased distributed capacitance as now turns with a large voltage differential are layered right +on top of each other. Before the invention of ferrites, a number of ways were devised to decrease distributed capacitance in multilayer inductors. These methods can be divided into two general categories: Optimizing the connecting order of turns to minimize the voltage differential between adjacent turns---a technique that is still used to this -day\cite{lopeFirstSelfresonantFrequency2021}, and optimizing the winding schema to increase the separation between +day~\cite{lopeFirstSelfresonantFrequency2021}, and optimizing the winding schema to increase the separation between turns. The main technique in the first category concerns winding the turns of a cylindrical multilayer inductor not layer by layer, but instead layering them diagonally, effectively connecting adjacent turns in a diagonal zigzag pattern. Then as now, wound inductors applying this technique were not feasible to manufacture reliably by machine, but @@ -344,7 +351,7 @@ Both construction techniques apply similar principles to those leading to the im twisted inductors that we describe in this paper.\footnote{Interestingly, the winding schemes of both honeycomb and basket-woven coils are also governed by the same coprimality condition between the number of turns and the number of inversions within each turn that we describe for our twisted inductors below, although we could not find an example in -historic literature where this condition was explicitly stated \cite{eppenAnforderungenEinzelteileRundfunkempfanger1927, +historic literature where this condition was explicitly stated~\cite{eppenAnforderungenEinzelteileRundfunkempfanger1927, kleinSpulenUndSchwingungskreise1941, wiggeRundfunktechnischesHandbuch1930, querfurthCoilWindingDescription1954}.} \section{Twisted Inductor Design} @@ -543,16 +550,16 @@ case. To allow for easy design with twisted inductors and to speed up the laboratory prototyping we performed for this paper, we created a tool that generates arbitrary twisted inductor layouts, and that is able to output these layouts as PCB -footprint files for the open source KiCad EDA CAD tool\cite{KiCadEDA}. We integrated the ESR and inductance +footprint files for the open source KiCad EDA CAD tool~\cite{KiCadEDA}. We integrated the ESR and inductance approximations as derived above with our tool, so that it provides immediate design feedback when generating inductors. In order to minimize ESR and maximize PCB area utilization, we made the tool automatically calculate the largest possible trace width when given a minimum clearance specification. To handle outputting PCB geometry in a format that can be read from KiCad, we utilized the open source EDA file format -library \emph{gerbonara}\cite{GerbonaraToolsHandle}. To support the FEM simulations that are described in the next +library \emph{gerbonara}~\cite{GerbonaraToolsHandle}. To support the FEM simulations that are described in the next section below, our tool contains functionality to map gerbonara's geometry representation into that of -gmsh\cite{geuzaineGmsh3DFinite2009}, the FEM mesher that we chose to interface with Elmer -FEM\cite{ruokolainenElmerCSCElmerfemElmer2023}. +gmsh~\cite{geuzaineGmsh3DFinite2009}, the FEM mesher that we chose to interface with Elmer +FEM~\cite{ruokolainenElmerCSCElmerfemElmer2023}. Our inductor design tool is available in this paper's supplementary material as well as at the git repository linked at the end of this paper. @@ -580,7 +587,7 @@ We let Elmer determine inductance by first using its coil solver to determine th given a test current, then applying its magnetodynamics solver to solve the electromagnetic field. Elmer provides routines to derive the total magnetic field energy $U_\text{mag}$ from an EM field solution. Since we have only our inductor under test inside the simulation volume, with test current $I_\text{test}$, we can then derive the inductor's -inductance according to the well-known relation\cite{meeekerFiniteElementMethod2015}: +inductance according to the well-known relation~\cite{meeekerFiniteElementMethod2015}: \begin{equation} L = \frac{2\cdot U_\text{mag}}{I_\text{test}^2} @@ -619,7 +626,7 @@ inductors almost perfectly matches that of simple two-layer inductors. Finally, while not particularly relevant for our application, we decided to evaluate the high-frequency performance of twisted inductors. It is well-known that self-resonant frequency decreases when going from a single-layer spiral inductor to a two-layer spiral inductor while keeping inductance and dimensions -constant\cite{zhangImprovedCompensationMethod2025}. Our measurements show this effect, with it being more pronounced +constant~\cite{zhangImprovedCompensationMethod2025}. Our measurements show this effect, with it being more pronounced with higher turn count. Intuitively, this makes sense if we consider the mechanism of inductor self-resonance. The primary contributor to self resonance, particularly in higher turn count inductors, is capacitive coupling between the inductor's windings. In a single-layer spiral inductor, this effect gets partially mitigated since the strongest