From 2f13da79f667381f70019455a7798dbd9d32c027 Mon Sep 17 00:00:00 2001 From: jaseg Date: Wed, 11 Dec 2024 13:37:24 +0100 Subject: [PATCH] Straighten up citations. --- paper/paper.tex | 93 +++++++++++++++++++++++++++---------------------- 1 file changed, 51 insertions(+), 42 deletions(-) diff --git a/paper/paper.tex b/paper/paper.tex index cabf4d0..b4e8387 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -83,12 +83,18 @@ Achieving Rotation-Invariant Coupling using Twisted Multi-Layer PCB Inductors} \end{figure} Inductive Wireless Power Transfer (WPT) is a widely used technology supported by a large corpus of research literature -\cite{awuahNovelCoilDesign2023, batraEffectFerriteAddition2015, curranModelingCharacterizationPCB2015, -fanSimultaneousWirelessPower2024, leeSimpleWirelessPower2017, liWirelessPowerTransfer2015, -maierContributionSystemDesign2019, mooreApplicationsWirelessPower2019, mouEnergyEfficientAdaptiveDesign2017, -mouWirelessPowerTransfer2015, mullenEffectMisalignmentInductive, rezmeritaSelfMutualInductance2017, -zhangWirelessPowerTransfer2019}. -% FIXME todo too many refs, weed out ones that don't appear elsewhere. +\cite{ + awuahNovelCoilDesign2023, + batraEffectFerriteAddition2015, + curranModelingCharacterizationPCB2015, + fanSimultaneousWirelessPower2024, + leeSimpleWirelessPower2017, + liWirelessPowerTransfer2015, + maierContributionSystemDesign2019, + mooreApplicationsWirelessPower2019, + mouEnergyEfficientAdaptiveDesign2017, + mouWirelessPowerTransfer2015, + zhangWirelessPowerTransfer2019}. While working on an application of Inductive WPT in a Inertial Hardware Security Module (IHSM) as previously published by \textcite{gotteCantTouchThis2022}, we found ourselves presented with an unusual set of constraints attempting WPT through a rotating joint using a planar inductor implemented in a Printed Circuit Board (PCB)---a set of @@ -160,8 +166,8 @@ operating frequency and improving its efficiency at lower operating frequencies. \subsection{Contributions} Our contributions in this paper include: \begin{itemize} - \item We introduce twisted inductors, a planar inductor layout that both improves rotational symmetry in rotating - wireless power transfer interface as well as quality factor in other applications. + \item We introduce twisted inductors, a planar inductor layout that improves rotational symmetry in WPT through + rotating joins, and promises improved high-frequency behavior in other applications. \item We provide detailed instructions for the construction of such layouts, including a mathematical analysis of the available parameter space. \item We provide an analytical model of inductance and DC equivalent series resistance of our scheme. @@ -176,8 +182,6 @@ Our contributions in this paper include: \section{Related Work} -% TODO cite \cite{mullenEffectMisalignmentInductive} below (misaligned coils) - \subsection{Inductive WPT in Practice} Inductive WPT has been proposed in a large number of @@ -204,36 +208,41 @@ transfer for the charging of electric vehicles (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 (almost) no concern, but at charging rates up to tens of kilowatt, -efficiency becomes critical. When charging an EV at a rate of \qty{10}{\kilo\watt}, an efficiency improvement of just -$0.1\%$ corresponds to a reduction in power dissipation of \qty{10}{\watt}. Besides the monetary cost of the power lost -this way, each small improvement enables a reduction in size of heat sinks and other cooling components, which directly -translates to a decrease in cost. +water-cooled cables. In this application, size is of little concern, but at charging rates up to tens of kilowatt, +efficiency becomes critical. +%When charging an EV at a rate of \qty{10}{\kilo\watt}, an efficiency improvement of just +%$0.1\%$ corresponds to a reduction in power dissipation of \qty{10}{\watt}. Besides the monetary cost of the power lost +%this way, each small improvement enables a reduction in size of heat sinks and other cooling components, which directly +%translates to a decrease in cost. -\subsection{Air-Core Inductors in WPT} +\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, and adding a ferrite core would not change the system's performance by much in these -circumstances. 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}. +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 +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}. \subsection{PCB inductor design for wireless power transfer} Today, air-core inductors are the standard solution in inductive WPT links. Since in most WPT applications an air gap of 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. +air-core inductors used, or by tiling multiple +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 -also serve as structural support. - -Implementing inductors in PCBs has several disadvantages. First, due to the limited layer count of common PCB -processes and due to structure size limitations, the number of windings that can be fit into a given volume is much -lower than in wire-wound inductors. Second, due to a PCB's copper layers being thin compared to its dielectric -substrate\footnote{common values are \qtyrange{15}{30}{\micro\meter} copper thickness and +also serve as structural support. However, implementing inductors in PCBs has several disadvantages. First, due to the +limited layer count of common PCB processes and due to structure size limitations, the number of windings that can be +fit into a given volume is much lower than in wire-wound inductors. Second, due to a PCB's copper layers being thin +compared to its dielectric substrate\footnote{common values are \qtyrange{15}{30}{\micro\meter} copper thickness and \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 @@ -250,13 +259,12 @@ through the PCB's substrate, not air. The relative permittivity $\epsilon_r$ of 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{Twisted Inductors in RFIC Design} +\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 to reduce distributed -capacitance\cite{lopez-villegasImprovementQualityFactor2000}, and applying variable trace width to decrease equivalent -series resistance while preserving total inductance and quality factor\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 @@ -609,16 +617,17 @@ $k=1$ to $k=3$ irrespective of turn count. From these measurements we can conclu 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. We found that going from a single-layer spiral inductor to a two-layer spiral inductor decreases the -self-resonant frequency, this effect being more pronounced with higher turn count. Intuitively, this makes sense if we -consider the mechanics 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 coupling exists between adjacent windings, which here have only a -small voltage differential as only a fraction of the inductor's total voltage appears across each winding. Compared to -this, when the inductor is constructed as a simple two-layer inductor with $k=1$, now the start and end windings of the -inductor, which have the highest voltage differential, are located right on top of each other with the substrate in -between. Making things worse, common PCB substrates have a relative permittivity much larger than air (usually around -$4$). +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 +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 +coupling exists between adjacent windings, which here have only a small voltage differential as only a fraction of the +inductor's total voltage appears across each winding. Compared to this, when the inductor is constructed as a simple +two-layer inductor with $k=1$, now the start and end windings of the inductor, which have the highest voltage +differential, are located right on top of each other with the substrate in between. Making things worse, common PCB +substrates have a relative permittivity much larger than air (usually around $4$). We observe that this decrease in high-frequency performance is eventually counteracted by increasing inversion count $k$. While our test samples focused on smaller turn counts, we observe a notable increase from a self-resonant frequency