From 8c76006f5f093e1668896c2da613ed66bd34bba5 Mon Sep 17 00:00:00 2001 From: jaseg Date: Mon, 17 Feb 2025 16:52:54 +0100 Subject: [PATCH] Update paper for newer submission template --- paper/Makefile | 2 +- paper/paper.tex | 222 ++++++++++++++++++++++------------------------ paper/version.tex | 2 +- 3 files changed, 108 insertions(+), 118 deletions(-) diff --git a/paper/Makefile b/paper/Makefile index 71a6704..987562f 100644 --- a/paper/Makefile +++ b/paper/Makefile @@ -36,7 +36,7 @@ submission.zip: figures/setup_probe_small.jpg version.tex: ${main_tex}.tex paper.bib - echo "${VERSION_STRING}" > $@ + echo -n "${VERSION_STRING}" > $@ .PHONY: clean clean: diff --git a/paper/paper.tex b/paper/paper.tex index 33cc371..c018e8b 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -1,4 +1,4 @@ -\documentclass[journal,12pt,onecolumn,draftclsnofoot]{IEEEtran} +\documentclass[journal,10pt,a4paper]{IEEEtran} \usepackage[T1]{fontenc} \usepackage[ @@ -32,9 +32,8 @@ \newcolumntype{P}[1]{>{\centering\arraybackslash}p{#1}} \newcommand{\partnum}[1]{\texttt{#1}} \newcommand{\todo}[1]{\textbf{TODO}\footnote{#1}} -% Set to 1.0 for final two-column export \newlength{\figurescale} -\setlength{\figurescale}{0.75\textwidth} +\setlength{\figurescale}{\linewidth} \begin{document} @@ -43,7 +42,10 @@ University of Darmstadt, 64283 Darmstadt, Germany (e-mail: jan.goette@tu-darmstadt.de).} \and \IEEEauthorblockN{Björn Scheuermann}\thanks{Björn Scheuermann is with the Technical University of Darmstadt, -64283 Darmstadt, Germany (e-mail: scheuermann@kom.tu-darmstadt.de).}} +64283 Darmstadt, Germany (e-mail: scheuermann@kom.tu-darmstadt.de).} +\thanks{This work has been funded by the LOEWE initiative (Hesse, Germany) within the emergenCITY center + (LOEWE/1/12/519/03/05.001(0016)/72) as well as by Technical University of Darmstadt.} +} \title{Wireless Power Transfer with a Twist: Achieving Rotation-Invariant Coupling using Twisted Multi-Layer PCB Inductors} \maketitle @@ -61,24 +63,6 @@ Achieving Rotation-Invariant Coupling using Twisted Multi-Layer PCB Inductors} \section{Introduction} -\begin{figure} - \begin{center} - \subcaptionbox{\raggedright A classic planar spiral inductor}{ - \includegraphics[width=0.3\figurescale]{figures/svg_vis_paper_plain.png}} - \subcaptionbox{\raggedright A honeycomb coil in \textcite{saackeRadiotechnikIIIEmpfanger1926}}{ - \includegraphics[width=0.2\figurescale]{figures/saacke-radiotechnik-3-ledionspule.jpg}} - \subcaptionbox{\raggedright A basket-woven coil in \textcite{kleinSpulenUndSchwingungskreise1941}}{ - \includegraphics[width=0.2\figurescale]{figures/klein-spulen-schwingkreise-korbspule.jpg}} - \subcaptionbox{\raggedright Our proposed inductor layout}{ - \includegraphics[width=0.3\figurescale]{figures/svg_vis_paper.png}} - \end{center} - \caption{Illustration of our proposed inductor layout compared to contemporary conventional planar inductors and - honeycomb as well as basket-woven coils from the early days of wireless radio.} - \textbf{Note}: Not final graphics. Higher-quality scans of the middle two graphics will be submitted with the final - camera-ready version. - \label{fig_illust_honeycomb_basket} -\end{figure} - Inductive Wireless Power Transfer (WPT) is a widely used technology supported by a large corpus of research literature \cite{ awuahNovelCoilDesign2023, @@ -125,6 +109,22 @@ the often higher turn count and the tightly packed, circular wires render this e ripple caused by this oscillation can be filtered through a voltage regulator or by using a large decoupling capacitor on the secondary side if the application can accomodate such components on the rotating part. +\begin{figure} + \begin{center} + \subcaptionbox{\raggedright A classic planar spiral inductor}{ + \includegraphics[width=0.25\figurescale]{figures/svg_vis_paper_plain.png}} + \subcaptionbox{\raggedright Our proposed inductor layout}{ + \includegraphics[width=0.25\figurescale]{figures/svg_vis_paper.png}} + \subcaptionbox{\raggedright A honeycomb coil in \textcite{saackeRadiotechnikIIIEmpfanger1926}}{ + \includegraphics[width=0.15\figurescale]{figures/saacke-radiotechnik-3-ledionspule.jpg}} + \subcaptionbox{\raggedright A basket-woven coil in \textcite{kleinSpulenUndSchwingungskreise1941}}{ + \includegraphics[width=0.15\figurescale]{figures/klein-spulen-schwingkreise-korbspule.jpg}} + \end{center} + \caption{Illustration of our proposed inductor layout compared to contemporary conventional planar inductors and + honeycomb as well as basket-woven coils from the early days of wireless radio.} + \label{fig_illust_honeycomb_basket} +\end{figure} + 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}, @@ -174,7 +174,7 @@ Our contributions in this paper include: \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. - \item We validate our scheme, we provide laboratory measurements of the basic parameters of 39 test specimens + \item We validate our scheme and provide laboratory measurements of the basic parameters of 39 test specimens comparing our scheme to conventional layouts. \item We further present the results of Finite Element Method (FEM) simulations to validate our inductance and ESR approximations. @@ -330,7 +330,7 @@ layer of such windings forms a helix whose pitch is equal to the wire diameter. helical scheme reversing at the coil ends, but uses a helical pitch larger than the wire diameter to form a structure similar to a spool of sewing thread. -Other winding techniques include honeycomb and basket woven coils, some historic examples of which are shown in Figure\ +Other winding techniques include honeycomb and basket woven coils, some historic examples of which are shown in Fig.\ \ref{fig_illust_honeycomb_basket}. In a honeycomb coil, like in an universal winding, subsequent winding layers are wound at a criss-cross pattern. The characteristic feature of honeycomb coils is that the winding machine is adjusted to produce large air gaps between adjacent windings, resulting in a three-dimensional rhomboid pattern that is vaguely @@ -374,7 +374,7 @@ To improve layer utilization, a common technique in PCB inductor design is to us inductor's spiral trace, instead of only using the bottom layer for a straight jumper trace. Using both layers this way allows for wider traces, which lowers resistive losses. We can accomodate this optimization in our definition by re-defining our normalized radius to allow both positive and negative values, defining negative values to designate -traces on the PCB's bottom layer as follows. Figure\ \ref{fig_nk_combined} shows both a simple and a two-layer +traces on the PCB's bottom layer as follows. Fig.\ \ref{fig_nk_combined} shows both a simple and a two-layer spiral inductor in the first two columns. Let $n$ be the turn count of our inductor. The resulting parametrization is: @@ -398,7 +398,7 @@ two core observations: \begin{description}[\IEEEsetlabelwidth{foo}] \item[Observation 1.]\hfill\\When using an archimedean spiral, multiple such spirals using the same pitch can be interleaved by spreading out their start and end points at regular angular intervals. - \item[Observation 2.]\hfill\\In a two-layer spiral inductor (Figure\ \ref{fig_nk_combined}), we can adjust the turn + \item[Observation 2.]\hfill\\In a two-layer spiral inductor (Fig.\ \ref{fig_nk_combined}), we can adjust the turn count of the pair of traces to move the end point of the bottom layer trace anywhere on the inductor's outer radius. \end{description} @@ -408,10 +408,10 @@ scheme~\cite{lopeFirstSelfresonantFrequency2021,sproHighVoltageInsulationDesign2 Combining these two observations, we find that by choosing a number $k$ of inversions, i.e. layer jumps, that is coprime to the number of total turns of the inductor $n$, we achieve a layout where all $k$ pairs of top and bottom-layer traces -naturally connect in series, with the resulting spirals on the top and bottom layers interleaving cleanly. Figure\ +naturally connect in series, with the resulting spirals on the top and bottom layers interleaving cleanly. Fig.\ \ref{fig_nk_combined} shows a layout with $n=3$ turns with both a single inversion ($k=1$), which results in a conventional two-layer inductor, and with $k=2$ inversions, creating two interleaved spirals on both the top and the -bottom layer of the PCB. Figure\ \ref{fig_nk_complex_illust} in Appendix\ \ref{sec_appendix_layout_examples} shows +bottom layer of the PCB. Fig.\ \ref{fig_nk_complex_illust} in the Appendix of this paper shows additional layout examples for other values of $n$ and $k$. For $k=\frac{1}{2}$, we get a standard single-layer planar spiral inductor for any turn count $n$, and for $k=1$ we get a standard two-layer planar spiral inductor for any turn count $n$. In this paper, we will call all layouts with $k\ge 2$ \emph{Twisted Inductors}. The coordinate description of @@ -446,7 +446,7 @@ Equation\ \ref{eqn_twolayer_spiral} thus becomes: \end{figure} Topologically, the shape of our inductors can be described as a $(k, n)$-torus knot. From knot theory, we know that such -a torus knot exists if and only if both $n$ and $k$ are co-prime. Figure\ \ref{fig_nk_combined} illustrates a derivation +a torus knot exists if and only if both $n$ and $k$ are co-prime. Fig.\ \ref{fig_nk_combined} illustrates a derivation of the coprimality requirement. If we plot the spiral in polar coordinates on a cartesian plot we observe that for a $n$-turn coil with $k$ inversions, the trace crosses the $\varphi$ axis once for each inversion, wrapping around $r$. Likewise, it crosses the $r$ axis once for each turn of the inductor, wrapping around $\varphi$. Based on this, we can @@ -558,10 +558,9 @@ In order to minimize ESR and maximize PCB area utilization, we made the tool aut 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 -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}. +library \emph{gerbonara}. 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}. 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. @@ -650,58 +649,65 @@ inductors allow for lowers resistive losses by approximately a factor of four. I lead to the choice of a two-layer inductor, twisted inductors provide improved high-frequency performance at no additional cost and without compromising other performance parameters. -\begin{table*} - \begin{tabular}{cc|cccc|cccc|ccc} - \multicolumn{2}{c|}{\textbf{Parameters}}& - \multicolumn{4}{c|}{\textbf{Design values}}& - \multicolumn{4}{c|}{\textbf{Simulation results}}& - \multicolumn{3}{c}{\textbf{Measurements}}\\ - $n$& - $k$& - $L \left[\unit{\micro\henry}\right]$& - Error $\left[\unit{\percent}\right]$& - $R \left[\unit{\ohm}\right]$& - Error $\left[\unit{\percent}\right]$& - $L \left[\unit{\micro\henry}\right]$& - Error $\left[\unit{\percent}\right]$& - $R \left[\unit{\ohm}\right]$& - Error $\left[\unit{\percent}\right]$& - $L \left[\unit{\micro\henry}\right]$& - $f_\text{res} \left[\unit{\mega\hertz}\right]$& - $R \left[\unit{\ohm}\right]$\\\hline - - \rowcolor[gray]{0.9} - $1$& $3$& $0.03$& $-93.1$& $0.0095$& $-49.9$& $0.039$& $-43.6$& $0.008$& $-78.8$& $0.056$& $\textbf{465.07}$& $\textbf{0.0143}$\\ - $1$& $4$& $0.03$& $-103.4$& $0.0108$& $-38.6$& $0.040$& $-47.5$& $0.008$& $-87.5$& $\textbf{0.059}$& $460.08$& $0.015$\\ - $1$& $5$& $0.03$& $-89.7$& $0.0123$& $-35.3$& $0.041$& $-34.1$& $0.009$& $-84.4$& $0.055$& $460.08$& $0.0166$\\ - \hline\rowcolor[gray]{0.9} - $2$& $1$& $0.12$& $-28.4$& $0.0253$& $-12.1$& $0.127$& $-17.3$& $0.024$& $-18.3$& $0.149$& $\textbf{245.51}$& $\textbf{0.0284}$\\ - $2$& $3$& $0.12$& $-31.0$& $0.0270$& $-7.9$& $0.128$& $-18.8$& $0.025$& $-16.4$& $\textbf{0.152}$& $240.52$& $0.0291$\\ - $2$& $5$& $0.12$& $-26.7$& $0.0299$& $-0.2$& $0.130$& $-13.1$& $0.027$& $-11.1$& $0.147$& $225.5$& $0.03$\\ - \hline\rowcolor[gray]{0.9} - $3$& $1$& $0.26$& $-10.0$& $0.0454$& $-1.6$& $0.262$& $-9.5$& $0.044$& $-4.8$& $\textbf{0.287}$& $\textbf{145.71}$& $0.0461$\\ - $3$& $4$& $0.26$& $-9.6$& $0.0479$& $5.0$& $0.265$& $-7.9$& $0.046$& $1.1$& $\textbf{0.286}$& $\textbf{145.71}$& $\textbf{0.0455}$\\ - \hline\rowcolor[gray]{0.9} - $5$& $1$& $0.73$& $4.5$& $0.0755$& $-3.1$& $0.670$& $-3.4$& $0.074$& $-5.1$& $\textbf{0.693}$& $61.345$& $0.0778$\\ - $5$& $3$& $0.73$& $4.3$& $0.0763$& $4.7$& $0.671$& $-3.4$& $0.074$& $1.8$& $\textbf{0.694}$& $\textbf{70.285}$& $0.0727$\\ - $5$& $7$& $0.73$& $4.4$& $0.0802$& $16.2$& $0.675$& $-2.8$& $0.077$& $12.7$& $\textbf{0.694}$& $68.05$& $\textbf{0.0672}$\\ - \hline\rowcolor[gray]{0.9} - $10$& $1$& $2.90$& $6.3$& $0.2513$& $7.6$& $2.700$& $-0.7$& $0.250$& $7.1$& $\textbf{2.718}$& $24.076$& $0.2322$\\ - $10$& $3$& $2.90$& $6.4$& $0.2520$& $10.5$& $2.700$& $-0.5$& $0.250$& $9.8$& $2.714$& $\textbf{28.571}$& $0.2255$\\ - $10$& $7$& $2.90$& $6.4$& $0.2554$& $16.9$& $2.700$& $-0.5$& $0.252$& $15.8$& $2.713$& $28.072$& $\textbf{0.2122}$\\ - \hline\rowcolor[gray]{0.9} - $25$& $1$& $18.15$& $6.7$& $1.8843$& $9.7$& $16.900$& $-0.2$& $1.900$& $10.4$& $16.938$& $8.84$& $1.7024$\\ - $25$& $3$& $18.15$& $6.8$& $1.8851$& $13.2$& N/A& N/A& N/A& N/A& $16.919$& $8.595$& $1.636$\\ - $25$& $13$& $18.15$& $6.7$& $1.9016$& $18.9$& $16.900$& $-0.2$& $1.900$& $18.8$& $16.931$& $\textbf{10.555}$& $\textbf{1.5429}$\\ - $25$& $37$& $18.15$& $6.0$& $2.0197$& $15.9$& $17.100$& $0.2$& $2.000$& $15.1$& $\textbf{17.066}$& $10.31$& $1.698$\\ - - \end{tabular} +\setlength{\tabcolsep}{4pt} +\begin{table} \caption{Inductor sample design parameters and measured characteristics. All inductors have outer diameter \qty{35}{\milli\meter} and inner diameter \qty{15}{\milli\meter}. The missing values in the simulation results - columns result from the solver failing to converge. Bolded values highlight the best performing coil of each - turn count. Shaded rows indicate conventional two-layer planar inductors ($k=1$).} + columns result from the solver failing to converge.} + \begin{tabular}{cc|cc|cc|ccc} + \multicolumn{2}{c|}{}& + \multicolumn{2}{c|}{\textbf{Design}}& + \multicolumn{2}{c|}{\textbf{Simulation}}& + \multicolumn{3}{c}{\textbf{Measured}}\\ + + $n$& + $k$& + $L$& + $R$& + $L$& + $R$& + $L$& + $f_\text{res}$& + $R$\\ + + & + & + $\left[\unit{\micro\henry}\right]$& + $\left[\unit{\ohm}\right]$& + $\left[\unit{\micro\henry}\right]$& + $\left[\unit{\ohm}\right]$& + $\left[\unit{\micro\henry}\right]$& + $\left[\unit{\mega\hertz}\right]$& + $\left[\unit{\ohm}\right]$\\\hline + + \rowcolor[gray]{0.9} + $1$& $3$& $0.03$& $0.0095$& $0.039$& $0.008$& $0.056$& ${465}$& ${0.0143}$\\ + $1$& $4$& $0.03$& $0.0108$& $0.040$& $0.008$& ${0.059}$& $460$& $0.0150$\\ + $1$& $5$& $0.03$& $0.0123$& $0.041$& $0.009$& $0.055$& $460$& $0.0166$\\ + \hline\rowcolor[gray]{0.9} + $2$& $1$& $0.12$& $0.0253$& $0.127$& $0.024$& $0.149$& ${246}$& ${0.0284}$\\ + $2$& $3$& $0.12$& $0.0270$& $0.128$& $0.025$& ${0.152}$& $241$& $0.0291$\\ + $2$& $5$& $0.12$& $0.0299$& $0.130$& $0.027$& $0.147$& $226$& $0.0300$\\ + \hline\rowcolor[gray]{0.9} + $3$& $1$& $0.26$& $0.0454$& $0.262$& $0.044$& ${0.287}$& ${146}$& $0.0461$\\ + $3$& $4$& $0.26$& $0.0479$& $0.265$& $0.046$& ${0.286}$& ${146}$& ${0.0455}$\\ + \hline\rowcolor[gray]{0.9} + $5$& $1$& $0.73$& $0.0755$& $0.670$& $0.074$& ${0.693}$& $61.3$& $0.0778$\\ + $5$& $3$& $0.73$& $0.0763$& $0.671$& $0.074$& ${0.694}$& ${70.3}$& $0.0727$\\ + $5$& $7$& $0.73$& $0.0802$& $0.675$& $0.077$& ${0.694}$& $68.0$& ${0.0672}$\\ + \hline\rowcolor[gray]{0.9} + $10$& $1$& $2.90$& $0.2513$& $2.700$& $0.250$& ${2.718}$& $24.1$& $0.2322$\\ + $10$& $3$& $2.90$& $0.2520$& $2.700$& $0.250$& $2.714$& ${28.6}$& $0.2255$\\ + $10$& $7$& $2.90$& $0.2554$& $2.700$& $0.252$& $2.713$& $28.1$& ${0.2122}$\\ + \hline\rowcolor[gray]{0.9} + $25$& $1$& $18.15$& $1.8843$& $16.900$& $1.900$& $16.938$& $8.84$& $1.7024$\\ + $25$& $3$& $18.15$& $1.8851$& N/A& N/A& $16.919$& $8.60$& $1.6360$\\ + $25$& $13$& $18.15$& $1.9016$& $16.900$& $1.900$& $16.931$& ${10.56}$& ${1.5429}$\\ + $25$& $37$& $18.15$& $2.0197$& $17.100$& $2.000$& ${17.066}$& $10.31$& $1.6980$\\ + + \end{tabular} \label{tab_coupons} -\end{table*} +\end{table} \subsection{Inductance and Frequency Behavior of Larger Coils} @@ -726,6 +732,9 @@ see that this effect exceeds what one would reach by a simple series configurati indicating a contribution from flux linkage. \begin{table} + \caption{Parameters and measurement results of a set of larger sample inductors. Bold values indicate best + performance at a given size. Shaded rows indicate conventional planar toroidal ($n=1$) or two-layer planar + spiral inductors ($k=1$).} \begin{tabular}{cc|cc|ccc|c} $d_1$& $d_2$& @@ -765,9 +774,6 @@ indicating a contribution from flux linkage. $75$&$90$&$53$ &$320$& $461$& $76.2$& $8.75$& $0.72$\\ $75$&$90$&$53$ &$480$& $\mathbf{470}$& $92.9$& $8.00$& $0.84$\\ \end{tabular} - \caption{Parameters and measurement results of a set of larger sample inductors. Bold values indicate best - performance at a given size. Shaded rows indicate conventional planar toroidal ($n=1$) or two-layer planar - spiral inductors ($k=1$).} \label{tab_wide_coils} \end{table} @@ -777,7 +783,7 @@ indicating a contribution from flux linkage. To evaluate twisted inductors in our WPT application, we measured the variation of the coupling between a pair of inductors using an automated measurement setup consisting of a 3D gantry built from an old 3D printer, with a fourth rotation axis provided by a small servo that allows us to position two inductor test coupons at arbitrary offsets and -angles to one another (cf.\ Figure\ \ref{fig_setup_probe}). +angles to one another (cf.\ Fig.\ \ref{fig_setup_probe}). \begin{figure} \begin{center} @@ -800,21 +806,21 @@ angles to one another (cf.\ Figure\ \ref{fig_setup_probe}). To approximate our application, we loaded the secondary inductor with a \qty{10}{\ohm} resistor while providing a signal at a \qty{300}{\kilo\hertz} carrier frequency to the primary inductor from a Siglent SDG6022X function generator as -shown in Figure\ \ref{fig_test_schematic}. We measured both the input and output voltages of the coupled inductor pair +shown in Fig.\ \ref{fig_test_schematic}. We measured both the input and output voltages of the coupled inductor pair using Keysight 34465A multimeters in AC Root Mean Square (RMS) mode. \begin{figure} \begin{center} \includegraphics[width=\figurescale]{figures/symmetry_3turn_n_twist.pdf} \end{center} - \caption{RMS output voltage of the test circuit from Figure\ \ref{fig_test_schematic} for three pairs of matching + \caption{RMS output voltage of the test circuit from Fig.\ \ref{fig_test_schematic} for three pairs of matching inductors with one inductor rotating w.r.t.\ the other. The inductors have $n=3$ turns each and $k=\frac{1}{2}$, $k=1$, and $k=3$, respectively. For each $k$, voltage curves are plotted for a number of different radial offsets between the two inductor's centers.} \label{fig_symmetry_3turn_n_twist} \end{figure} -Figure\ \ref{fig_symmetry_3turn_n_twist} shows the ratio between input and output voltage of our test link for a set of +Fig.\ \ref{fig_symmetry_3turn_n_twist} shows the ratio between input and output voltage of our test link for a set of three-turn inductors with multiple inversion numbers $k$ when one inductor is rotated. In practical WPT setups, the transmitter and receiver coils are rarely aligned perfectly, so we show measurements across a range of radial offsets. In line with our inductance measurements, coupling is lower at $k>0$ compared to a single-layer spiral inductor. Across @@ -824,12 +830,12 @@ into higher frequencies that are easier to passively filter on the WPT link's se Expanding our measurements in the previous section, we performed a series of measurements rotating both inductors. In these measurements, the coils' distance is fixed \qty{1}{\milli\meter} and the radial offset is set to a worst-case -value of \qty{4}{\milli\meter}. Figure\ \ref{fig_rms_ripple_n3} shows the normalized output voltage of a WPT link made +value of \qty{4}{\milli\meter}. Fig.\ \ref{fig_rms_ripple_n3} shows the normalized output voltage of a WPT link made from three-turn inductors with rotation of one inductor shown on the horizontal axis, and the rotation of the other shown on the vertical axis. We performed similar measurements on 24 of our test coupons at \qty{1}{\milli\meter} and \qty{4}{\milli\meter} radial -offsets. Figure\ \ref{fig_k_ripple_plot} shows the combined results of these measurements, with worst-case voltage +offsets. Fig.\ \ref{fig_k_ripple_plot} shows the combined results of these measurements, with worst-case voltage variation plotted across inversion count $k$ for multiple turn counts $n$ and radial offsets $r$. In this graph, we see that twisted inductors improve ripple compared to conventional designs, even at a low inversion count such as $k=3$. @@ -842,12 +848,11 @@ pitch, as their turns deviate the furthest from a set of ideal, concentric circl \begin{center} \includegraphics[width=.85\figurescale]{figures/k_ripple_plot.pdf} \end{center} - \caption{RMS Voltage ripple in a model rotating WPT setup with $R_L=\qty{10}{\ohm}$ as a percentage of total RMS - output voltage, plotted against inductor inversion count $k$. Measurements were taken with a number of different - coils with turn count $n$ between a single turn and $25$ turns. Measurements were taken at two different radial coil - offsets of $r=\qty{1}{\milli\meter}$ and $\qty{4}{\milli\meter}$. Coil distance was $d=\qty{1}{\milli\meter}$ in all - cases. The shaded area indicates conventional coil layouts, with the remainder of the plot showing twisted - inductors.} + \caption{RMS Voltage ripple as a percentage of total RMS + output voltage in a rotating WPT setup with $R_L=\qty{10}{\ohm}$, coil distance $d=\qty{1}{\milli\meter}$ plotted + w.r.t. inductor inversion count $k$. Measurements were taken at two radial offsets of $r=\qty{1}{\milli\meter}$ and + $\qty{4}{\milli\meter}$. The shaded area indicates conventional coil layouts, with the remainder of the plot showing + twisted inductors.} \label{fig_k_ripple_plot} \end{figure} @@ -921,24 +926,8 @@ four-dimensional mapping of the coupling between a pair of identical inductors. description of twisted inductor construction as well as a set of Open-Source tools for their design, available at the link at the end of this paper. -\section*{Acknowledgement} -\addcontentsline{toc}{section}{Acknowledgment} -This work has been funded by the LOEWE initiative (Hesse, Germany) within the emergenCITY center -[LOEWE/1/12/519/03/05.001(0016)/72] as well as by Technical University of Darmstadt. - - -\section*{Availability} -This is version \texttt{\input{version.tex}\unskip} of this paper, generated on \today. - -After publication, the git repository with the LaTeX source for this paper, the data analysis code underlying our -measurements as well the set of tools for the generation of twisted inductor layouts that we wrote can be found at: - - \center{\url{https://git.jaseg.de/nice-coils.git}} - \printbibliography[heading=bibintoc] -\FloatBarrier -\appendix %\section{Supplemental plots} %\begin{figure} @@ -966,10 +955,12 @@ measurements as well the set of tools for the generation of twisted inductor lay % \label{fig_rms_ripple_n25} %\end{figure} -\section{Layout examples} -\label{sec_appendix_layout_examples} +\FloatBarrier +%\section{Layout examples} +%\label{sec_appendix_layout_examples} \begin{figure*} + \appendix \begin{center} \includegraphics[width=.75\textwidth]{figures/nk_complex_illust.pdf} \end{center} @@ -977,5 +968,4 @@ measurements as well the set of tools for the generation of twisted inductor lay illustration we chose values for $n$ and $k$ such that all pairs are coprime.} \label{fig_nk_complex_illust} \end{figure*} - \end{document} diff --git a/paper/version.tex b/paper/version.tex index cab9b1c..7d7cb6a 100644 --- a/paper/version.tex +++ b/paper/version.tex @@ -1 +1 @@ -v1.0-0-gcfae60e +final-tpel-submission-2025-01-27-0-g99d4905 \ No newline at end of file