From 53a9b9f87cbd013943d4ed3f17524ae107c2c932 Mon Sep 17 00:00:00 2001 From: jaseg Date: Wed, 13 Nov 2024 09:43:08 +0100 Subject: [PATCH] annotate tables --- paper/paper.tex | 96 ++++++++++++++++++++++++++++++++----------------- 1 file changed, 63 insertions(+), 33 deletions(-) diff --git a/paper/paper.tex b/paper/paper.tex index 02c3a18..49be2c3 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -19,6 +19,7 @@ \DeclareSIUnit{\year}{a} \usepackage{commath} \usepackage{graphicx,color} +\usepackage{colortbl} \usepackage{subcaption} \usepackage{array} \usepackage{censor} @@ -594,35 +595,48 @@ performance parameters. $f_\text{res} \left[\unit{\mega\hertz}\right]$& $R_\text{meas} \left[\unit{\ohm}\right]$\\\hline -$1$& $0$& $0.03$& $-86.2$& $0.0076$& $-86.8$& $0.038$& $-42.1$& $0.008$& $-77.5$& $0.054$& $457.585$&$0.0142$\\ -$1$& $3$& $0.03$& $-93.1$& $0.0095$& $-49.9$& $0.039$& $-43.6$& $0.008$& $-78.8$& $0.056$& $465.07$& $0.0143$\\ -$1$& $4$& $0.03$& $-103.4$& $0.0108$& $-38.6$& $0.040$& $-47.5$& $0.008$& $-87.5$& $0.059$& $460.08$& $0.015$\\ -$1$& $5$& $0.03$& $-89.7$& $0.0123$& $-35.3$& $0.041$& $-34.1$& $0.009$& $-84.4$& $0.055$& $460.08$& $0.0166$\\\hline -$2$& $0$& $0.16$& $10.0$& $0.0252$& $-26.7$& $0.126$& $-14.3$& $0.026$& $-22.7$& $0.144$& $266.24$& $0.0319$\\ -$2$& $1$& $0.12$& $-28.4$& $0.0253$& $-12.1$& $0.127$& $-17.3$& $0.024$& $-18.3$& $0.149$& $245.51$& $0.0284$\\ -$2$& $3$& $0.12$& $-31.0$& $0.0270$& $-7.9$& $0.128$& $-18.8$& $0.025$& $-16.4$& $0.152$& $240.52$& $0.0291$\\ -$2$& $5$& $0.12$& $-26.7$& $0.0299$& $-0.2$& $0.130$& $-13.1$& $0.027$& $-11.1$& $0.147$& $225.5$& $0.03$\\\hline -$3$& $0$& $0.26$& $-19.6$& $0.0755$& $-5.0$& $0.285$& $-9.1$& $0.077$& $-2.9$& $0.311$& $192.95$& $0.0792$\\ -$3$& $1$& $0.26$& $-10.0$& $0.0454$& $-1.6$& $0.262$& $-9.5$& $0.044$& $-4.8$& $0.287$& $145.71$& $0.0461$\\ -$3$& $4$& $0.26$& $-9.6$& $0.0479$& $5.0$& $0.265$& $-7.9$& $0.046$& $1.1$& $0.286$& $145.71$& $0.0455$\\\hline -$5$& $0$& $0.73$& $-9.6$& $0.2357$& $-0.4$& $0.760$& $-5.3$& $0.240$& $1.4$& $0.8$& $125.415$&$0.2366$\\ -$5$& $1$& $0.73$& $4.5$& $0.0755$& $-3.1$& $0.670$& $-3.4$& $0.074$& $-5.1$& $0.693$& $61.345$& $0.0778$\\ -$5$& $3$& $0.73$& $4.3$& $0.0763$& $4.7$& $0.671$& $-3.4$& $0.074$& $1.8$& $0.694$& $70.285$& $0.0727$\\ -$5$& $7$& $0.73$& $4.4$& $0.0802$& $16.2$& $0.675$& $-2.8$& $0.077$& $12.7$& $0.694$& $68.05$& $0.0672$\\\hline -$10$& $0$& $2.90$& $-2.4$& $0.7539$& $-2.3$& $2.900$& $-2.4$& $0.761$& $-1.4$& $2.97$& $62.835$& $0.7713$\\ -$10$& $1$& $2.90$& $6.3$& $0.2513$& $7.6$& $2.700$& $-0.7$& $0.250$& $7.1$& $2.718$& $24.076$& $0.2322$\\ -$10$& $3$& $2.90$& $6.4$& $0.2520$& $10.5$& $2.700$& $-0.5$& $0.250$& $9.8$& $2.714$& $28.571$& $0.2255$\\ -$10$& $7$& $2.90$& $6.4$& $0.2554$& $16.9$& $2.700$& $-0.5$& $0.252$& $15.8$& $2.713$& $28.072$& $0.2122$\\\hline -$25$& $0$& $18.15$& $1.1$& $3.7693$& $-3.9$& $18.000$& $0.3$& $3.800$& $-3.0$& $17.955$& $24.84$& $3.9156$\\ -$25$& $1$& $18.15$& $6.7$& $1.8843$& $9.7$& $16.900$& $-0.2$& $1.900$& $10.4$& $16.938$& $8.84$& $1.7024$\\ -$25$& $3$& $18.15$& $6.8$& $1.8851$& $13.2$& N/A& N/A& N/A& N/A& $16.919$& $8.595$& $1.636$\\ -$25$& $13$& $18.15$& $6.7$& $1.9016$& $18.9$& $16.900$& $-0.2$& $1.900$& $18.8$& $16.931$& $10.555$& $1.5429$\\ -$25$& $37$& $18.15$& $6.0$& $2.0197$& $15.9$& $17.100$& $0.2$& $2.000$& $15.1$& $17.066$& $10.31$& $1.698$\\ + \rowcolor[gray]{0.9} + $1$& $0$& $0.03$& $-86.2$& $0.0076$& $-86.8$& $0.038$& $-42.1$& $0.008$& $-77.5$& $0.054$& $457.585$&$0.0142$\\ + $1$& $3$& $0.03$& $-93.1$& $0.0095$& $-49.9$& $0.039$& $-43.6$& $0.008$& $-78.8$& $0.056$& $\textbf{465.07}$& $\textbf{0.0143}$\\ + $1$& $4$& $0.03$& $-103.4$& $0.0108$& $-38.6$& $0.040$& $-47.5$& $0.008$& $-87.5$& $\textbf{0.059}$& $460.08$& $0.015$\\ + $1$& $5$& $0.03$& $-89.7$& $0.0123$& $-35.3$& $0.041$& $-34.1$& $0.009$& $-84.4$& $0.055$& $460.08$& $0.0166$\\\hline + \rowcolor[gray]{0.9} + $2$& $0$& $0.16$& $10.0$& $0.0252$& $-26.7$& $0.126$& $-14.3$& $0.026$& $-22.7$& $0.144$& $266.24$& $0.0319$\\ + \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} + $3$& $0$& $0.26$& $-19.6$& $0.0755$& $-5.0$& $0.285$& $-9.1$& $0.077$& $-2.9$& $0.311$& $192.95$& $0.0792$\\ + \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} + $5$& $0$& $0.73$& $-9.6$& $0.2357$& $-0.4$& $0.760$& $-5.3$& $0.240$& $1.4$& $0.8$& $125.415$&$0.2366$\\ + \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} + $10$& $0$& $2.90$& $-2.4$& $0.7539$& $-2.3$& $2.900$& $-2.4$& $0.761$& $-1.4$& $2.97$& $62.835$& $0.7713$\\ + \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} + $25$& $0$& $18.15$& $1.1$& $3.7693$& $-3.9$& $18.000$& $0.3$& $3.800$& $-3.0$& $17.955$& $24.84$& $3.9156$\\ + \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} \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.} + \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 two-layer coil + of each turn count. Shaded rows indicate conventional single-layer ($k=0$) or two-layer ($k=1$) planar + inductors.} \end{table*} \subsection{Inductance and Frequency Behavior of Larger Coils} @@ -645,28 +659,35 @@ $25$& $37$& $18.15$& $6.0$& $2.0197$& $15.9$& $17.100$& $0.2$& $2.000$& $\left[\unit{\ohm}\right]$& $\left[\unit{\mega\hertz}\right]$& $\left[\unit{\pico\farad}\right]$\\\hline + \rowcolor[gray]{0.9} $25$&$40$&$1$ &$150$& $5.00$& $11.0$& N/A& N/A\\ + \rowcolor[gray]{0.9} $25$&$40$&$53$ &$1$& $120$& $\mathbf{19.6}$& $18.0$& $0.65$\\ $25$&$40$&$53$ &$50$& $121$& $22.6$& $\mathbf{27.5}$& $\mathbf{0.28}$\\ $25$&$40$&$53$ &$100$& $123$& $26.9$& $26.5$& $0.29$\\ $25$&$40$&$53$ &$150$& $\mathbf{125}$& $33.2$& $24.0$& $0.35$\\\hline + \rowcolor[gray]{0.9} $50$&$65$&$1$ &$300$& $10.2$& $21.9$& N/A& N/A\\ + \rowcolor[gray]{0.9} $50$&$65$&$53$ &$1$& $270$& $\mathbf{35.7}$& $10.0$& $0.94$\\ $50$&$65$&$53$ &$100$& $272$& $41.9$& $\mathbf{15.8}$& $\mathbf{0.37}$\\ $50$&$65$&$53$ &$200$& $277$& $50.1$& $13.3$& $0.52$\\ $50$&$65$&$53$ &$300$& $\mathbf{280}$& $65.0$& $13.8$& $0.48$\\\hline + \rowcolor[gray]{0.9} $75$&$90$&$1$ &$480$& $17.3$& $35.5$& N/A& N/A\\ + \rowcolor[gray]{0.9} $75$&$90$&$53$ &$1$& $441$& $\mathbf{50.7}$& $7.00$& $1.17$\\ $75$&$90$&$53$ &$160$& $444$& $60.8$& $\mathbf{10.0}$& $\mathbf{0.57}$\\ $75$&$90$&$53$ &$320$& $461$& $76.2$& $8.75$& $0.72$\\ $75$&$90$&$53$ &$480$& $\mathbf{470}$& $92.9$& $8.00$& $0.84$\\ \end{tabular} \caption{Inductor sample design parameters and measured characteristics for a number of physically larger, - ring-shaped inductors. $L$ and $R_\text{ESR}$ have been measured with a Keysight U1733C handheld LCR meter. - $f_\text{Res}$ has been measured with a LiteVNA VNA. $C_p$ has been calculated for the simple parallel LC resonator - model from $f_\text{Res}$ and $L$. $f_\text{Res}$ could not be measured for the $n=1$ case since these are just - planar toroidal inductors, which show different resonance characteristics compared to planar spiral or multi-turn - twisted inductors.} + ring-shaped inductors. $L$ and $R_\text{ESR}$ have been measured with a Keysight U1733C handheld LCR meter. + $f_\text{Res}$ has been measured with a LiteVNA VNA. $C_p$ has been calculated for the simple parallel LC + resonator model from $f_\text{Res}$ and $L$. $f_\text{Res}$ was not be measured for the $n=1$ case since these + are just planar toroidal inductors, which show different resonance characteristics compared to planar spiral or + multi-turn twisted inductors. Bolded values highlight the best performance among the coils of one size. Shaded + rows indicate conventional planar toroidal ($n=1$) or two-layer planar spiral inductors ($k=1$).} \label{tab_wide_coils} \end{table} @@ -731,6 +752,10 @@ the resulting coupling plot for a set of three-turn inductors, and Figure\ \ref{ five-turn inductors. Measurements for 10- and for 25-turn inductors are shown in Figures \ref{fig_rms_ripple_n10} and \ref{fig_rms_ripple_n25} in the Appendix. +Plotting the results of these experiments as well as a series of experiments at a \qty{1}{\milli\meter} radial offset +against inversion count $k$, we arrive at the graph in Figure\ \ref{fig_k_ripple_plot}. In this graph, we see that +twisted inductors improve ripple compared to conventional designs, even at a low inversion count such as $k=3$. + From these plots, we can draw a number of conclusions. First, our primary objective of reducing coupling variation across rotations works, with twisted inductors ($k>1$) showing a further improvement over simple two-layer inductors, which prove to be better than simple single-layer spiral inductors. As one would expect, this gain is greatest for @@ -745,8 +770,13 @@ for $k=7$ inversions. \begin{center} \includegraphics[width=.85\linewidth]{figures/k_ripple_plot.pdf} \end{center} - \caption{} - \label{fig_test_schematic} + \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.} + \label{fig_k_ripple_plot} \end{figure} \begin{figure}