From 82eaace7fa284727463b1630fd861b933e4dbd80 Mon Sep 17 00:00:00 2001 From: jaseg Date: Wed, 13 Nov 2024 10:06:26 +0100 Subject: [PATCH] paper: more text --- paper/paper.tex | 61 ++++++++++++++++++++++++++++++++++--------------- 1 file changed, 43 insertions(+), 18 deletions(-) diff --git a/paper/paper.tex b/paper/paper.tex index 49be2c3..67c3f64 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -530,12 +530,12 @@ twisted inductors with winding count $n$ between $1$ and $25$, and twist count r spiral inductor) to $k=37$. All test inductors had an inner diameter of \qty{15}{\milli\meter} and an outer diameter of \qty{35}{\milli\meter}. -\subsection{Inductance, Q-factor and DC resistance} +\subsection{Inductance and DC resistance} -We measured inductance and Q-factor of each test coupon using a Keysight U1733C LCR meter at \qty{100}{\kilo\hertz}. We -measured DC resistance using a Keysight 34465A multimeter in four-wire resistance mode. We further determined the -self-resonant frequency of each inductor using a LiteVNA64 handheld vector network analyzer. The results of our -measurements are shown in Table\ \ref{tab_inductor_params}. +We measured the inductance and DC resistance of each test coupon using a Keysight U1733C LCR meter at +\qty{100}{\kilo\hertz} for inductance and a Keysight 34465A multimeter in four-wire configuration for DC resistance. We +further determined the self-resonant frequency of each inductor using a LiteVNA64 handheld vector network analyzer. The +results of our measurements are shown in Table\ \ref{tab_inductor_params}. We found our inductance approximation to be accurate within \qty{10}{\percent} and our ESR approximation to be accurate within \qty{20}{\percent} for inductors with three turns or more. For lower turn-count inductors, inductance @@ -637,10 +637,29 @@ performance parameters. 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.} + \label{tab_coupons} \end{table*} \subsection{Inductance and Frequency Behavior of Larger Coils} +To investigate the high-frequency behavior of twisted inductors further, we produced and measured several additional +sample inductors, this time larger than before, and with more turns. The results of these measurements are shown in +Table\ \ref{tab_wide_coils}. In these results, we can identify three clear trends. First, the ESR of twisted inductors +is generally poorer when compared to two-layer spiral inductors. This increase in ESR is due to the large number of vias +used in these sample inductors. It should be noted that while twisted inductors have worse ESR compared to conventional +two-layer inductors, their ESR is still better than that of a single-layer inductor. + +Our second observation is that in all cases we tested, twisted inductors outperform conventional inductors in +self-resonant frequency by a considerable margin with an increase in SRF of up to \qty{50}{\percent} in our samples. + +Our third observation is that unlike in the smaller inductors from Table\ \ref{tab_coupons}, in these larger instances, +twisted inductors show increased inductance by approximately \qty{3.7}{\percent} for our smallest samples, and +\qty{6.5}{\percent} for our largest samples. This behavior indicates that large twisted inductors indeed behave like a +combination between a conventional planar spiral inductor and a conventional planar toroidal inductor. Comparing the +magnitude of this increase with the measurements listed in Table\ \ref{tab_wide_coils} for planar toroidal inductors, we +see that this effect exceeds what one would reach by a simple series configuration of both styles of inductor, +indicating a contribution from flux linkage. + \begin{table} \begin{tabular}{cc|cc|ccc|c} $d_1$& @@ -694,11 +713,13 @@ performance parameters. \subsection{Coupling and its Sensitivity to Radial Offset} -The key performance criterion in our application is the voltage ripple that appears on the secondary side of a WPT link -when one of the inductors is rotating. To experimentally evaluate the magnitude of this ripple in a realistic scenario -across a large set of rotations and relative displacements, we created a test 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 while measuring their coupling. +While our accidential findings that twisted inductors improve high-frequency performance are certainly welcome and may +benefit many applications, the key performance criterion in our application is the voltage ripple that appears on the +secondary side of a WPT link when one of the inductors is rotating. To experimentally evaluate the magnitude of this +ripple in a realistic scenario across a large set of rotations and relative displacements, we created a test 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 while measuring their +coupling. \todo{pics of 3d printer test setup} @@ -836,14 +857,18 @@ measurements for some of these choices of parameters in a future paper. \section{Conclusion} -In this paper, we introduced a novel layout approach for planar, multi-layer inductors inspired by classic basket-wound -inductors used in the early days of radio. Our \emph{twisted} inductors produce field distributions that have better -rotational symmetry along the inductor's main axis compared to either simple single-layer spiral inductors or -counter-wound two-layer spiral inductors. Furthermore, we found that our sample twisted inductors have slightly higher -self-resonant frequency compared to both traditional layouts. We base this evaluation on laboratory measurements on a -set of 24 test inductors, which include an automated, four-dimensional mapping of the coupling between a pair of -identical inductors. We provide both an analytical description of twisted inductor construction as well as a set of -Open-Source tools for their design. +In this paper, we introduced a novel layout approach for planar, multi-layer inductors loosely inspired by classic +basket-wound inductors used in the early days of radio. Our \emph{twisted} inductors produce field distributions that +have better rotational symmetry along the inductor's main axis compared to either simple single-layer spiral inductors +or counter-wound two-layer spiral inductors, which yields lower output ripple in our rotating wireless power transfer +application, enabling smaller and lighter secondary-side circuitry and improving efficiency. + +Furthermore, besides the advantages twisted inductors show in our particular application, we found that our sample +twisted inductors have improved self-resonant frequency, and slightly increased inductance compared to both conventional +single-layer and two-layer planar inductors. We base this evaluation on laboratory measurements on a set of 39 sample +inductors in total, including an automated, four-dimensional mapping of the coupling between a pair of identical +inductors. We provide both an analytical description of twisted inductor construction as well as a set of Open-Source +tools for their design. \section*{Availability} This is version \texttt{\input{version.tex}\unskip} of this paper, generated on \today.