From 4d0fab02485c7c297fa135788b3b06c0be27f1e4 Mon Sep 17 00:00:00 2001 From: jaseg Date: Tue, 3 Dec 2024 13:07:45 +0100 Subject: [PATCH] More Leo fixes --- paper/paper.tex | 56 ++++++++++++++++++++++++++----------------------- 1 file changed, 30 insertions(+), 26 deletions(-) diff --git a/paper/paper.tex b/paper/paper.tex index 7ba235f..190c360 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -63,9 +63,10 @@ Achieving Rotation-Invariant Coupling using Twisted Multi-Layer PCB Inductors} planar toroidal inductors. Compared to conventional planar spiral inductors, twisted inductors generate a magnetic field with better rotational symmetry, resulting in decreased output ripple in Wireless Power Transfer (WPT) applications with an axially rotating receiver. Additionally, we found that twisted inductors can simultaneously - yield a significantly improved self-resonant frequency and a higher inductance in the same area as a conventional - planar spiral inductor, up to \qty{50}{\percent} improved SRF and \qty{6.5}{\percent} increased inductance among our - test samples. We base our conclusions on several simulations and an extensive set of practical measurements. + yield a significantly improved Self-Resonant Frequency (SRF) and a higher inductance in the same area as a + conventional planar spiral inductor, up to \qty{50}{\percent} improved SRF and \qty{6.5}{\percent} increased + inductance among our test samples. We base our conclusions on several simulations and an extensive set of practical + measurements. \end{abstract} \section{Introduction} @@ -132,10 +133,10 @@ approach thus generalizes a number of previous approaches to the design of plana We observe that in high-frequency applications, a moderate number of twists increases the spacing between the beginning and end of the inductor's conductor, where the majority of the inductor's AC current flows. This decreases the parasitic -capacitance of the inductor and raises its self-resonant frequency, raising its maximum possible operating frequency and -improving its efficiency at lower operating frequencies. We note that the principle behind this reduction in distributed -capacitance coincides with the intuition that led to the creation of honeycomb or basket-woven inductors in early radio -sets more than a hundred years ago, before the invention of ferrites. +capacitance of the inductor and raises its Self-Resonant Frequency (SRF), raising its maximum possible operating +frequency and improving its efficiency at lower operating frequencies. We note that the principle behind this reduction +in distributed capacitance coincides with the intuition that led to the creation of honeycomb or basket-woven inductors +in early radio sets more than a hundred years ago, before the invention of ferrites. \subsection{Contributions} In this paper, we introduce twisted inductors, a novel technique of laying out planar inductors that both improves @@ -143,10 +144,10 @@ rotational symmetry in rotating wireless power transfer interface as well as qua provide detailed layout instructions, including a mathematical analysis of the available parameter space and an analytical model of both inductance and DC equivalent series resistance of our scheme. Validating our scheme, we provide laboratory measurements of the basic parameters of a number of test specimens comparing our scheme to conventional -techniques. We furhter present the results of FEM simulations to validate our inductance and ESL approximations. -Finally, to analyze the degree of rotational symmetry in our proposed scheme, we provide the results of a large number -of automated measurements of coupling between pairs of inductors under various rotations, offsets, distances and load -conditions. +techniques. We further present the results of Finite Element Method (FEM) simulations to validate our inductance and ESR +approximations. Finally, to analyze the degree of rotational symmetry in our proposed scheme, we provide the results of +a large number of automated measurements of coupling between pairs of inductors under various rotations, offsets, +distances and load conditions. \section{Related Work} @@ -543,8 +544,11 @@ gmsh/Elmer toolchain, we were unable to run simulations for parasitic capacitanc behavior of coil pairs. We found that for these cases which require larger, more complex meshes, gmsh would frequently crash during meshing, and where we were able to produce meshes, Elmer would only converge for some of them. While these are problems that can be solved through either a more skillful description of the problem in gmsh and Elmer, or by using -more robust software such as Simulia CST, we decided to instead experimentally measure these quantities instead -(Section\ \ref{sec_experiments}). +more robust software such as Simulia CST, we decided to instead experimentally measure these quantities instead (cf.\ +Section\ \ref{sec_experiments}). While our measurements only cover a small number of inductor samples, their results are +more reliable than results from FEM and can serve as a baseline for future work on such simulations. + +We conducted our FEM simulations as follows: \paragraph{Ohmic Resistance} Determining ohmic resistance by FEM is reasonably easy. In Elmer FEM, we can use the built-in joint static current and @@ -567,7 +571,7 @@ inductance according to the well-known relation\todo{Find decent source}: To experimentally validate our design with real-world inductors, we produced test coupons with a number of variations of twisted inductors with winding count $n$ between $1$ and $25$, and twist count ranging from $k=0$ (simple single-sided 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}. +\qty{35}{\milli\meter} corresponding to the space available in our IHSM implementation. \subsection{Inductance and DC resistance} @@ -604,10 +608,10 @@ between. Making things worse, common PCB substrates have a relative permittivity $4$). Interestingly, 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 an increase from an SRF of -\qty{8.9}{\mega\hertz} for a standard $n=25,k=1$ inductor to \qty{10.6}{\mega\hertz} for $n=25,k=13$. Prompted by this -observation, we produced another set of samples focusing on this aspect. We report our results of this investigation in -the following section. +inversion count $k$. While our test samples focused on smaller turn counts, we observe an increase from a self-resonant +frequency of \qty{8.9}{\mega\hertz} for a standard $n=25,k=1$ inductor to \qty{10.6}{\mega\hertz} for $n=25,k=13$. +Prompted by this observation, we produced another set of samples focusing on this aspect. We report our results of this +investigation in the following section. In conclusion to the above measurement results, we observe that twisted inductors \emph{improve} high-frequency performance compared to simple two-layer inductors while closely matching them in ESR and inductance. While they peform @@ -773,14 +777,14 @@ measuring their coupling. To evaluate a realistic scenario, we loaded the secondary inductor with a resistive load of \qty{10}{\ohm}, 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 using Keysight 34465A multimeters in AC RMS mode. The results of these measurements, with -the voltage ratio between the coupled inductors' input and output voltages graphed across one revolution in Figure\ -\ref{fig_symmetry_3turn_n_twist} for a set of three-turn inductors with multiple inversion numbers $k$. A plot for a set -of 10-turn inductors is shown in Figure\ \ref{fig_symmetry_10turn_n_twist} in the Appendix. A key observation here is -that while the asymmetry in the inductor's field is impossible to distinguish visually in field plots, the ripple -induced by rotation is considerable. The sharp dropoff of coupling with radial offset magnifies any small asymmetry and -leads to the ripple voltages we have listed in Table\ \ref{tab_coupons}, in some cases amounting to several percent of -total RMS output voltage. +of the coupled inductor pair using Keysight 34465A multimeters in AC Root Mean Square (RMS) mode. The results of these +measurements, with the voltage ratio between the coupled inductors' input and output voltages graphed across one +revolution in Figure\ \ref{fig_symmetry_3turn_n_twist} for a set of three-turn inductors with multiple inversion numbers +$k$. A plot for a set of 10-turn inductors is shown in Figure\ \ref{fig_symmetry_10turn_n_twist} in the Appendix. A key +observation here is that while the asymmetry in the inductor's field is impossible to distinguish visually in field +plots, the ripple induced by rotation is considerable. The sharp dropoff of coupling with radial offset magnifies any +small asymmetry and leads to the ripple voltages we have listed in Table\ \ref{tab_coupons}, in some cases amounting to +several percent of total RMS output voltage. \begin{figure} \begin{center}