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@ -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 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}.
\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 We measured the inductance and DC resistance of each test coupon using a Keysight U1733C LCR meter at
measured DC resistance using a Keysight 34465A multimeter in four-wire resistance mode. We further determined the \qty{100}{\kilo\hertz} for inductance and a Keysight 34465A multimeter in four-wire configuration for DC resistance. We
self-resonant frequency of each inductor using a LiteVNA64 handheld vector network analyzer. The results of our further determined the self-resonant frequency of each inductor using a LiteVNA64 handheld vector network analyzer. The
measurements are shown in Table\ \ref{tab_inductor_params}. 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 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 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 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 of each turn count. Shaded rows indicate conventional single-layer ($k=0$) or two-layer ($k=1$) planar
inductors.} inductors.}
\label{tab_coupons}
\end{table*} \end{table*}
\subsection{Inductance and Frequency Behavior of Larger Coils} \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{table}
\begin{tabular}{cc|cc|ccc|c} \begin{tabular}{cc|cc|ccc|c}
$d_1$& $d_1$&
@ -694,11 +713,13 @@ performance parameters.
\subsection{Coupling and its Sensitivity to Radial Offset} \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 While our accidential findings that twisted inductors improve high-frequency performance are certainly welcome and may
when one of the inductors is rotating. To experimentally evaluate the magnitude of this ripple in a realistic scenario benefit many applications, the key performance criterion in our application is the voltage ripple that appears on the
across a large set of rotations and relative displacements, we created a test setup consisting of a 3D gantry built from secondary side of a WPT link when one of the inductors is rotating. To experimentally evaluate the magnitude of this
an old 3D printer, with a fourth rotation axis provided by a small servo that allows us to position two inductor test ripple in a realistic scenario across a large set of rotations and relative displacements, we created a test setup
coupons at arbitrary offsets and angles to one another while measuring their coupling. 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} \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} \section{Conclusion}
In this paper, we introduced a novel layout approach for planar, multi-layer inductors inspired by classic basket-wound In this paper, we introduced a novel layout approach for planar, multi-layer inductors loosely inspired by classic
inductors used in the early days of radio. Our \emph{twisted} inductors produce field distributions that have better basket-wound inductors used in the early days of radio. Our \emph{twisted} inductors produce field distributions that
rotational symmetry along the inductor's main axis compared to either simple single-layer spiral inductors or have better rotational symmetry along the inductor's main axis compared to either simple single-layer spiral inductors
counter-wound two-layer spiral inductors. Furthermore, we found that our sample twisted inductors have slightly higher or counter-wound two-layer spiral inductors, which yields lower output ripple in our rotating wireless power transfer
self-resonant frequency compared to both traditional layouts. We base this evaluation on laboratory measurements on a application, enabling smaller and lighter secondary-side circuitry and improving efficiency.
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 Furthermore, besides the advantages twisted inductors show in our particular application, we found that our sample
Open-Source tools for their design. 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} \section*{Availability}
This is version \texttt{\input{version.tex}\unskip} of this paper, generated on \today. This is version \texttt{\input{version.tex}\unskip} of this paper, generated on \today.