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@ -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}