Paper structure WIP

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paper/paper.tex

@@ -38,16 +38,132 @@ Achieving Rotation-Invariant Coupling using Multi-Layer PCB Inductors}
 \maketitle
 
 \begin{abstract}
+    % FIXME
 \end{abstract}
 
 \section{Introduction}
 
+Inductive wireless power transfer (WPT) is a widely used technology supported by a large corpus of research literature.
+% FIXME cite
+While working on a novel application of Inductive wireless power transfer in a Inertial Hardware Security Module (IHSM)
+as proposed by Götte and Scheuermann, % FIXME cite
+we found ourselves presented with an unusual set of constraints around inductive wireless power transfer through a
+rotating joint using a PCB inductor that does not yet seem to be addressed adequately in the existing literature on
+inductive wireless power transfer.
+
+Our application poses the challenge of transferring power between a stationary and a rotating part. To reduce
+manufacturing cost of both parts, and to reduce weight, and thereby inertia as well as susceptibility to vibration in
+the rotating part, we decided to use inductors that are directly patterned onto the IHSM's printed circuit boards.
+The primary constraint that results from this choice is a highly constrained turn count that is limited by the PCB
+manufacturing processes' pattern resolution and by ohmic heating.
+
+We found that the limited turn count of PCB inductors results in a \emph{slightly} asymmetric field, which means that
+the coupling coefficient of two such inductors oscillates at one oscillation per revolution when the inductors are
+rotated on-axis, even if both inductors are perfectly coaxially aligned.
+
+In other inductive wireless power transfer systems, this oscillation is mitigated by one of several factors: First, for
+this effect to matter in the first place, the two coils have to be rotating with respect to one another. In ferrite or
+iron-cored inductors, the core shapes the magnetic field and evens out any such imperfection. In wire-wound inductors,
+the (much) higher turn count and circular aspect ratio of the wires reduces this effect to almost nothing. Finally, the
+output ripple caused by this oscillation can be filtered through a voltage regulator or by using a large decoupling
+capacitor on the secondary side.
+
+While there exist a number of prior works focusing on efficient power transfer between two coils whose position relative
+to one another cannot be precisely controlled as is the case in wireless phone charging systems, it is generally assumed
+that the two coils remain (almost) stationary with respect to one another throughout the charging process. % FIXME cite
+
+There exists a small body of work on inductive power transfer through rotating joints, % FIXME cite
+but here the focus lies on higher power budgets than our application requires, which often requires ferrite or iron-core
+inductors.
+
+Our application is unique in that it requires power transfer through a joint that is constantly rotating at high speed,
+while we simultaneously want to avoid heavy components on the (rotating) receiver side. (Liquid) electrolytic capacitors
+cannot be used due to the large centrifugal acceleration that the rotating part experiences, and other heavy components
+such as large ceramic or polymer electrolytic capacitors or ferrite-core power inductors are inadvisable since they will
+exert large stresses onto the assembly due to the same centrifugal acceleration, and any imbalance caused by tolerances
+in the placement of heavy components will quickly cause a strong vibration.
+
+\subsection{Twisted inductors}
+
+Applying a principle inspired by rectangular or octagonal RFIC inductor design as well as by the polygonal basket-woven
+air coils used in early radio set, we propose a novel way of laying out circular PCB inductors that twists the
+inductor's windings around one another using a ring of vias each on the inside and outside of the inductor's windings.
+Applying some math, we show that we can layout a twisted inductor for any number of twists that is co-prime to the
+inductor's turn count.
+
+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. This is the same effect that is exploited in basket-woven
+air core inductors that were commonly used in old radio sets.
+% FIXME citation on this, citation on basket weaving -> It's hard to find reliable references on that.
+
 \section{Related Work}
+
+\subsection{Inductive Wireless Power Transfer in Practice}
+
+Inductive WPT has been proposed in a large number of scenarios, each of which comese with a set of
+unique constraints. When WPT is used to charge an electric toothbrush, the implementation cost of the system is
+critical, while efficiency and total power output are of little concern. Mechanically, in an electric toothbrush's
+charging system, the position and spacing of the transmitter and receiver coils can easily be controlled down to
+millimeter precision.
+
+In contrast to this, wireless smartphone charging is a much more demanding application. Here, the total cost of the
+system is only secondary, but the receiver's form factor is critical, and total power output as well as efficiency
+become major objectives. At the same time, in wireless smartphone charging, position tolerances are very coarse, and the
+two coils in the charging base and in the phone may be positioned more than a centimeter off-axis, with a gap of several
+millimeters and potentially not even in parallel planes.
+
+Power transfer across large distances is even more of a concern in implantable medical devices. Where a wireless phone
+charger must be able to bridge distances of a few millimeters, an implantable medical device might be situated
+underneath several centimeter of tissue and bones. At the same time, cost is of (almost) no concern in this medical
+application, which enables the use of complex manufacturing techniques, customized electronic components and exotic
+materials.
+
+While all of the aforementioned applications transfer somewhere between a few hundred milliwatts and several watts of
+power, at the other end of the spectrum there is a large body of research suggesting the use of inductive wireless power
+transfer for the charging of electric vehicles (EVs). In this application, the wireless power transfer system replaces
+the conventional wired charging connector, which improves the systems' user experience given the strong force required
+to seat or unseat these rather large connectors, as well as the heft of the required water-cooled cables. In this
+application, size is of (almost) no concern, but at several kilowatt up to dozens or even a hundred kilowatt, the
+transferred power is enormous and consequentially efficiency becomes of utmost importance. When charging an EV at a
+rate of 30 kW, an efficiency improvement of just $0.1\%$ corresponds to a reduction in power dissipation of 30 W.
+Besides the monetary cost of the power lost this way, each small improvement enables a reduction in size of heat sinks
+and other cooling components, which directly translates to a decrease in cost.
+
 \subsection{Twisted Inductors in RFIC Design}
 \subsection{Basket-Woven Air Coils}
+\subsection{Air-Core Inductors for Inductive Power Transfer}
+\subsection{Ferrite or Iron-Core Inductors for Inductive Power Transfer}
 
 \section{Twisted Inductor Design} 
 
+\subsection{From Spiral to Twisted Inductor}
+
+\subsubsection{Ohmic Resistance}
+
+\subsubsection{Inductance}
+
+\subsection{CAD Integration}
+
+\section{FEM Simulation}
+
+\subsection{Ohmic Resistance}
+
+\subsection{Inductance}
+
+\subsection{Parasitic Capacitance and Self-Resonant Frequency}
+
+\subsection{Coupling}
+
+\section{Experimental Validation}
+
+\subsection{Inductance and Parasitic Capacitance}
+
+\subsection{Self-Resonant Frequency}
+
+\subsection{Coupling}
+
 \section{Conclusion}
 
 \section*{Availability}