Related work mostly done

paper/paper.tex

@@ -178,7 +178,6 @@ condition between the number of turns and the number of inversions within each t
 inductors below, although in contemporary literature, this condition is never explicitly stated
 \cite{eppenAnforderungenEinzelteileRundfunkempfanger1927, kleinSpulenUndSchwingungskreise1941,
 wiggeRundfunktechnischesHandbuch1930}.
-% TODO cite \cite{querfurthCoilWindingDescription1954}
 
 \subsection{PCB inductor design for wireless power transfer}
 
@@ -213,27 +212,34 @@ a pure air-core inductor.
 
 \subsection{Twisted Inductors in RFIC Design}
 
+Planar inductors are commonly used in RF ICs. In RFIC design, the major challenges are area optimization, and precisely
+predicting the inductor's characteristics during the design phase. Common optimizations include applying a variable
+trace pitch to reduce distributed capacitance\cite{lopez-villegasImprovementQualityFactor2000}, and applying variable
+trace width to decrease equivalent series resistance while preserving total inductance and quality
+factor\cite{hsuAnalyticalDesignAlgorithm2008}.
+
+In RFICs, inductors are commonly designed as \emph{balanced} inductors with a grounded central node. Such designs
+interleave two counter-wound planar spiral inductors on the same layer with the help of some jumper connections on a
+second layer\cite{daneshDifferentiallyDrivenSymmetric2002,martinMultiturnTwistedInductor2016}. The use of such designs
+in RFIC design is mainly focused on their electrical symmetry, so that the two input ports can be fed with a fully
+differential signal, with the inductor loading both driver outputs equally across the inductor's frequency range.
+
 The simplest twisted inductor as shown below with $k=1$ inversion corresponds to the counterwound scheme that is
 commonly used for two-layer planar
 inductors\cite{lopeFirstSelfResonant2021,sproHighVoltageInsulationDesign2021,leePrintedSpiralWinding2011a}, and
 which has been used to stack planar coils for more than a century\cite{flemingPrinciplesElectricWave1910}.
 
-Another, more recent design interleaves two counter-wound planar spiral inductors on the same layer with the help of
-some jumper connections on a second layer, as shown in \cite{daneshDifferentiallyDrivenSymmetric2002}. The use of this
-design in RFIC design is mainly focused on its electrical symmetry, so that the two input ports can be fed with a fully
-differential signal, with both driver outputs being loaded equally across the inductor's frequency range.
-
 % They note that the main point behind the design is electrical symmetry of the two ports to make driving the thing
 % differentially cleaner. We should adopt this observation for our inductors, which likewise are electrically symmetric
 % when compared to a single-layer spiral inductor.
 
 \subsection{Inductive Wireless Power Transfer in Practice}
 
-Inductive WPT has been proposed in a large number of scenarios\cite{zhangWirelessPowerTransfer2019}, each of which comes
-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.
+Inductive WPT has been proposed in a large number of
+scenarios\cite{zhangWirelessPowerTransfer2019,mouWirelessPowerTransfer2015}, each of which comes 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
@@ -241,33 +247,33 @@ become major objectives. At the same time, in wireless smartphone charging, posi
 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.
+Power transfer across large distances is even more of a concern in implantable medical
+devices\cite{mooreApplicationsWirelessPower2019}. 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.
+transfer for the charging of electric vehicles
+(EVs)\cite{liWirelessPowerTransfer2015,mouEnergyEfficientAdaptiveDesign2017}. In this application, the wireless power
+transfer system usually 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 charging rates up to tens of kilowatt,
+efficiency becomes critical. When charging an EV at a rate of 10 kW, an efficiency improvement of just $0.1\%$
+corresponds to a reduction in power dissipation of 10 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{Air-Core Inductors for Inductive Power Transfer}
 
-In inductive wireless power transfer, air-core inductors are often used since in most applications, an air gap of
-several millimeters or more is expected, and adding a ferrite core would not change the system's performance by much in
-these circumstances. A common way to use ferrites in WPT applications is magnetically shielding the inductor's back side
-with a ferrite plate such that the field does not extend beyond the coil's back side, and to reduce eddy current losses
-when the WPT coils are placed near metal
+Across application areas, air-core inductors are often used for wireless power transfer since in most applications, an
+air gap of several millimeters or more is expected, and adding a ferrite core would not change the system's performance
+by much in these circumstances. A common way to use ferrites in WPT applications is magnetically shielding the
+inductor's back side with a ferrite plate such that the field does not extend beyond the coil's back side, and to reduce
+eddy current losses when the WPT coils are placed near metal
 objects\cite{batraEffectFerriteAddition2015,leeSimpleWirelessPower2017,muehlmannMutualCouplingModeling2012}.
 
-
 \section{Twisted Inductor Design} 
 
 We can approach twisted inductors by construction. Let us first consider a simple, planar, circular spiral coil with a