From 87f83fdb95e029e25a67882f44da18269a5c5b02 Mon Sep 17 00:00:00 2001 From: jaseg Date: Wed, 30 Oct 2024 12:17:50 +0100 Subject: [PATCH] Extend related work section --- paper/paper.tex | 41 +++++++++++++++++++++++++++++++++++++++-- 1 file changed, 39 insertions(+), 2 deletions(-) diff --git a/paper/paper.tex b/paper/paper.tex index 6bec2cb..7e60a1b 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -162,6 +162,36 @@ inductors below, although in contemporary literature, this condition is never ex \cite{eppenAnforderungenEinzelteileRundfunkempfanger1927, kleinSpulenUndSchwingungskreise1941, wiggeRundfunktechnischesHandbuch1930}. +\subsection{PCB inductor design for wireless power transfer} + +For wireless power transfer, air-core inductors with or without ferrite magnetic shielding are the standard solution. +Since in most applications, an air gap of several millimeters between the sending and receiving assemblies is expected, +adding a ferrite core does not result in a large improvement in coupling. Meanwhile, in many WPT applications, +especially for charging portable devices or medical implants, some misalignment between the sending and receiving coils +is expected. Using the available space with an air-core inductor that has a large cross-sectional area reduces the +impact of this misalignment. + +Looking at such WPT inductors, they tend to be mostly planar coils with only a few layers, so implementing them in a PCB +process seems natural. Using a PCB for the inductor has the potential to reduce implementation cost since PCBs are +cheap, and they can also serve as structural support. + +Implementing inductors in PCBs has a number of disadvantages. First, due to the limited layer count of common PCB +processes, and due to structure size limitations, the number of windings that can be fit into a given volume is much +lower than in wire-wound inductors. Second, due to a PCB's copper layers being thin compared to its dielectric +substrate, PCB inductors tend to have poor DC resistance. A PCBs' thin but wide trace cross-section helps with +skin effect compared to a solid conductor. However, PCBs can still not approach the performance of litz wire used in +high-frequency WPT coils, which commonly use wire diameters in the tens of micrometer +range\cite{zhaoDesignOptimizationLitzWire2023}. \textcite{lopeFrequencyDependentResistancePlanar2014} propose a +mitigation that aims to emulate a litz wire's structure in large, high-current PCB inductors, but their mitigation is +heavily limited by the structure size achievable in common PCB manufacturing processes. + +A further factor that limits the high-frequency performance of PCB inductors is distributed capacitance. Not only do +large air coils exhibit more parasitic capacitance than much smaller ferrite-core inductors simply due to their size, +when implemented in a PCB process a large fraction of the electrical fields responsible for this capacitance pass +through the PCB's substrate, not air. The relative permittivity $\epsilon_r$ of common PCB substrates typically lies in +the range of $4$ to $5$\cite{mumbyDielectricPropertiesFR41989}, which increases the distributed capacitance compared to +a pure air-core inductor. + \subsection{Twisted Inductors in RFIC Design} The simplest twisted inductor as shown below with $k=1$ inversion corresponds to the counterwound scheme that is @@ -200,7 +230,14 @@ Besides the monetary cost of the power lost this way, each small improvement ena and other cooling components, which directly translates to a decrease in cost. \subsection{Air-Core Inductors for Inductive Power Transfer} -\subsection{Ferrite or Iron-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 +objects\cite{batraEffectFerriteAddition2015,leeSimpleWirelessPower2017,muehlmannMutualCouplingModeling2012}. + \section{Twisted Inductor Design} @@ -462,7 +499,7 @@ effect gets partially mitigated since the strongest coupling exists between adja the SRF have a small voltage differential as only a fraction of the inductor's total voltage appears across each winding. Compared to this, when the inductor is constructed as a simple two-layer inductor with $k=1$, now the start and end windings of the inductor, which have the highest voltage differential, are located right on top of each other with -the substrate in between. Making things worse, common PCB substrates have a dielectric constant much larger than air +the substrate in between. Making things worse, common PCB substrates have a relative permittivity much larger than air (usually around $4$). Interestingly, we observe that this decrease in high-frequency performance is counteracted by larger inversion count