diff --git a/paper/paper.tex b/paper/paper.tex index 46b13e3..6cc2d35 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -293,18 +293,20 @@ decrease in cost. 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 +by much in these circumstances. A common way to use ferrites in WPT applications is by magnetically shielding the +inductor's back side with a ferrite plate such that the field does not extend beyond the coil's back side, thereby +increasing the intended mutual inductance while simultaneously reducing 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 -fixed pitch. We will ignore trace width for now, and consider the trace a thin wire. We will assume the inductor's ports -are both located on the positive $x$-Axis. We can rotate it so its first port aligns with the $x$-Axis. To -minimize the loop area of the inductor's connections, inductors are usually designed with both ports close to one -another, so we can also assume its second port aligns with the $x$-Axis. +In this section, we will provide a detailed derivation of the layout of twisted inductors. We can approach this layout +by construction. Let us first consider a simple, planar, circular spiral coil with a fixed pitch. We will ignore trace +width for now, and consider the trace a thin wire. We will assume the inductor's ports are both located on the positive +$x$-Axis. We can rotate it so its first port aligns with the $x$-Axis. To minimize the loop area of the inductor's +connections, inductors are usually designed with both ports close to one another, so we can also assume its second port +aligns with the $x$-Axis. The trace trajectory of a standard planar spiral inductor can be parameterized in polar coordinates $r, \varphi$ based on an Archimedean spiral: \todo{For the lulz, cite Archimedes here}