First proof intro and related work done.

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}