diff --git a/paper/figures/symmetry_3turn_n_twist.pdf b/paper/figures/symmetry_3turn_n_twist.pdf index 1cfd58d..5629093 100644 Binary files a/paper/figures/symmetry_3turn_n_twist.pdf and b/paper/figures/symmetry_3turn_n_twist.pdf differ diff --git a/paper/paper.tex b/paper/paper.tex index cf49f8f..fbd051a 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -306,10 +306,10 @@ In conclusion, we observe that twisted inductors \emph{improve} high-frequency p inductors while closely matching them in ESR and inductance. While they peform worse than simple single-layer inductors in high-frequency performance, the increased trace width that two-layer inductors allow for lowers resistive losses by approximately a factor of four. In applications where resistive losses lead to the choice of a two-layer inductor, -twisted inductors provide improved high-frequency performance at no additional cost and without compromising on other +twisted inductors provide improved high-frequency performance at no additional cost and without compromising other performance parameters. -\begin{table} +\begin{table*} \begin{tabular}{cc|ccc|} Turn Count $n$& Trace pair count $k$& @@ -319,10 +319,33 @@ performance parameters. \end{tabular} \caption{Inductor sample design parameters and measured characteristics. All inductors have outer diameter \qty{35}{\milli\meter} and inner diameter \qty{15}{\milli\meter}.} -\end{table} +\end{table*} \subsection{Coupling} +The key performance criterion in our application is the voltage ripple that appears on the secondary side of a WPT link +when one of the inductors is rotating. To experimentally evaluate the magnitude of this ripple in a realistic scenario +across a large set of rotations and relative displacements, we created a test setup consisting of a 3D gantry built from +an old 3D printer, with a fourth rotation axis provided by a small servo that allows us to position two inductor test +coupons at arbitrary offsets and angles to one another while measuring their coupling. + +To evaluate a realistic scenario, we loaded the secondary inductor with a resistive load of \qty{10}{\ohm}, while +providing a signal at a \qty{300}{\kilo\hertz} carrier frequency to the primary inductor from a Siglent SDG6022X +function generator. We measured both the input and output voltages of the coupled inductor pair using Keysight 34465A +multimeters in AC RMS mode. The results of these measurements, with the voltage ratio between the coupled inductors' +input and output voltages graphed across one revolution in Figure\ \ref{symmetry_3turn_n_twist} for a set of three-turn +inductors and in Figure\ \ref{symmetry_10turn_n_twist} for a set of 10-turn inductors with multiple trace pair amounts +$k$. + +From these graphs we observe slightly lower coupling for $k>0$ compared to a single-layer spiral inductor, which is +in line with our previous inductance measurements. Across one revolution, we find that single-layer spiral inductors +exhibit the worst voltage ripple, with simple two-layer inductors with $k=1$ already improving ripple by a large margin. +Increasing $k$ above $1$ does not decrease the amplitude of this ripple further, but it does shift the ripple into +higher frequencies that are easier to passively filter, as we originally intended. + +\todo{new ripple measurements, concrete coupling factor measurements} +\todo{schematics for illustration of measeurement circuits} + \begin{figure} \begin{center} %\includegraphics[width=0.7\linewidth]{figures/symmetry_3turn_n_twist.pdf}