\section{Hardware-Based Six-Step Commutation Controller}
\label{sec:sixstep}

The basis of this section is the replacement of components who are highly complex, technical and/or are dependant on global supply chains to manufacture. An additional goal is, as for the preceding section, to make a repairable, reliable and manufacturable circuit, this time using these more basic components, based on open-source principles. The controller needs to be performant enough to drive one of the two electric motors used on the LaMAD (La Manufacture Autonome Décentralisée) bicycle cargo trailer. %ref moteur qu'utilise lamad

\subsection{Constraints}
The electric motors used are supplied using 36/48 Volts at 1000 W. This means that the six-step chopper transistors need to be able to supply up to 28 Amperes of current. This is a lot, considering our restrictions. Additionally, the heat will need to be managed, which may be an even bigger challenge than the current.

\subsection{Semiconductor facilities in Occitanie}
The most challenging part of this section is the replacement of semiconductor parts, as these are the most complicated parts to manufacture. Luckily, the city in which the team is located, Toulouse, offers possibilities in semiconductor manufacturing. This may not be a complete list, but the following were identified:

\begin{enumerate}
	\item ST Microelectronics Labège-Innopôle (formerly Exagan, formerly CEA-Leti) 
	\item AIME (Atelier Interuniversitaire de Micro-nano Électronique) on-campus at INSA Toulouse
\end{enumerate}

ST Microelectronics at Labège designs and manufactures gallium nitride transistors under the commercial designation STPOWER PowerGaN, this confirmed by a colleague who visited the plant and engineering teams in late 2022, Etienne Gadefait. Gallium nitride transistors are great for high speed power electronics % ref https://www.st.com/en/power-transistors/powergan.html
but this is a very recent technology, and none of the big material players in GaN are European, let alone French or Occitanian (US, China, Japan and India are predominant). % ref https://us.metoree.com/categories/7137/
 Because of this and very high costs, we chose to consider this a supply chain-constrained technology, which could not be relied on in a non-global future, and we moved on to option 2; AIME.

The AIME is a small research lab located on our campus. Their capabilities and projects were not publicly available, so we decided to contact them. We met two researchers Reasmey Tan and Jean-Baptiste Lincelles to enquire about the manufacturability of certain components, and eventual costs. The AIME specialises in logic circuits, and has not developed any power components at least a decade. Therefore, the research teams have not maintained any know-how in power semiconductors. However, they were very interested in developing this field in their lab, and came with the following proposal to start, based on their existing knowledge. Here are the AIME capabilities, prices and proposal:

\begin{table}[htbp]
	\caption{AIME capabilities}
	\label{tab:AIME_capabilities}
	\centering
	\begin{tabular}{lcc}
		\toprule
		\textbf{Proposal or capability} & \textbf{Value, if relevant} & \textbf{Price, if relevant} \\
		\midrule
		Silicon wafer & 2'' (~50mm) & 10 € \\
		Epitaxial Silicon Carbide wafer & 2'' (~50mm) & 100-200 €   \\
		Lithography mask &  10µm width & 300 € \\
		Lab rental & 1 day & ~2000 € \\
		Transistor canal width & ~1µm \\
		Hardware cost 							 & \\
		Dynamic response 					&  \\
		\bottomrule
	\end{tabular}
\end{table}

\begin{table}[htbp]
\caption{The project proposed by the AIME}
\label{tab:AIME_project}
\centering
\begin{tabular}{lcc}
\toprule
\textbf{Proposal or capability} & \textbf{Value} & \textbf{Price, if relevant} \\
\midrule
Wafer size 	   &  \\
Low-load efficiency 				  &   \\
High-speed switching loss     &  \\
Position sensor requirement &  \\
Implementation complexity  & \\
Hardware cost 							 & \\
Dynamic response 					&  \\
\bottomrule
\end{tabular}
\end{table}



\subsection{Replacing an IC}

Replacing the IC of a motor controller requires using traditional logic gates. This approach is 

\subsection{Power components}


\subsection{Clock}

To calculate the maximum rotation speed, we take the worst conditions of the motor used in the MAD cargo bike; 50 km/h\footnote{http://www.mxusebikekit.com/pro\_info.asp?Pid=25} with a 50 cm wheel\footnote{http://www.mxusebikekit.com/pro\_info.asp?Pid=25}\footnote{https://veloma.org/2022/10/05/la-charrette-version-montagne-ou-comment-transporter-250kg-a-velo-par-monts-et-par-vaux/} (not measured, assumed from the images and the motor specifications). 

\begin{equation*}
  \omega=\frac{v}{\pi d}=\frac{50\cdot 10^3m/h\cdot\frac{1}{60}h/min}{3,14\cdot 50\cdot 10^{-2}m}=530\ rpm
\end{equation*}

The motor being a three-phase brushless motor, the switching speed needs to be 


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