exjobb/rapport/results.tex

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\chapter{Results}\label{cha:results}
This chapter presents the results achieved using the methods described in \autoref{cha:methods}. Each section in this chapter corresponds to a section in the method chapter with the same name.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Prestudy}
Since not much was known about the project at this time, it was difficult to find relevant papers on the topic of the standards. Most of the literature was found during the project to solve problems as they were discovered.

Since the test equipment was mostly in line with the new standards, the first project path was chosen. There was not enough time available to investigate any of the extra tasks as intended.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Comparison Between the Old and the New Standard}
The differences of importance between the old and new standards will be presented in this chapter to see what parameters might be a problem for the older equipment to fulfil.

One of the most notable differences is the removal of a test pulse from ISO~7637\nd2 that was called \emph{Pulse 5a}. This was instead introduced to the ISO~16750\nd2 under the name \emph{Load~dump~A}.

Only the properties that were found to differ are mentioned in the results.

%%%%%%%%%%%%%%%%%%%%
\subsection{Supply voltages}
The specification of the DC supply voltage for the DUT, $U_A$ in \autoref{fig:doubleexp}, differs between the old and the new version of the standard. \autoref{tab:supplyVoltageDiff} presents the supply voltage specifications from the different standards. The supply voltages are provided by an external PSU and will thus not be dependent on the test equipment.

\begin{table}[H]
    \caption{Comparison of the different supply voltage specifications.}
\begin{adjustbox}{center}
    %\centering
    \begin{tabular}{|l|r|r|} 
       \hline
        & \multicolumn{2}{c|}{Supply voltage} \\
       Standard & $U_N=$\SI{12}{\volt} & $U_N=$\SI{24}{\volt} \\
       \hline
       \multicolumn{1}{|c}{} & \multicolumn{2}{c|}{$U_A$}    \\
       \hline
       ISO 7637-2:2004   & \SIrange{13}{14}{\volt}    & \SIrange{26}{28}{\volt}  \\
       ISO 7637-2:2011   & \SIrange{12}{13}{\volt}    & \SIrange{24}{28}{\volt}  \\
       ISO 16750-1:2018 &  \SIrange{13.8}{14.2}{\volt}    & \SIrange{27.8}{28.2}{\volt}   \\
       \hline
    \end{tabular}
\end{adjustbox}
    \label{tab:supplyVoltageDiff}
\end{table}

%%%%%%%%%%%%%%%%%%%%
\subsection{Surge voltages}
Several of the surge voltages has a wider specified range, as can be seen in \autoref{tab:UADiff}. Notice how the old pulse 5a and the new load dump A have different specifications for $U_S$, but they describe the same pulse because of the different definition of $U_S$ in ISO~7637\nd2 and ISO~16750\nd2 as described in \autoref{sec:theory-load-dump-test-a}.

\begin{table}[H]
    \caption{Comparison of the different surge voltage specifications.}
\begin{adjustbox}{center}
    %\centering
    \begin{tabular}{|l|r|r|} 
       \hline
        & \multicolumn{2}{c|}{$U_S$}    \\
       Standard & $U_N=$\SI{12}{\volt}  &  $U_N=$\SI{24}{\volt}    \\
       \hline
       \multicolumn{3}{|l|}{Pulse 1}    \\
       \hline
       ISO 7637-2:2004   & \SIrange{-75}{-100}{\volt}    & \SIrange{-450}{-600}{\volt}  \\
       ISO 7637-2:2011   & \SIrange{-75}{-150}{\volt}    & \SIrange{-300}{-600}{\volt}  \\
       \hline
       \multicolumn{3}{|l|}{Pulse 2a}    \\
       \hline
       ISO 7637-2:2004   & \multicolumn{2}{c|}{\SIrange{37}{50}{\volt}}  \\
       ISO 7637-2:2011   & \multicolumn{2}{c|}{\SIrange{37}{112}{\volt}}  \\
       \hline
       \multicolumn{3}{|l|}{Pulse 3a}    \\
       \hline
       ISO 7637-2:2004   & \SIrange{-112}{-150}{\volt}    & \SIrange{-150}{-200}{\volt}  \\
       ISO 7637-2:2011   & \SIrange{-112}{-220}{\volt}    & \SIrange{-150}{-300}{\volt}  \\
       \hline
       \multicolumn{3}{|l|}{Pulse 3b}    \\
       \hline
       ISO 7637-2:2004   & \SIrange{75}{100}{\volt}    & \SIrange{150}{200}{\volt}  \\
       ISO 7637-2:2011   & \SIrange{75}{150}{\volt}    & \SIrange{150}{300}{\volt}  \\
       \hline
       \multicolumn{3}{|l|}{Pulse 5a/Load dump A}    \\
       \hline
       ISO 7637-2:2004   & \SIrange{65}{87}{\volt}    & \SIrange{123}{174}{\volt}  \\
       ISO 16750-2:2012 & \SIrange{79}{101}{\volt}    & \SIrange{151}{202}{\volt}   \\
       ISO 16750-2:2012\tablefootnote{Recalculated values to fit the same $U_S$ definitions as the older standard. $U_{S_{7637}} = U_{S_{16750}}-U_{N_{16750}}$} & \SIrange{65}{87}{\volt}    & \SIrange{123}{174}{\volt}   \\
       \hline
    \end{tabular}
\end{adjustbox}
    \label{tab:UADiff}
\end{table}

%%%%%%%%%%%%%%%%%%%%
\subsection{Time constraints}
The only time constraint that is stricter in the newer standard is the risetime of pulse 3a and pulse 3b, $t_r$, as shown in \autoref{tab:timingDiff}

\begin{table}[H]
    \caption{Comparison of the different time constraints.}
\begin{adjustbox}{center}
    %\centering
    \begin{tabular}{|l|r|} 
       \hline
        & \multicolumn{1}{c|}{Timing} \\
       Standard & \multicolumn{1}{c|}{$t_d$} \\
       \hline
       ISO 7637-2:2004   & \SIrange{100}{200}{\micro\second} \\
       ISO 7637-2:2011   & \SIrange{105}{195}{\micro\second} \\
       \hline
    \end{tabular}
\end{adjustbox}
    \label{tab:timingDiff}
\end{table}

%%%%%%%%%%%%%%%%%%%%
\subsection{Limits in verification}

Most of the limits are the same in all standards. The only differences found are presented in \autoref{tab:caldiff}. The tolerances for pulse 1 has been widened to \SI{20}{\percent}. The nominal voltage for pulse 2a has been changed to \SI{75}{\volt} for calibration but the tolerance is still \SI{10}{\percent} with no load.

\begin{table}[H]
    \caption{Comparison of the limits for calibration.}
\begin{adjustbox}{center}
    %\centering
    \begin{tabular}{|l|r|} 
       \hline
       \multicolumn{2}{|l|}{Pulse 1, $U_S$, \SI{24}{\volt}, \SI{50}{\ohm} load}    \\
       \hline
       ISO 7637-2:2004   & \SI{-300}{\volt} $\pm$ \SI{30}{\volt}  \\
       ISO 7637-2:2011   & \SI{-300}{\volt} $\pm$ \SI{60}{\volt}  \\
       \hline
       \multicolumn{2}{|l|}{Pulse 2a, $U_S$, no load}    \\
       \hline
       ISO 7637-2:2004   & \SI{50}{\volt} $\pm$ \SI{5}{\volt}  \\
       ISO 7637-2:2011   & \SI{75}{\volt} $\pm$ \SI{7.5}{\volt}  \\
       \hline
       \multicolumn{2}{|l|}{Pulse 2a, $U_S$, \SI{2}{\ohm} load}    \\
       \hline
       ISO 7637-2:2004   & \SI{25}{\volt} $\pm$ \SI{5}{\volt}  \\
       ISO 7637-2:2011   & \SI{37.5}{\volt} $\pm$ \SI{7.5}{\volt}  \\
       \hline
    \end{tabular}
\end{adjustbox}
    \label{tab:caldiff}
\end{table}

%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Examination and Initial Measurement of the Old Equipment}

At first, the test equipment itself needed some care before it was possible to operate it. A couple of screws were loose inside of the LD~200 and a bridge had to be made for the optional external resistor on the MPG~200 for the pulses to even reach the pulse output connectors.

The result from the initial measurements are presented, along with the limits, in \autoref{tab:initial_measurements} without the CNA~200 connected and in \autoref{tab:initial_measurements_cna} with the CNA~200 connected.

\begin{table}[h]
    \caption{The initial manual measurements, measured directly at each generator's output. Values highlighted in red are not within their specifications.}
\begin{adjustbox}{width=\columnwidth,center}
    %\centering
    \begin{tabular}{|l|r|r|r|r|r|r|} 
        \hline
         & \multicolumn{3}{c|}{Limits} & \multicolumn{3}{c|}{Measured} \\
        Pulse & $U_S$ (\si{\volt}) & $t_d$ (\si{\second}) & $t_r$ (\si{\second}) & $U_S$ (\si{\volt}) & $t_d$ (\si{\second}) & $t_r$ (\si{\second}) \\ [0.5ex]
        \hline
        Pulse 1, 12 V, Open     & $[ -110, -90 ]$   & $[1.6,2.4]$ \si{\milli}   & $[0.5,1]$ \si{\micro}     & $-99.0$   & $2.10$ \si{\milli}    & $540$ \si{\nano} \\
        Pulse 1, 24 V, Open     & $[ -660, -540 ]$  & $[0.8,1.2]$ \si{\milli}   & $[1.5,3]$ \si{\micro}     & $-630$    & $1.18$ \si{\milli}    & $2.6$ \si{\micro} \\
        Pulse 2a, Open          & $[ 67.5, 82.5 ]$  & $[40,60]$ \si{\micro}     & $[0.5,1]$ \si{\micro}     & $76.0$    & $51.0$ \si{\micro}    & $750$ \si{\nano} \\
        Pulse 3a, Open (1k)     & $[ -220, -180 ]$  & $[105,195]$ \si{\nano}    & $[3.5,6.5]$ \si{\nano}    & $-202$    & $163$ \si{\nano}      & $5.2$ \si{\nano} \\
        Pulse 3a, Match         & $[ -120, -80 ]$   & $[105,195]$ \si{\nano}    & $[3.5,6.5]$ \si{\nano}    & $-104$    & $134$ \si{\nano}      & $5.0$ \si{\nano} \\
        Pulse 3b, Open (1k)     & $[ 180, 220 ]$    & $[105,195]$ \si{\nano}    & $[3.5,6.5]$ \si{\nano}    & $202$    & \cellcolor{red!60} $208$ \si{\nano}      & $5.1$ \si{\nano} \\
        Pulse 3b, Match         & $[ 80, 120 ]$     & $[105,195]$ \si{\nano}    & $[3.5,6.5]$ \si{\nano}    & $102$     & $166$ \si{\nano}      & $5.0$ \si{\nano} \\
        Load dump A, 12 V, Open & $[ 90, 110 ]$     & $[320,480]$ \si{\milli}   & $[5,10]$ \si{\milli}      & $93.4$    & $390$ \si{\milli}     & $5.8$ \si{\milli} \\
        Load dump A, 24 V, Open & $[ 180, 220 ]$    & $[280,420]$ \si{\milli}   & $[5,10]$ \si{\milli}      & $190$     & $365$ \si{\milli}     & $5.2$ \si{\milli} \\
        \hline
    \end{tabular}
\end{adjustbox}
    \label{tab:initial_measurements}
\end{table}

\begin{table}[h]
    \caption{The initial manual measurements on the equipment, including the CNA~200. Values highlighted in red are not within their specifications.}
\begin{adjustbox}{width=\columnwidth,center}
    %\centering
    \begin{tabular}{|l|r|r|r|r|r|r|} 
        \hline
         & \multicolumn{3}{c|}{Limits} & \multicolumn{3}{c|}{Measured} \\
        Pulse & $U_S$ (\si{\volt}) & $t_d$ (\si{\second}) & $t_r$ (\si{\second}) & $U_S$ (\si{\volt}) & $t_d$ (\si{\second}) & $t_r$ (\si{\second}) \\ [0.5ex]
        \hline
        Pulse 1, 12 V, Open     & $[ -110, -90 ]$   & $[1.6,2.4]$ \si{\milli}   & $[0.5,1]$ \si{\micro}     & $-99.2$   & $2.00$ \si{\milli}    & \cellcolor{red!60} $450$ \si{\nano} \\
        Pulse 1, 24 V, Open     & $[ -660, -540 ]$  & $[0.8,1.2]$ \si{\milli}   & $[1.5,3]$ \si{\micro}     & $-632$    & $1.18$ \si{\milli}    & $2.6$ \si{\micro} \\
        Pulse 2a, Open          & $[ 67.5, 82.5 ]$  & $[40,60]$ \si{\micro}     & $[0.5,1]$ \si{\micro}     & $76.0$    & $50.0$ \si{\micro}    & $770$ \si{\nano} \\
        Pulse 3a, Open (1k)     & $[ -220, -180 ]$  & $[105,195]$ \si{\nano}    & $[3.5,6.5]$ \si{\nano}    & $-213$    & $163$ \si{\nano}      & $6.2$ \si{\nano} \\
        Pulse 3a, Match         & $[ -120, -80 ]$   & $[105,195]$ \si{\nano}    & $[3.5,6.5]$ \si{\nano}    & $-93.2$   & $138$ \si{\nano}      & $6.0$ \si{\nano} \\
        Pulse 3b, Open (1k)     & $[ 180, 220 ]$    & $[105,195]$ \si{\nano}    & $[3.5,6.5]$ \si{\nano}    & \cellcolor{red!60} $222$     & \cellcolor{red!60} $200$ \si{\nano}      & $6.3$ \si{\nano} \\
        Pulse 3b, Match         & $[ 80, 120 ]$     & $[105,195]$ \si{\nano}    & $[3.5,6.5]$ \si{\nano}    & $94.0$    & $171$ \si{\nano}      & $5.7$ \si{\nano} \\
        Load dump A, 12 V, Open & $[ 90, 110 ]$     & $[320,480]$ \si{\milli}   & $[5,10]$ \si{\milli}      & $93.2$    & $394$ \si{\milli}     & $5.8$ \si{\milli} \\
        Load dump A, 24 V, Open & $[ 180, 220 ]$    & $[280,420]$ \si{\milli}   & $[5,10]$ \si{\milli}      & $186$     & $400$ \si{\milli}     & $5.1$ \si{\milli} \\
        \hline
    \end{tabular}
\end{adjustbox}
    \label{tab:initial_measurements_cna}
\end{table}

%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Test Architecture}
\label{result-test-architecture}
The 3rd alternative was chosen because of the convenience of a fully automatic system and because of the electrical safety hazard that alternative 2 would pose to the operator due to its live voltages on the measurement connectors.

%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Design of Dummy Loads}
The design of the dummy loads is described in this chapter.

%%%%%%%%%%%%%%%%%%
\subsection{Components}
The results of the maximum momentary power is shown in \autoref{tab:dummy_load_worst_case}. The highest momentary power delivered from the MPG~200 is as high as \SI{45}{\kilo\watt}. This might sound too much to be possible, but the power $P = \frac{U^2}{R}$ which with the \SI{2}{\ohm} dummy load attached gives $\frac{\left({\SI{300}{\volt}}\right)^2}{\SI{2}{\ohm}}\si{\watt} = \frac{90000}{2}\si{\watt} = \SI{45}{\kilo\watt}$.

\begin{table}[h]
    \caption{Calculated momentary worst cases for each dummy load. The LD~200 is included for comparison to the MPG~200 even though it does not result in the highest power.}
\begin{adjustbox}{width=\columnwidth,center}
    \centering
    \begin{tabular}{|l|r|r|r|r|r|r|} 
        \hline
        Dummy load & Generator & $R_S$ & Generator voltage & Resistor peak voltage & Peak resistor power \\
        \hline
        \SI{2}{\ohm}  & LD 200  & \SI{0.5}{\ohm} & \SI{200}{\volt} & \SI{160}{\volt} & \SI{12.8}{\kilo\watt} \\
        \SI{2}{\ohm}  & MPG 200 & \SI{2}{\ohm}   & \SI{600}{\volt} & \SI{300}{\volt} & \SI{45  }{\kilo\watt} \\
        \SI{10}{\ohm} & MPG 200 & \SI{2}{\ohm}   & \SI{600}{\volt} & \SI{500}{\volt} & \SI{ 5  }{\kilo\watt} \\ 
        \SI{50}{\ohm} & MPG 200 & \SI{2}{\ohm}   & \SI{600}{\volt} & \SI{577}{\volt} & \SI{266 }{\watt} \\
        \hline
    \end{tabular}
\end{adjustbox}
    \label{tab:dummy_load_worst_case}
\end{table}

The maximum energy transferred to the \SI{2}{\ohm}, however, is delivered by the LD~200 generator as shown in \autoref{fig:dummy2_energy}.

\begin{figure}[H]
	\centering
	\begin{subfigure}[t]{0.48\textwidth}
		\includegraphics[width=\textwidth]{mpg200_energy}
		\caption{The MPG~200 transfers approximately \SI{23}{\joule} to the dummy load.}
   	    \label{fig:mpg200_energy}
	\end{subfigure}
	\begin{subfigure}[t]{0.48\textwidth}
		\includegraphics[width=\textwidth]{ld200_energy}
		\caption{The LD~200 transfers approximately \SI{1.2}{\kilo\joule} to the dummy load.}
   	    \label{fig:ld200_energy}
	\end{subfigure}
	\caption{The maximum energies transferred from the pulse generators to the \SI{2}{\ohm} dummy load. The vertical scale represents the energy in Joule, but is presented in voltage because of the way it is calculated in the simulation.}
   	\label{fig:dummy2_energy}
\end{figure}

The LTO100 resistor series\footnote{\url{https://www.vishay.com/docs/50051/lto100.pdf}} from Vishay was chosen because of its high power characteristics and because the maximum overload energy curve was specified in its datasheet. Whith the datasheet and simulation side by side, a worst ratio between the simulated energy and the energy specified in the datasheet was determined. The worst case found for the different pulses and dummy loads can be found in \autoref{tab:dummy_load_energies}.

\begin{table}[h]
    \caption{The worst case ratio between the simulation energies and the datasheet specification. The ratio equals the minimum number of resistors needed to share the energy.}
%\begin{adjustbox}{width=\columnwidth,center}
    \centering
    \begin{tabular}{|r|r|l|} 
        \hline
        Dummy load & Ratio & Limiting property \\
        \hline
        \SI{2}{\ohm}  & 26 & Pulse 5 energy after \SI{50}{\milli\second} \\
        \SI{10}{\ohm} & 10 & Pulse 5 energy after \SI{100}{\milli\second} \\ 
        \SI{50}{\ohm} & 2 & Pulse 5 energy after \SI{50}{\milli\second} \\
        \hline
    \end{tabular}
%\end{adjustbox}
    \label{tab:dummy_load_energies}
\end{table}

When the least number of resistors required had been determined, some different resistor topologies were considered before setteling on the configuration seen in \autoref{fig:dummy_load_schematic}. The number of different resistor values were kept as low as considered possible to keep things easy.

\begin{figure}[H]
    %\captionsetup{width=.5\linewidth}
    \centering
    \includegraphics[width=\textwidth]{dummy_load_schematic}
    \caption{The topology chosen for the \SI{2}{\ohm}, \SI{10}{\ohm} and \SI{50}{\ohm} dummy loads.}
    \label{fig:dummy_load_schematic}
\end{figure}

%%%%%%%%%%%%%%%%%%
\subsection{PCB}

Because of the high voltages present on the board, a minimum creepage of \SI{3}{\milli\meter} was used. This is in line with the \mbox{EN 60664-1} standard \cite{en_60664_1}. The board was perforated to allow for better air flow past the resistors, improving the cooling. The mounting holes for the card was placed in a \SI[product-units=single]{105 x 105}{\milli\meter} square, allowing a \SI{120}{\milli\meter} fan to be mounted on top of the card using mounting hardware.

A two layer board was chosen, and all of the traces were mirrored on both layers to get as much conductive cross sectional area as possible, and thus lowering the resistance and power dissipation in the traces. The default copper thickness from the manufacturer\footnote{Cogra Pro AB \url{ https://www.cogra.se/produkter/monsterkort/}},  was \SI{18}{\micro\meter}, but this PCB was ordered with \SI{60}{\micro\meter} thick copper layer to further extend the cross sectional areas. The width of the traces for the \SI{2}{\ohm} load was chosen as wide as possible without violating the \SI{3}{\milli\meter} creepage distance.

\begin{figure}[H]
	\centering
	\begin{subfigure}[t]{0.48\textwidth}
	    \includegraphics[width=\textwidth]{dummy-load-prototype}
	    \caption{Card board was used to test the PCB layout before it was sent for manufacturing.}
	    \label{fig:dummy-load-prototype}
	\end{subfigure}
	\begin{subfigure}[t]{0.48\textwidth}
    	\includegraphics[width=\textwidth]{dummy-load-assembled}
	    \caption{The assembled dummy load.}
	    \label{fig:dummy-load-assembled}
	\end{subfigure}
	\caption{The resulting board was predicted using a card board mockup PCB.}
   	\label{fig:dummy-load-development}
\end{figure}

When the PCB was delivered, it was visually inspected before assembling. The component placement was correct, but some modification was made to improve the isolation distance by drilling away the plating and pads of the ventilation holes. The modified board's top and bottom side can be seen in \autoref{fig:dummy-load-top} and \autoref{fig:dummy-load-bottom} respectively.

\begin{figure}[H]
	\centering
	\begin{subfigure}[t]{0.48\textwidth}
	    \includegraphics[width=\textwidth]{dummy-load-top}
	    \caption{Top.}
	    \label{fig:dummy-load-top}
	\end{subfigure}
	\begin{subfigure}[t]{0.48\textwidth}
    	\includegraphics[width=\textwidth]{dummy-load-bottom}
	    \caption{Bottom.}
	    \label{fig:dummy-load-bottom}
	\end{subfigure}
	\caption{The plating in the ventilation holes was removed by hand using a drill to increase the creepage distance between the resistor terminals. All holes without annular ring are ventilation holes.}
   	\label{fig:dummy-load-pcb}
\end{figure}

\pagebreak
%%%%%%%%%%%%%%%%%%
\subsection{Measurements}
The resistance of the dummy loads are presented in \autoref{tab:four-wire-result}.

\begin{table}[h]
    \captionsetup{width=.6\linewidth}
    \caption{The measured resistance of the dummy loads, and the error compared to the nominal values.}
%\begin{adjustbox}{width=0.6\columnwidth,center}
    \centering
    \begin{tabular}{|l|r|r|} 
        \hline
        Nominal (\si{\ohm}) & Measured $R$ (\si{\ohm}) & Error (\si{\percent}) \\
        \hline
        2   & $2.004$   & $+ 0.2$    \\
        10  & $9.973$   & $ - 0.27 $  \\
        50  & $49.954$  & $ - 0.09 $  \\
        \hline
    \end{tabular}
%\end{adjustbox}
    \label{tab:four-wire-result}
\end{table}

%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Design of the Switching Fixture and the Embedded Attenuators}
The design of the switching fixture and its attenuators is described in this chapter. The designed attenuator is referred to as \emph{BK 50} and \emph{BK 1000} in the figures in this section to differentiate them from the commercially available \emph{PAT 50} and \emph{PAT 1000}.

%%%%%%%%%%%%%%%%%%
\subsection{Components}
The 1206 package from Vishay's CRCW-HP series\footnote{\url{https://datasheet.octopart.com/CRCW120682R0FKEAHP-Vishay-datasheet-8359436.pdf}} was used for the embedded attenuators. They are high pulse tolerant thick-film resistors. However, they don't specify the maximum energy vs time as the LTO100 that were used for the dummy loads, but only power and voltage limits. The maximum voltage allowed for the short duration of Pulse 3, \SI{200}{\nano\second}, is specified to \SI{700}{\volt} and the maximum power to \SI{900}{\watt}.

The maximum power dissipated into the \SI{50}{\ohm} attenuator will be approximately $\frac{\left(\SI{750}{\volt}\right)^2}{\SI{50}{\ohm}} = \SI{11250}{\watt}$. For the \SI{1000}{\ohm} attenuator it will be approximately $\frac{\left(\SI{1429}{\volt}\right)^2}{\SI{1000}{\ohm}} \approx \SI{2042}{\watt}$, where \SI{1429}{\volt} is the approximate voltage that would result over a \SI{1000}{\ohm} load from a \SI{1500}{\volt} source with \SI{50}{\ohm} series resistance.

The Panasonic's LF-G relays were chosen as switching elements as they have a high breakdown voltage between the open contacts and had a small form factor making them suitable for the relay box.

%%%%%%%%%%%%%%%%%%
\subsection{Attenuators}
\label{sec:result-attenuators}
The \SI{54.7}{\deci\bel} attenuator was divided into two \SI{27.35}{\deci\bel} $\Pi$\nd{}attenuator links. The values obtained from the online calculator was \SI{54.48}{\ohm} as the parallel resistors and \SI{581.62}{\ohm} as the series resistor for each link. The real values for the resistors, when replaced by several resistors connected in series and parallel, was chosen to \SI{54.67}{\ohm} and \SI{560}{\ohm} for parallel and series resistors respectively. The final attenuation was \SI{53.76}{\deci\bel} for the two links according to the simulation, as seen in \autoref{fig:ltspice-54db-attenuator}. The design was realized as seen in \autoref{fig:ltspice-54db-attenuator-comp}, with the number of resistors based on the maximum voltages and powers. Capacitors were placed in the schematic to allow for phase compensation.

Since the uncompensated simulated circuit had its \SI{3}{\deci\bel} limit at only \SI{190}{\mega\hertz} the circuit had to be compensated. The values used for compensating the circuit was \SI{130}{\pico\farad} for the first parallel resistance and \SI{10}{\pico\farad} for the second parallel link as seen in \autoref{fig:ltspice-54db-attenuator-comp}. The results before and after the compensation can be seen in \autoref{fig:50-ohm-result-response} where the new \SI{3}{\deci\bel} limit is instead over \SI{1}{\giga\hertz}.

\begin{figure}[H]
	\centering
	\begin{subfigure}[t]{0.7\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{ltspice-54db-attenuator}
		\caption{The ideal circuit simulated.}
		\label{fig:ltspice-54db-attenuator}
	\end{subfigure}
	
	\begin{subfigure}[t]{0.7\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{ltspice-54db-attenuator-comp}
		\caption{Chosen topology simulated with parasitics and compensation capacitors. The components with designator X are the non-ideal resistors depicted in \autoref{fig:nonIdealResistor}}
		\label{fig:ltspice-54db-attenuator-comp}
	\end{subfigure}
	\caption{The \SI{50}{\ohm} attenuator circuit in the simulator.}
	\label{fig:50-ohm-result-circuit}
\end{figure}

\begin{figure}[H]
	\centering
	\begin{subfigure}[t]{0.7\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{simulated-50-w-vs-wo-comp-mag}
	\end{subfigure}
	
	\begin{subfigure}[t]{0.7\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{simulated-50-w-vs-wo-comp-phase}
	\end{subfigure}
	\caption{The \SI{50}{\ohm} attenuator simulated with and without compensation.}
	\label{fig:50-ohm-result-response}
\end{figure}

The \SI{60.1}{\deci\bel} attenuator was divided into one \SI{27.35}{\deci\bel} $\Pi$\nd{}attenuator link, the same as used in the \SI{54.7}{\deci\bel} attenuator, preceded by a \SI{32.75}{\deci\bel} $\Pi$ link with \SI{1000}{\ohm} in-impedance. When the closest values for the resistors had been chosen, using \SI{56}{\ohm} as parallel resistors and \SI{56}{\ohm} as series resistor, the final attenuation was \SI{60.33}{\deci\bel} for the two links according to the simulation, seen in \autoref{fig:ltspice-60db-attenuator}. The attenuator was then realized as seen in \autoref{fig:ltspice-60db-attenuator-comp}, based on the maximum voltages and powers.

Since the uncompensated circuit had its \SI{3}{\deci\bel} limit at only \SI{130}{\mega\hertz} the circuit had to be compensated. The values used for compensating the circuit was \SI{40}{\pico\farad} for the first parallel resistance and \SI{30}{\pico\farad} for the second parallel link as seen in \autoref{fig:ltspice-60db-attenuator-comp}. The results before and after the compensation can be seen in \autoref{fig:1k-ohm-result-response} where the new \SI{3}{\deci\bel} limit is instead above \SI{1}{\giga\hertz}. 

\begin{figure}[H]
	\centering
	\begin{subfigure}[t]{0.7\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{ltspice-60db-attenuator}
		\caption{The ideal circuit simulated.}
		\label{fig:ltspice-60db-attenuator}
	\end{subfigure}
	
	\begin{subfigure}[t]{0.7\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{ltspice-60db-attenuator-comp}
		\caption{Chosen topology simulated with parasitics and compensation capacitors. The components with designator X are the non-ideal resistors depicted in \autoref{fig:nonIdealResistor}}
		\label{fig:ltspice-60db-attenuator-comp}
	\end{subfigure}
	
	\caption{The \SI{1000}{\ohm} attenuator simulated.}
	\label{fig:1k-ohm-result-circuit}
\end{figure}
	
\begin{figure}[H]
	\centering
	\begin{subfigure}[t]{0.7\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{simulated-1k-w-vs-wo-comp-mag}
	\end{subfigure}

	\begin{subfigure}[t]{0.7\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{simulated-1k-w-vs-wo-comp-phase}
	\end{subfigure}
	
	\caption{The \SI{1000}{\ohm} attenuator simulated with and without compensation.}
	\label{fig:1k-ohm-result-response}
\end{figure}
	

%%%%%%%%%%%%%%%%%%
\subsection{PCB}
The prototype and finished PCB can be seen side by side in \autoref{fig:attenuator-development}. The PCB had to be modified after it was delivered, since the creepage distance was to low at a few places and because the footprint for the relays was wrong. The modified PCB can be seen in \autoref{fig:attenuator-pcb}.

The manufacturer's default values for dual layer boards was used for this PCB, i.e. \SI{18}{\micro\meter} copper layers on a \SI{1.6}{\milli\meter} laminate.

To attach the relay card fixture to the \SI{4}{\mm} banana connectors on the CNA~200, three banana plugs was designed to be screwed directly to the PCB. This makes the conductors as short as possible, and also act as mechanical fastening of the PCB to the case.


\begin{figure}[h]
	\centering
	\begin{subfigure}[t]{0.48\textwidth}
	    \includegraphics[width=\textwidth]{attenuator-prototype}
	    \caption{Card board was used to test the PCB layout before it was sent for manufacturing.}
	    \label{fig:attenuator-prototype}
	\end{subfigure}
	\begin{subfigure}[t]{0.48\textwidth}
    	\includegraphics[width=\textwidth]{attenuator-assembled}
	    \caption{The assembled switching fixture.}
	    \label{fig:attenuator-assembled}
	\end{subfigure}
	\caption{The resulting board was predicted using a card board mockup PCB.}
	\label{fig:attenuator-development}
\end{figure}

\begin{figure}[h]
	\centering
	\begin{subfigure}[t]{0.48\textwidth}
	    \includegraphics[width=\textwidth]{attenuator-top}
	    \caption{Top.}
	    \label{fig:attenuator-top}
	\end{subfigure}
	\begin{subfigure}[t]{0.48\textwidth}
    	\includegraphics[width=\textwidth]{attenuator-bottom}
	    \caption{Bottom.}
	    \label{fig:attenuator-bottom}
	\end{subfigure}
	\caption{The PCB was modified to correct the mistakes.  The footprint for the relay was slightly wrong (1) and some of the creepage distances were to short (2)}
   	\label{fig:attenuator-pcb}
\end{figure}

%%%%%%%%%%%%%%%%%%
\subsection{Measurements}
Since the designed attenuators deviated very much at frequencies above \SI{100}{\mega\hertz} the measurement sweep was only set to \SI{200}{\mega\hertz}.

The designed attenuators were not compensated, thus they are compared to the uncompensated simulated circuits. The frequency response for these are presented in \autoref{fig:50-ohm-comparison-result-response} and \autoref{fig:1k-ohm-comparison-result-response} for the \SI{50}{\ohm} and the \SI{1000}{\ohm} attenuator respectively.

A comparison to the commercially available \emph{PAT 50} can be seen in \autoref{fig:50-ohm-real-vs-pat} and a comparison to the \emph{PAT 1000} can be seen in \autoref{fig:1k-ohm-real-vs-pat}.

In \autoref{fig:bk50-signal-paths} and \autoref{fig:bk1000-signal-paths} the tree different signal paths are compared to each other to show the differences between them for the \SI{50}{\ohm} and the \SI{1000}{\ohm} attenuator respectively.

Any disconnected signal path should not affect the measured output. The results in \mbox{\autoref{fig:bk50-suppression}} and \mbox{\autoref{fig:bk1000-suppression}} shows how much of the unwanted signal is transferred to the output for the \SI{50}{\ohm} and the \SI{1000}{\ohm} attenuator respectively. The magnitude response of the single relay is also plotted in this figure to show how much attenuation it contributes with.
	
\begin{figure}[h]
	\centering
	\begin{subfigure}[t]{0.8\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{simulated-vs-bk50-mag}
	\end{subfigure}

	\begin{subfigure}[t]{0.8\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{simulated-vs-bk50-phase}
	\end{subfigure}
	
	\caption{The simulated \SI{50}{\ohm} attenuator compared to the designed.}
	\label{fig:50-ohm-comparison-result-response}
\end{figure}
	
\begin{figure}[h]
	\centering
	\begin{subfigure}[t]{0.8\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{pat50-vs-bk50-mag}
	\end{subfigure}

	\begin{subfigure}[t]{0.8\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{pat50-vs-bk50-phase}
	\end{subfigure}
	
	\caption{The designed \SI{50}{\ohm} attenuator compared to the commercially available PAT 50.}
	\label{fig:50-ohm-real-vs-pat}
\end{figure}

\begin{figure}[h]
    \centering
    \includegraphics[width=0.8\textwidth]{bk50-paths}    
    \caption{Comparison of the three different signal paths of the designed \SI{50}{\ohm} attenuator.}
    \label{fig:bk50-signal-paths}
\end{figure}

\begin{figure}[h]
    \centering
    \includegraphics[width=0.8\textwidth]{bk50-suppression}    
    \caption{Comparison between one of the signal paths against several paths that are disconnected on the \SI{50}{\ohm} attenuator. This measurement was made to see if the disconnected paths can influence the measured path. A single open relay was also measured to show its attenuation.}
    \label{fig:bk50-suppression}
\end{figure}

\begin{figure}[h]
	\centering
	\begin{subfigure}[t]{0.8\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{simulated-vs-bk1000-mag}
	\end{subfigure}

	\begin{subfigure}[t]{0.8\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{simulated-vs-bk1000-phase}
	\end{subfigure}
	
	\caption{The simulated \SI{1000}{\ohm} attenuator compared to the designed.}
	\label{fig:1k-ohm-comparison-result-response}
\end{figure}
	
\begin{figure}[h]
	\centering
	\begin{subfigure}[t]{0.8\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{pat1k-vs-bk1000-mag}
	\end{subfigure}

	\begin{subfigure}[t]{0.8\textwidth}
		\captionsetup{width=\linewidth}
		\centering
		\includegraphics[width=\textwidth]{pat1k-vs-bk1000-phase}
	\end{subfigure}
	
	\caption{The designed \SI{1000}{\ohm} attenuator compared to the commercially available PAT 1000.}
	\label{fig:1k-ohm-real-vs-pat}
\end{figure}

\begin{figure}[h]
    \centering
    \includegraphics[width=0.8\textwidth]{bk1000-paths}    
    \caption{Comparison of the three different signal paths of the designed \SI{50}{\ohm} attenuator.}
    \label{fig:bk1000-signal-paths}
\end{figure}

\begin{figure}[h]
    \centering
    \includegraphics[width=0.8\textwidth]{bk1000-suppression}    
    \caption{Comparison between one of the signal paths versus several paths that are disconnected on the \SI{1000}{\ohm} attenuator. This measurement was made to see if the disconnected paths can influence the measured path. A single open relay was also measured to show its attenuation.}
    \label{fig:bk1000-suppression}
\end{figure}

The time measurements are shown in \autoref{fig:time-measurements}

\begin{figure}[h]
	\centering
	\begin{subfigure}[t]{0.4\textwidth}
		\includegraphics[width=\textwidth]{bk50_time}
		\caption{The designed \SI{50}{\ohm} attenuator}
		\label{fig:bk50-time}
	\end{subfigure}\hfill
	\begin{subfigure}[t]{0.4\textwidth}
		\includegraphics[width=\textwidth]{bk1000_time}
		\caption{The designed \SI{1}{\kilo\ohm} attenuator}
		\label{fig:bk1000-time}
	\end{subfigure}
	
	\begin{subfigure}[t]{0.4\textwidth}
		\includegraphics[width=\textwidth]{pat50_time}
		\caption{PAT50}
		\label{fig:pat-50-time}
	\end{subfigure}\hfill
	\begin{subfigure}[t]{0.4\textwidth}
		\includegraphics[width=\textwidth]{pat1000_time}
		\caption{PAT1000}
		\label{fig:pat-1000}
	\end{subfigure}
	\caption{The attenuator measurements in time domain, measured with the oscilloscope.}
	\label{fig:time-measurements}
\end{figure}