\documentclass{PELsmallreport}

%\usepackage{subcaption}

\graphicspath{{gfx/}}
\bibliography{Bibliography.bib}

\setAuthorOne{{Name1 Surname1 SCIPER ID}}
\setAuthorTwo{{Name2 Surname2 SCIPER ID}}

\begin{document}
\maketitle

\tableofcontents
\vfill

\clearpage
\section{Flyback Converter Sizing}

    The first part of the project deals with sizing of the main elements of a Flyback converter, according to given converter specifications and design requirements. Throughout the whole project continuous conduction mode (CCM) of the converter will be assumed. Fill out Table \ref{Tab:Specs} with the parameters assigned to your group. Regarding the results, please provide them with two digits after the decimal point in the unit provided in the solution box and use the framed boxes below each question to insert your answers and explanations.\\
\begin{minipage}{\linewidth}
    \begin{minipage}[t][][t]{0.3\linewidth}
    \begin{table}[H]
    \captionof{table}{Given parameters and design requirements for the Flyback converter.}
    \centering
    \label{Tab:Specs}
    \begin{tabular}{|l|l|l|}
        \hline
        \textbf{Property} & \textbf{Value} & \textbf{Unit} \\
        \hline
        $P_{out,nom}$ &  & \si{\watt} \\ \hline
	    $P_{out,min,CCM}$ &  & \si{\watt} \\ \hline
	    $U_{in,nom}$ &  & \si{\volt} \\ \hline
        $U_{in,min}$ &  & \si{\volt} \\ \hline
        $U_{in,max}$ &  & \si{\volt} \\ \hline  
        $U_{out}$ &  & \si{\volt} \\ \hline
        $ \Delta U_{out,pp}/U_{out}$ &  & \% \\ \hline
        $f_{sw}$ &  & \si{\kilo\hertz} \\ \hline
    \end{tabular}
    \end{table}
\end{minipage}
\hfill
\begin{minipage}[t][][t]{0.63\linewidth}
        \vspace{0.45cm}
        \captionof{figure}{Schematic of the double switch Flyback.}
        \includegraphics[width=1\linewidth]{gfx/DS_Flyback.png}
        \label{fig:schematic}
\end{minipage}
\end{minipage}    


\subsection{Q1: Voltage transfer function} 
    Derive the input-output voltage transfer function $\frac{U_{out}}{U_{in}}=f\left(D\right)$ of a Flyback converter and solve it for the duty cycle $D=f\left(U_{in}, U_{out}\right)$.
	
    \begin{framed}
        \vspace{2em}
	    \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}

    \fbox{$\frac{U_{in}}{U_{out}}\left(D\right)\ =$\qquad} \quad 
    \fbox{$D\ =$} \qquad \hfill
    \fbox{\qquad / 4 pt.}



\subsection{Q2: Winding ratio} 
    To determine the winding ratio, the following steps should be followed:: 
    \begin{enumerate}[label=\alph*)]
		\item Define a maximum duty ratio $D_{max}$ for your further calculations (please note that the datasheet of the UCC38C44 limits the duty cycle to 0.50)
        \item Calculate the winding ratio $N=\frac{N_P}{N_S}$ to match the requested voltages with your selection of $D_{max}$. 
    \end{enumerate}

    \begin{framed}
        \vspace{2em}
	    \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
	    \vspace{2em}
    \end{framed}

    \fbox{a) $D_{max}\ =$ \qquad} \quad 
    \fbox{b) $N\ =$ \qquad} \quad \hfill
    \fbox{\qquad / 3 pt.}


\subsection{Q3: Duty cycle} Calculate the duty cycle under the following operating conditions:         
    \begin{enumerate}[label=\alph*)]
        \item Nominal operation $\left.D\right|_{U_{in,nom}}$;
        \item Minimum input voltage $\left.D\right|_{U_{in,min}}$;
        \item Maximum input voltage $\left.D\right|_{U_{in,max}}$.
    \end{enumerate} 

    \begin{framed}
        \vspace{2em}
	    \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
	    \vspace{2em}
    \end{framed}

    \fbox{a) $\left.D\right|_{U_{in,nom}}$ = } \quad 
    \fbox{b)$\left.D\right|_{U_{in,min}}$ = } \quad 
    \fbox{c) $\left.D\right|_{U_{in,max}}$ = \qquad} \hfill
    \fbox{\qquad / 2 pt.}


\subsection{Q4: Magnetizing inductance and stray inductance} \label{sec:Q4}
    Derive an expression and calculate the required magnetizing inductance $L_m$ of your transformer, considering that the Flyback converter should operate down to $P_{out,min,CCM}$ in continuous conduction mode.\\ 
    A specific stray inductance cannot be calculated easily, therefore an estimation is needed. To design this converter, use the assumption $L_\sigma \approx 0.05 \cdot L_m$.
    \begin{framed}
        \vspace{2em}
	    \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
	    \vspace{2em}
    \end{framed}

    \fbox{$L_m\ =$ \qquad \si{\micro\henry}}\qquad
    \fbox{$L_\sigma\ =$ \qquad \si{\micro\henry}} \hfill
    \fbox{\qquad / 6 pt.}


\subsection{Q5: Output capacitance} 
    Derive an expression and calculate the required output capacitance $C_{out}$ to fulfill the output voltage ripple requirements under all operating conditions.

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}

    \fbox{$C_{out}\ =$ \qquad \si{\micro\farad} } \hfill
    \fbox{\qquad / 4 pt.}


\subsection{Q6: Input capacitance} 
    Similar to the output capacitance, the input capacitance has to be calculated. The constraint is that the converter should survive the loss of a half-period of the supplying 50 Hz-grid, i.e. \SI{10}{\milli\second}. During this so called 'Hold-up time', the voltage should not drop below $U_{in,min}$ when starting from $U_{in,nom}$.

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}

    \fbox{$C_{in}\ =$ \qquad \si{\micro\farad}} \hfill
    \fbox{\qquad / 4 pt.}

\clearpage

\subsection{Q7: \textsc{Plecs} validation at nominal operation} 
    Using the provided \textsc{Plecs} model, verify your calculations during steady state at nominal operation by presenting the following waveforms over five switching periods: \begin{enumerate}[label=\alph*)]
        \item Output voltage, also provide the measured voltage ripple $\left.\Delta U_{out,pp}\right|_{nom}$;
        \item Inductor current, also provide the minimum measured inductor current $\left.I_{m,min}\right|_{nom}$;
        \item Voltage and current of the transistors;
        \item Voltage and current of the rectifying diode.
    \end{enumerate}
    Start with configuring the Plecs model by clicking on the configuration block in the model. The stray inductance can be neglected here and should be put to 0.
    \begin{framed}
        \vspace{2em}
        \textbf{A dummy figure is given below, exchange it with the one you obtained in \textsc{Plecs}. \\ Delete this before writing anything. }
        \begin{center}
            \includegraphics[width=0.9\textwidth]{gfx/PlecsDummy}
            \captionof{figure}{Voltage and current waveforms of interest. From top to bottom: output voltage $U_{out}\left(t\right)$, magnetizing current $I_m\left(t\right)$, transistor voltage $U_T\left(t\right)$, diode voltage $U_D\left(t\right)$, diode current $I_D\left(t\right)$; all as a function of time.}
            \label{fig:Scope}
        \end{center}
    \end{framed}

    \fbox{a) $\left.U_{out,pp}\right|_{nom}\ =$ \qquad \si{\milli\volt}} \quad 
    \fbox{b) $\left.I_{m,min}\right|_{nom}\ =$ \qquad \si{\milli\ampere}} \hfill
    \fbox{\qquad / 2 pt.}

\clearpage

\subsection{Q8: \textsc{Plecs} validation for CCM} 
    Using the provided \textsc{Plecs} model, verify that your design stays in continuous conduction in steady state mode under worst case operating conditions (\texttt{OP: Limit CCM}) by presenting the following waveforms over five switching periods: 
    \begin{enumerate}[label=\alph*)]
        \item Output voltage, also provide the measured voltage ripple $\left.\Delta U_{out,pp}\right|_{P_{out,min,CCM}}$;
        \item Inductor current, also provide the measured minimum inductor current $\left.I_{m,min}\right|_{P_{out,min,CCM}}$;
        \item Voltage and current of the transistors;
        \item Voltage and current of the rectifying diode.
    \end{enumerate}
    PS: If the output voltage $U_{out}$ does not exactly correspond to the desired value, check the inductor current $i_m$ carefully. It may be that $i_m$ drops to zero for a very short time. This does not mean that your calculation from Q4 are wrong, but is rather due to numerical reasons. Slightly increase your magnetizing inductance $L_m$ and try it again.

    \begin{framed}
        \vspace{2em}
        \textbf{A dummy figure is given below, exchange it with the one you obtained in \textsc{Plecs}. \\ Delete this before writing anything. }
        \begin{center}
            \includegraphics[width=0.9\textwidth]{gfx/PlecsDummy}
            \captionof{figure}{Voltage and current waveforms of interest. From top to bottom: output voltage $U_{out}\left(t\right)$, magnetizing current $I_m\left(t\right)$, transistor voltage $U_T\left(t\right)$, diode voltage $U_D\left(t\right)$, diode current $I_D\left(t\right)$; all as a function of time.}
            \label{fig:Scope}
        \end{center}
    \end{framed}

    \fbox{a) $\left.U_{out,pp}\right|_{P_{out,min,CCM}}\ =$ \qquad \si{\milli\volt}} \quad 
    \fbox{b) $\left.I_{m,min}\right|_{P_{out,min,CCM}}\ =$ \qquad \si{\milli\ampere}} \hfill
    \fbox{\qquad / 2 pt.}

\clearpage

\subsection{Q9: \textsc{Plecs} validation for maximum duty ratio} 
    Using the provided \textsc{Plecs} model, verify that your design does not exceed your selection of neither $D_{max}$ nor $\Delta U_{out,pp}$ (\texttt{OP: Limit ripple and duty cycle;}) by presenting the following waveforms with $U_{in,min}$ and $P_{out,nom}$ in steady state (again five switching periods): \begin{enumerate}[label=\alph*)]
        \item Output voltage, also provide the measured voltage ripple $\left.\Delta U_{out,pp}\right|_{D_{max}}$;
        \item Inductor current, also provide the measured minimum inductor current $\left. I_{m,min}\right|_{D_{max}}$;
	    \item Voltage and current of the transistors;
	    \item Voltage and current of the rectifying diode.
    \end{enumerate}

    \begin{framed}
        \vspace{2em}
        \textbf{A dummy figure is given below, exchange it with the one you obtained in \textsc{Plecs}. \\ Delete this before writing anything. }
        \begin{center}
            \includegraphics[width=0.9\textwidth]{gfx/PlecsDummy}
            \captionof{figure}{Voltage and current waveforms of interest. From top to bottom: output voltage $U_{out}\left(t\right)$, magnetizing current $I_m\left(t\right)$, transistor voltage $U_T\left(t\right)$, diode voltage $U_D\left(t\right)$, diode current $I_D\left(t\right)$; all as a function of time.}
            \label{fig:Scope}
        \end{center}
    \end{framed}

    \fbox{a) $\left.U_{out,pp}\right|_{D_{max}}\ =$ \qquad \si{\milli\volt}} \quad 
    \fbox{b) $\left.I_{m,min}\right|_{D_{max}}\ =$ \qquad \si{\milli\ampere}} \hfill
    \fbox{\qquad / 2 pt.}


\clearpage


\section{Semiconductor Components}

    The second part of this report focuses on the semiconductors. You will have to derive equations for your design, eventually leading to the selection of proper semiconductors that you will use in your design. To achieve this, the highest occurring voltage and biggest current needs to determined for every device. As in the first set of questions, provide numeric answers with a precision of two digits after the decimal point in the provided unit. From now on, you can use the assumption for $L_\sigma$ you made in \ref{sec:Q4}.

\subsection{Q10: Transistor stresses} 
    To select an appropriate transistors for your design, you need to determine maximum voltage and current stress that it has to handle in the Flyback converter. For this purpose, derive analytically. Also provide the results for your converter in normal operation mode in table \ref{tab:stresses}:
    \begin{enumerate}[label=\alph*)]
        \item The maximum voltage over each transistor $u_{T1,max}$ and $u_{T2,max}$;
        \item The maximum current flowing through each transistor $i_{T1,max}$ and $i_{T2,max}$.
    \end{enumerate}

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}
    \hfill\fbox{\qquad / 6 pt.}

\subsection{Q11: Rectifying diode stresses} 
    Identical to the transistors, the maximum values of the rectifying diode have to be identified. Thus, derive analytically. Provide the results for your converter in normal operation mode in table \ref{tab:stresses}:
    \begin{enumerate}[label=\alph*)]
        \item The maximum voltage over the diode $u_{D,rec,max}$;
        \item The maximum current flowing through the diode $i_{D,rec,max}$.
    \end{enumerate}

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}
    \hfill \fbox{\qquad / 6 pt.}

\subsection{Q12: Clamping diodes stresses} 
    Furthermore the maximum values of the clamping diodes on the primary side have to be considered. Derive analytically. Provide the results for your converter in normal operation mode in table \ref{tab:stresses}:
    \begin{enumerate}[label=\alph*)]
        \item The maximum voltage over the diode $u_{D,c,max}$;
        \item The maximum current flowing through the diode $i_{D,c,max}$.
    \end{enumerate}

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}
    \hfill \fbox{\qquad / 4 pt.}

\subsection{Q13: Worst case conditions} 
    Consider the equations you derived in the three previous questions. Identify and explain briefly when the highest voltage and current stress occur for every component. Also calculate the values under their respective worst case condition (that means $U_{in,min}\leq U_{in}\leq U_{in,max}$ and $P_{out,min,CCM}\leq P_{out}\leq P_{out,nom}$). Please note that the worst case may be different for the different values:

    \begin{framed}
        \vspace{2em}
       \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}
    \hfill\fbox{\qquad / 4 pt.}

    
    \begin{table}
        \centering
        \begin{tabular}{|r||r|r||r|r|}
            \hline
             & \multicolumn{2}{c||}{Normal conditions} & \multicolumn{2}{c|}{Worst conditions} \\ \hline             
             Semiconductors & $u_{max}$ & $i_{max}$ & $u_{max}$ & $i_{max}$ \\ \hline \hline
             $T_1$      & \qquad \si{\volt} & \qquad \si{\ampere} & \qquad \si{\volt} & \qquad \si{\ampere} \\ \hline
             $T_2$      & \qquad \si{\volt} & \qquad \si{\ampere} & \qquad \si{\volt} & \qquad \si{\ampere} \\ \hline
             $D_{rec}$  & \qquad \si{\volt} & \qquad \si{\ampere} & \qquad \si{\volt} &  \qquad \si{\ampere} \\ \hline
             $D_{c,1}$  & \qquad \si{\volt} & \qquad \si{\ampere} & \qquad \si{\volt} &  \qquad \si{\ampere} \\ \hline
             $D_{c,2}$  & \qquad \si{\volt} & \qquad \si{\ampere} & \qquad \si{\volt} &  \qquad \si{\ampere} \\ \hline
        \end{tabular}
        \caption{Currents and voltages for all semiconductor devices in normal and (respective) worst case condition,}
        \label{tab:stresses}
    \end{table}

\subsection{Q14: Semiconductor selection} 
    Based on the obtained values from Q12, select from the offered lists in Tables \ref{Tab:MOSFET} and \ref{Tab:Diode} MOSFET (Metal Oxide Semiconductor Field-Effect Transistor) devices and diodes for your design. For all five, the blocking voltage of the device should be at least 1.5-times your result to provide sufficient safety margin during operation (e.g. overvoltages due to parasitic effects). Elaborate briefly why you chose exactly these models and highlight them in the tables, as it is exemplary done for the first device. Note that due to the low operating voltage, Schottky diodes are offered, and thus reverse recovery is not of concern for the design. All devices are built in a TO-220 case as shown in Fig.~\ref{fig:TO220}.

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}

    \fbox{Upper transistor model No. : \qquad} \quad
    \fbox{Lower transistor model No. : \qquad} \quad 
    \fbox{Rectifying diode model No. : \qquad}\\ \\
    \fbox{Upper clamping diode model No. : \qquad} \quad
    \fbox{Lower clamping diode model No. : \qquad} \quad 
    \hfill
    \fbox{\qquad / 2 pt.}

    \begin{table}[h!]
        \begin{minipage}[t]{0.50\textwidth}
            \caption{The list of offered MOSFET devices. The parameter $U_{ds}$ is the rated drain-source voltage, whereas the $I_{cont}$ stands for continuous drain-source current. All devices are in the TO-220 package (see Fig.~\ref{fig:TO220}).}
            \centering
            \footnotesize
            \label{Tab:MOSFET}
            \begin{tabular}{|l|l|l|l|l|l|}
                \hline
                \textbf{No.} & \textbf{Manufacturer} & \textbf{Product} & \textbf{\begin{tabular}[c]{@{}l@{}}$U_{ds}$ \\ (\si{\volt}) \end{tabular}} & \textbf{\begin{tabular}[c]{@{}l@{}}$I_{cont}$ \\ (\si{\ampere}) \end{tabular}} & \textbf{\begin{tabular}[c]{@{}l@{}}$R_{ds,on}$ @ \SI{25}{\degreeCelsius} \\ (\si{\milli\ohm}) \end{tabular}} \\
                \hline
                \rowcolor{blue!20}
                % \rowcolor highlights the next row!
                1  & Infineon 			& IRFB5620PbF 	& 200 & 18 	 & 60 \\ \hline 
                2  & Rohm               & RCX300N20     & 200 & 16.3 & 60				\\ \hline
                3  & Onsemi             & FDPF18N20FT-G & 200 & 10.8 & 120    \\ \hline
                4  & Rohm               & RCX200N20     & 200 & 10.8 & 100  \\ \hline
                5  & Onsemi             & FQPF630       & 200 & 6.3  & 340    \\ \hline
                6  & Nexperia           & PHP18NQ11T    & 110 & 13   & 80   \\ \hline
                7 & Vishay             & SiHF530       & 100 & 10   & 160    \\ \hline
                8 & ST					& STP16NF06     & 60  & 11   & 80 \\ \hline
            \end{tabular}
            \normalsize
        \end{minipage}
        \hfill
        \begin{minipage}[t]{0.48\textwidth}
            \caption{The list of offered Schottky diode devices. The parameter $U_{dc}$ refers to the maximum dc blocking voltage, whereas $I_{cont}$ is the continuous forward current. All devices are in the TO-220 package (see Fig.~\ref{fig:TO220}).}
            \centering
            \footnotesize
            \label{Tab:Diode}
            \begin{tabular}{|l|l|l|l|l|l|}
                \hline
                \textbf{No.} & \textbf{Manufacturer} & \textbf{Product} & \textbf{\begin{tabular}[c]{@{}l@{}}$U_{dc}$ \\ (\si{\volt}) \end{tabular}} & \textbf{\begin{tabular}[c]{@{}l@{}}$I_{cont}$ \\ (\si{\ampere}) \end{tabular}} & \textbf{\begin{tabular}[c]{@{}l@{}}$U_f$ @ \SI{25}{\degreeCelsius} \\ (\si{\volt}) \end{tabular}} \\
                \hline
                 \rowcolor{green!20} % This here highlights the next row! Use green for the rectifying diode
                1  & Taiwan & MBR16150      & 150 & 16 & 0.95 \\ \hline
                \rowcolor{red!20} % This here highlights the next row! Use red for the clamping diodes
                2  & Taiwan & SRAF10150     & 150 & 10 & 0.95 \\ \hline
                3  & Onsemi & MBR10100G     & 100 & 10 & 0.70  \\ \hline
                4  & ST     & STPS20SM60    & 60  & 20 & 0.57 \\ \hline
                5  & Onsemi & MBR1660       & 60  & 16 & 0.75 \\ \hline
                6  & Vishay & VT3045BP      & 45  & 30 & 0.58 \\ \hline
                7  & Vishay & VFT2045BP     & 45  & 20 & 0.57 \\ \hline
                8 & Vishay & VS-12TQ045-M3 & 45  & 15 & 0.56 \\ \hline
            \end{tabular}
            \normalsize
        \end{minipage}
    \end{table}

    \begin{figure}[h!]
        \centering
        \includegraphics[width=0.4\textwidth]{TO220}
        \caption{A semiconductor in a TO-220 case.}
        \label{fig:TO220}
    \end{figure}

\clearpage

\section{Calculation of current average and rms values}
    To serve as a basis for the loss calculation using simplified models, expressions for average and rms currents have to be derived and calculated. In addition, this also reveals the current condition in a given operating point. The results have to be given with two digits after the decimal point using the given unit.

\subsection{Q15: Transistor current} 
    Consider the current passing through the transistors in the steady state operation of the Flyback converter. Derive an analytical expression for the average current $I_{T,avg}$ and for the rms current $I_{T,rms}$. To make the calculations easier, you can assume pulse-shaped waveforms (e.g. neglecting the output voltage ripple). Provide the results for your converter in table \ref{tab:currents}.

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}
    
    \hfill\fbox{\qquad / 6 pt.}


\subsection{Q16: Rectifying diode current} 
    Consider now the current passing through the rectifying diode in the steady state operation of the Flyback converter. Derive an analytical expression for the average current $I_{D,rec,avg}$ for the rms current $I_{D,rec,rms}$. Also here, the simplifications can be used.

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}

    \hfill    \fbox{\qquad / 6 pt.}

\subsection{Q17: Clamping diode current} 
    Consider again the current passing through the diode. Derive an analytical expression for the rms current during steady state $I_{D,c1,rms}$ with the simplified assumptions.

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}
    \hfill \fbox{\qquad / 4 pt.}

\subsection{Q18: \textsc{Plecs} verification for the current calculations} 
    Using the provided \textsc{Plecs} model, verify your formulas by calculating the values during nominal operation and comparing them with the model output (for nominal operation, in the model \texttt{OP = 1;} has to be selected): 
    \begin{enumerate}[label=\alph*)]
        \item The transistor rms current $\left.I_{T,rms}\right|_{nom}$;
        \item The transistor average current $\left.I_{T,avg}\right|_{nom}$;
        \item The diode rms current $\left.I_{D,rms}\right|_{nom}$;
        \item The diode average current $\left.I_{D,avg}\right|_{nom}$.
    \end{enumerate}

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. } 
        \vspace{2em}
    \end{framed}   
    \hfill \fbox{\qquad / 2 pt.}
    
 \begin{table}
        \centering
        \begin{tabular}{|r||r|r||r|r|}
            \hline
             & \multicolumn{2}{c||}{Calculated} & \multicolumn{2}{c|}{Plecs Model} \\ \hline             
             Semiconductors & $I_{avg}$ & $I_{rms}$ & $I_{avg}$ & $I_{rms}$ \\ \hline \hline
             $T_1$      & \qquad \si{\ampere} & \qquad \si{\ampere} & \qquad \si{\ampere} & \qquad \si{\ampere} \\ \hline
             $T_2$      & \qquad \si{\ampere} & \qquad \si{\ampere} & \qquad \si{\ampere} & \qquad \si{\ampere} \\ \hline
             $D_{rec}$  & \qquad \si{\ampere} & \qquad \si{\ampere} & \qquad \si{\ampere} &  \qquad \si{\ampere} \\ \hline
             $D_{c,1}$  & \qquad \si{\ampere} & \qquad \si{\ampere} & \qquad \si{\ampere} &  \qquad \si{\ampere} \\ \hline
             $D_{c,2}$  & \qquad \si{\ampere} & \qquad \si{\ampere} & \qquad \si{\ampere} &  \qquad \si{\ampere} \\ \hline
        \end{tabular}
        \caption{Currents and voltages for all semiconductor devices in normal and (respective) worst case condition,}
        \label{tab:currents}
    \end{table}

\clearpage


\section{Thermal Design based on the expected semiconductor losses}

    Based on your previously calculated results, losses in the semiconductors for normal operation condition will be calculated. These results will be compared with the results of the provided Loss Tool in \textsc{Matlab}. Results from the Loss Tool will also be used to select appropriate heatsinks for your design. As in the other questions, results should be given with two digits after the decimal point in the unit indicated by the answer.

\subsection{Q19: Rectifying Diode conduction losses} 
    Using the datasheet of your selected diode as well as the results from your calculations, calculate the conduction losses of your diode at steady state operation with nominal data $\left.P_{D,cond}\right|_{nom}$. Note that the datasheet values may not be at the temperature your diode will operate, which is assumed to be \SI{125}{\degreeCelsius}. The provided Application Notes of \textsc{Infineon} may serve you as a guideline for this calculation.

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}

    \fbox{$\left.P_{D,rec,cond}\right|_{nom}\ = $ \qquad \si{\watt}} \hfill
    \fbox{\qquad / 4 pt.}

\subsection{Q20: Transistor conduction losses} 
    Using the datasheet of your selected transistor as well as the results from your calculations, calculate the conduction losses for one of your transistors at steady state operation with nominal data $\left.P_{T,cond}\right|_{nom}$. Identical to the diode, the transistor operates at a temperature of \SI{125}{\degreeCelsius} (for temperature scaling, follow the instructions of the provided \textsc{Infineon} Application Note and/or the figures provided in the datasheet).

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. }
        \vspace{2em}
    \end{framed}

    \fbox{$\left.P_{T,cond}\right|_{nom}\ = $ \qquad \si{\watt}} \hfill
    \fbox{\qquad / 4 pt.}

\subsection{Q21: Transistor switching losses} 
    Calculate the switching losses for one of your transistors at steady state operation with nominal data $\left.P_{T,sw}\right|_{nom}$. Here not the temperature, but the proper scaling of the switching times and electrical values is crucial, for which the procedure can be found again in the provided \textsc{Infineon} Application Notes.

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. } 
        \vspace{2em}
    \end{framed}
    
    \fbox{$\left.P_{T,sw}\right|_{nom}\ =$ \qquad \si{\watt}} \hfill
    \fbox{\qquad / 6 pt.}

\subsection{Q22: Comparison with the Loss Tool} 
   Use the Loss Tool to calculate the semiconductor losses in detail for the nominal operation point and compare them to your results. Comment deviations in case they appear.
   \underline{Read the comments in the code carefully to obtain valid results!}

    \begin{framed}
        \vspace{2em}
        \textbf{A dummy figure is given below, exchange it with the one you obtained in \textsc{Matlab}. \\ Delete this before writing anything. }
        \begin{center}
	       \includegraphics[width=0.85\textwidth]{gfx/LossToolDummy}
            \captionof{figure}{Semiconductor power losses and efficiencies achieved for different operating points.}
            \label{fig:Min_input}
        \end{center}
        \vspace{2em}
    \end{framed}

  \hfill\fbox{\qquad / 3 pt.}

\subsection{Q23: Efficiency} 
    Calculate the efficiency of your Flyback converter in nominal operation $\left.\eta\right|_{nom}$, when only semiconductor losses are considered. Please note that there will be other losses in your converter that will appear during the design. Nevertheless, semiconductor losses are a good indication of the overall converter performance.

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. } 
        \vspace{2em}
    \end{framed}

    \fbox{$\left.\eta\right|_{nom}$ = \qquad} \hfill\fbox{\qquad / 3 pt.}

\subsection{Q24: Loss tool} 
    Use the provided Loss Tool to investigate the semiconductor losses for a set of different values of $U_{in}$ and $P_{out}$. Comment on how the efficiency changes for the different operating points.

    \begin{framed}
        \vspace{2em}
        \textbf{A dummy figure is given below, exchange it with the one you obtained in \textsc{Matlab}. \\ Delete this before writing anything. }
        \begin{center}
	       \includegraphics[width=0.85\textwidth]{gfx/LossToolDummy}
            \captionof{figure}{Semiconductor power losses and efficiencies achieved for different operating points.}
            \label{fig:Min_input}
        \end{center}
    \end{framed}

\hfill\fbox{\qquad / 2 pt.}

\subsection{Q25: Transistor heatsink} 
    To choose a proper heatsink, answer the following questions. For the calculations, assume a maximum ambient temperature of $\vartheta_a=\SI{40}{\degreeCelsius}$, whereas the semiconductor junction temperature should not exceed $\vartheta_j=\SI{125}{\degreeCelsius}$. Please note that there is already a thermal resistance from the junction to the case of the semiconductor.:
    \begin{enumerate}[label=\alph*)]
        \item Considering the output of the previous question, determine the worst case operation condition for the transistor in terms of power losses $\left.P_{T}\right|_{wc}$. 
        \item Calculate the maximum allowed thermal resistance $R_{th,T,j-a}$ (where $_{c-a}$ indicates junction to ambient).
        \item Based on b), choose a heatsink from the selection provided in Table~\ref{tab:HS}, they are also presented graphically in Fig.~\ref{fig:Heatsinks} (all images from the manufacturer websites). Elaborate briefly on your choice. Don't forget to highlight your selection in \colorbox{blue!20}{blue}.
    \end{enumerate}

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. } 
        \vspace{2em}
    \end{framed}

    \fbox{$\left.P_{T1}\right|_{wc}\ =$ \qquad \si{\watt}} \quad 
    \fbox{$R_{th,T1,j-a}\ =$ \qquad \si{\kelvin\per\watt}} \quad 
    \fbox{T1 heatsink model No. : \qquad} \hfill \\
    \fbox{$\left.P_{T2}\right|_{wc}\ =$ \qquad \si{\watt}} \quad 
    \fbox{$R_{th,T2,j-a}\ =$ \qquad \si{\kelvin\per\watt}} \quad 
    \fbox{T2 heatsink model No. : \qquad} \hfill
    \fbox{\qquad / 3 pt.}

\subsection{Q26: Rectifying diode heatsink} 
    Similar to the transistor, a diode heatsink has to be selected. Assuming the same thermal constraints, answer the following questions:
    \begin{enumerate}[label=\alph*)]
        \item Considering the output of the Loss Tool, determine the worst case operation condition for the diode in terms of losses $\left.P_D\right|_{wc}$. 
        \item Calculate the maximum allowed thermal resistance $R_{th,D,rec,j-a}$.
        \item Select a suitable heatsink from the selection provided in Table~\ref{tab:HS} (highlight in \colorbox{green!20}{green}) Elaborate briefly on your choice..
    \end{enumerate}

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. } 
        \vspace{2em}
    \end{framed}

    \fbox{$\left.P_D\right|_{wc}\ =$ \qquad} \quad 
    \fbox{$R_{th,D,rec,j-a}\ =$ \qquad \si{\kelvin\per\watt}} \quad 
    \fbox{Diode heatsink model No. : \qquad} \hfill
    \fbox{\qquad / 3 pt.}

\subsection{Q27: Clamping diode heatsink} 
    Also the cooling for the clamping diode needs to be assessed. Assuming the same thermal constraints, answer the following questions:
    \begin{enumerate}[label=\alph*)]
        \item Considering the output of the Loss Tool, determine the worst case operation condition for the diode in terms of losses $\left.P_D\right|_{wc}$. 
        \item Calculate the maximum allowed thermal resistance $R_{th,D,C,j-a}$.
        \item Select a suitable cooling option. Provide an explanation for your choice.
    \end{enumerate}

    \begin{framed}
        \vspace{2em}
        \textbf{Please write your answer inside the frame. Be concise and punctual. Keep it simple and short. \\ Delete this before writing anything. } 
        \vspace{2em}
    \end{framed}

    \fbox{$\left.P_D\right|_{wc}\ =$ \qquad} \quad 
    \fbox{$R_{th,D,C1,j-a}\ =$ \qquad \si{\kelvin\per\watt}} \quad 
    \fbox{Diode $D_{C1}$ heatsink model No. : \qquad} \hfill \\
    \fbox{$\left.P_D\right|_{wc}\ =$ \qquad} \quad 
    \fbox{$R_{th,D,C1,j-a}\ =$ \qquad \si{\kelvin\per\watt}} \quad 
    \fbox{Diode $D_{C2}$ heatsink model No. : \qquad} \hfill
    \fbox{\qquad / 3 pt.}

    \begin{table}[h!]
        \caption{List of the offered heatsinks.}
        \centering
        \label{tab:HS}
        \begin{tabular}{|l|l|l|l|l|}
            \hline
            \textbf{No.} & \textbf{Manufacturer} & \textbf{Product} & \textbf{$R_{th}$ (\si{\kelvin\per\watt})} & \textbf{Figure} \\ \hline
            1 & Ohmite                & FA-T220-64E      & 3.00     & \ref{subfig:Ohmite-FA}              \\ \hline
            2 & Ohmite                & FA-T220-25E      & 4.70     & \ref{subfig:Ohmite-FA}                   \\ \hline
            3 & Ohmite                & EA-T220-51E      & 7.50     & \ref{subfig:Ohmite-EA}                   \\ \hline
            4 & Ohmite                & EA-T220-38E      & 10.40    & \ref{subfig:Ohmite-EA}                  \\ \hline
            5 & Wakefield-Vette       & 265-118ABHE-22   & 14.00    & \ref{subfig:Wakefield-265}                  \\ \hline
            6 & Ohmite                & E2A-T220-25E     & 16.40    & \ref{subfig:Ohmite-E2A}                  \\ \hline
            7 & Wakefield-Vette       & OMNI-220-18-25-1C  & 24     & \ref{subfig:WV-OMNI-1C}                       \\ \hline
            8 & Wakefield-Vette       & OMNI-220-18-50-2C  & 12     & \ref{subfig:WV-OMNI-2C}                       \\ \hline
            9 & Wakefield-Vette       & OMNI-220-18-75-3C  & 8      & \ref{subfig:WV-OMNI-3C}                       \\ \hline
        \end{tabular}
    \end{table}

    \begin{figure}[h!]
        \centering
        \begin{subfigure}[b]{0.2\textwidth}
            \centering
            \includegraphics[height=32mm]{Ohmite-FA.jpg}
            \caption{Ohmite FA-T220-xxE}
            \label{subfig:Ohmite-FA}
        \end{subfigure}
        \hfill
        \begin{subfigure}[b]{0.2\textwidth}
            \centering
            \includegraphics[height=32mm]{Ohmite-EA.jpg}
            \caption{Ohmite EA-T220-xxE}
            \label{subfig:Ohmite-EA}
        \end{subfigure}
        \hfill
        \begin{subfigure}[b]{0.2\textwidth}
	       \centering
	       \includegraphics[height=32mm]{Wakefield-265.jpg}
	       \caption{Wakefield 265-118ABHE-xx}
	       \label{subfig:Wakefield-265}
        \end{subfigure}
        \hfill
        \begin{subfigure}[b]{0.18\textwidth}
	       \centering
	       \includegraphics[height=32mm]{Ohmite-E2A.jpg}
	       \caption{Ohmite E2A-T220-xxE}
	       \label{subfig:Ohmite-E2A}
        \end{subfigure}
        %\caption{The heatsinks with screw mechanism.}
        \hfill \\
        \begin{subfigure}[b]{0.22\textwidth}
	       \centering
	       \includegraphics[height=38mm]{gfx/Wakefield_OMNI-220-18-25-1C.jpg}
	       \caption{Wakefield OMNI 220 18 25 1C}
	       \label{subfig:WV-OMNI-1C}
        \end{subfigure}
        \begin{subfigure}[b]{0.22\textwidth}
	       \centering
	       \includegraphics[height=38mm]{gfx/Wakefield_OMNI-220-18-50-2C.jpg}
	       \caption{Wakefield OMNI 220 18 50 2C}
	       \label{subfig:WV-OMNI-2C}
        \end{subfigure}
        \begin{subfigure}[b]{0.22\textwidth}
	       \centering
	       \includegraphics[height=38mm]{gfx/Wakefield_OMNI-220-18-75-3C.jpg}
	       \caption{Wakefield OMNI 220 18 75 3C}
	       \label{subfig:WV-OMNI-3C}
        \end{subfigure}
        \caption{The available heatsinks.}
        \label{fig:Heatsinks}
    \end{figure}

\newpage

\section{Report 1 Summary}
    Fill out the table below with your results as well as your chosen devices:

    \begin{framed}
        \begin{center}
            \label{Tab:Specs_calculated}
            \captionof{table}{Calculated parameter values, selected components and efficiency.}
            \begin{tabular}{|l|l|l|}
                \hline
                \textbf{Property} & \textbf{Value} & \textbf{Unit} \\
                \hline
                $N$ &  & --- \\ \hline
			    $\left.D\right|_{U_{in,nom}}$ &  & --- \\ \hline
			    $L_m$ &  & \si{\micro\henry} \\ \hline
			    $C_{out}$ &  & \si{\micro\farad} \\ \hline
    			$C_{in}$ &  & \si{\micro\farad} \\ \hline
    			Switch no. &  & --- \\ \hline
    			Diode no. &  & --- \\ \hline
    			$\left.\eta\right|_{U_{in,nom}}$ &  & --- \\ \hline
    			Switch heatsink no. &  & --- \\ \hline
    			Diode heatsink no. &  & --- \\ \hline
            \end{tabular}
        \end{center}
    \end{framed}
    \hfill\fbox{\textbf{Total: \qquad\quad / 100 pt.}}


\end{document}