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corr of ex03
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wallscheid committed Nov 22, 2024
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2 changes: 1 addition & 1 deletion exercise/fig/ex02/Fig_ECDTeTa.tex
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\end{circuitikz}
\end{tabular}
\caption{ECD of the boost converter for different switching states.}
\label{fig:switching_states_step-down_converter}
\label{fig:switching_states_step-down_converter-Ex02}
\end{solutionfigure}
6 changes: 3 additions & 3 deletions exercise/fig/ex03/Fig_courseILminmaxOutputPower.tex
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major grid style={line width=.2pt,draw=gray!50},
minor grid style={line width=.1pt,draw=gray!20},
xlabel={$t$ / µs},
ylabel={$i_\mathrm{L}(\mathrm{2~W})$ / A},
ylabel={$i_\mathrm{L}(P_2=\SI{2}{\watt})$ / A},
title={$i_\mathrm{L}$ for minimum output power},
xmin=0, xmax=14,
ymin=0, ymax=0.6,
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major grid style={line width=.2pt,draw=gray!50},
minor grid style={line width=.1pt,draw=gray!20},
xlabel={$t$ / µs},
ylabel={$i_\mathrm{L}(\mathrm{15~W})$ / A},
ylabel={$i_\mathrm{L}(P_2=\SI{15}{\watt})$ / A},
title={$i_\mathrm{L}$ for maximum output power},
xmin=0, xmax=100,
ymin=0, ymax=5,
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};
\end{axis}
\end{tikzpicture}
\caption{Display of the current $i_\mathrm{L}$ for minimum and maximum output power.}
\caption{Current $i_\mathrm{L}$ for minimum and maximum output power.}
\label{fig:InductorCurrentEx03}
\end{solutionfigure}
2 changes: 1 addition & 1 deletion exercise/fig/ex03/sFigTab_PowerminSepic.tex
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\end{tabular}
\caption{Minimal necessary power of SEPIC topology for CCM mode.}
\label{table:PowerminSepic}
\end{solutiontable}
\end{solutiontable}%

2 changes: 1 addition & 1 deletion exercise/tex/exercise02.tex
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\begin{solutionblock}
\input{./fig/ex02/Fig_ECDTeTa.tex}
The equivalent circuit diagram (ECD) is shown in \autoref{fig:switching_states_step-down_converter}.
The equivalent circuit diagram (ECD) is shown in \autoref{fig:switching_states_step-down_converter-Ex02}.
As there are no losses at the transistor, the voltage $U_{\mathrm{1}}$ is equal to $u_{\mathrm{L}}$ for the switch-on period $T_{\mathrm{on}}$ and is defined as
\begin{equation}
U_{\mathrm{1}} = \overline u_{\mathrm{L}} = L \frac{\Delta i_{\mathrm{L}} }{\Delta t}.
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27 changes: 12 additions & 15 deletions exercise/tex/exercise03.tex
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\end{equation}
The previously obtained maximum and minimum switching frequencies lead to:
\begin{equation}
T_\mathrm{s}(P_\mathrm{2}=\SI{2}{\watt}) =\frac{1}{f_{\mathrm{s,2W}}} = \frac{1}{\SI{150}{\kilo \hertz}}= \SI{6.67}{\micro \s},
T_\mathrm{s}(P_\mathrm{2}=\SI{2}{\watt}) = \frac{1}{\SI{150}{\kilo \hertz}}= \SI{6.67}{\micro \s},
\end{equation}
\begin{equation}
T_\mathrm{s}(P_\mathrm{2}=\SI{15}{\watt}) =\frac{1}{f_{\mathrm{s,15W}}} = \frac{1}{\SI{20}{\kilo \hertz}}= \SI{50}{\micro \s}.
T_\mathrm{s}(P_\mathrm{2}=\SI{15}{\watt}) = \frac{1}{\SI{20}{\kilo \hertz}}= \SI{50}{\micro \s}.
\end{equation}
The transistor switch-on times can be determined using
\begin{equation}
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The relationship between the voltage ripple and the capacitance is identical to the step-up converter, which is defined as:
\begin{equation}
\Delta u_{\mathrm{C}} = \frac{I_2}{C} D T_{\mathrm{s}},
\Delta u_{\mathrm{C}} = \frac{I_2}{C} D T_{\mathrm{s}}.
\end{equation}
applying for the maximum power ($P = \SI{15}{\watt}$) results into:
Considering the maximum power ($P_2 = \SI{15}{\watt}$) results into:
\begin{equation}
C_2 = \frac{I_{\mathrm{2}}(P_\mathrm{2}=\SI{15}{\watt}) D T_{\mathrm{s}}(P_\mathrm{2}=\SI{15}{\watt})}{\Delta u_{\mathrm{C}}}
= \frac{\SI{1.25}{\ampere} \cdot 0.4 \cdot \SI{50}{\micro\second}}{\SI{0.24}{\volt}}
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\label{eq:U2}
\end{equation}
where the diode voltage is assumed to be zero during the conduction phase.
Hence, the maximum blocking voltage of the transistor is calculated with \eqref{eq:U2} and \eqref{eq:uT}, which results in:
Hence, the maximum blocking voltage of the transistor is calculated with \eqref{eq:uT} and \eqref{eq:U2}, which results in:
\begin{equation}
u_{\mathrm{T}} = U_1 - (-U_2)
= U_1 + U_2 = \SI{18}{\volt} + \SI{12}{\volt} = \SI{30}{\volt}.
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For the boost-buck converter the voltage transfer ratio delivers:
\begin{equation}
\frac{U_\mathrm{2}}{U_\mathrm{1}} = \frac{D} {1-D}
\hspace{1cm} \Rightarrow \hspace{1cm}
\quad \Leftrightarrow \quad
D = \frac{\frac{U_\mathrm{2}}{U_\mathrm{1}}} {1+{\frac{U_\mathrm{2}}{U_\mathrm{1}}}}.
\label{eq:DutyCycleEx03}
\end{equation}
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of $\SI{285}{\volt}$, the intermediate circuit voltage $U_\mathrm{0}$ is calculated as
\begin{equation}
U_\mathrm{0}=U_\mathrm{1} \frac{1}{1-D}
\hspace{1cm} \Rightarrow \hspace{1cm}
=
\SI{380}{\volt} \frac{1}{1-0.429} = \SI{665}{\volt}.
\label{eq:DCLinkEx03}
\end{equation}
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\begin{solutionblock}
% Solution
Here \eqref{eq:DutyCycleEx03} and \eqref{eq:DCLinkEx03} are used to calculate results summarized in \autoref{table:DutyCycleDCLinkVoltageAtOutputVoltage}
Here, \eqref{eq:DutyCycleEx03} and \eqref{eq:DCLinkEx03} are used to calculate results summarized in \autoref{table:DutyCycleDCLinkVoltageAtOutputVoltage}
and displayed in \autoref{fig:DCLinkVoltageAtOutputVoltage} and \autoref{fig:DutyCycleAtOutputVoltage}.

%Result table
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\begin{solutionblock}
% Solution
Based on the schematic \autoref{fig:ex03_boost_buck_converter} following voltages are applied to the semiconductor components.
Based on the schematic from \autoref{fig:ex03_boost_buck_converter}, following voltage ratings of the semiconductor components can be derived:
\begin{itemize}
\item Reverse voltage across $D_1$: In case of $T_1$ is active, the potential at the T$T_1$'s drain is pulled down.
The diode $D_1$ hat to block $U_0$.
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$U_\mathrm{C}$ corresponds to the input voltage $U_\mathrm{1}$, because the voltage transfer ratio of the SEPIC-topology
is calculated by:
\begin{equation}
\frac{U_\mathrm{2}}{U_\mathrm{1}}= \frac{D}{1-D} \Rightarrow
\frac{U_\mathrm{2}}{U_\mathrm{1}}= \frac{D}{1-D} \quad \Leftrightarrow \quad
U_\mathrm{1}=\frac{1-D}{D}U_\mathrm{2}=\left( \frac{1}{D}-1\right)U_\mathrm{2}=U_\mathrm{C}
\end{equation}
The result shows, that the transistor and the diode needs to block the sum of input and output voltage,
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P_\mathrm{min}=U_\mathrm{1}\frac{\Delta i_\mathrm{L1}}{2}D.
\label{eq:PowerL1ripplesepic}
\end{equation}
Entering the values in \eqref{eq:PowerL1ripplesepic} leads to \autoref{table:PowerminSepic}.
%Solution table Minimal Power
\input{./fig/ex03/sFigTab_PowerminSepic}
The minimal power, which ensures continuous operation across the entire output voltage range
yields $\SI{849}{\watt}$.
\input{./fig/ex03/sFigTab_PowerminSepic} %Solution table Minimal Power
Entering the values in \eqref{eq:PowerL1ripplesepic} leads to \autoref{table:PowerminSepic}. The minimal power, which ensures continuous operation across the entire output voltage range yields $\SI{849}{\watt}$.

\end{solutionblock}

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