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more minor typo mistakes
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wallscheid committed Feb 2, 2025
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2 changes: 1 addition & 1 deletion exercise/fig/ex04/Fig_currentI1I2PeriodTask1.tex
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Expand Up @@ -49,6 +49,6 @@
};
\end{axis}
\end{tikzpicture}
\caption{Display of the current $i_\mathrm{1}(t)$.}
\caption{Input and output currents.}
\label{fig:currentSecondarySideTask1}
\end{solutionfigure}
2 changes: 1 addition & 1 deletion exercise/fig/ex04/Fig_voltageTransistorUsPeriodTask1.tex
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Expand Up @@ -49,7 +49,7 @@
};
\end{axis}
\end{tikzpicture}
\caption{Display of the voltage $u_\mathrm{T}(t)$ and $u_\mathrm{s}(t)$.}
\caption{Display of the voltages $u_\mathrm{T}(t)$ and $u_\mathrm{s}(t)$.}
\label{fig:voltageTransistorPeriodTask1}


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Expand Up @@ -59,7 +59,7 @@
\node[black, fill=white, inner sep = 1pt, anchor = south] at (axis cs:0.55,200) {$U_{\mathrm{1}}=\SI{240}{\volt}$};
\end{axis}
\end{tikzpicture}
\caption{Voltage at transistor.}
\caption{Voltage at the transistor.}
\label{fig:ex04_VoltageAtTransistor}
\begin{tikzpicture}
\begin{axis}[
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14 changes: 7 additions & 7 deletions exercise/tex/exercise04.tex
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Expand Up @@ -65,17 +65,17 @@

\end{solutionblock}

\subtask{The input voltage is $U_\mathrm{1}=\SI{382}{\volt}$ at nominal load. Calculate and sketch the following voltage and current curves for this operating points over two cycle periods: $u_\mathrm{T}(t), u_\mathrm{s}(t), i_\mathrm{2}(t), i_\mathrm{1}(t)$. Here, $u_\mathrm{T}(t)$ is the transistor voltage and $u_\mathrm{s}(t)$ is the voltage on the secondary side of the transformer.}
\subtask{The input voltage is $U_\mathrm{1}=\SI{382}{\volt}$ at nominal load. Calculate and sketch the following voltage and current curves for this operating point over two cycle periods: $u_\mathrm{T}(t), u_\mathrm{s}(t), i_\mathrm{2}(t), i_\mathrm{1}(t)$. Here, $u_\mathrm{T}(t)$ is the transistor voltage and $u_\mathrm{s}(t)$ is the voltage on the secondary side of the transformer.}

\begin{solutionblock}
Because of a different input voltage, the duty cycle $D$ has changed:
Because of the different input voltage, the duty cycle $D$ has changed:
\begin{equation}
\Delta i_\mathrm{m,max}= \frac{T_\mathrm{s} \cdot U_1}{L_\mathrm{m}} = \frac{\frac{1}{\SI{50}{\kilo\hertz}}\cdot \SI{382}{\volt}}{\SI{760}{\micro\henry}}=\SI{10.05}{\ampere}.
\end{equation}
\begin{equation}
D = \sqrt{\frac{2U_2\overline{i}_2}{U_1\Delta i_\mathrm{m,max}}} = \sqrt{\frac{2\cdot \SI{15}{\volt}\cdot\SI{30}{\watt}}{\SI{382}{\volt}\cdot\SI{15}{\volt}\cdot\SI{10.05}{\ampere}}} = 0.125.
\end{equation}
Trough this result $T_\mathrm{on}$ can be calculated as:
Based on this result, $T_\mathrm{on}$ can be calculated as:
\begin{equation}
T_\mathrm{on} = D T_\mathrm{s} = 0.125 \cdot \frac{1}{\SI{50}{\kilo\hertz}} = \SI {2.5}{\micro\s}.
\end{equation}
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u_\mathrm{T} = \SI{382}{\volt} + \frac{60}{12}\cdot\SI{15}{\volt} = \SI{457}{\volt}.
\end{equation}
Because of the conducting diode, for the voltage $U_\mathrm{2}$ is following $U_\mathrm{2} = u_\mathrm{s} = \SI{15}{\volt}$.
The third interval is $T_\mathrm{on}+T'_\mathrm{off}$ < t < $T_\mathrm{s}$. In this interval the diode is not conducting and the transistor blocks. From this follows $u_\mathrm{T} = U_1$ and $u_\mathrm{s}=0$.
The third interval is $T_\mathrm{on}+T'_\mathrm{off} < t < T_\mathrm{s}$. In this interval the diode is not conducting and the transistor blocks. From this follows $u_\mathrm{T} = U_1$ and $u_\mathrm{s}=0$.
Looking at the current $i_\mathrm{1}(t)$ over the entire course, the current can only be present when the transistor is switched on. When the transistor is switched on, the current value rises to the peak value $\hat i_\mathrm{1}= \SI{1.257}{\ampere}$. Current $i_\mathrm{2}(t)$ is the discharge current of the secondary winding when the diode is conducting and the transistor blocks. The discharge current starts at the peak value of the secondary side $\hat i_\mathrm{2}= \SI{6.28}{\ampere}$.
\input{./fig/ex04/Fig_voltageTransistorUsPeriodTask1.tex}
\input{./fig/ex04/Fig_currentI1I2PeriodTask1.tex}
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\subtask{Calculate the peak value $\hat{i}_\mathrm{m}$ of the magnetizing current $i_\mathrm{m}$.}
\begin{solutionblock}
The duty cycle is less than $0.5$, i.e. the magnetizing current $i_\mathrm{m}$ increase
The duty cycle is less than $0.5$, i.e., the magnetizing current $i_\mathrm{m}$ increase
while the transistors are active and decrease to $\SI{0}{\ampere}$ before the next period starts.
This means that
This leads to
\begin{equation}
\hat{i}_\mathrm{m}=\Delta i_\mathrm{m,max}= \frac{D \cdot U_\mathrm{1}}{L_\mathrm{m} \cdot f_\mathrm{s}} =
\frac{0.4615 \cdot \SI{325}{\volt}}{\SI{2}{\milli\henry} \cdot \SI{50}{\kilo\hertz}} = \SI{1.5}{\ampere}.
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I_\mathrm{2}=P_\mathrm{2}/U_\mathrm{2}=\frac{\SI{125}{\watt}}{\SI{5}{\volt}}=\SI{25}{\ampere}
\label{eq:ex04ouputcurrent}.
\end{equation}
This is corresponds to the current at the primary side of
This corresponds to the current at the primary side of
\begin{equation}
I_\mathrm{2s}'=I_\mathrm{2}\frac{N_\mathrm{2}}{N_\mathrm{1}}.
\end{equation}
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2 changes: 1 addition & 1 deletion lecture/main.ist
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@@ -1,5 +1,5 @@
% makeindex style file created by the glossaries package
% for document 'main' on 2025-1-28
% for document 'main' on 2025-2-2
actual '?'
encap '|'
level '!'
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5 changes: 3 additions & 2 deletions lecture/tex/Lecture03.tex
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Expand Up @@ -1197,6 +1197,7 @@ \subsection{Forward converter}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Forward converter: demagnetization via negative input voltage}
\vspace{-0.25cm}
\begin{figure}
\begin{circuitikz}[]
%Asym. half-bridge
Expand All @@ -1216,7 +1217,7 @@ \subsection{Forward converter}
to [short, -o] (B)
(F) to [short,*-] ++(1,0) coordinate (I)
to [short] ++(1,0) coordinate (H)
(J) to [open,v^= $u_\mathrm{p}(t)\hspace{1.6cm}$, voltage = straight] (I);
(J) to [open,v_= $u_\mathrm{p}(t)\hspace{0.5cm}$, voltage = straight] (I);
\draw let \p1 = (npn1.B) in node[anchor=east] at (\x1,\y1) {$T_1$};
\draw let \p1 = (npn2.B) in node[anchor=east] at (\x1,\y1) {$T_2$};

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to [short, -o] (B)
(F) to [short,*-] ++(1,0) coordinate (I)
to [short] ++(1,0) coordinate (H)
(J) to [open,v^= $u_\mathrm{p}(t)\hspace{1.6cm}$, voltage = straight] (I);
(J) to [open,v_= $u_\mathrm{p}(t)\hspace{0.5cm}$, voltage = straight] (I);
\draw let \p1 = (npn1.B) in node[anchor=east] at (\x1,\y1) {$T_1$};
\draw let \p1 = (npn2.B) in node[anchor=east] at (\x1,\y1) {$T_2$};
\draw let \p1 = (npn3.B) in node[anchor=east] at (\x1,\y1) {$T_3$};
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