diff --git a/exercise/fig/ex02/Fig_diode_switchOff.tex b/exercise/fig/ex02/Fig_diode_switchOff.tex new file mode 100644 index 0000000..427ad4c --- /dev/null +++ b/exercise/fig/ex02/Fig_diode_switchOff.tex @@ -0,0 +1,62 @@ +\begin{figure}[htb] + \centering + \begin{tikzpicture} + \tikzmath{ + real = \t0, \t1, \t2 \x1; + \x1 = 3; + \t1 = 6; + \t2 = 8; + \t0 = (\t1-\x1)/0.71; + } + \begin{axis}[ + xlabel={$t$}, + axis lines=middle, + ymin=-1.5, ymax=1.2, + xmin=0, xmax=10, + xtick={\t0,\t1,\t2}, + xticklabels={$t_0$,$t_1$,$t_2$}, + ticklabel style ={yshift=0.2cm,anchor=south}, + yticklabels={}, + width=12cm, + height=5cm, + thick, + smooth, + no markers, + grid + ] + \draw[white,pattern=north east lines, pattern color=signalorange] (\t0,0) -- (\t1,-1) -- (\t1,0); + % + \node[signalorange, fill=white, inner sep = 1pt, anchor = south] at (axis cs:\t0+1.3,-0.45) {$Q_1$}; + % + \draw[white,pattern=north west lines, pattern color=signalgreen] (\t1,0) -- (\t1,-1) -- (\t2,0); + % + \node[signalgreen, fill=white, inner sep = 1pt, anchor = south] at (axis cs:\t1+0.6,-0.45) {$Q_2$}; + % + \draw[thick,signalred] (0,0.7) -- (\x1,0.7) -- (\t1,-1) -- (\t2,0); + % + \node[signalred, fill=white, inner sep = 1pt, anchor = south] at (axis cs:2,0.8) {$i_{\mathrm{D}}$}; + % + \draw[thin, signalred] (3.5,0.6) -- (4,0.7); + \node[signalred, fill=white, inner sep = 1pt, anchor = south] at (axis cs:4.5,0.55) {$\frac{\mathrm{d}i_{\mathrm{D}}}{\mathrm{d}t}$}; + % + \draw[thin, signalred] (7,-0.6) -- (7.8,-0.85); + \node[signalred, fill=white, inner sep = 1pt, anchor = south] at (axis cs:8,-1) {$\frac{\mathrm{d}i_{\mathrm{rr}}}{\mathrm{d}t}$}; + % + \draw[thin, signalred] (\t1-0.05,-1.02) -- (\t1-0.3,-1.2); + % + \node[signalred, inner sep = 1pt, anchor = south] at (axis cs:\t1-0.4,-1.45) {$\hat{i}_{\mathrm{rr}}$}; + % + \node[black, fill=white, inner sep = 1pt, anchor = south] at (axis cs:2,-0.7) {$Q_{\mathrm{rr}} = Q_{1} + Q_{2}$}; + % + \draw[thick, signalblue, dashed] (0,0.1) -- (\t0,0.1) -- (\t0,-0.1) -- (\t1,-0.1) -- (\t1,-1.3) -- (\t2,-1.3) -- (\t2,-1) -- (10,-1); + % + \draw[thin, signalblue] (8.1, -1.3) -- (8.5,-1.3); + % + \node[signalblue, fill=white, inner sep = 1pt, anchor = south] at (axis cs:8.8,-1.5) {${U}_{\mathrm{RB}}$}; + % + \node[signalblue, fill=white, inner sep = 1pt, anchor = south] at (axis cs:2,0.15) {${u}_{\mathrm{D}}$}; + \end{axis} + \end{tikzpicture} + \caption{Turn-off behavior of a fast silicon diode.} + \label{fig:TurnOffSiliconDiode} +\end{figure} \ No newline at end of file diff --git a/exercise/fig/ex02/sFig_boost_voltage_efficiency.tex b/exercise/fig/ex02/sFig_boost_voltage_efficiency.tex new file mode 100644 index 0000000..adb2238 --- /dev/null +++ b/exercise/fig/ex02/sFig_boost_voltage_efficiency.tex @@ -0,0 +1,58 @@ +\begin{solutionfigure}[htb] + \centering + \begin{subfigure}{0.45\textwidth} + \centering + \begin{tikzpicture} + \begin{axis}[ + xlabel={$D$}, + ylabel={$U_{\mathrm{1}}/U_{\mathrm{2}}$}, + axis lines=left, + ymin=0, ymax=10, + xmin=0, xmax=1, + xtick={0,0.2,0.4,0.6,0.8,1.0}, + ytick={0,1,2,3,4,5,6,7,8,9,10}, + xticklabels={0,0.2,0.4,0.6,0.8,1.0}, + yticklabels={0,1,2,3,4,5,6,7,8,9,10}, + thick, + smooth, + no markers, + height=7cm, + width = 0.99\textwidth, + grid + ] + \addplot[signalblue, domain=0:0.95] {(1-x)/((1-x)^2)}; + \node[signalblue, fill=white, inner sep = 1pt, anchor = south] at (axis cs:0.5,8) {ideal function}; + \addplot[signalred, domain=0:1.0] {(1-x)/((1-x)^2+0.2/30)}; + \node[signalred, fill=white, inner sep = 1pt, anchor = south] at (axis cs:0.5,7) {function with losses}; + \end{axis} + \end{tikzpicture} + \end{subfigure}% + \begin{subfigure}{0.45\textwidth} + \begin{tikzpicture} + \begin{axis}[ + xlabel={$D$}, + ylabel={$\eta$}, + axis lines=left, + ymin=0, ymax=1.1, + xmin=0, xmax=1, + xtick={0,0.2,0.4,0.6,0.8,1.0}, + ytick={0,0.2,0.4,0.6,0.8,1.0}, + xticklabels={0,0.2,0.4,0.6,0.8,1.0}, + yticklabels={0,0.2,0.4,0.6,0.8,1.0}, + thick, + smooth, + no markers, + height=7cm, + width = 0.99\textwidth, + grid + ] + \addplot[signalblue, domain=0:1] {1}; + \node[signalblue, fill=white, inner sep = 1pt, anchor = south] at (axis cs:0.5,0.4) {ideal function}; + \addplot[signalred, domain=0:1] {1/(1+(0.2/30)/(1-x)^2)}; + \node[signalred, fill=white, inner sep = 1pt, anchor = south] at (axis cs:0.5,0.3) {function with losses}; + \end{axis} + \end{tikzpicture} + \end{subfigure} + \caption{Voltage ratio (on the left) and the efficiency function (on the right) are visualized. Both functions are dependant on the duty cycle $D$.} + \label{fig:voltageRatioAndEfficiency} +\end{solutionfigure} \ No newline at end of file diff --git a/exercise/fig/ex02/sFig_diode_sw_off_esb.tex b/exercise/fig/ex02/sFig_diode_sw_off_esb.tex new file mode 100644 index 0000000..2764722 --- /dev/null +++ b/exercise/fig/ex02/sFig_diode_sw_off_esb.tex @@ -0,0 +1,19 @@ +\begin{solutionfigure}[htb] + \centering + \begin{circuitikz}[european currents,european resistors,american inductors] + \draw (0,2) to [open, o-o, v = $\hspace{2cm}u_2(t)$, voltage = straight] ++(0,-2) + to ++(-5.3,0); + \draw (0,2) to (2,2); + \draw (2,0) to (0,0); + \draw (2,2) to [R, l=$R$](2,0); + \draw (-6.375,2) ++(0.625,0) node [cuteopenswitchshape, anchor = out, rotate=180] (S) {} + let \p1 = (S.mid) in (S.in) to [short, i=$i_\mathrm{D}(t)$] ++(1,0) + to [inductor, l=$L_{\mathrm{c}}$, v = $u_\mathrm{L}(t)$, voltage = straight] ++(2,0) + to [short] ++(1,0) + to [short, -o, i=$i_2(t)$] (0,2) + (S.mid) to [short, o-*](\x1,0); + \draw (-1.5,2) to [capacitor, *-*, l=$C$, i>^=$i_\mathrm{C}(t)$] ++(0,-2); + \end{circuitikz} + \caption{Equivalent circuit diagram of the diode switch-off event.} + \label{fig:DiodeSwitchOff} +\end{solutionfigure} \ No newline at end of file diff --git a/exercise/tex/exercise02.tex b/exercise/tex/exercise02.tex index 46be516..e450d63 100644 --- a/exercise/tex/exercise02.tex +++ b/exercise/tex/exercise02.tex @@ -277,64 +277,8 @@ The voltage ratio dependant on the duty cycle $D$ is shown in \autoref{fig:voltageRatioAndEfficiency} on the left side. Both functions for the loss-free and lossy operation are visualized. Moreover, on the right side of \autoref{fig:voltageRatioAndEfficiency} the resulting efficiency cures are shown. -\begin{solutionfigure}[htb] - \centering - \begin{subfigure}{0.45\textwidth} - \centering - \begin{tikzpicture} - \begin{axis}[ - xlabel={$D$}, - ylabel={$U_{\mathrm{1}}/U_{\mathrm{2}}$}, - axis lines=left, - ymin=0, ymax=10, - xmin=0, xmax=1, - xtick={0,0.2,0.4,0.6,0.8,1.0}, - ytick={0,1,2,3,4,5,6,7,8,9,10}, - xticklabels={0,0.2,0.4,0.6,0.8,1.0}, - yticklabels={0,1,2,3,4,5,6,7,8,9,10}, - thick, - smooth, - no markers, - height=7cm, - width = 0.99\textwidth, - grid - ] - \addplot[signalblue, domain=0:0.95] {(1-x)/((1-x)^2)}; - \node[signalblue, fill=white, inner sep = 1pt, anchor = south] at (axis cs:0.5,8) {ideal function}; - \addplot[signalred, domain=0:1.0] {(1-x)/((1-x)^2+0.2/30)}; - \node[signalred, fill=white, inner sep = 1pt, anchor = south] at (axis cs:0.5,7) {function with losses}; - \end{axis} - \end{tikzpicture} - \end{subfigure}% - \begin{subfigure}{0.45\textwidth} - \begin{tikzpicture} - \begin{axis}[ - xlabel={$D$}, - ylabel={$\eta$}, - axis lines=left, - ymin=0, ymax=1.1, - xmin=0, xmax=1, - xtick={0,0.2,0.4,0.6,0.8,1.0}, - ytick={0,0.2,0.4,0.6,0.8,1.0}, - xticklabels={0,0.2,0.4,0.6,0.8,1.0}, - yticklabels={0,0.2,0.4,0.6,0.8,1.0}, - thick, - smooth, - no markers, - height=7cm, - width = 0.99\textwidth, - grid - ] - \addplot[signalblue, domain=0:1] {1}; - \node[signalblue, fill=white, inner sep = 1pt, anchor = south] at (axis cs:0.5,0.4) {ideal function}; - \addplot[signalred, domain=0:1] {1/(1+(0.2/30)/(1-x)^2)}; - \node[signalred, fill=white, inner sep = 1pt, anchor = south] at (axis cs:0.5,0.3) {function with losses}; - \end{axis} - \end{tikzpicture} - \end{subfigure} - \caption{Voltage ratio (on the left) and the efficiency function (on the right) are visualized. Both functions are dependant on the duty cycle $D$.} - \label{fig:voltageRatioAndEfficiency} -\end{solutionfigure} + + \input{fig/ex02/sFig_boost_voltage_efficiency.tex} \end{solutionblock} @@ -420,68 +364,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subtask{Beside the conduction losses, also switching losses need to be considered in practice. In \autoref{fig:TurnOffSiliconDiode} the voltage and current waveforms are visualized for the turn-off event of a diode (reverse recovery effect). Therefore, calculate the turn-off losses for a fast diode with a commutation inductivity loop of $L_{\mathrm{c}} = \SI{500}{\nano\henry}$. The peak reverse recovery current is $\hat{i}_{\mathrm{rr}} = \SI{4}{\ampere}$ and the reverse recovery time is $t_{\mathrm{rr}} = t_2 - t_0 = \SI{46.6}{\nano\second}$.} -\begin{figure}[htb] - \centering - \begin{tikzpicture} - \tikzmath{ - real = \t0, \t1, \t2 \x1; - \x1 = 3; - \t1 = 6; - \t2 = 8; - \t0 = (\t1-\x1)/0.71; - } - \begin{axis}[ - xlabel={$t$}, - axis lines=middle, - ymin=-1.5, ymax=1.2, - xmin=0, xmax=10, - xtick={\t0,\t1,\t2}, - xticklabels={$t_0$,$t_1$,$t_2$}, - ticklabel style ={yshift=0.2cm,anchor=south}, - yticklabels={}, - width=12cm, - height=5cm, - thick, - smooth, - no markers, - grid - ] - \draw[white,pattern=north east lines, pattern color=signalorange] (\t0,0) -- (\t1,-1) -- (\t1,0); - % - \node[signalorange, fill=white, inner sep = 1pt, anchor = south] at (axis cs:\t0+1.3,-0.45) {$Q_1$}; - % - \draw[white,pattern=north west lines, pattern color=signalgreen] (\t1,0) -- (\t1,-1) -- (\t2,0); - % - \node[signalgreen, fill=white, inner sep = 1pt, anchor = south] at (axis cs:\t1+0.6,-0.45) {$Q_2$}; - % - \draw[thick,signalred] (0,0.7) -- (\x1,0.7) -- (\t1,-1) -- (\t2,0); - % - \node[signalred, fill=white, inner sep = 1pt, anchor = south] at (axis cs:2,0.8) {$i_{\mathrm{D}}$}; - % - \draw[thin, signalred] (3.5,0.6) -- (4,0.7); - \node[signalred, fill=white, inner sep = 1pt, anchor = south] at (axis cs:4.5,0.55) {$\frac{\mathrm{d}i_{\mathrm{D}}}{\mathrm{d}t}$}; - % - \draw[thin, signalred] (7,-0.6) -- (7.8,-0.85); - \node[signalred, fill=white, inner sep = 1pt, anchor = south] at (axis cs:8,-1) {$\frac{\mathrm{d}i_{\mathrm{rr}}}{\mathrm{d}t}$}; - % - \draw[thin, signalred] (\t1-0.05,-1.02) -- (\t1-0.3,-1.2); - % - \node[signalred, inner sep = 1pt, anchor = south] at (axis cs:\t1-0.4,-1.45) {$\hat{i}_{\mathrm{rr}}$}; - % - \node[black, fill=white, inner sep = 1pt, anchor = south] at (axis cs:2,-0.7) {$Q_{\mathrm{rr}} = Q_{1} + Q_{2}$}; - % - \draw[thick, signalblue, dashed] (0,0.1) -- (\t0,0.1) -- (\t0,-0.1) -- (\t1,-0.1) -- (\t1,-1.3) -- (\t2,-1.3) -- (\t2,-1) -- (10,-1); - % - \draw[thin, signalblue] (8.1, -1.3) -- (8.5,-1.3); - % - \node[signalblue, fill=white, inner sep = 1pt, anchor = south] at (axis cs:8.8,-1.5) {${U}_{\mathrm{RB}}$}; - % - \node[signalblue, fill=white, inner sep = 1pt, anchor = south] at (axis cs:2,0.15) {${u}_{\mathrm{D}}$}; - \end{axis} - \end{tikzpicture} - \caption{Turn-off behavior of a fast silicon diode.} - \label{fig:TurnOffSiliconDiode} -\end{figure} + \input{fig/ex02/Fig_diode_switchOff.tex} \begin{solutionblock} Switching losses occur when the diode voltage or current is not zero. In \autoref{fig:TurnOffSiliconDiode} the voltage and current waveforms are shown. The voltage $u_{\mathrm{D}}$ is for the interval $t_0$ until $t_1$ small and, therefore, the switching losses. At the time step $t_1$ the diode is blocking and the reverse breakdown voltage $U_{\mathrm{RB}}$ applies. Due to this much bigger value, the switching losses increases significantly, resulting that only the interval between $t_1$ and $t_2$ is responsible for the switching losses. Hence, the losses are calculated as follows @@ -504,25 +387,7 @@ \end{equation} The equivalent circuit diagram of the diode switch-off event is shown in \autoref{fig:DiodeSwitchOff}. - \begin{solutionfigure}[htb] - \centering - \begin{circuitikz}[european currents,european resistors,american inductors] - \draw (0,2) to [open, o-o, v = $\hspace{2cm}u_2(t)$, voltage = straight] ++(0,-2) - to ++(-5.3,0); - \draw (0,2) to (2,2); - \draw (2,0) to (0,0); - \draw (2,2) to [R, l=$R$](2,0); - \draw (-6.375,2) ++(0.625,0) node [cuteopenswitchshape, anchor = out, rotate=180] (S) {} - let \p1 = (S.mid) in (S.in) to [short, i=$i_\mathrm{D}(t)$] ++(1,0) - to [inductor, l=$L_{\mathrm{c}}$, v = $u_\mathrm{L}(t)$, voltage = straight] ++(2,0) - to [short] ++(1,0) - to [short, -o, i=$i_2(t)$] (0,2) - (S.mid) to [short, o-*](\x1,0); - \draw (-1.5,2) to [capacitor, *-*, l=$C$, i>^=$i_\mathrm{C}(t)$] ++(0,-2); - \end{circuitikz} - \caption{Equivalent circuit diagram of the diode switch-off event.} - \label{fig:DiodeSwitchOff} - \end{solutionfigure} + \input{fig/ex02/sFig_diode_sw_off_esb.tex} The current $i_{\mathrm{D}}(t)$ is dependant on the voltage $U_2$ by: \begin{equation} \Delta i_{\mathrm{D}} = \frac{\mathrm{d}i_{\mathrm{D}}(t)}{\mathrm{d}t} = \frac{U_2}{L_{\mathrm{c}}} = \frac{\SI{60}{\volt}}{\SI{500}{\nano\henry}} = \SI{120}{\ampere\per\micro\second}.