From 020600c9eddf6f21411fb42ce30235704eebd833 Mon Sep 17 00:00:00 2001 From: "[SilasElter]" <[SilasElter]> Date: Thu, 21 Nov 2024 12:55:02 +0100 Subject: [PATCH 1/5] improve schematic task 4 --- exercise/fig/ex04/Fig_FlybackConverter.tex | 11 ++++++++--- exercise/main.tex | 3 ++- 2 files changed, 10 insertions(+), 4 deletions(-) diff --git a/exercise/fig/ex04/Fig_FlybackConverter.tex b/exercise/fig/ex04/Fig_FlybackConverter.tex index db2a04a..dcb94ed 100644 --- a/exercise/fig/ex04/Fig_FlybackConverter.tex +++ b/exercise/fig/ex04/Fig_FlybackConverter.tex @@ -1,6 +1,10 @@ - - \begin{figure} - \begin{circuitikz}[] +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % Flyback converter Schematic +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + \begin{figure}[htb] + \begin{center} + \begin{circuitikz}[european currents,european resistors,american inductors] \draw (0.5,0) to [short] ++(0.5,0) to [diode, l=$D$] ++(1.0,0) to [short, -o, i=$i_2(t)$] ++(1.0,0) @@ -19,6 +23,7 @@ (l2.midtap) node[right]{$N_2$}; \draw[double, double distance=3pt, thick] let \p1=(l1.core west), \p2=(l2.core east) in (\x1/2+\x2/2, \y1) -- (\x1/2+\x2/2, \y2); \end{circuitikz} + \end{center} \caption{Flyback converter topology} \label{fig:flyback_converter_topology} \end{figure} diff --git a/exercise/main.tex b/exercise/main.tex index 01be547..13e9136 100644 --- a/exercise/main.tex +++ b/exercise/main.tex @@ -1,10 +1,11 @@ \documentclass[solution]{../course_template/exerciseClass} \title{Power Electronics} -\includeonly{tex/exercise03} +\includeonly{tex/exercise04} \begin{document} \include{tex/exercise01} \include{tex/exercise02} \include{tex/exercise03} + \include{tex/exercise04} \end{document} From 804252b7e3c66691f6f23c6d31cd188f952325cc Mon Sep 17 00:00:00 2001 From: "[SilasElter]" <[SilasElter]> Date: Thu, 21 Nov 2024 15:36:10 +0100 Subject: [PATCH 2/5] Starting solution ex 4 --- exercise/fig/ex04/Fig_FlybackConverter.tex | 12 ++--- .../fig/ex04/Fig_currentI2PeriodTask1.tex | 0 .../ex04/Fig_voltageTransistorPeriodTask1.tex | 30 +++++++++++++ .../fig/ex04/Fig_voltageUsPeriodTask1.tex | 0 exercise/tex/exercise04.tex | 44 ++++++++++++++++++- 5 files changed, 78 insertions(+), 8 deletions(-) create mode 100644 exercise/fig/ex04/Fig_currentI2PeriodTask1.tex create mode 100644 exercise/fig/ex04/Fig_voltageTransistorPeriodTask1.tex create mode 100644 exercise/fig/ex04/Fig_voltageUsPeriodTask1.tex diff --git a/exercise/fig/ex04/Fig_FlybackConverter.tex b/exercise/fig/ex04/Fig_FlybackConverter.tex index dcb94ed..60173aa 100644 --- a/exercise/fig/ex04/Fig_FlybackConverter.tex +++ b/exercise/fig/ex04/Fig_FlybackConverter.tex @@ -7,15 +7,15 @@ \begin{circuitikz}[european currents,european resistors,american inductors] \draw (0.5,0) to [short] ++(0.5,0) to [diode, l=$D$] ++(1.0,0) - to [short, -o, i=$i_2(t)$] ++(1.0,0) - to [open, o-o, v = $\hspace{2cm}u_2(t)$, voltage = straight] ++(0,-2) coordinate (A) - (-0.5,0) to [short, -o, i_<=$i_1(t)$] ++(-1.5,0) - to [open, o-o, v_= $u_1(t)\hspace{0.75cm}$, voltage = straight] ++(0,-3.75) coordinate (B) + to [short, -, i=$i_2(t)$] ++(1.0,0) + to [open, V=$U_2(t)$, voltage = straight] ++(0,-2) coordinate (A) + (-0.5,0) to [short, -, i_<=$i_1(t)$] ++(-1.5,0) + to [open, V_=$U_1(t)$, voltage = straight] ++(0,-3.75) coordinate (B) (-0.5,0) to [inductor, n=l1] ++(0,-2) to [Tnpn, n=npn1, mirror] ++(0,-1.75) coordinate (C) (0.5,0) to [inductor, n=l2, mirror] ++(0,-2) coordinate (D) - (D) to [short, -o] (A) - (C) to [short, -o] (B); + (D) to [short, -] (A) + (C) to [short, -] (B); \draw let \p1 = (npn1.B) in node[anchor=south] at (\x1,\y1) {$T$}; \path (l1.ul dot) node[circ]{} (l2.ur dot) node[circ]{}; diff --git a/exercise/fig/ex04/Fig_currentI2PeriodTask1.tex b/exercise/fig/ex04/Fig_currentI2PeriodTask1.tex new file mode 100644 index 0000000..e69de29 diff --git a/exercise/fig/ex04/Fig_voltageTransistorPeriodTask1.tex b/exercise/fig/ex04/Fig_voltageTransistorPeriodTask1.tex new file mode 100644 index 0000000..f4b6f7f --- /dev/null +++ b/exercise/fig/ex04/Fig_voltageTransistorPeriodTask1.tex @@ -0,0 +1,30 @@ +\begin{solutionfigure}[htb] + \centering + \begin{tikzpicture} + \begin{axis}[ + width=7cm, height=4.5cm, + grid=both, + major grid style={line width=.2pt,draw=gray!50}, + minor grid style={line width=.1pt,draw=gray!20}, + xlabel={$t$ / µs}, + ylabel={$u_\mathrm{T}(t)$ / V}, + title={$i_\mathrm{L}$ for minimum output power}, + xmin=0, xmax=40, + ymin=-100, ymax=600, + xtick={0, 20, 40}, + ytick={-100, 0, 225, 500}, + ] + % Einschaltverhalten graph + \addplot[ + thick, + mark=none, + color=black, + ] coordinates { + (0,0) (2.5,0) (2.5, 500) (12.7, 500) (12.7, 382) (20, 382) (20, 0) (22.5, 0)(22.5, 500) (32.7, 500) (32.7, 382) (40, 382) + }; + \end{axis} + \end{tikzpicture} + \hspace{1cm} % Abstand zwischen den beiden Diagrammen + \caption{Display of the voltage $u_\mathrm{T}(t)$.} + \label{fig:voltageTransistorPeriodTask1} + \end{solutionfigure} \ No newline at end of file diff --git a/exercise/fig/ex04/Fig_voltageUsPeriodTask1.tex b/exercise/fig/ex04/Fig_voltageUsPeriodTask1.tex new file mode 100644 index 0000000..e69de29 diff --git a/exercise/tex/exercise04.tex b/exercise/tex/exercise04.tex index e6e6cd3..c9256f0 100644 --- a/exercise/tex/exercise04.tex +++ b/exercise/tex/exercise04.tex @@ -18,7 +18,7 @@ \toprule Input voltage: & $U_{\mathrm{1}} = \SI{300}{\volt} \, \dots \, \SI{900}{\volt}$ & Output voltage: & $U_{\mathrm{2}} = \SI{15}{\volt}$ \\ - Output power: & $P_2 = \SI{15}{\watt}$ & Transformation ratio: & $N_\mathrm{1}/N_\mathrm{2}=60/12$ \\ + Output power: & $P_2 = \SI{30}{\watt}$ & Transformation ratio: & $N_\mathrm{1}/N_\mathrm{2}=60/12$ \\ Inductance of the primary winding: & $L_\mathrm{1} = \SI{760}{\micro\henry}$ & Switching frequency: & $f_{\mathrm{s}} = \SI{50}{\kilo\hertz}$ \\ \bottomrule \end{tabular} @@ -26,10 +26,50 @@ \label{table:ex04_Parameters of the circuit} \end{table} -\subtask{The input voltage is $U_\mathrm{1}=\SI{760}{\volt}$ at rated power at the output. What is the peak value $\hat I_\mathrm{1}$ of the primary current $i_\mathrm{1}$? What is the peak value $\hat I_\mathrm{2}$ of the primary current $i_\mathrm{2}$? Calculate the duty cycle of the transistor for this operating case.} +\subtask{The input voltage is $U_\mathrm{1}=\SI{760}{\volt}$ at rated power at the output. What is the peak value $\hat I_\mathrm{1}$ of the primary current $i_\mathrm{1}$? What is the peak value $\hat I_\mathrm{2}$ of the secundary current $i_\mathrm{2}$? Calculate the duty cycle of the transistor for this operating case.} + +\begin{solutionblock} +\begin{equation} + P_\mathrm{2} = W_\mathrm{L} f_\mathrm{p} +\end{equation} + +\begin{equation} + W_\mathrm{L} = \frac{1}{2}L_\mathrm{1}\hat I_\mathrm{1}^2 +\end{equation} + +\begin{equation} + \hat I_\mathrm{1} = \sqrt{\frac{2P_\mathrm{2}}{L_\mathrm{1}f_\mathrm{p}}}= \sqrt{\frac{2\cdot\SI{30}{\watt}}{\SI{760}{\micro\henry}\cdot\SI{50}{\kilo\hertz}}}=\SI{1.257}{\ampere} +\end{equation} + +\begin{equation} + \hat I_\mathrm{1} = \hat I_\mathrm{2} +\end{equation} + +\begin{equation} + \hat I_\mathrm{2} = \hat I_\mathrm{1} \frac{N_\mathrm{1}}{N_\mathrm{2}} = \SI{1.257}{\ampere} \cdot \frac{60}{12} = \SI{6.28}{\ampere} +\end{equation} +Because of CCM the duty cycle $D$ is expressed ..... +\begin{equation} + \frac{U_2}{U_1} = \frac{D^2}{2} \frac{\Delta i_\mathrm{m,max}}{\overline{i}_2} \label{eq:Duty cycle ex04} +\end{equation} +Because of the unknown $\Delta i_\mathrm{m,max}$ this value has to be calculate first as +\begin{equation} + \Delta i_\mathrm{m,max}= \frac{T_\mathrm{s} \cdot U_1}{L} = \frac{\frac{1}{\SI{50}{\kilo\hertz}}\cdot \SI{760}{\volt}}{\SI{760}{\micro\henry}}=\SI{20}{\ampere}. +\end{equation} +Now $\Delta i_\mathrm{m,max}=\SI{20}{\ampere}$ can be used in \eqref{eq:Duty cycle ex04}: + +\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{760}{\volt}\cdot\SI{15}{\volt}\cdot\SI{20}{\ampere}}} = 0.063. +\end{equation} + +\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 case over one cycle period: $u_\mathrm{T}(t), u_\mathrm{s}(t), i_\mathrm{2}(t), i_\mathrm{1}(t)$ (Note: corresponds to the switch-on time of the transistor).} +\input{./fig/ex04/Fig_voltageTransistorPeriodTask1.tex} + + + \subtask{The input voltage is $U_\mathrm{1}=\SI{382}{\volt}$ at nominal load. Determine the mean value $\overline i_\mathrm{T}$ and the effective value of the current $i_\mathrm{T, rms}$ through the transistor. Determine the mean value $\overline i_\mathrm{D}$ and the effective value of the current $i_\mathrm{D, rms}$ through the diode. What is the maximum reverse voltage load $u_\mathrm{T, max}$ of the transistor? What is the maximum reverse voltage load $u_\mathrm{D, max}$ of the diode? Calculate the fluctuation range $\Delta i_\mathrm{C, pp}$ of the current $i_\mathrm{C}$ in the output capacitor.} \subtask{The input voltage is $U_\mathrm{1}=\SI{382}{\volt}$ at nominal load.How much energy is transferred from the input to the output per switching period $\Delta E$ and what is the resulting average power? What happens if there is no ideal voltage source on the output side but an unloaded capacitor and the circuit is operated with $D>0$?} \ No newline at end of file From 5b2016a4e2db8a4a6488229a210e4b7743e15731 Mon Sep 17 00:00:00 2001 From: SevenOfNinePE Date: Thu, 21 Nov 2024 18:23:35 +0100 Subject: [PATCH 3/5] Ex04: Add figure for task3 and start figure for task2 --- ...Fig_ForwardConverterWithAsymHalfBridge.tex | 107 ++++++++++++++++++ .../ex04/Fig_SingledEndedForwardConverter.tex | 105 +++++++++++++++++ exercise/main.tex | 3 +- exercise/tex/exercise04.tex | 71 +++++++++++- lecture/main.tex | 1 - 5 files changed, 284 insertions(+), 3 deletions(-) create mode 100644 exercise/fig/ex04/Fig_ForwardConverterWithAsymHalfBridge.tex create mode 100644 exercise/fig/ex04/Fig_SingledEndedForwardConverter.tex diff --git a/exercise/fig/ex04/Fig_ForwardConverterWithAsymHalfBridge.tex b/exercise/fig/ex04/Fig_ForwardConverterWithAsymHalfBridge.tex new file mode 100644 index 0000000..c9ea1ca --- /dev/null +++ b/exercise/fig/ex04/Fig_ForwardConverterWithAsymHalfBridge.tex @@ -0,0 +1,107 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Forward converter with asymmetric half-bridge +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{figure}[ht] + \begin{center} + \begin{circuitikz}[european currents,european resistors,american inductors] + \draw + % Base point for voltage supply + (0,0) coordinate (jU1v) + % Add supply U1 + (jU1v) to [V=$U_1$] ++(0,-7.5) coordinate (jU1g) + % Add junction for Transistor TBc + (jU1v) to [short,-*] ++(2,0) coordinate (jTBc) + % Add junction for Transistor TBe + (jTBc) ++ (0,-2) coordinate (jTBe) + % Add transistor TB + % (jTBc) ++ (0,-1) [Tnpn, n=npn1](TB){} + (jTBc) ++ (0,-2) node[npn, anchor=E](TB){} + % At transistor label T2 + (TB) node[anchor=east,color=black]{$T_\mathrm{B}$} + % Connect Transistor + (jTBe) to [short,-] (TB.E) + (jTBc) to [short,-] (TB.C) + (TB.B) to [sqV] ++(-1,0); + % Add inductor transistor TB + %(jTBe) to [L,l=$L_\mathrm{T}$,n=L1,v_<=$U_\text{s}$, voltage shift=0.5, voltage=straight] (jTBc); + \draw + % Add connection point of the diode DFP + (jTBe) ++(0,-3) coordinate (jDFPa) + % Add diode DFP + (jDFPa) to [D,l^=$D_\mathrm{Fp}$] (jTBe) + % Add connection to U1g + (jDFPa) to [short,-] (jU1g) + % Add junction for transformer Ltpv + (jTBc) to [short,-] ++(2,0) coordinate (jLtpv) + % Add arrow and Text + (jTBc) ++(1,0) node[currarrow](IP){} + (IP) node[anchor=south,color=black]{$i_\mathrm{p}$} + % Add junction for Transistor + (jLtpv) ++(0,-3) coordinate (jTd) + % Add junction for Transistor + (jTd) ++(0,-3) coordinate (jTs) + % Add transistor T2 + (jTs) ++ (0,1.5) node[nigfete,xscale=-1](Trans1){} + % At transistor label T2 + (Trans1) node[anchor=east,color=black]{$T$} + % Connect Transistor + (jTs) to [short,-] (Trans1.S) + (jTd) to [short,-] (Trans1.D) + (Trans1.G) to [sqV] ++(1,0) + % Add connection to diode DFp + (jTs) to [short,-*] (jDFPa) + % Assign Transistor drain junction to primary junction point + (jTd) coordinate (jLtpg) + % Add transformer primary inductor with voltage arrow + (jLtpv) to [L, n=Ltp, v_=$U_\text{p}$, voltage=straight] ++(0,-3) coordinate (jLtpg) + % Add junctions for secondary inductor + (jLtpv) ++(0.8,0) coordinate (jLtsv) + (jLtpg) ++(0.8,-0.5) coordinate (jLtsgx) + % Add winding text + (jLtpg) node[left] {$N_\mathrm{p}$}; + % Add iron core + \draw + (jLtpv) ++(0.5,-0.5) coordinate (jLtcorev) + (jLtpg) ++(0.5,0.5) coordinate (jLtcoreg) + (jLtcorev) to [short, double, double distance=3pt, thick] (jLtcoreg) + let \p1 = (jLtcorev), \p2 = (jLtcoreg) in [double, double distance=3pt, thick] + (\x1/2+\x2/2, \y1) -- (\x1/2+\x2/2, \y2); + \draw + % Add transformer secondary inductor with voltage arrow + (jLtsv) to [L,n=Lts,v^=$U_\text{s}$, voltage shift=0.5, voltage=straight] ++(0,-3) coordinate (jLtsg) + % Add winding text + (jLtsg) node[right] {$N_\mathrm{s}$}; + \path (Ltp.ul dot) node[circ]{}; + \path (Lts.ul dot) node[circ]{}; + \draw + % Add arrow and Text + (jLtsv) ++(0.5,0) node[currarrow](IS){} + (IS) node[anchor=south,color=black]{$i_\mathrm{s}$} + % Add D1 + (jLtsv) to [D,l^=$D_1$] ++ (2,0) coordinate (jD1k) + % Add junction point for DFsk + (jD1k) to [short,-*] ++(0,0) coordinate (jDFsk) + % Add junction point for DFsa + (jDFsk) ++ (0,-3.5) coordinate (jDFsa) + % Add diode DFs + (jDFsa) to [D,l^=$D_\mathrm{Fs}$] (jDFsk) + % Add inductor L + (jDFsk) to [L,l=$L$,n=L1] ++(3,0) coordinate (jU2v) + % Add arrow and Text + (jDFsk) ++(0.5,0) node[currarrow](IL){} + (IL) node[anchor=south,color=black]{$i_\mathrm{L}$} + % Add output voltage U2 + (jU2v) to [V=$U_2$] ++(0,-3.5) coordinate (jU2g) + % Add connection to DFs + (jU2g) to [short,-*] (jDFsa) + % Add connection to LTsgx + (jDFsa) to [short,-] (jLtsgx) + % Add connection to LTsgx + (jLtsgx) to [short,-] (jLtsg); + + \end{circuitikz} + \end{center} + \caption{Forward converter with asymmetric half-bridge.} + \label{fig:ex04_ForwardConverterWithAsymHalfBridge} +\end{figure} diff --git a/exercise/fig/ex04/Fig_SingledEndedForwardConverter.tex b/exercise/fig/ex04/Fig_SingledEndedForwardConverter.tex new file mode 100644 index 0000000..54b1657 --- /dev/null +++ b/exercise/fig/ex04/Fig_SingledEndedForwardConverter.tex @@ -0,0 +1,105 @@ + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Single Ended Forward Converter +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{figure}[ht] + \begin{center} + \begin{circuitikz}[european currents,european resistors,american inductors] + \draw + % Base point for voltage supply + (0,0) coordinate (jU1v) + % Add supply U1 + (jU1v) to [V=$U_1$] ++(0,-6) coordinate (jU1g) + % Add junction for capacitor C1+ + (jU1v) to [short,-*] ++(2,0) coordinate (jLTv) + % Add junction for diode DFP + (jLTv) ++ (0,-3) coordinate (jDFPk) + % Add inductor LTv + (jDFPk) to [L,l=$L_\mathrm{T}$,n=L1,v_<=$U_\text{s}$, voltage shift=0.5, voltage=straight] (jLTv) + % Add winding text + (jDFPk) node[right] {$N_\mathrm{T}$}; + \path (L1.ul dot) node[circ]{}; + \draw + % Add arrow and Text + (jDFPk) ++(0,-0.5) node[currarrow,rotate=90](IT){} + (IT) node[anchor=east,color=black]{$i_\mathrm{T}$} + % Add connection point of the diode DFP + (jDFPk) ++(0,-3) coordinate (jDFPa) + % Add diode DFP + (jDFPa) to [D,l^=$D_\mathrm{Fp}$] (jDFPk) + % Add connection to U1g + (jDFPa) to [short,-] (jU1g) + % Add junction for transformer Ltpv + (jLTv) to [short,-] ++(2,0) coordinate (jLtpv) + % Add arrow and Text + (jLTv) ++(1,0) node[currarrow](IP){} + (IP) node[anchor=south,color=black]{$i_\mathrm{p}$} + % Add junction for Transistor + (jLtpv) ++(0,-3) coordinate (jTd) + % Add junction for Transistor + (jTd) ++(0,-3) coordinate (jTs) + % Add transistor T2 + (jTs) ++ (0,1.5) node[nigfete,xscale=-1](Trans1){} + % At transistor label T2 + (Trans1) node[anchor=east,color=black]{$T$} + % Connect Transistor + (jTs) to [short,-] (Trans1.S) + (jTd) to [short,-] (Trans1.D) + (Trans1.G) to [sqV] ++(1,0) + % Add connection to diode DFp + (jTs) to [short,-*] (jDFPa) + % Assign Transistor drain junction to primary junction point + (jTd) coordinate (jLtpg) + % Add transformer primary inductor with voltage arrow + (jLtpv) to [L, n=Ltp, v_=$U_\text{p}$, voltage=straight] ++(0,-3) coordinate (jLtpg) + % Add junctions for secondary inductor + (jLtpv) ++(0.8,0) coordinate (jLtsv) + (jLtpg) ++(0.8,-0.5) coordinate (jLtsgx) + % Add winding text + (jLtpg) node[left] {$N_\mathrm{p}$}; + % Add iron core + \draw + (jLtpv) ++(0.5,-0.5) coordinate (jLtcorev) + (jLtpg) ++(0.5,0.5) coordinate (jLtcoreg) + (jLtcorev) to [short, double, double distance=3pt, thick] (jLtcoreg) + let \p1 = (jLtcorev), \p2 = (jLtcoreg) in [double, double distance=3pt, thick] + (\x1/2+\x2/2, \y1) -- (\x1/2+\x2/2, \y2); + \draw + % Add transformer secondary inductor with voltage arrow + (jLtsv) to [L,n=Lts,v^=$U_\text{s}$, voltage shift=0.5, voltage=straight] ++(0,-3) coordinate (jLtsg) + % Add winding text + (jLtsg) node[right] {$N_\mathrm{s}$}; + \path (Ltp.ul dot) node[circ]{}; + \path (Lts.ul dot) node[circ]{}; + \draw + % Add arrow and Text + (jLtsv) ++(0.5,0) node[currarrow](IS){} + (IS) node[anchor=south,color=black]{$i_\mathrm{s}$} + % Add D1 + (jLtsv) to [D,l^=$D_1$] ++ (2,0) coordinate (jD1k) + % Add junction point for DFsk + (jD1k) to [short,-*] ++(0,0) coordinate (jDFsk) + % Add junction point for DFsa + (jDFsk) ++ (0,-3.5) coordinate (jDFsa) + % Add diode DFs + (jDFsa) to [D,l^=$D_\mathrm{Fs}$] (jDFsk) + % Add inductor L + (jDFsk) to [L,l=$L$,n=L1] ++(3,0) coordinate (jU2v) + % Add arrow and Text + (jDFsk) ++(0.5,0) node[currarrow](IL){} + (IL) node[anchor=south,color=black]{$i_\mathrm{L}$} + % Add output voltage U2 + (jU2v) to [V=$U_2$] ++(0,-3.5) coordinate (jU2g) + % Add connection to DFs + (jU2g) to [short,-*] (jDFsa) + % Add connection to LTsgx + (jDFsa) to [short,-] (jLtsgx) + % Add connection to LTsgx + (jLtsgx) to [short,-] (jLtsg); + + \end{circuitikz} + \end{center} + \caption{Single Ended Forward Converter circuit.} + \label{fig:ex04_SingledEndedForwardConverter} +\end{figure} diff --git a/exercise/main.tex b/exercise/main.tex index 01be547..13e9136 100644 --- a/exercise/main.tex +++ b/exercise/main.tex @@ -1,10 +1,11 @@ \documentclass[solution]{../course_template/exerciseClass} \title{Power Electronics} -\includeonly{tex/exercise03} +\includeonly{tex/exercise04} \begin{document} \include{tex/exercise01} \include{tex/exercise02} \include{tex/exercise03} + \include{tex/exercise04} \end{document} diff --git a/exercise/tex/exercise04.tex b/exercise/tex/exercise04.tex index e6e6cd3..54a08fd 100644 --- a/exercise/tex/exercise04.tex +++ b/exercise/tex/exercise04.tex @@ -32,4 +32,73 @@ \subtask{The input voltage is $U_\mathrm{1}=\SI{382}{\volt}$ at nominal load. Determine the mean value $\overline i_\mathrm{T}$ and the effective value of the current $i_\mathrm{T, rms}$ through the transistor. Determine the mean value $\overline i_\mathrm{D}$ and the effective value of the current $i_\mathrm{D, rms}$ through the diode. What is the maximum reverse voltage load $u_\mathrm{T, max}$ of the transistor? What is the maximum reverse voltage load $u_\mathrm{D, max}$ of the diode? Calculate the fluctuation range $\Delta i_\mathrm{C, pp}$ of the current $i_\mathrm{C}$ in the output capacitor.} -\subtask{The input voltage is $U_\mathrm{1}=\SI{382}{\volt}$ at nominal load.How much energy is transferred from the input to the output per switching period $\Delta E$ and what is the resulting average power? What happens if there is no ideal voltage source on the output side but an unloaded capacitor and the circuit is operated with $D>0$?} \ No newline at end of file +\subtask{The input voltage is $U_\mathrm{1}=\SI{382}{\volt}$ at nominal load.How much energy is transferred from the input to the output per switching period $\Delta E$ and what is the resulting average power? What happens if there is no ideal voltage source on the output side but an unloaded capacitor and the circuit is operated with $D>0$?} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Task 2: Forward converter with asymmetric half-bridge +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\task{Forward converter with asymmetric half-bridge} + +Betrachten Sie den in \autoref{fig:ex04_ForwardConverterWithAsymHalfBridge} dargestellten Zwei-Transistor Durchflusswandler unter Annahme idealer Transisto- +ren und Dioden. + +\input{./fig/ex04/Fig_ForwardConverterWithAsymHalfBridge} + +Die Eingangsspannung betrage u 1 = U 1 = 325 V entsprechend der gleichgerichteten, ideal +kapazitiv geglätteten Netzspannung. Die Ausgangskapazität C ist so gross gewählt, dass die Ausgangsspan- +nung praktisch konstant ist, u 2 = U 2 = 15 V . Die an die Last abgegebene Leistung bei Nennbetrieb beträgt +P 2 = 50W . Die Taktfrequenz beträgt f p = 50 kHz . Das Transformator hat das Windungszahlverhältnis +N 1 ⁄ N 2 = 10 ⁄ 1 und eine Induktivität der Primärwicklung L 1 = 2mH . Die Streuinduktivität, die ohmschen Ver- +luste und die Kernverluste des Transformators sind vernachlässigbar. Der Wandler arbeite im stationären Be- +trieb. + +\subtask{Mit welchem Tastverhältnis D 1 (= relative Leitdauer von T A und T B ) arbeitet die Schaltung?} +\subtask{Berechnen Sie den Mittelwert von i 2 und i 1 über eine Taktperiode unter Annahme idealer Glättung von +i2.} +\subtask{Berechnen Sie den Spitzenwert $\hat{i}_\mu$ des Magnetisierungsstromes $i_\mu$.} +\subtask{Skizzieren Sie auf dem Beiblatt 1 für den Fall nichtidealer Stromglättung $L \neq \infty$ den Verlauf von $U_\mathrm{p}$, $U_\mathrm{D2}$' , + $i_\mu$, $i_2$ , $i_\mathrm{2}$ , $i_\mathrm{p}$ und $i_\mathrm{1}$ . Hinweis: $i_\mathrm{2}$ $( t = 0 )$ = $I_\mathrm{2min}$ .} +\subtask{Berechnen Sie die minimal notwendige Eingangsspannung $U_\mathrm{1}$ , wenn die Ausgangsspannung +$U_\mathrm{2}$ = \SI{20}{\volt} konstant bleiben soll.} +\subtask{Berechnen Sie die Induktivität $L$ , wenn der peak-to-peak Wert} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Task 3: Singled-ended forward converter (demagnetization winding) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\task{Singled-ended forward converter (demagnetization winding)} + +Zur Stromversorgung einer Datenverarbeitunganlage soll ein Eintakt-Durchflusswandler nach \autoref{fig:ex04_SingledEndedForwardConverter} +eingesetzt werden. + +\input{./fig/ex04/Fig_SingledEndedForwardConverter} + +Entsprechend dem Toleranzbereich der Netzspannung und der Schwankung der Spannung am +Eingangskondensator liegt die Eingangsspannung des Systems im Bereich U1 = 240...360V. Die +Schaltfrequenz wird mit fP = 48kHz gewählt. Die Ausgangdiode D1 weise einen stromunabhängigen +Durchlassspannungsabfall von 0.4V auf. Die Ausgangsinduktivität sei so dimensioniert, dass iL einen +kontinuierlichen Verlauf zeigt. Die Streuung des Transformators kann vernachlässigt werden. +\subtask{Berechnen Sie das Windungszahlverhältnis NT/NP so, dass während der Entmagnetisierung +eine maximale Sperrspannung am Transistor von 600V auftritt.} +\subtask{Welches maximale Tastverhältnis des Leistungstransistors ist dann zulässig?} +\subtask{Wie ist das Windungszahlverhältnis NP/NS zu wählen damit die geforderte Sekundärspannung +gebildet wird?} +\subtask{Muss das stationäre Tastverhältnis des Transistors bei Änderung der Ausgangsleistung +verändert werden? In welchem Bereich muss das Tastverhältnis des Transistors unter +Berücksichtigung des Eingangsspannungsbereiches einstellbar sein?} +\subtask{Welche maximale Sperrspannung tritt an der Diode D1 und an der Diode DFs auf?} +\subtask{Wie hoch muss die Primärinduktivität LP sein damit der Spitzenwert des Magnetisierungsstrom +auf kleiner 10\% des auf die Primärseite übersetzen Stromes iL in der Ausgangsinduktivität bei +Nennlast P2 = 125W beschränkt bleibt? ( iL kann als näherungsweise konstant angenommen +werden).} +\subtask{Skizzieren Sie auf Beiblatt 1 den Verlauf der Spannung am Leistungstransistor, den Verlauf +des Stromes in der Entmagnetisierungswicklung und des Stromes in der Freilaufdiode DFs für +U1 = 240V und U1 = 360V.} +\subtask{Berechnen Sie den jeweiligen Spitzenwert des Magnetisierungsstromes. +Der Strom in der Ausgangsinduktivität sei für die folgenden Überlegungen als ideal geglättet +angenommen.} +\subtask{Könnte bei Verdopplung der Schaltfrequenz des Konverters eine höhere Leistung übertragen +werden?} diff --git a/lecture/main.tex b/lecture/main.tex index 0058a32..0f286cc 100644 --- a/lecture/main.tex +++ b/lecture/main.tex @@ -31,7 +31,6 @@ \include{tex/Lecture01} % Initial overview \include{tex/Lecture02} % DC-DC converters (non-isolated) \include{tex/Lecture03} % Isolated DC-DC converters -\include{tex/Lecture04} % Diode-based rectifiers \include{tex/dict} % English-German dictionary \include{tex/nomen} % Nomenclature \end{document} \ No newline at end of file From c46f4e7d101d751aa2d537cf252a85116ff78e47 Mon Sep 17 00:00:00 2001 From: Wallscheid Date: Thu, 21 Nov 2024 19:44:23 +0100 Subject: [PATCH 4/5] abc --- lecture/main.ist | 2 +- lecture/main.nom | 16 ---------------- lecture/main.nomc | 6 ------ lecture/main.tex | 2 +- 4 files changed, 2 insertions(+), 24 deletions(-) diff --git a/lecture/main.ist b/lecture/main.ist index fe931ad..6aa243d 100644 --- a/lecture/main.ist +++ b/lecture/main.ist @@ -1,5 +1,5 @@ % makeindex style file created by the glossaries package -% for document 'main' on 2024-11-20 +% for document 'main' on 2024-11-21 actual '?' encap '|' level '!' diff --git a/lecture/main.nom b/lecture/main.nom index 384c9c9..e69de29 100644 --- a/lecture/main.nom +++ b/lecture/main.nom @@ -1,16 +0,0 @@ -\glossarysection[\glossarytoctitle]{\glossarytitle}\glossarypreamble -\begin{theglossary}\glossaryheader -\glsgroupheading{glsnumbers}\relax \glsresetentrylist % -\glossentry{scalar_signal}{\glossaryentrynumbers{\relax - \setentrycounter[]{page}\glsignore{191}}}% -\glossentry{vectorial_signal}{\glossaryentrynumbers{\relax - \setentrycounter[]{page}\glsignore{191}}}% -\glossentry{const_signal}{\glossaryentrynumbers{\relax - \setentrycounter[]{page}\glsignore{191}}}% -\glossentry{matrix}{\glossaryentrynumbers{\relax - \setentrycounter[]{page}\glsignore{191}}}% -\glossentry{average_signal}{\glossaryentrynumbers{\relax - \setentrycounter[]{page}\glsignore{191}}}% -\glossentry{derivative_signal}{\glossaryentrynumbers{\relax - \setentrycounter[]{page}\glsignore{191}}}% -\end{theglossary}\glossarypostamble diff --git a/lecture/main.nomc b/lecture/main.nomc index 15df7a8..e69de29 100644 --- a/lecture/main.nomc +++ b/lecture/main.nomc @@ -1,6 +0,0 @@ -\glossaryentry{010?\glossentry{scalar_signal}|setentrycounter[]{page}"\glsignore}{191} -\glossaryentry{020?\glossentry{vectorial_signal}|setentrycounter[]{page}"\glsignore}{191} -\glossaryentry{021?\glossentry{const_signal}|setentrycounter[]{page}"\glsignore}{191} -\glossaryentry{022?\glossentry{matrix}|setentrycounter[]{page}"\glsignore}{191} -\glossaryentry{030?\glossentry{average_signal}|setentrycounter[]{page}"\glsignore}{191} -\glossaryentry{040?\glossentry{derivative_signal}|setentrycounter[]{page}"\glsignore}{191} diff --git a/lecture/main.tex b/lecture/main.tex index 0058a32..0d7b1e8 100644 --- a/lecture/main.tex +++ b/lecture/main.tex @@ -5,7 +5,7 @@ \author{Oliver Wallscheid} \date{} -%\includeonly{tex/Lecture03} % build only selected sections +\includeonly{tex/Lecture04} % build only selected sections \begin{document} From d1dfef76d40da712bbb7902d13cf5683fd6f44a1 Mon Sep 17 00:00:00 2001 From: Wallscheid Date: Thu, 21 Nov 2024 19:51:15 +0100 Subject: [PATCH 5/5] min corr to ex03 --- exercise/main.tex | 2 +- exercise/tex/exercise03.tex | 16 ++++++++-------- 2 files changed, 9 insertions(+), 9 deletions(-) diff --git a/exercise/main.tex b/exercise/main.tex index 13e9136..e66f6d9 100644 --- a/exercise/main.tex +++ b/exercise/main.tex @@ -1,7 +1,7 @@ \documentclass[solution]{../course_template/exerciseClass} \title{Power Electronics} -\includeonly{tex/exercise04} +\includeonly{tex/exercise03} \begin{document} \include{tex/exercise01} diff --git a/exercise/tex/exercise03.tex b/exercise/tex/exercise03.tex index 1b53e0b..d151ce0 100644 --- a/exercise/tex/exercise03.tex +++ b/exercise/tex/exercise03.tex @@ -57,17 +57,17 @@ As the output power is specified as a value range, the highest and lowest values can be used. The lowest and highest current should be determined from these two values, from which the value range of the frequency $f_\mathrm{s}$ can then be determined. The average inductor current is calculated as: \begin{equation} - \overline{i}_\mathrm{L}(P_\mathrm{2}=(\SI{2}{\watt}))= \frac{P_\mathrm{2}}{U_\mathrm{2}}\frac{1}{D}=\frac{\SI{2}{\watt}}{\SI{12}{\volt}}\frac{5}{3}=\SI{0.278}{\ampere}, + \overline{i}_\mathrm{L}(P_\mathrm{2}=\SI{2}{\watt})= \frac{P_\mathrm{2}}{U_\mathrm{2}}\frac{1}{D}=\frac{\SI{2}{\watt}}{\SI{12}{\volt}}\frac{5}{3}=\SI{0.278}{\ampere}, \end{equation} \begin{equation} - \overline{i}_\mathrm{L}(P_\mathrm{2}=(\SI{15}{\watt}))= \frac{P_\mathrm{2}}{U_\mathrm{2}}\frac{1}{D}=\frac{\SI{15}{\watt}}{\SI{12}{\volt}}\frac{5}{3}=\SI{2.0833}{\ampere}. + \overline{i}_\mathrm{L}(P_\mathrm{2}=\SI{15}{\watt})= \frac{P_\mathrm{2}}{U_\mathrm{2}}\frac{1}{D}=\frac{\SI{15}{\watt}}{\SI{12}{\volt}}\frac{5}{3}=\SI{2.0833}{\ampere}. \end{equation} With \eqref{eq:equation switching frequencies ex03} the resulting switching frequencies are: \begin{equation} - f_\mathrm{s}(P_\mathrm{2}=(\SI{2}{\watt}))=\frac{0.4\cdot\SI{18}{\volt}}{\SI{86.4}{\micro\henry}\cdot 2\cdot \SI{0.278}{\ampere}}=\SI{150}{\kilo \hertz}, + f_\mathrm{s}(P_\mathrm{2}=\SI{2}{\watt})=\frac{0.4\cdot\SI{18}{\volt}}{\SI{86.4}{\micro\henry}\cdot 2\cdot \SI{0.278}{\ampere}}=\SI{150}{\kilo \hertz}, \end{equation} \begin{equation} - f_\mathrm{s}(P_\mathrm{2}=(\SI{15}{\watt}))=\frac{0.4\cdot\SI{18}{\volt}}{\SI{86.4}{\micro\henry}\cdot 2\cdot \SI{2.0833}{\ampere}}=\SI{20}{\kilo \hertz}. + f_\mathrm{s}(P_\mathrm{2}=\SI{15}{\watt})=\frac{0.4\cdot\SI{18}{\volt}}{\SI{86.4}{\micro\henry}\cdot 2\cdot \SI{2.0833}{\ampere}}=\SI{20}{\kilo \hertz}. \end{equation} The switching frequency $f_\mathrm{s}$ varies in the range from $\SI{20}{\kilo \hertz} \, \dots \, \SI{150}{\kilo \hertz}$ for the specified output power range in the task. \end{solutionblock} @@ -88,7 +88,7 @@ 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}, \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}{f_{\mathrm{s,15W}}} = \frac{1}{\SI{20}{\kilo \hertz}}= \SI{50}{\micro \s}. \end{equation} The transistor switch-on times can be determined using \begin{equation} @@ -96,10 +96,10 @@ \end{equation} leading to: \begin{equation} - T_\mathrm{on}(P_\mathrm{2}=(\SI{2}{\watt})) = 0.4 \cdot \SI{6.67}{\micro \s} = \SI{2.67}{\micro \s}, + T_\mathrm{on}(P_\mathrm{2}=\SI{2}{\watt}) = 0.4 \cdot \SI{6.67}{\micro \s} = \SI{2.67}{\micro \s}, \end{equation} \begin{equation} - T_\mathrm{on}(P_\mathrm{2}=(\SI{15}{\watt})) = 0.4 \cdot \SI{50}{\micro \s}= \SI{20}{\micro \s}. + T_\mathrm{on}(P_\mathrm{2}=\SI{15}{\watt}) = 0.4 \cdot \SI{50}{\micro \s}= \SI{20}{\micro \s}. \end{equation} \end{solutionblock} @@ -142,7 +142,7 @@ \end{equation} applying for the maximum power ($P = \SI{15}{\watt}$) 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}}} + 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}} = \SI{104}{\micro\farad}. \end{equation}