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@SevenOfNinePE
SevenOfNinePE committed Nov 22, 2024
2 parents 2be3f7a + d1dfef7 commit bbb0d92
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23 changes: 14 additions & 9 deletions exercise/fig/ex04/Fig_FlybackConverter.tex
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\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)
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]{};
\draw (l1.midtap) node[left]{$N_1$}
(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}
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107 changes: 107 additions & 0 deletions exercise/fig/ex04/Fig_ForwardConverterWithAsymHalfBridge.tex
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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}
105 changes: 105 additions & 0 deletions exercise/fig/ex04/Fig_SingledEndedForwardConverter.tex
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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}
Empty file added exercise/fig/ex04/Fig_currentI2PeriodTask1.tex
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30 changes: 30 additions & 0 deletions exercise/fig/ex04/Fig_voltageTransistorPeriodTask1.tex
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\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}
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1 change: 1 addition & 0 deletions exercise/main.tex
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Expand Up @@ -7,4 +7,5 @@
\include{tex/exercise01}
\include{tex/exercise02}
\include{tex/exercise03}
\include{tex/exercise04}
\end{document}
16 changes: 8 additions & 8 deletions exercise/tex/exercise03.tex
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Expand Up @@ -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}
Expand All @@ -88,18 +88,18 @@
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}
T_\mathrm{on} = D T_\mathrm{s} \label{absolut value switch-on-times}
\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}

Expand Down Expand Up @@ -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}
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