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Merge branch 'main' of https://github.com/IAS-Uni-Siegen/PE_course
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@wallscheid
wallscheid committed Nov 25, 2024
2 parents f062dc0 + d666b76 commit d4d2e60
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6 changes: 3 additions & 3 deletions exercise/fig/ex04/FigTab_ForwardConverterWithAsymHalfBridge.tex
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Expand Up @@ -2,15 +2,15 @@
% Parameter of the forward converter with asymmetric half-bridge
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{table}[ht]
\begin{table}[htb]
\centering % Zentriert die Tabelle
\begin{tabular}{llll}
\toprule
Input voltage: & $U_{\mathrm{1}} = \SI{325}{\volt}$ & Output voltage: & $U_{\mathrm{2}} = \SI{15}{\volt}$ \\
Output power: & $P_{\mathrm{2}} = \SI{50}{\watt}$ & Switching frequency: & $f_{\mathrm{s}} = \SI{50}{\kilo\hertz}$ \\
Winding ration: & $N_{\mathrm{1}}/N_{\mathrm{2}}=10$ & Inductance: & $L_{\mathrm{1}}=\SI{2}{\milli\henry}$ \\
Turns ration: & $N_{\mathrm{1}}/N_{\mathrm{2}}=10$ & Magnetizing inductance: & $L_{\mathrm{m}}=\SI{2}{\milli\henry}$ \\
\bottomrule
\end{tabular}
\caption{Parameter of the circuit.}
\caption{Parameter overview of the circuit.}
\label{table:Ex04_Forward converter with asymmetric half-bridge}
\end{table}
4 changes: 2 additions & 2 deletions exercise/fig/ex04/Fig_ForwardConverterWithAsymHalfBridge.tex
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Expand Up @@ -64,7 +64,7 @@
(jLtpv) ++(-0.5,0) node[currarrow](IP){}
(IP) node[anchor=south,color=black]{$i_\mathrm{p}$}
% Add transformer primary inductor with voltage arrow
(jLtpv) to [L,l_=$N_\mathrm{1}$, n=Ltp, v_=$U_\text{p}$, voltage shift=5, voltage=straight] (jLtpg)
(jLtpv) to [L,l_=$N_\mathrm{1}$, n=Ltp, v_=$u_\text{p}$, voltage shift=5, voltage=straight] (jLtpg)
% Add connections point for secondary inductor
(jLtpv) ++(0.8,0) coordinate (jLtsv);
% Add iron core
Expand All @@ -78,7 +78,7 @@
% Add transformer secondary inductor with voltage arrow
(jLtsv) ++(0,-2) coordinate (jLtsg)
% Add transformer secondary inductor with voltage arrow
(jLtsv) to [L,l^=$N_\mathrm{2}$,n=Lts,mirror,v^=$U_\text{s}$, voltage shift=5, voltage=straight] (jLtsg);
(jLtsv) to [L,l^=$N_\mathrm{2}$,n=Lts,mirror,v^=$u_\text{s}$, voltage shift=5, voltage=straight] (jLtsg);
\path (Ltp.ul dot) node[circ]{};
\path (Lts.ul dot) node[circ]{};
\draw
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62 changes: 32 additions & 30 deletions exercise/fig/ex04/Fig_SingledEndedForwardConverter.tex
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Expand Up @@ -10,26 +10,26 @@
% Base point for voltage supply
(0,0) coordinate (jU1v)
% Add supply U1
(jU1v) to [V=$U_1$] ++(0,-4) coordinate (jU1g)
(jU1v) to [V=$U_\mathrm{1}$] ++(0,-4) coordinate (jU1g)
% Add junction for inductor LT
(jU1v) to [short,-*] ++(2,0) coordinate (jLTv)
% Add junction for diode DFP
(jLTv) ++ (0,-2) coordinate (jDFPk)
% Add junction for diode D3
(jLTv) ++ (0,-2) coordinate (jD3k)
% Add inductor LTv
(jDFPk) to [L,l=$L_\mathrm{T}$,n=L1,v_<=$U_\text{T}$, voltage shift=0.5, voltage=straight] (jLTv)
(jD3k) to [L,l=$L_\mathrm{3}$,n=L1,v_<=$U_\mathrm{3}$, voltage shift=0.5, voltage=straight] (jLTv)
% Add winding text
(jDFPk) node[right] {$N_\mathrm{T}$};
(jD3k) node[right] {$N_\mathrm{3}$};
\path (L1.ul dot) node[circ]{};
\draw
% Add arrow and Text
(jDFPk) ++(0,-0.5) node[currarrow,rotate=90](IT){}
(jD3k) ++(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,-2) coordinate (jDFPa)
% Add diode DFP
(jDFPa) to [D,l^=$D_\mathrm{Fp}$] (jDFPk)
% Add connection point of the diode D3
(jD3k) ++(0,-2) coordinate (jD3a)
% Add diode D3
(jD3a) to [D,l^=$D_\mathrm{3}$] (jD3k)
% Add connection to U1g
(jDFPa) to [short,-] (jU1g)
(jD3a) to [short,-] (jU1g)
% Add junction for transformer Ltpv
(jLTv) to [short,-] ++(2.5,0) coordinate (jLtpv)
% Add arrow and Text
Expand All @@ -47,12 +47,14 @@
(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)
% Add connection to diode D3
(jTs) to [short,-*] (jD3a)
% Assign Transistor drain junction to primary junction point
(jTd) coordinate (jLtpg)
% Add transformer primary inductor with voltage arrow
(jLtpv) to [L,l_=$N_\mathrm{1}$, n=Ltp, v_=$U_\text{p}$,voltage shift=5, voltage=straight] ++(0,-2) coordinate (jLtpg)
(jLtpv) to [L,l_=$L_\mathrm{1}$, n=Ltp, v_=$U_\mathrm{p}$,voltage shift=5, voltage=straight] ++(0,-2) coordinate (jLtpg)
% Add turn name of primary inductor
(jLtpg) node[left] {$N_\mathrm{1}$}
% Add junctions for secondary inductor
(jLtpv) ++(0.8,0) coordinate (jLtsv)
(jLtpg) ++(0.8,0) coordinate (jLtsg);
Expand All @@ -65,35 +67,35 @@
(\x1/2+\x2/2, \y1) -- (\x1/2+\x2/2, \y2);
\draw
% Add transformer secondary inductor with voltage arrow
(jLtsv) to [L,l^=$N_\mathrm{2}$,n=Lts,mirror,v^=$U_\text{s}$, voltage shift=5, voltage=straight] (jLtsg);
(jLtsv) to [L,l^=$N_\mathrm{2}$,n=Lts,mirror,v^=$U_\mathrm{s}$, voltage shift=5, voltage=straight] (jLtsg);
\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^=$D_1$] ++ (3,0) coordinate (jD1k)
% Add junction point for DFsk
(jD1k) to [short,-*] ++(0,0) coordinate (jDFsk)
% Add junction point for DFsa
(jDFsk) ++ (0,-2) 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)
(jLtsv) to [D,l^=$D_\mathrm{1}$] ++ (3,0) coordinate (jD1k)
% Add junction point for D2k
(jD1k) to [short,-*] ++(0,0) coordinate (jD2k)
% Add junction point for D2a
(jD2k) ++ (0,-2) coordinate (jD2a)
% Add diode D2
(jD2a) to [D,l^=$D_\mathrm{2}$] (jD2k)
% Add inductor L4
(jD2k) to [L,l=$L_\mathrm{4}$,n=L1] ++(3,0) coordinate (jU2v)
% Add arrow and Text
(jDFsk) ++(0.5,0) node[currarrow](IL){}
(jD2k) ++(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,-2) coordinate (jU2g)
% Add connection to DFs
(jU2g) to [short,-*] (jDFsa)
(jU2v) to [V=$U_\mathrm{2}$] ++(0,-2) coordinate (jU2g)
% Add connection to D2
(jU2g) to [short,-*] (jD2a)
% Add connection to secondary transformer LTsg
(jDFsa) to [short,-] (jLtsg);
(jD2a) to [short,-] (jLtsg);

\end{circuitikz}
\end{center}
\caption{Single Ended Forward Converter circuit.}
\caption{Single ended forward converter circuit.}
\label{fig:ex04_SingledEndedForwardConverter}
\end{figure}
39 changes: 20 additions & 19 deletions exercise/tex/exercise04.tex
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Expand Up @@ -115,26 +115,27 @@

\task{Forward converter with asymmetric half-bridge}

The schematic of a forward converter with asymmetric half-bridge is shown in \autoref{fig:ex04_ForwardConverterWithAsymHalfBridge}.
The schematic of a forward converter with an asymmetric half-bridge is shown in \autoref{fig:ex04_ForwardConverterWithAsymHalfBridge}.
For the calculations the diodes and transistors are considered as ideal components.

\input{./fig/ex04/Fig_ForwardConverterWithAsymHalfBridge}

The parameters are listed in \autoref{fig:ex04_ForwardConverterWithAsymHalfBridge}
\input{./fig/ex04/FigTab_ForwardConverterWithAsymHalfBridge}
The parameters are listed in \autoref{fig:ex04_ForwardConverterWithAsymHalfBridge}.

\input{./fig/ex04/FigTab_ForwardConverterWithAsymHalfBridge}
\FloatBarrier
The leakage inductance, the resistive losses, and the core losses of the transformer are negligible.
The converter operates in steady-state conditions. Both transistors are controlled by the same signal.

\subtask{At what duty cycle $D$ does the circuit operate?}
\subtask{Calculate the average value of $i_\mathrm{2}$ and $i_\mathrm{1}$ over a clock cycle,
\subtask{Calculate the average value of $\overline{i_\mathrm{2}}$ and $\overline{i_\mathrm{1}}$ over a switching cycle,
assuming ideal filtering of $i_\mathrm{2}$.}
\subtask{Calculate the peak value of $\hat{i}_\mathrm{m}$ the magnetizing current $i_\mathrm{m}$.}
\subtask{Sketch the waveforms of $U_\mathrm{p}$, $i_\mathrm{m}$, $i_\mathrm{p}$ and $i_\mathrm{1}$
for the case of non-ideal current smoothing $L \neq \infty$.}
\subtask{Sketch the waveforms of $u_\mathrm{p}$, $i_\mathrm{m}$, $i_\mathrm{p}$ and $i_\mathrm{1}$
considering switching-induced ripples.}
\subtask{Calculate the minimal necessary input voltage $U_\mathrm{1}$, if the output voltage $U_\mathrm{2}$ = \SI{20}{\volt} shall being constant.}
\subtask{Calculate the inductance of $L$, if the peak-to-peak value $\Delta i_\mathrm{pp}$ of the
switching frequency ripple current $\Delta i_\mathrm{2}$ is to be 10\% of the average value $I_\mathrm{2}$?}
\subtask{Calculate the inductance of $L$,such that the ripple current $\Delta i_\mathrm{2}$ is to be $\SI{10}{\percent}$ of the
average output current $\overline{I_\mathrm{2}}$?}



Expand All @@ -149,25 +150,25 @@
\input{./fig/ex04/Fig_SingledEndedForwardConverter}

The parameters are listed in \autoref{table:Ex04_Parameters of the singled ended forward converter.}.
The output inductance is dimensioned so that the current $i_\mathrm{L}$ exhibits a continuous waveform.
The output inductance $L_\mathrm{4}$ is dimensioned so that the current $i_\mathrm{L4}$ exhibits a continuous waveform.
The transformer's leakage inductance can be neglected.

\input{./fig/ex04/FigTab_SingledEndedForwardConverter}

\subtask{Calculate the turns ratio $N_\mathrm{T}$/$N_\mathrm{1}$ so that the maximum blocking voltage
\subtask{Calculate the turns ratio $N_\mathrm{3}$/$N_\mathrm{1}$ so that the maximum blocking voltage
across the transistor during demagnetization is $\SI{600}{\volt}$.}
\subtask{What is the maximum permissible duty cycle of the power transistor in this case?}
\subtask{What turns ratio $N_\mathrm{1}$/$N_\mathrm{2}$ should be chosen to achieve the required secondary voltage?}
\subtask{Does the steady-state duty cycle of the transistor need to be adjusted when the output power changes?
Over what range must the transistor's duty cycle be adjustable, considering the input voltage range?}
\subtask{What is the maximum blocking voltage occurring across diode $D_\mathrm{1}$ and diode $U_\mathrm{DFs}$?}
\subtask{What should be the value of the primary inductance $L_\mathrm{p}$ to ensure
that the peak value of the magnetizing current remains below 10\% of the current $i_\mathrm{L'}$.
The current $i_\mathrm{L'}$ corresponds to the current $i_\mathrm{L}$ through the output inductance
at a nominal load of $P_2=\SI{125}{\watt}$, which is translated to the primary side.
(Assume $i_\mathrm{L}$ is approximately constant).}
\subtask{What are the resulting maximum blocking voltages of the diodes $D_\mathrm{1}$ and $D_\mathrm{2}$?}
\subtask{What should be the value of the primary inductance $L_\mathrm{1}$ to ensure
that the peak value of the magnetizing current remains below $\SI{10}{\percent}$ of the current $\overline{i_\mathrm{L4'}}$.
The current $\overline{i_\mathrm{L4'}}$ corresponds to the average current $\overline{i_\mathrm{L4}}$ through the output inductance
at a nominal load of $P_2=\SI{125}{\watt}$, which is translated to the primary side.}
\subtask{Sketch the waveform of the voltage across the power transistor, the current through the demagnetization
winding, and the current through the freewheeling diode $D_\mathrm{Fs}$
winding, and the current through the freewheeling diode $D_\mathrm{2}$
for $U_\mathrm{1}=\SI{240}{\volt}$ and $U_\mathrm{1}=\SI{360}{\volt}$.}
\subtask{Calculate the peak value of the magnetizing current for each case. Consider the current in the output
inductance as ideally filtered.}
\subtask{Could a higher power be transferred by doubling the switching frequency of the converter?}
inductor as ideally filtered.}
\subtask{Could a higher power be transferred by doubling the switching frequency of the converter?}

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