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Ex03Task2 Translate subtask and add table and picture
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SevenOfNinePE committed Nov 7, 2024
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17 changes: 17 additions & 0 deletions exercise/fig/ex03/FigTab_BoostBuckConverter.tex
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Boost buck converter parameter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{table}[ht]
\centering % Zentriert die Tabelle
\begin{tabular}{llll}
\toprule

Input voltage: & $U_{\mathrm{1}} = \SI{380}{\volt}$ & Output voltage: & $U_{\mathrm{2}} = \SI{285}{\volt}$ to $\SI{450}{\volt}$\\
Output power: & $P_{\mathrm{2}} = \SI{3000}{\watt}$ & Switching frequency: & $f_{\mathrm{s}} = \SI{50}{\kilo\hertz}$ \\
\multicolumn{4}{l}{$P_{\mathrm{2}}$ is constant (unless otherwise stated)} \\
\bottomrule
\end{tabular}
\caption{Parameters of the circuit.} % Beschriftung der Tabelle
\label{table:Parameters of the buck-boost converter.}
\end{table}
60 changes: 60 additions & 0 deletions exercise/fig/ex03/Fig_BoostBuckConverter.tex
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\begin{figure}[htb]
\begin{center}
\begin{circuitikz}[european currents,european resistors,american inductors]
\draw
% Base coordinates
(0,0) coordinate (jU1v)
(0,-3) coordinate (jU1g)
% Add components
% Add primary source U1
(jU1v) to [V=$U_1$] (jU1g)
% Add current symbol and T1 with Control
(jU1v) ++(2,0) node[nigfete,rotate=90](Trans1){} -- ++(2.5,0) coordinate(T1)
(Trans1.G) to [sqV] ++(0,-1)
% At transistor label T1
(Trans1) node[anchor=south,color=black]{$T_1$}
% Short horizontal line
(jU1v) to [short,-] (Trans1.D)
% Add junction point for M-buck diode
(T1) to [short,-*] ++(0,0) coordinate (jDBuckM)
% Add junction point for P-buck diode
(jDBuckM) ++(0,-3) coordinate (jDBuckP)
% Add Inductance
(jDBuckM) to [L, l=$L$] ++ (3,0) coordinate (jT2v)
% Add arrow and Text
++(-0.5,0) node[currarrow](IL){}
(IL) node[anchor=south,color=black]{$i_\mathrm{L}$}
% Add junction point for Transistor
(jT2v) to [short,-*] ++(0,0)
% Add junction for Transistor
(jT2v) ++(0,-3) coordinate (jT2g)
% Add Diode
(jT2v) to [D-,l^=$D_{\mathrm{boost}}$] ++ (2,0) coordinate (jU2v)
% Add coordinate jU2v and jU2g
(jU2v) to [short,-] ++(0,-3) coordinate (jU2g)
% Add secondary source U2
(jU2v) to [V=$U_2$] (jU2g)
% Add junction point for transistor T2g
(jU2g) to [short,-*] (jT2g)
% Add transistor T2
(jT2v) ++ (0,-1.5) node[nigfete](Trans2){}
% At transistor label T2
(Trans2) node[anchor=west,color=black]{$T_2$}
% Connect Transistor
(jT2v) to [short,-] (Trans2.D)
(jT2g) to [short,-] (Trans2.S)
(Trans2.G) to [sqV] ++(-1,0)
% Add Junction point for diode D2g
(jT2g) to [short,-*] (jDBuckP)
% Add diode D2g
% (jDBuckP) to [D-,l^=$D_{buck}$,v =$U$,voltage shift=0, voltage=straight] (jDBuckM)
(jDBuckP) to [D-, l^=$D_{\mathrm{buck}}$, v_<=$U_0$, voltage=straight] (jDBuckM)
% Connect U1
(jDBuckP) to [short,-] (jU1g)
;
\end{circuitikz}
\end{center}
\caption{Buck-boost converter circuit.}
\label{fig:ex02_step_down_with_load_resistor}
\end{figure}
2 changes: 1 addition & 1 deletion exercise/tex/exercise02.tex
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Yes, the relationsships are independent from the switching frequency and switching points.
\end{solutionblock}

\vspace{2em}\par
\vspace{2em}\par
% Explaining text for the next subtask
If the transistors $T_1$ and $T_2$ are switched on, a constant voltage drop $U_\mathrm{F}=\SI{2.5}{\volt}$ occurs at the transistors
regardless of the current. All other components are considered ideal and loss-free.
Expand Down
72 changes: 27 additions & 45 deletions exercise/tex/exercise03.tex
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As the maximum current through the transistor is the current $I_1$, these values are the same. Since the BCM is considered in this circuit, the maximum current is the peak current, which corresponds to the value of $\SI{4.16}{\ampere}$.
\end{solutionblock}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Task 2: Boost-Buck converter and SEPIC topology
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\task {Boost-Buck converter and SEPIC topology}

Versorgung einer Plasmabeschichtungsanlage mit variabler Spannung U2 ausgehend von einer
geregelten Spannung U1 über Kopplung eines Hochsetzstellers und eines Tiefsetzstellers (mit
gemeinsamer Kapazität).


Bild


Angaben:
T2
DBoost
T1
C
U
L2
DBuck
U2
U1 = 380V
U2 = 285V ... 450V
P2 = 3000W konstant (falls nicht anders angegeben)
Schaltfrequenz: fP = 50kHz

The supply of a plasma coating system is realized by a boost converter and a buck converter (with common capacitance).
The converter is connected to a voltage $U_\mathrm{1}$ and provides a variable output voltage $U_\mathrm{2}$.

Die Ausgangsspannung wird durch entsprechende Einstellung der Tastverhältnisse D1 (von Transistor
T1) und D2 (von Transistor T2) mittels einer Regelung auf den vorgegebenen Wert eingestellt. Beide
Transistoren arbeiten mit gleicher Schaltfrequenz. Die schaltfrequente Schwankung der
Zwischenkreisspannung und der Ströme in den Induktivitäten können falls nicht anders
angegeben vernachlässigt werden. Die Ströme in L1 und L2 zeigen kontinuierlichen Verlauf.

Beide Transistoren werden mit gleicher relativer Einschaltdauer D1 = D2 = D betrieben.
\par
% Schematic of Buck Boost Converter cascade
\input{./fig/ex03/Fig_BoostBuckConverter}
\par
%Table of parameter values
\input{./fig/ex03/FigTab_BoostBuckConverter}

\subtask{Berechnen Sie die zur Realisierung einer Ausgangsspannung U2 einzustellende relative
Einschaltdauer D der Transistoren T1 und T2.}
The output voltage is set to the specified value by adjusting the duty cycles $D_\mathrm{1}$ (of transistor $T_\mathrm{1}$)
and $D_\mathrm{2}$ (of transistor $T_\mathrm{2}$) using a control system. Both transistors operate at the same switching frequency.
The switching frequency fluctuation of the intermediate circuit voltage and the currents in the inductors can be ignored unless otherwise stated.
The currents in $L_\mathrm{1}$ and $L_\mathrm{2}$ show a continuous course. Both transistors are operated with the
same relative duty cycle $D_\mathrm{1}$ = $D_\mathrm{2}$ = $D$.

\subtask{Welche Zwischenkreisspannung U stellt sich in Abhängigkeit von U2 ein?}
\subtask{Calculate the relative duty cycle $D$ of the transistors $T_\mathrm{1}$ and $T_\mathrm{1}$ to be set to achieve an output voltage $U_\mathrm{2}$.}

\subtask{Stellen Sie D und U über U2 graphisch dar und geben Sie die Zahlenwerte für U2 = 285V, U2 =
380V und U2 = 450V an.}
\subtask{Which intermediate circuit voltage U is determined depending on $U_\mathrm{2}$?}

\subtask{Welche Sperrspannungsfestigkeit müssen die Transistoren T1 und T2 und die Dioden DBoost und
DBuck aufweisen?}
\subtask{Plot $D$ and the voltage against $U_\mathrm{2}$ and calculate the numerical values for $U_\mathrm{2}$ = 285V, $U_\mathrm{2}$ =
380V and $U_\mathrm{2}$ = 450V.}

Die Steuerung erfolge weiterhin mit D1 = D2 = D. Die ein- und ausgangsseitigen Induktivitäten
weisen gleichen Wert L1 = L2 = L = 0.5mH auf.
\subtask{What blocking voltage strength must the transistors $T_\mathrm{1}$ and $T_\mathrm{2}$ and the diodes DBoost and
DBuck have?}
\vspace{2em}\par
The control continues with $D_\mathrm{1}$ = $D_\mathrm{2}$ = $D$. The input and output inductances
have the same value $L_\mathrm{1}$ = $L_\mathrm{2}$ = $L$ = $\SI{0.5}{m\henry}$.

% \subtask{Berechnen Sie allgemein die Abhängigkeit des eingangs- und ausgangsseitigen Induktivitätsstromrippels $\Delta$iL1,pp(D) und $\Delta$i_{L2},pp(D) ausschliesslich vom Tastverhältnis D.}
\subtask {Berechnen Sie allgemein die Abhängigkeit des eingangs- und ausgangsseitigen Induktivitätsrippels $\Delta i_{L1}$, pp(D) und $\Delta i_{L2}$,pp(D)}
\subtask{Write the formula for the dependence of the input and output inductance ripple $\Delta i_{L1}$ and $\Delta i_{L2}$}

\subtask{Wie weit darf die Ausgangleistung reduziert werden, um gerade noch kontinuierlichen Betrieb für
den gesamten Ausgangsspannungsbereich sicherzustellen (d.h. kontinuierlicher Stromverlauf in L1
und L2)?}
\subtask{To what minimum value can the output power be reduced while still ensuring continuous operation across the entire output voltage range?
(i.e. continuous current flow in $L_\mathrm{1}$ and L$L_\mathrm{2}$)?}

\subtask{In welchem Abschnitt des Ausgangsspannungsbereiches wird diese Grenze zuerst
eingangsseitig, in welchem zuerst ausgangsseitig erreicht?}
\subtask{In which section of the output voltage range is this limit reached first on the input side and in which section is it reached first on the output side?}

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