From 950a46368d81127f3b262cc3012fdd9eb28fc632 Mon Sep 17 00:00:00 2001 From: =?utf8?q?Nils=20Forss=C3=A9n?= Date: Tue, 30 Sep 2025 16:08:20 +0200 Subject: [PATCH] lab 3 completed --- gitlab | 2 +- lab3/Figures/150.png | Bin 0 -> 100013 bytes lab3/Figures/1k.png | Bin 0 -> 96559 bytes lab3/main.aux | 37 ++ lab3/main.fdb_latexmk | 175 +++++++++ lab3/main.fls | 886 ++++++++++++++++++++++++++++++++++++++++++ lab3/main.log | 607 +++++++++++++++++++++++++++++ lab3/main.out | 8 + lab3/main.pdf | Bin 0 -> 357969 bytes lab3/main.synctex.gz | Bin 0 -> 40723 bytes lab3/main.tex | 36 ++ lab3/main.toc | 8 + lab3/prep_task.tex | 79 ++++ lab3/sim_task.tex | 96 +++++ 14 files changed, 1933 insertions(+), 1 deletion(-) create mode 100644 lab3/Figures/150.png create mode 100644 lab3/Figures/1k.png create mode 100644 lab3/main.aux create mode 100644 lab3/main.fdb_latexmk create mode 100644 lab3/main.fls create mode 100644 lab3/main.log create mode 100644 lab3/main.out create mode 100644 lab3/main.pdf 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+\maketitle + +\tableofcontents +\newpage + +\input{prep_task.tex}\pagebreak +\input{sim_task.tex} + +\end{document} \ No newline at end of file diff --git a/lab3/main.toc b/lab3/main.toc new file mode 100644 index 0000000..9c6aecb --- /dev/null +++ b/lab3/main.toc @@ -0,0 +1,8 @@ +\contentsline {section}{\numberline {1}Preperations: MOSFET switching performance calculations}{2}{section.1}% +\contentsline {subsection}{\numberline {1.1}Turn-on delay calculations}{2}{subsection.1.1}% +\contentsline {subsection}{\numberline {1.2}Drain current rise time}{2}{subsection.1.2}% +\contentsline {subsection}{\numberline {1.3}Rate of change of drain-source voltage}{2}{subsection.1.3}% +\contentsline {subsection}{\numberline {1.4}Gate-source voltage due to complimentary MOSFET turn-off}{3}{subsection.1.4}% +\contentsline {section}{\numberline {2}Simulation of MOSFET gate drive and switching}{4}{section.2}% +\contentsline {subsection}{\numberline {2.1}Simulation results}{4}{subsection.2.1}% +\contentsline {subsection}{\numberline {2.2}Model validation}{5}{subsection.2.2}% diff --git a/lab3/prep_task.tex b/lab3/prep_task.tex new file mode 100644 index 0000000..7e4fd5e --- /dev/null +++ b/lab3/prep_task.tex @@ -0,0 +1,79 @@ +\section{Preperations: MOSFET switching performance calculations}\label{sec:lab2_prep} +In this section, the gate control of the MOSFETs in a full- or half-bridge circuit will be analyzed. For simplicity, the focus will be on the half-bridge, which is a building block in the full-bridge circuit. + +Consider $V_{gg} = 15$\,V at turn-on and $V_{gg} = 0$\,V at turn-off. Using the MOSFET datasheet fill Table~\ref{tab:MOSFETcaps}. +\begin{table}[h!] + \centering + \caption{MOSFET capacitances.} + \label{tab:MOSFETcaps} + \begin{tabular}{c|c|c|c} + \hline + $C_{iss}$ & pF & 1700 & at $V_{ds} = 25\,$V\\ + \hline + $C_{rss}$ & pF & 850 & at $V_{ds} = 25\,$V\\ + \hline + $C_{rss}$ & pF & 100 & at $V_{ds} = 0\,$V\\ + \hline + \end{tabular} +\end{table} + +\subsection{Turn-on delay calculations} + +% \subsubsection{Draw the equivalent circuit during the turn-on delay and use this equivalent circuit to derive the expression.} + +% Draw the equivalent circuit drawing goes here. + +% \vspace{50pt} + +% The derivation of the turn-on delay, +% \begin{align} +% \text{your derivation here} +% \end{align} + +Calculate $t_1$ considering two values of $R_{g1}$, i.e, 150\,$\Omega$ and 1\,k$\Omega$, and the turn-on delay $t_1$ is +\begin{align} + t_1 &= -R_{g1}C_{iss}\ln\left(1 - \frac{V_{th}}{V_{gg}}\right). \label{eq:lab2_turnondly} +\end{align} +For $R_{g1} = 150\,\Omega$ and $R_{g1} = 1\,\text{k}\Omega$, the turn-on delays are + +\begin{align} + t_1|_{150\,\Omega} &= 54 \text{ ns}, & t_1|_{1\,\text{k}\Omega} &= 357 \text{ ns}. +\end{align} + +\subsection{Drain current rise time} +To determine the drain current rise time, assume that the plateau voltage $V_{gp}=5\,$V, +\begin{align} + t_2 = -R_{g1}C_{iss}\ln\left(1 - \frac{V_{gp}}{V_{gg}}\right). \label{eq:lab2_turnonplat} +\end{align} +The drain current rise time $t_{ri}$ is +\begin{equation} + t_{ri} = t_2 - t_1. +\end{equation} +For $R_{g1} = 150\,\Omega$ and $R_{g1} = 1\,\text{k}\Omega$, the turn-on delays are + +\begin{align} + t_{ri}|_{150\,\Omega} &= 43 \text{ ns}, & t_{ri}|_{1\,\text{k}\Omega} &= 292 \text{ ns}. +\end{align} + +\subsection{Rate of change of drain-source voltage}\label{ssec:lab2_dvdt} +to determine, the rate of change of drain-source voltage $dV_{ds}/dt$, the average capacitance of $C_{rss}$ between 25\,V to 0\,V is used, and +\begin{align} + C_{rss}|_{\text{avg}} &= 730 \text{ pF}. +\end{align} + +The rate of change of drain-source voltage is calculated from +\begin{align} + i_g &= C_{rss}\frac{dV_{ds}}{dt}, \quad \text{where } i_g = \frac{V_{gg} - V_{gp}}{R_{g1}}. \nonumber \\ + \implies \frac{dV_{ds}}{dt} &= \frac{V_{gg} - V_{gp}}{R_{g1}C_{rss}} \\ + & = 91.3 \text{ MV/s when } R_{g1} = 150 \Omega. \\ + & = 13.7 \text{ MV/s when } R_{g1} = 1 \text{k}\Omega. +\end{align} + +\subsection{Gate-source voltage due to complimentary MOSFET turn-off} +When the high-side MOSFET (Q1) is turning off, due to the $C_{ds}$ of the low-side MOSFET (Q2), the gate-source voltage $V_{gs2}$ of Q2 will be affected. This is calcuated as +\begin{align} + V_{gs} &= V_{d4} + i_g R_{4}, \quad \text{where } i_g = C_{rss}\frac{dV_{ds}}{dt}. \nonumber \\ + \implies V_{gs} &= V_{d4} + \frac{C_{rss}}{R_{g1}}\left(V_{gg} - V_{gp}\right) \\ + & = 1.37 \text{ V when } R_{g1} = 150 \Omega. \\ + & = 0.8 \text{ V when } R_{g1} = 1 \text{k} \Omega. +\end{align} diff --git a/lab3/sim_task.tex b/lab3/sim_task.tex new file mode 100644 index 0000000..c6d2f56 --- /dev/null +++ b/lab3/sim_task.tex @@ -0,0 +1,96 @@ +\section{Simulation of MOSFET gate drive and switching}\label{sec:sim_mosfet} +This section presents the simulation results of the MOSFET gate drive and switching analysis. The simulation is performed using Simulink, and the results are compared with the analytical calculations from Section~\ref{sec:lab2_prep}. + +\subsection{Simulation results} +Figure \ref{fig:150} and \ref{fig:1000} shows the simulated waveforms for the gate voltage ($V_{gs}$) and the drain-source voltage ($V_{ds}$), drain current ($I_d$), gate current ($I_g$) and several other relevant signals during the switching events of the MOSFET. + +\begin{figure}\label{fig:150} + \centering + \includegraphics[width=0.8\textwidth]{Figures/150.png} + \caption{Simulation results, Rg = 150 Ohm} +\end{figure} + +\begin{figure}\label{fig:1000} + \centering + \includegraphics[width=0.8\textwidth]{Figures/1k.png} + \caption{Simulation results, Rg = 1000 Ohm} +\end{figure} + +From Figure \ref{fig:150} and \ref{fig:1000}, the following observations can be made: +\begin{enumerate} + \item Explain the relation between: \par + \begin{enumerate} + \item The gate-source voltage ($V_{gs}$) and gate current ($I_g$) of the switch $Q_1$. + \begin{tcolorbox} + When $V_{gs}$ start rising the gate current is at its maximum. As the voltage rises the current decreases + until eventually the gate is completely charged and the current is zero. The gate current stays constant during the Miller plateau + since $V_{gs}$ is constant and the current will charge the miller capacitance. + \end{tcolorbox} + \item The gate-source voltage ($V_{gs}$) and drain current ($I_q$) of the switch $Q_1$. + \begin{tcolorbox} + When $V_{gs}$ start rising the drain current is zero. As the voltage rises above the threshold voltage + of the transistor the drain current starts rising until the current saturates at its maximum value during the Miller plateau. + \end{tcolorbox} + \item The gate-source voltage ($V_{gs}$) and drain-to-source voltage ($V_{ds}$) of the switch $Q_1$. + \begin{tcolorbox} + When $V_{gs}$ start rising the drain to source voltage is at its maximum since the transistor starts in the off-state. + As the voltage rises above the threshold voltage the drain to source voltage will start falling. Once the the $V_{gs}$ + reaches the Miller plateau the drain to source voltage will fall rapidly until the transistor is fylly turned on. + \end{tcolorbox} + \item The drain current ($I_q$) and drain-to-source voltage ($V_{ds}$) of the switch $Q_1$. + \begin{tcolorbox} + The drain current will reach its maximum value before the drain to source voltage reaches its minimum. This is because + once the transistor reaches the Miller plateau the + \end{tcolorbox} + \end{enumerate} + \item Although the turn-on transients for the switch $Q_1$ are different for the two cases, the turn-off transients are similar, Why? + \begin{tcolorbox} + The gate resistor only affects the speed of the turn on transients since it limits the current that can charge the gate and miller capacitances. The turn-off transients are not affected. + \end{tcolorbox} + \item Observing the transients for the switch $Q_2$, at $t<0$, i.e., when the gate pulse is zero, why is there a current through the switch, $I_{q(2)} \neq 0$? + \begin{tcolorbox} + The body diode of the mosfet $Q_2$ will still conduct when the mosfet is off. Only when $Q_1$ is fully turned on the current through $Q_2$ will be zero. + \end{tcolorbox} + \item Observing the transients for the switch $Q_2$, why is there no plateau for $V_{gs(2)}$? + \begin{tcolorbox} + The lower transistor $Q_2$ has its source tied to ground instead of the switching node. The gate voltage will therefore not be affected by the miller capacitance and there will be no plateau. + \end{tcolorbox} + \item Which of the two cases (case 1 or 2) has higher switching losses? Is there a consequence with the case that has the lower switching loss? + \begin{tcolorbox} + The case with the lower gate resistance will have lower switching losses since the switching will be faster and less time will be spent in the transistors resistive region . This however also leads to higher rates of change which will lead to higher voltage spikes (see disturbance of the off-state mosfet). + \end{tcolorbox} +\end{enumerate} + +\subsection{Model validation} +Table~\ref{tab:simres_lab2} shows the results of the gate drive analysis for the power MOSFET. The table includes both simulated and calculated values, allowing for a comparison of the two methods. +\begin{table}[!h] + \centering + \caption{Simulated and analytical results of gate drive analysis for power MOSFET.} + \label{tab:simres_lab2} + \begin{tabular}{c|c|c|c|c|c|p{0.4\textwidth}} + & & \multicolumn{2}{c|}{Calculated} & \multicolumn{2}{c|}{Simulated} & \\ + & & \multicolumn{2}{c|}{Section~\ref{sec:lab2_prep}} & \multicolumn{2}{c|}{\textsf{Simulink}} & \\ + \hline + $R_{g}$ & $\Omega$ & 1000 & 150 & 1000 & 150 & \\ + \hline + $V_{th}$ for $Q_1$ & V & 3 & 3 & 2.36 & 2.51 & Gate threshold voltage \\ + \hline + $V_{gp}$ for $Q_1$ & V & & & 6.39 & 6.41 & Miller gate voltage plateau \\ + \hline + $I_{q}$ for $Q_1$ & A & - & - & 17 & 17 & MOSFET on-state current, i.e., the level after complete turn-on \\ + \hline + $t_{1}$ for $Q_1$ & ns & 357 & 54 & 366 & 47 & Time taken for $I_q$ to start rising from 0\,A \\ + \hline + $t_{ri}$ for $Q_1$ & ns & 292 & 43 & 645 & 102 & $I_q$ rise time \\ + \hline + $t_{3}$ mean for $Q_1$ & ns & - & - & 900 & 136 & Duration of Miller plateau \\ + \hline + $dV_{ds}/dt$ mean for $Q_1$ & V/$\mu$s & 13.7 & 91.3 & 19.5 & 141 & Average $dV/dt$ during Miller plateau \\ + \hline + $dV_{ds}/dt$ max for $Q_1$ & V/$\mu$s & - & - & 54.3 & 318 & maximum $dV/dt$ during initial steep part \\ + \hline + $dV_{ds}/dt$ max for $Q_2$ & V/$\mu$s & - & - & 49.3 & 502 & maximum $dV/dt$ during initial steep part \\ + \hline + $V_{gs}^{max}$ for $Q_2$ & V & 0.8 & 1.37 & 0.7 & 1.56 & Disturbance of the off-state MOSFET\\ + \end{tabular} +\end{table} \ No newline at end of file -- 2.30.2