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\begin{document}

\section*{Monofazni ispravljači}

\subsection*{Monofazni ispravljač sa prostim kapacitivnim filtrom}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=0.75]{monofazni-C.ps}  
	\caption{Monofazni ispravljač sa prostim kapacitivnim filtrom.}
\end{figure}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{ciinvin.ps}  
	\caption{Monofazni ispravljač sa prostim kapacitivnim filtrom, ulazni napon i ulazna struja.}
\end{figure}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{ciout.ps}  
	\caption{Monofazni ispravljač sa prostim kapacitivnim filtrom, izlazna struja diodnog mosta.}
\end{figure}

\[ v_{IN} = V_m \sin \omega_0 t \]

\[ V_{OUTmax} = V_m \]

\[ C \left( 2 \Delta v_{OUT} \right) = \dfrac{T_0}{2} \; I_{OUT} \]

\[ \Delta V_{OUT} = \dfrac{I_{OUT}}{4 f_0 C} \]

\[ V_{OUT} = V_{OUTmax} - \Delta V_{OUT} = V_m - \dfrac{I_{OUT}}{4 f_0 C} \]

\[ i_{IN} = \dfrac{I_{OUT}}{2 f_0} \sum_{k=-\infty}^{\infty}{\left( \delta \left( t - \dfrac{T_0}{4} - k T_0 \right) - \delta \left( t - \dfrac{3 T_0}{4} - k T_0 \right) \right)} \]


\clearpage

\subsection*{Nekontrolisan strujom opterećen monofazni ispravljač}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=0.75]{monofazni-strujni.ps}  
	\caption{Nekontrolisan strujom opterećen monofazni ispravljač.}
\end{figure}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{siinvin.ps}  
	\caption{Nekontrolisan strujom opterećen monofazni ispravljač, ulazni napon i ulazna struja.}
\end{figure}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{svout.ps}  
	\caption{Nekontrolisan strujom opterećen monofazni ispravljač, izlazni napon.}
\end{figure}

\[ I_{1m} = \dfrac{4}{\pi} I_{OUT} \]

\[ I_{1RMS} = \dfrac{1}{\sqrt{2}} I_{1m} = \dfrac{2 \sqrt{2}}{\pi} I_{OUT} \]

\[ I_{RMS} = I_{OUT} \]

\[ cos \varphi_1 = 1 \]

\[ PF = \dfrac{I_{1RMS}}{I_{RMS}} \cos \varphi_1 = \dfrac{2 \sqrt{2}}{\pi} \approx 90.032 \%  \]

\[ THD = \sqrt{\left( \dfrac{I_{RMS}}{I_{1RMS}} \right) ^2 - 1} = \sqrt{ \dfrac{\pi^2}{8} - 1} \approx 48.34 \%\]

\clearpage

\subsection*{Potpuno kontrolisan monofazni tiristorski most}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=0.75]{monofazni-full.ps}  
	\caption{Potpuno kontrolisan monofazni tiristorski most.}
\end{figure}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{tiinvin.ps}  
	\caption{Potpuno kontrolisan monofazni tiristorski most, ulazna struja i ulazni napon.}
\end{figure}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{tvout.ps}  
	\caption{Potpuno kontrolisan monofazni tiristorski most, izlazni napon.}
\end{figure}

\[ V_{OUT} = \dfrac{1}{\pi} \int_{\alpha}^{\pi+\alpha}{V_m \sin(\omega_0 t) \; d(\omega_0 t)} = \dfrac{2}{\pi} V_m \cos \alpha \]

\[ I_{1RMS} = \dfrac{1}{\sqrt{2}} I_{1m} = \dfrac{2 \sqrt{2}}{\pi} I_{OUT} \]

\[ I_{RMS} = I_{OUT} \]

\[ cos \varphi_1 = \cos \alpha \]

\[ PF = \dfrac{I_{1RMS}}{I_{RMS}} \cos \varphi_1 = \dfrac{2 \sqrt{2}}{\pi} \cos \alpha \approx 90.032 \% \cos \alpha \]

\[ THD = \sqrt{\left( \dfrac{I_{RMS}}{I_{1RMS}} \right) ^2 - 1} = \sqrt{ \dfrac{\pi^2}{8} - 1} \approx 48.34 \%\]

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{t-Vout.ps}  
	\caption{Potpuno kontrolisan monofazni tiristorski most, zavisnost izlaznog napona od ugla uključenja tiristora.}
\end{figure}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{t-PFDPF.ps}  
	\caption{Potpuno kontrolisan monofazni tiristorski most, zavisnost $PF$ (puna linija) i $DPF$ (tanka linija) od ugla uključenja tiristora.}
\end{figure}

\clearpage

\subsection*{Polukontrolisan monofazni tiristorski most}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=0.75]{monofazni-half.ps}  
	\caption{Polukontrolisan monofazni tiristorski most.}
\end{figure}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{hiinvin.ps}  
	\caption{Polukontrolisan monofazni tiristorski most, ulazna struja i ulazni napon.}
\end{figure}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{hvout.ps}  
	\caption{Polukontrolisan monofazni tiristorski most, izlazni napon.}
\end{figure}

\[ V_{OUT} = \dfrac{1}{\pi} \int_{\alpha}^{\pi}{V_m \sin(\omega_0 t) \; d(\omega_0 t)} = \dfrac{1}{\pi} V_m \left( 1 + \cos \alpha \right) \]

\[ P_{OUT} = V_{OUT} I_{OUT} = \dfrac{1}{\pi} V_m I_{OUT} \left( 1 + \cos \alpha \right) \]

\[ I_{RMS} = I_{OUT} \sqrt{\dfrac{\pi-\alpha}{\pi}} \]

\[ S = V_{RMS} I_{RMS} = V_m I_{OUT} \sqrt{\dfrac{\pi-\alpha}{2 \pi}} \]

\[ P = P_{IN} = P_{OUT} = \dfrac{1}{\pi} V_m I_{OUT} \left( 1 + \cos \alpha \right) \]

\[ PF = \dfrac{P}{S} = \sqrt{\dfrac{2}{\pi (\pi-\alpha)}} \; \left( 1 + \cos \alpha \right) \]

\[ I_{1S} = \dfrac{2}{\pi} I_{OUT} \int_{\alpha}^{\pi}{\sin (\omega_0t) \; d(\omega_0t)} = \dfrac{2}{\pi} I_{OUT} \left( 1 + \cos \alpha \right) \]

\[ I_{1C} = \dfrac{2}{\pi} I_{OUT} \int_{\alpha}^{\pi}{\cos (\omega_0t) \; d(\omega_0t)} = - \dfrac{2}{\pi}  I_{OUT} \sin \alpha \]

\[ I_{1m} = \dfrac{2 \sqrt{2}}{\pi} I_{OUT} \sqrt{1 + \cos \alpha} \]

\[ I_{1RMS} = \dfrac{2}{\pi} I_{OUT} \sqrt{1 + \cos \alpha} \]

\[ DPF = \cos \varphi_1 = \sqrt{\dfrac{1 + \cos \alpha}{2}} = \cos \dfrac{\alpha}{2}\]

\[ THD = \sqrt{\dfrac{\pi (\pi - \alpha)}{4 (1 + \cos \alpha)} - 1} \]

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{h-Vout.ps}  
	\caption{Polukontrolisan monofazni tiristorski most, zavisnost izlaznog napona od ugla uključenja tiristora.}
\end{figure}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{h-PFDPF.ps}  
	\caption{Polukontrolisan monofazni tiristorski most, zavisnost $PF$ (puna linija) i $DPF$ (tanka linija) od ugla uključenja tiristora.}
\end{figure}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=1]{h-THD.ps}  
	\caption{Polukontrolisan monofazni tiristorski most, zavisnost $THD$ od ugla uključenja tiristora.}
\end{figure}
\clearpage

\subsection*{Nekontrolisan naponom opterećen monofazni ispravljač}

\begin{figure}[!h]
	\centering
	\includegraphics[scale=0.75]{monofazni-LV.ps}  
	\caption{Nekontrolisan naponom opterećen monofazni ispravljač.}
\end{figure}

\end{document}