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% Rectifier Tables % Diego Trapero

Rectifier Tables

  1. Monophasic Uncontrolled Rectifiers with R load
  2. Monophasic Uncontrolled Full Wave Rectifier loads
  3. Monophasic Controlled Full Wave Rectifier, R vs RL load
  4. Triphasic Uncontrolled Rectifiers with R load
  5. Triphasic Controlled Half Wave Rectifier, R vs RL load
  6. Triphasic Controlled Full Wave Rectifier, R vs RL load

\newpage

Monophasic Uncontrolled Rectifiers with R load

\tabulinesep=1mm \begin{longtabu} to\linewidth{|X[0.6,m,c]|X[2,m,c]|X[2,m,c]|}

\hline
What & Half Wave Rectifier & Full Wave Rectifier \\
\hline

Circuit Diagram
&
$$ % AC to DC Half Wave rectifier, by Diego Trapero
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	(0,0) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](0,4)
	(0,4) to[diode, l^=$D$](4,4)
	(0,0) to[short](4,0)
	(4,4) to[R, l=$R$, v_<=$v_o$](4,0)
	;
\end{circuitikz}
$$
&
$$ % AC to DC Full Wave rectifier, by Diego Trapero
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	%Sinusoidal source and connections
	(0,2) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](0,4)
	(0,2) to[short](4,2)
	(4,2) node[circ] {}
	(0,4) to[short](2,4)
	(2,4) node[circ] {}
	%Rectifier branch left
	(2,0) to[diode, l^=$D3$](2,2)
	(2,2) to[short](2,4)
	(2,4) to[diode, l^=$D1$](2,6)
	%Rectifier branch right
	(4,0) to[diode, l^=$D4$](4,2)
	(4,2) to[short](4,4)
	(4,4) to[diode, l^=$D2$](4,6)
	%Load and connections
	(2,6) to[short](8,6) %upper node
	(2,0) to[short](8,0) %lower node
	(8,6) to[R](8,0) %load
	;
\end{circuitikz}
$$
\\
\hline

$v_i > 0$ equivalent
&
$$ % AC to DC Half Wave rectifier, by Diego Trapero
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	(0,0) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](0,4)
	(0,4) to[short](4,4)
	(0,0) to[short](4,0)
	(4,4) to[R, l=$R$, v_<=$v_o$](4,0)
	;
\end{circuitikz}
$$
&
$$ % AC to DC Full Wave rectifier, by Diego Trapero
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	%Sinusoidal source and connections
	(0,2) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](0,4)
	(0,2) to[short](4,2)
	(4,2) node[circ] {}
	(0,4) to[short](2,4)
	(2,4) node[circ] {}
	%Rectifier branch left
	(2,0) to[open](2,2)
	(2,4) to[short](2,6)
	%Rectifier branch right
	(4,0) to[short](4,2)
	(4,4) to[open](4,6)
	%Load and connections
	(2,6) to[short](8,6) %upper node
	(4,0) to[short](8,0) %lower node
	(8,6) to[R](8,0) %load
	;
\end{circuitikz}
$$
\\
\hline

$v_i < 0$ equivalent
&
$$ % AC to DC Half Wave rectifier, by Diego Trapero
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	(0,0) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](0,4)
	(0,4) to[open](4,4)
	(0,0) to[short](4,0)
	(4,4) to[R, l=$R$, v_<=$v_o$](4,0)
	;
\end{circuitikz}
$$
&
$$ % AC to DC Full Wave rectifier, by Diego Trapero
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	%Sinusoidal source and connections
	(0,2) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](0,4)
	(0,2) to[short](4,2)
	(4,2) node[circ] {}
	(0,4) to[short](2,4)
	(2,4) node[circ] {}
	%Rectifier branch left
	(2,0) to[short](2,2)
	(2,2) to[short](2,4)
	(2,4) to[open](2,6)
	%Rectifier branch right
	(4,0) to[open](4,2)
	(4,2) to[short](4,4)
	(4,4) to[short](4,6)
	%Load and connections
	(4,6) to[short](8,6) %upper node
	(2,0) to[short](8,0) %lower node
	(8,6) to[R](8,0) %load
	;
\end{circuitikz}
$$
\\
\hline

Diode table
&
\vspace{30mm}
&
\vspace{30mm}
\\
\hline

$v_o$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:2*pi,samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=2*pi:3*pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:4*pi,samples=20, line width=2]{0};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:2*pi,samples=20, line width=2]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=2*pi:3*pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:4*pi,samples=20, line width=2]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$\bar{v_o}$
&
$$\bar{v_o} = \frac{V_{i p}}{\pi}$$
&
$$\bar{v_o} = \frac{2V_{i p}}{\pi}$$
\\
\hline

$i_o = i_R$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:pi,samples=50, line width=2]{0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:2*pi,samples=50, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=2*pi:3*pi,samples=50, line width=2]{0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:4*pi,samples=50, line width=2]{0};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:pi,samples=50, line width=2]{0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:2*pi,samples=50, line width=2]{-0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=2*pi:3*pi,samples=50, line width=2]{0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:4*pi,samples=50, line width=2]{-0.5*sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$i_i$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:pi,samples=50, line width=2]{0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:2*pi,samples=50, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=2*pi:3*pi,samples=50, line width=2]{0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:4*pi,samples=50, line width=2]{0};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:4*pi,samples=50, line width=2]{0.5*sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline

Diodes Voltage $v_D$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\

\end{longtabu}

\newpage

Monophasic Uncontrolled Full Wave Rectifier loads

\tabulinesep=1mm \begin{longtabu} to\linewidth{|X[1,m,c]|X[2,m,c]|X[2,m,c]|X[2,m,c]|}

\hline
What & R load & RC load & RLC load \\
\hline

Circuit Diagram
&
$$ % AC to DC Full Wave Rectifier with R load, by Diego Trapero
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) node[fullWaveRectifier](FWR){}
	(-19mm, -5mm) to[sinusoidal voltage source](-19mm, 5mm)
	(9mm, 5mm) to[short](19mm,5mm)
	(19mm, 5mm) to[open](19mm,-5mm)
	(29mm, 5mm) to[R](29mm,-5mm)
	(-19mm, 5mm) -- (FWR.1)
	(-19mm, -5mm) -- (FWR.2)
	(19mm,5mm) -- (29mm, 5mm)
	(FWR.3) -- (29mm,-5mm)
	;
\end{circuitikz}
$$	
&
$$ % AC to DC Full Wave Rectifier with RC load, by Diego Trapero
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) node[fullWaveRectifier](FWR){}
	(-19mm, -5mm) to[sinusoidal voltage source](-19mm, 5mm)
	(9mm, 5mm) to[short](19mm,5mm)
	(19mm, 5mm) to[C](19mm,-5mm)
	(29mm, 5mm) to[R](29mm,-5mm)
	(-19mm, 5mm) -- (FWR.1)
	(-19mm, -5mm) -- (FWR.2)
	(19mm,5mm) -- (29mm, 5mm)
	(FWR.3) -- (29mm,-5mm)
	;
\end{circuitikz}
$$
&
$$ % AC to DC Full Wave Rectifier with RLC load, by Diego Trapero
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) node[fullWaveRectifier](FWR){}
	(-19mm, -5mm) to[sinusoidal voltage source](-19mm, 5mm)
	(9mm, 5mm) to[L](19mm,5mm)
	(19mm, 5mm) to[C](19mm,-5mm)
	(29mm, 5mm) to[R](29mm,-5mm)
	(-19mm, 5mm) -- (FWR.1)
	(-19mm, -5mm) -- (FWR.2)
	(19mm,5mm) -- (29mm, 5mm)
	(FWR.3) -- (29mm,-5mm)
	;
\end{circuitikz}
$$
\\
\hline

$v_o$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:2*pi,samples=20, line width=2]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=2*pi:3*pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:4*pi,samples=20, line width=2]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:pi,samples=50, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:2*pi,samples=50, line width=2]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=2*pi:3*pi,samples=50, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:4*pi,samples=50, line width=2]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$v_R$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:2*pi,samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=2*pi:3*pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:4*pi,samples=20, line width=2]{0};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\

$\bar{v_R}$
&
$$\bar{v_R} = \frac{2}{\pi} V_{ip}$$
&
$$\bar{v_R} = V_{ip} - \frac{1}{2} \Delta v_R$$
&
$$\bar{v_R} = \frac{2}{\pi} V_{ip}$$
\\

$v_R$ ripple
&
Not considered
&
Triangular approximation
$$\Delta v_R = \frac{V_{ip}T}{2RC}$$
&
Considering only 1st harmonic
$$\Delta v_R = H V$$
\\
\hline

$i_R$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:pi,samples=50, line width=2]{0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:2*pi,samples=50, line width=2]{-0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=2*pi:3*pi,samples=50, line width=2]{0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:4*pi,samples=50, line width=2]{-0.5*sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$i_o$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:pi,samples=50, line width=2]{0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:2*pi,samples=50, line width=2]{-0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=2*pi:3*pi,samples=50, line width=2]{0.5*sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:4*pi,samples=50, line width=2]{-0.5*sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$i_i$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:4*pi,samples=50, line width = 2]{0.5*sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$i_{D1}$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$i_{D3}$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$i_C$
&
No capacitor
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=50]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\

\end{longtabu}

\newpage

Monophasic Controlled Full Wave Rectifier, R vs RL load

\tabulinesep=1mm \begin{longtabu} to\linewidth{|X[0.6,m,c]|X[2,m,c]|X[2,m,c]|}

\hline
What & Controlled FWR R load & Controlled FWR RL load \\
\hline

Circuit Diagram
&
$$ % AC to DC Full Wave rectifier, by Diego Trapero
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	%Sinusoidal source and connections
	(0,2) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](0,4)
	(0,2) to[short](4,2)
	(4,2) node[circ] {}
	(0,4) to[short](2,4)
	(2,4) node[circ] {}
	%Rectifier branch left
	(2,0) to[thyristor, l^=$T3$](2,2)
	(2,2) to[short](2,4)
	(2,4) to[thyristor, l^=$T1$](2,6)
	%Rectifier branch right
	(4,0) to[thyristor, l^=$T4$](4,2)
	(4,2) to[short](4,4)
	(4,4) to[thyristor, l^=$T2$](4,6)
	%Load and connections
	(2,6) to[short](8,6) %upper node
	(2,0) to[short](8,0) %lower node
	(8,6) to[R](8,0) %load
	;
\end{circuitikz}
$$
&
$$ % AC to DC Full Wave rectifier, by Diego Trapero
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	%Sinusoidal source and connections
	(0,2) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](0,4)
	(0,2) to[short](4,2)
	(4,2) node[circ] {}
	(0,4) to[short](2,4)
	(2,4) node[circ] {}
	%Rectifier branch left
	(2,0) to[thyristor, l^=$T3$](2,2)
	(2,2) to[short](2,4)
	(2,4) to[thyristor, l^=$T1$](2,6)
	%Rectifier branch right
	(4,0) to[thyristor, l^=$T4$](4,2)
	(4,2) to[short](4,4)
	(4,4) to[thyristor, l^=$T2$](4,6)
	%Load and connections
	(2,6) to[short](8,6) %upper node
	(2,0) to[short](8,0) %lower node
	(8,6) to[L](8,3) %load
	(8,0) to[R](8,3)
	;
\end{circuitikz}
$$
\\
\hline

$v_o$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:0.53,samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=0.53:pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:(pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(pi+0.53):2*pi,samples=20, line width=2]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=2*pi:(2*pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(2*pi+0.53):3*pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:(3*pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(3*pi+0.53):4*pi,samples=20, line width=2]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0.53:(pi+0.53),samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=(pi+0.53):(2*pi+0.53),samples=20, line width=2]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=(2*pi+0.53):(3*pi+0.53),samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=(3*pi+0.53):4*pi,samples=20, line width=2]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\

$\bar{v_o}(\alpha)$
&
$$ \bar{v_o} = \frac{V_i}{\pi} ( \cos{\alpha} + 1 ) $$
&
$$ \bar{v_o} = \frac{2 V_i}{\pi} \cos{\alpha} $$
\\
\hline

$v_R$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:0.53,samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=0.53:pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:(pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(pi+0.53):2*pi,samples=20, line width=2]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=2*pi:(2*pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(2*pi+0.53):3*pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:(3*pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(3*pi+0.53):4*pi,samples=20, line width=2]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:4*pi,samples=100, line width=2]{0.55+0.015*sin(deg(x))+0.01*sin(2*deg(x))+0.025*sin(3*deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline



Thyristor table
&
\vspace{30mm}
&
\vspace{30mm}
\\
\hline

$i_o(t)$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:0.53,samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=0.53:pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:(pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(pi+0.53):2*pi,samples=20, line width=2]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=2*pi:(2*pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(2*pi+0.53):3*pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:(3*pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(3*pi+0.53):4*pi,samples=20, line width=2]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:4*pi,samples=100, line width=2]{0.55+0.015*sin(deg(x))+0.01*sin(2*deg(x))+0.025*sin(3*deg(x))};
	\end{axis}
\end{tikzpicture}
\\

$\bar{i_o}$
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) to[voltage source, l=$\bar{v_o}$](0,2)
	(0,2) to[diode](2,2)
	(2,2) to[R](2,0)
	(0,0) to[short](2,0)
	(0,0) node[ground](){}
	;
\end{circuitikz}
$$\bar{i_o} = \frac{\bar{v_o}}{R} = \frac{\frac{V_i}{\pi} ( \cos{\alpha} + 1 )}{R}$$
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) to[voltage source, l=$\bar{v_o}$](0,2)
	(0,2) to[diode](2,2)
	(2,2) to[R](2,0)
	(0,0) to[short](2,0)
	(0,0) node[ground](){}
	;
\end{circuitikz}
$$\bar{i_o} = \frac{\bar{v_o}}{R} = \frac{\frac{2 V_i}{\pi} \cos{\alpha}}{R}$$
\\
\hline

$i_i(t)$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:0.53,samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=0.53:pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=pi:(pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(pi+0.53):2*pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=2*pi:(2*pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(2*pi+0.53):3*pi,samples=20, line width=2]{sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=3*pi:(3*pi+0.53),samples=20, line width=2]{0};
		\addplot[no marks,red,-] expression[domain=(3*pi+0.53):4*pi,samples=20, line width=2]{sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,red,-] expression[domain=0:0.53,samples=20, line width=2]{-0.55+0.015*sin(deg(x))+0.01*sin(2*deg(x))+0.025*sin(3*deg(x))};
		\addplot[no marks,red,-] expression[domain=0.53:(pi+0.53),samples=20, line width=2]{0.55+0.015*sin(deg(x))+0.01*sin(2*deg(x))+0.025*sin(3*deg(x))};
		\addplot[no marks,red,-] expression[domain=(pi+0.53):(2*pi+0.53),samples=20, line width=2]{-0.55+0.015*sin(deg(x))+0.01*sin(2*deg(x))+0.025*sin(3*deg(x))};
		\addplot[no marks,red,-] expression[domain=(2*pi+0.53):(3*pi+0.53),samples=20, line width=2]{0.55+0.015*sin(deg(x))+0.01*sin(2*deg(x))+0.025*sin(3*deg(x))};
		\addplot[no marks,red,-] expression[domain=(3*pi+0.53):4*pi,samples=20, line width=2]{-0.55+0.015*sin(deg(x))+0.01*sin(2*deg(x))+0.025*sin(3*deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$v_{T1}(t)$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=13,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28,9.42, 12.56},
		xticklabels={0, $\pi$, $2\pi$, $3\pi$, $4\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:4*pi,samples=100]{-sin(deg(x))};
	\end{axis}
\end{tikzpicture}
\\
\hline

Power
&
\vspace{30mm}
&
$$P = V_{1\text{ RMS}} I_{1\text{ RMS}} \cos{\varphi_1}$$
$$P = V_{ip} I_o \frac{2\sqrt{2}}{\pi} \cos{\alpha}$$
\\

Apparent Power
&
\vspace{30mm}
&
$$S = V_{\text{RMS}} I_{\text{RMS}}$$
$$S = \frac{V_{ip}}{\sqrt{2}} I_o$$
\\

Power factor
&
\vspace{30mm}
&
$$\text{PF} = \frac{2\sqrt{2}}{\pi} \cos{\alpha}$$
\\
\hline

\end{longtabu}

\newpage

Triphasic Uncontrolled Rectifiers with R load

\tabulinesep=1mm \begin{longtabu} to\linewidth{|X[0.6,m,c]|X[2,m,c]|X[2,m,c]|}

\hline
What & $3 \Phi$ Half Wave Rectifier & $3 \Phi$ Full Wave Rectifier \\
\hline

Circuit Diagram
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	%Sinusoidal source and connections
	(0,5) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](2,5)
	(0,4) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](2,4)
	(0,3) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](2,3)
	(2,5) to[diode](4,5)
	(2,4) to[diode](4,4)
	(2,3) to[diode](4,3)
	(0,5) to[short](0,0)
	(4,5) to[short](4,3)
	(4,4) to[short](5,4)
	(5,4) to[R](5,0)
	(0,0) to[short](5,0)
	(0,0) node[ground](){}
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	%Sinusoidal source and connections
	(0,2) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](1,2)
	(0,3) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](1,3)
	(0,4) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](1,4)
	(1,4) to[short, -*](2,4)
	(1,3) to[short, -*](3,3)
	(1,2) to[short, -*](4,2)
	(0,2) to[short](0,4)
	%Rectifier branch A
	(2,0) to[diode, l=$D4$](2,2)
	(2,2) to[short](2,4)
	(2,4) to[diode, l=$D1$](2,6)
	%Rectifier branch B
	(3,0) to[diode, l=$D3$](3,2)
	(3,2) to[short](3,4)
	(3,4) to[diode, l=$D2$](3,6)
	%Rectifier branch C
	(4,0) to[diode, l=$D6$](4,2)
	(4,2) to[short](4,4)
	(4,4) to[diode, l=$D3$](4,6)
	%Load and connections
	(2,6) to[short](6,6) %upper node
	(2,0) to[short](6,0) %lower node
	(6,6) to[R](6,0) %load
	;
\end{circuitikz}
\\
\hline

$v_o$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
\\

Peaks/period
&
3 peaks/period
&
3 peaks/period
\\

Period
&
$$ \frac{2\pi}{3} $$
&
$$ \frac{2\pi}{6} = \frac{\pi}{3} $$
\\

Integration limits
&
$$ \frac{\pi}{6}, \frac{5\pi}{6} $$
&
$$ \frac{\pi}{3}, \frac{2\pi}{3} $$
\\

Load Voltage
&
Phase Voltage
&
Line Voltage
\\

$\bar{v_o}$
&
$$\bar{v_o} = \frac{1}{\frac{2\pi}{3}} \int_{\frac{\pi}{6}}^{\frac{5\pi}{6}} { V_{PN} \sin{\theta} d\theta}$$
$$\bar{v_o} = \frac{3 V_{PN}}{2\pi} [ -\cos{\theta} ]_{\frac{\pi}{6}}^{\frac{5\pi}{6}}$$
$$\bar{v_o} = \frac{3 \sqrt{3}}{2\pi}  V_{PN}$$
&
$$\bar{v_o} = \frac{1}{\frac{\pi}{3}} \int_{\frac{\pi}{3}}^{\frac{2\pi}{3}} { V_{LL} \sin{\theta} d\theta}$$
$$\bar{v_o} = \frac{3 V_{LL}}{\pi} [ -\cos{\theta} ]_{\frac{\pi}{3}}^{\frac{2\pi}{3}}$$
$$\bar{v_o} = \frac{3}{\pi}  V_{LL}$$
\\
\hline

Diode table
&
\vspace{30mm}
&
\vspace{30mm}
\\
\hline

$i_o$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$i_i$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
\\

\end{longtabu}

\newpage

Triphasic Controlled Half Wave Rectifier, R vs RL load

\tabulinesep=1mm \begin{longtabu} to\linewidth{|X[0.6,m,c]|X[2,m,c]|X[2,m,c]|}

\hline
What & $3 \Phi$ Controlled HWR R load & $3 \Phi$ Controlled HWR RL load \\
\hline

Circuit Diagram
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	%Sinusoidal source and connections
	(0,5) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](2,5)
	(0,4) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](2,4)
	(0,3) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](2,3)
	(2,5) to[diode](4,5)
	(2,4) to[diode](4,4)
	(2,3) to[diode](4,3)
	(0,5) to[short](0,0)
	(4,5) to[short](4,3)
	(4,4) to[short](5,4)
	(5,4) to[R](5,0)
	(0,0) to[short](5,0)
	(0,0) node[ground](){}
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	%Sinusoidal source and connections
	(0,5) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](2,5)
	(0,4) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](2,4)
	(0,3) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](2,3)
	(2,5) to[diode](4,5)
	(2,4) to[diode](4,4)
	(2,3) to[diode](4,3)
	(0,5) to[short](0,0)
	(4,5) to[short](4,3)
	(4,4) to[short](5,4)
	(5,4) to[L](5,2)
	(5,2) to[R](5,0)
	(0,0) to[short](5,0)
	(0,0) node[ground](){}
	;
\end{circuitikz}
\\
\hline

$v_o$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$v_R$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
\\
\hline

Peaks/period
&
3 peaks/period
&
3 peaks/period
\\
\hline

Period
&
\vspace{10mm}
&
\vspace{10mm}
\\
\hline

Integration limits
&
\vspace{10mm}
&
\vspace{10mm}
\\
\hline

Load Voltage
&
\vspace{10mm}
&
\vspace{10mm}
\\
\hline

$\bar{v_o}(\alpha)$
&
\vspace{30mm}
&
$$\bar{v_o} = \frac{1}{\frac{2\pi}{3}} \int_{\frac{\pi}{6}+\alpha}^{\frac{5\pi}{6}+\alpha} { V_{PN} \sin{\theta} d\theta}$$
$$\bar{v_o} = \frac{3 V_{PN}}{2\pi} [ -\cos{\theta} ]_{\frac{\pi}{6}+\alpha}^{\frac{5\pi}{6}+\alpha}$$
$$\bar{v_o} = \frac{3 \sqrt{3}}{2\pi}  V_{PN} \cos{\alpha}$$
\\
\hline

Thyristor table
&
\vspace{30mm}
&
\vspace{30mm}
\\
\hline

$i_o$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$i_i$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
\\

\end{longtabu}

\newpage

Triphasic Controlled Full Wave Rectifier, R vs RL load

\tabulinesep=1mm \begin{longtabu} to\linewidth{|X[0.6,m,c]|X[2,m,c]|X[2,m,c]|}

\hline
What & $3 \Phi$ Controlled FWR R load & $3 \Phi$ Controlled FWR RL load \\
\hline

Circuit Diagram
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	%Sinusoidal source and connections
	(0,2) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](1,2)
	(0,3) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](1,3)
	(0,4) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](1,4)
	(1,4) to[short, -*](2,4)
	(1,3) to[short, -*](3,3)
	(1,2) to[short, -*](4,2)
	(0,2) to[short](0,4)
	%Rectifier branch A
	(2,0) to[thyristor, l=$T4$](2,2)
	(2,2) to[short](2,4)
	(2,4) to[thyristor, l=$T1$](2,6)
	%Rectifier branch B
	(3,0) to[thyristor, l=$T5$](3,2)
	(3,2) to[short](3,4)
	(3,4) to[thyristor, l=$T2$](3,6)
	%Rectifier branch C
	(4,0) to[thyristor, l=$T6$](4,2)
	(4,2) to[short](4,4)
	(4,4) to[thyristor, l=$T3$](4,6)
	%Load and connections
	(2,6) to[short](6,6) %upper node
	(2,0) to[short](6,0) %lower node
	(6,6) to[R](6,0) %load
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	%Sinusoidal source and connections
	(0,2) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](1,2)
	(0,3) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](1,3)
	(0,4) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](1,4)
	(1,4) to[short, -*](2,4)
	(1,3) to[short, -*](3,3)
	(1,2) to[short, -*](4,2)
	(0,2) to[short](0,4)
	%Rectifier branch A
	(2,0) to[thyristor, l=$T4$](2,2)
	(2,2) to[short](2,4)
	(2,4) to[thyristor, l=$T1$](2,6)
	%Rectifier branch B
	(3,0) to[thyristor, l=$T5$](3,2)
	(3,2) to[short](3,4)
	(3,4) to[thyristor, l=$T2$](3,6)
	%Rectifier branch C
	(4,0) to[thyristor, l=$T6$](4,2)
	(4,2) to[short](4,4)
	(4,4) to[thyristor, l=$T3$](4,6)
	%Load and connections
	(2,6) to[short](6,6) %upper node
	(2,0) to[short](6,0) %lower node
	(6,3) to[R](6,0) %load
	(6,6) to[L](6,3)
	;
\end{circuitikz}
\\
\hline

$v_o$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$v_R$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
\\
\hline

Peaks/period
&
6 peaks/period
&
6 peaks/period
\\
\hline

Period
&
\vspace{10mm}
&
\vspace{10mm}
\\
\hline

Integration limits
&
\vspace{10mm}
&
$$ \frac{\pi}{3} + \alpha, \frac{2\pi}{3} +\alpha $$
\\
\hline

Load Voltage
&
\vspace{10mm}
&
\vspace{10mm}
\\
\hline

$\bar{v_o}(\alpha)$
&
\vspace{30mm}
&
$$\bar{v_o} = \frac{1}{\frac{\pi}{3}} \int_{\frac{\pi}{3}+\alpha}^{\frac{2\pi}{3}+\alpha} { V_{LL} \sin{\theta} d\theta}$$
$$\bar{v_o} = \frac{3 V_{LL}}{\pi} [ -\cos{\theta} ]_{\frac{\pi}{3}+\alpha}^{\frac{2\pi}{3}+\alpha}$$
$$\bar{v_o} = \frac{3}{\pi}  V_{LL} \cos{\alpha}$$
\\
\hline

Thyristor table
&
\vspace{30mm}
&
\vspace{30mm}
\\
\hline

$i_o$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
\\
\hline

$i_i$
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
&
\begin{tikzpicture}[>=stealth, scale = 0.6, transform shape]
	\begin{axis}[
		xmin=0,xmax=6.5,
		ymin=-1,ymax=1,
		axis x line=middle,
		axis y line=middle,
		axis line style=->,
		%xlabel={$t$},
		%ylabel={$y$},
		ymajorgrids,
		xmajorgrids,
		xtick={0,3.14,6.28},
		xticklabels={0, $\pi$, $2\pi$},
		ytick={},
		yticklabels={}
		]
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{sin(deg(x-2.09440))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-1.04719))};
		\addplot[no marks,gray,-] expression[domain=0:2*pi,samples=100]{-sin(deg(x-2.09440))};
	\end{axis}
\end{tikzpicture}
\\

\end{longtabu}