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% Rectifier Tables: Monophasic Uncontrolled % 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}