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diegotrap committed Jan 9, 2014
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294 changes: 280 additions & 14 deletions dcacconv.mdown
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Expand Up @@ -14,36 +14,199 @@ $$ % AC to DC Inverter, by Diego Trapero
\begin{circuitikz}[scale = 1]
\draw
%Sinusoidal source and connections
(0,2) to[sinusoidal voltage source, v^>=$v_i$, i^>=$i_i$](0,4)
(0,4) |- (6,6)
(0,2) |- (6,0)
(0,0) to[battery1, v^>=$v_i$, i^>=$i_i$](0,6)
(0,0) -- (8,0)
(0,6) -- (8,6)
%Rectifier branch left
(2,0) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](2,2)
(2,2) to[short](2,4)
(2,4) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](2,6)
(4,0) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](4,3)
(4,3) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](4,6)
%Rectifier branch right
(6,0) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](6,2)
(6,2) to[short](6,4)
(6,4) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](6,6)
(8,0) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](8,3)
(8,3) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](8,6)
%Load
(2,3) to[R](6,3) %load
(4,3) to[R](8,3) %load
;
\end{circuitikz}
$$

$$ % AC to DC Inverter, by Diego Trapero
\begin{circuitikz}[scale = 1]
\draw
%Sinusoidal source and connections
(0,0) to[battery1, v^>=$v_i$, i^>=$i_i$](0,3)
(0,0) -- (4,0)
(0,3) -- (4,3)
%Rectifier branch left
(2,0) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](2,1.5)
(2,1.5) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](2,3)
%Rectifier branch right
(4,0) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](4,1.5)
(4,1.5) to[Tnigfete, i^>=$i_D$, v_<=$v_D$](4,3)
%Load
(2,1.5) to[R](4,1.5) %load
;
\end{circuitikz}
$$

**Direct polarization of the load.** S1 and S4

$$ % AC to DC Inverter, by Diego Trapero
\begin{circuitikz}[scale = 1]
\draw
%Sinusoidal source and connections
(0,0) to[battery1, v^>=$v_i$, i^>=$i_i$](0,3)
(0,0) -- (4,0)
(0,3) -- (4,3)
%Rectifier branch left
%S3
(2,0) to[short, -*](2,0.5)
(2,1) to[short, *-](2,1.5)
(2,0.5) to[open](2,1.5)
%S1
(2,1.5) to[short, -*](2,2)
(2,2.5) to[short, *-](2,3)
(2,2) to[short](2,2.5)
%Rectifier branch right
%S4
(4,0) to[short, -*](4,0.5)
(4,1) to[short, *-](4,1.5)
(4,0.5) to[short](4,1.5)
%S2
(4,1.5) to[short, -*](4,2)
(4,2.5) to[short, *-](4,3)
(4,2) to[open](4,2.5)
%Load
(2,1.5) to[generic, v^<=$v_{AB}$](4,1.5) %load
;
\end{circuitikz}
$$

$$v_{AB} = V_i$$


**Inverse polarization of the load.** S2 and S3

$$ % AC to DC Inverter, by Diego Trapero
\begin{circuitikz}[scale = 1]
\draw
%Sinusoidal source and connections
(0,0) to[battery1, v^>=$v_i$, i^>=$i_i$](0,3)
(0,0) -- (4,0)
(0,3) -- (4,3)
%Rectifier branch left
%S3
(2,0) to[short, -*](2,0.5)
(2,1) to[short, *-](2,1.5)
(2,0.5) to[short](2,1.5)
%S1
(2,1.5) to[short, -*](2,2)
(2,2.5) to[short, *-](2,3)
(2,2) to[open](2,2.5)
%Rectifier branch right
%S4
(4,0) to[short, -*](4,0.5)
(4,1) to[short, *-](4,1.5)
(4,0.5) to[open](4,1.5)
%S2
(4,1.5) to[short, -*](4,2)
(4,2.5) to[short, *-](4,3)
(4,2) to[short](4,2.5)
%Load
(2,1.5) to[generic, v^<=$v_{AB}$](4,1.5) %load
;
\end{circuitikz}
$$

$$v_{AB} = -V_i$$

**Grounding.** S1 and S3 OR S2 and S4

$$ % AC to DC Inverter, by Diego Trapero
\begin{circuitikz}[scale = 1]
\draw
%Sinusoidal source and connections
(0,0) to[battery1, v^>=$v_i$, i^>=$i_i$](0,3)
(0,0) -- (4,0)
(0,3) -- (4,3)
%Rectifier branch left
%S3
(2,0) to[short, -*](2,0.5)
(2,1) to[short, *-](2,1.5)
(2,0.5) to[open](2,1.5)
%S1
(2,1.5) to[short, -*](2,2)
(2,2.5) to[short, *-](2,3)
(2,2) to[short](2,2.5)
%Rectifier branch right
%S4
(4,0) to[short, -*](4,0.5)
(4,1) to[short, *-](4,1.5)
(4,0.5) to[open](4,1.5)
%S2
(4,1.5) to[short, -*](4,2)
(4,2.5) to[short, *-](4,3)
(4,2) to[short](4,2.5)
%Load
(2,1.5) to[generic, v^<=$v_{AB}$](4,1.5) %load
;
\end{circuitikz}
$$

$$ % AC to DC Inverter, by Diego Trapero
\begin{circuitikz}[scale = 1]
\draw
%Sinusoidal source and connections
(0,0) to[battery1, v^>=$v_i$, i^>=$i_i$](0,3)
(0,0) -- (4,0)
(0,3) -- (4,3)
%Rectifier branch left
%S3
(2,0) to[short, -*](2,0.5)
(2,1) to[short, *-](2,1.5)
(2,0.5) to[short](2,1.5)
%S1
(2,1.5) to[short, -*](2,2)
(2,2.5) to[short, *-](2,3)
(2,2) to[open](2,2.5)
%Rectifier branch right
%S4
(4,0) to[short, -*](4,0.5)
(4,1) to[short, *-](4,1.5)
(4,0.5) to[short](4,1.5)
%S2
(4,1.5) to[short, -*](4,2)
(4,2.5) to[short, *-](4,3)
(4,2) to[open](4,2.5)
%Load
(2,1.5) to[generic, v^<=$v_{AB}$](4,1.5) %load
;
\end{circuitikz}
$$

$$v_{AB} = 0$$

**Shorting the source.** The two switches of a branch cannot be closed at the same time because it would short the source. That's the reason why same-branch switch control signals have to be complementary:

$$S1 = \bar{S3}$$
$$S2 = \bar{S4}$$


# Non modulated control

# Square wave control

## Square wave control




## Phase shift control


# PWM control

## Unipolar control
## Unipolar PWM

## Bipolar control
## Bipolar PWM

# Triphasic inverters

Expand Down Expand Up @@ -74,4 +237,107 @@ $$
| -------------- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- |
| $n = 1$ | 0.087 | 0.173 | 0.260 | 0.346 | 0.433 | 0.520 | 0.606 | 0.693 | 0.779 | 0.866 |
| $n = mf +- 2$ | 0.003 | 0.013 | 0.030 | 0.053 | 0.801 | 0.114 | 0.150 | 0.190 | 0.232 | 0.275 |
| $n = 2mf +- 1$ | 0.086 | 0.165 | 0.232 | 0.282 | 0.313 | 0.321 | 0.307 | 0.272 | 0.221 | 0.157 |
| $n = 2mf +- 1$ | 0.086 | 0.165 | 0.232 | 0.282 | 0.313 | 0.321 | 0.307 | 0.272 | 0.221 | 0.157 |


**Fourier series table**

\tabulinesep=1mm

\begin{longtabu} to\linewidth{|X[1,m,c]|X[3,m,c]|}


\hline
Function & Fourier Series \\
\hline


\begin{tikzpicture}[>=stealth, scale = 0.4, transform shape]
\begin{axis}[
xmin=0,xmax=4,
ymin=-2,ymax=2,
axis x line=middle,
axis y line=middle,
axis line style=->,
%xlabel={$t$},
%ylabel={$y$},
ymajorgrids,
xmajorgrids,
xtick={0,1,2,3,4},
xticklabels={$0$, $1$, $2$, $3$, $4$},
ytick={},
yticklabels={}
]
\addplot[no marks,red,-] expression[domain=0:1,samples=100]{1};
\addplot[no marks,red,-] expression[domain=1:2,samples=100]{-1};
\addplot[no marks,red,-] expression[domain=2:3,samples=100]{1};
\addplot[no marks,red,-] expression[domain=3:4,samples=100]{-1};
\end{axis}
\end{tikzpicture}
&
$$ \frac{4}{\pi} \left( \frac{\sin{t}}{1} + \frac{\sin{3t}}{3} + \frac{\sin{5t}}{5} + ... \right) $$
\\
\hline

\begin{tikzpicture}[>=stealth, scale = 0.4, transform shape]
\begin{axis}[
xmin=0,xmax=4,
ymin=-2,ymax=2,
axis x line=middle,
axis y line=middle,
axis line style=->,
%xlabel={$t$},
%ylabel={$y$},
ymajorgrids,
xmajorgrids,
xtick={0,1,2,3,4},
xticklabels={$0$, $1$, $2$, $3$, $4$},
ytick={},
yticklabels={}
]
\addplot[no marks,red,-] expression[domain=0.00:0.33,samples=100]{0};
\addplot[no marks,red,-] expression[domain=0.33:0.66,samples=100]{1};
\addplot[no marks,red,-] expression[domain=0.66:1.33,samples=100]{0};
\addplot[no marks,red,-] expression[domain=1.33:1.66,samples=100]{-1};
\addplot[no marks,red,-] expression[domain=1.66:2.33,samples=100]{0};
\addplot[no marks,red,-] expression[domain=2.33:2.66,samples=100]{1};
\addplot[no marks,red,-] expression[domain=2.66:3.33,samples=100]{0};
\addplot[no marks,red,-] expression[domain=3.33:3.66,samples=100]{-1};
\addplot[no marks,red,-] expression[domain=3.66:4.00,samples=100]{-1};
\end{axis}
\end{tikzpicture}
&
$$\frac{4}{\pi} \left( \frac{\sin{t}\cos{\beta}}{1} + \frac{\sin{3t}\cos{3\beta}}{3} + \frac{\sin{5t}\cos{5\beta}}{5} + ... \right)$$
\\
\hline


\begin{tikzpicture}[>=stealth, scale = 0.4, 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,red,-] expression[domain=0:pi,samples=100]{sin(deg(x))};
\addplot[no marks,red,-] expression[domain=pi:2*pi,samples=100]{-sin(deg(x))};
\addplot[no marks,red,-] expression[domain=2*pi:3*pi,samples=100]{sin(deg(x))};
\addplot[no marks,red,-] expression[domain=3*pi:4*pi,samples=100]{-sin(deg(x))};
\end{axis}
\end{tikzpicture}
&
$$ \frac{2}{\pi} - \frac{4}{\pi} \left( \frac{\sin{t}}{1 \cdot 3} + \frac{\sin{2t}}{3 \cdot 5} + \frac{\sin{3t}}{5 \cdot 7} + ... \right) $$
\\
\hline

\end{longtabu}
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