% DC to DC Converter Tables % Diego Trapero

Non-Isolated DC to DC Converters

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

\hline
What & Buck & Boost & Buck-Boost \\
\hline

Circuit Diagram
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,2)
	(0,2) to[closing switch](2,2)
	(0,0) to[short](2,0)
	(2,0) to[diode, i^>=$i_D$, v_<=$v_D$](2,2)
	(2,0) to[short](4,0)
	(2,2) to[L, v^<=$v_L$, i_>=$i_L$](4,2)
	(4,2) to[C, i^>=$i_C$](4,0)
	(4,2) to[short, i^>=$i_o$](6,2)
	(4,0) to[short](6,0)
	(6,2) to[R, l=$R$, v_<=$v_o$](6,0)
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,2)
	(0,2) to[L, v^<=$v_L$, i_>=$i_L$](2,2)
	(0,0) to[short](2,0)
	(2,0) to[opening switch](2,2)
	(2,2) to[diode, i^>=$i_D$, v_<=$v_D$](4,2)
	(2,0) to[short](4,0)
	(4,2) to[C, i^>=$i_C$](4,0)
	(4,2) to[short, i^>=$i_o$](6,2)
	(4,0) to[short](6,0)
	(6,2) to[R, l=$R$, v_<=$v_o$](6,0)
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,2)
	(0,2) to[opening switch](2,2)
	(2,2) to[L, v^<=$v_L$, i_>=$i_L$](2,0)
	(0,0) to[short](2,0)
	(4,2) to[diode, i>=$i_D$, v_<=$v_D$](2,2)
	(2,0) to[short](4,0)
	(4,2) to[C, i^>=$i_C$](4,0)
	(4,2) to[short, i^>=$i_o$](6,2)
	(4,0) to[short](6,0)
	(6,2) to[R, l_=$R$, v^>=$v_o$](6,0)
	;
\end{circuitikz}
\\
\hline


ON Circuit
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) to[battery1](0,2)
	(0,2) to[short](0.66, 2) % Switch
	(1.33,2) to[short](2,2) 
	(1.33,2) node[circ] {}
	(0.66, 2) node[circ] {} % End switch
	(0,0) to[short](2,0)
	(2,0) to[short](2,0.66) %Diode
	(2,1.33) to[short](2,2)
	(2,0.66) node[circ] {}
	(2,1.33) node[circ] {} % End Diode
	(0,2) to[short](2,2) %Close switch
	(2,0) to[short](4,0)
	(2,2) to[L](4,2)
	(4,2) to[C](4,0)
	(4,2) to[short](6,2)
	(4,0) to[short](6,0)
	(6,2) to[R](6,0)
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,2)
	(0,2) to[L, v^<=$v_L$, i_>=$i_L$](2,2)
	(0,0) to[short](2,0)
	(2,0) to[short](2,0.66) %Switch
	(2,1.33) to[short](2,2)
	(2,0.66) to[short](2,1.33)%shorted switch
	(2,0.66) node[circ] {}
	(2,1.33) node[circ] {} % End Switch
	(2,2) to[short, -*](2.66,2) % Diode
	(3.33,2) to[short, *-](4,2) % End diode
	(2,0) to[short](4,0)
	(4,2) to[C, i^>=$i_C$](4,0)
	(4,2) to[short, i^>=$i_o$](6,2)
	(4,0) to[short](6,0)
	(6,2) to[R, l=$R$, v_<=$v_o$](6,0)
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,2)
	(0,2) to[short, -*](0.66,2)
	(1.33,2) to[short, *-](2,2)
	(0.66,2) to[short](1.33,2)
	(2,2) to[L, v^<=$v_L$, i_>=$i_L$](2,0)
	(0,0) to[short](2,0)
	(2,2) to[short, -*](2.66,2)
	(3.33,2) to[short, *-](4,2)
	(2.66,2) to[open](3.33,2)
	(2,0) to[short](4,0)
	(4,2) to[C, i^>=$i_C$](4,0)
	(4,2) to[short, i^>=$i_o$](6,2)
	(4,0) to[short](6,0)
	(6,2) to[R, l_=$R$, v^>=$v_o$](6,0)
	;
\end{circuitikz}
\\
\hline

OFF Circuit
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) to[battery1](0,2)
	(0,2) to[short](0.66, 2) % Switch
	(1.33,2) to[short](2,2) 
	(1.33,2) node[circ] {}
	(0.66, 2) node[circ] {} % End switch
	(0,0) to[short](2,0)
	(2,0) to[short](2,0.66) %Diode
	(2,1.33) to[short](2,2)
	(2,0.66) node[circ] {}
	(2,1.33) node[circ] {} % End Diode
	(2,0) to[short](2,2) %Close diode
	(2,0) to[short](4,0)
	(2,2) to[L](4,2)
	(4,2) to[C](4,0)
	(4,2) to[short](6,2)
	(4,0) to[short](6,0)
	(6,2) to[R](6,0)
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,2)
	(0,2) to[L, v^<=$v_L$, i_>=$i_L$](2,2)
	(0,0) to[short](2,0)
	(2,0) to[short](2,0.66) %Switch
	(2,1.33) to[short](2,2)
	(2,0.66) node[circ] {}
	(2,1.33) node[circ] {} % End %Switch
	(2,2) to[short, -*](2.66,2) % Diode
	(2.66,2) to[short](3.33,2) %shorted diode
	(3.33,2) to[short, *-](4,2) % End diode
	(2,0) to[short](4,0)
	(4,2) to[C, i^>=$i_C$](4,0)
	(4,2) to[short, i^>=$i_o$](6,2)
	(4,0) to[short](6,0)
	(6,2) to[R, l=$R$, v_<=$v_o$](6,0)
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.6, transform shape]
	\draw
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,2)
	(0,2) to[short, -*](0.66,2)
	(1.33,2) to[short, *-](2,2)
	(0.66,2) to[open](1.33,2)
	(2,2) to[L, v^<=$v_L$, i_>=$i_L$](2,0)
	(0,0) to[short](2,0)
	(2,2) to[short, -*](2.66,2)
	(3.33,2) to[short, *-](4,2)
	(2.66,2) to[short](3.33,2)
	(2,0) to[short](4,0)
	(4,2) to[C, i^>=$i_C$](4,0)
	(4,2) to[short, i^>=$i_o$](6,2)
	(4,0) to[short](6,0)
	(6,2) to[R, l_=$R$, v^>=$v_o$](6,0)
	;
\end{circuitikz}
\\
\hline

$V_o$ CCM
&
$$V_o = D V_i$$
&
$$V_o = \frac{1}{1-D} V_i$$
&
$$V_o = \frac{D}{1-D} V_i$$
\\
\hline

$D$ CCM
&
$$D = \frac{V_o}{V_i}$$
&
$$D = 1 - \frac{V_i}{V_o}$$
&
\vspace{20mm}
\\
\hline

$V_o$ DCM
&
\vspace{20mm}
&
$$V_o = V_i \frac{1+\sqrt{1+\frac{4D^2}{k}}}{2}$$
&
$$V_o = \frac{D}{\sqrt{k}}V_i$$
\\
\hline

$D$ DCM
&
$$D = \frac{V_o}{V_i} \sqrt{ \frac{k}{1-\frac{V_o}{V_i}} } $$
&
\vspace{20mm}
&
\vspace{20mm}
\\
\hline

$v_L$
&
\textbf{ON:}
$$v_L = V_i - V_o$$
\textbf{OFF:}
$$v_L = - V_o$$
\textbf{Waveform:}
\vspace{40mm}
&
\vspace{50mm}
&
\vspace{50mm}
\\
\hline

$i_L$
&
\textbf{Mean value:}
$$\bar{i_L} = \cancel{\bar{i_C}} + I_o$$
$$\bar{i_L} = \frac{V_o}{R}$$
\textbf{Ripple:}
$$\Delta i_L = \frac{(V_i - V_o)DT}{L}$$
$$\Delta i_L = \frac{V_o (1-D)T}{L}$$
\textbf{Waveform:}
\vspace{40mm}
&
\vspace{50mm}
&
\vspace{50mm}
\\
\hline

$i_o$
&
$$I_o = \frac{V_o}{R} = \frac{P_o}{V_o} = \sqrt{\frac{P_o}{R}}$$
&
$$I_o = \frac{V_o}{R} = \frac{P_o}{V_o} = \sqrt{\frac{P_o}{R}}$$
&
$$I_o = \frac{V_o}{R} = \frac{P_o}{V_o} = \sqrt{\frac{P_o}{R}}$$ 
\\
\hline

$v_S$
&
\textbf{ON:}
$$v_S = 0$$
\textbf{OFF:}
$$v_S = V_i - 0 = V_i$$
\vspace{40mm}
&
\vspace{40mm}
&
\vspace{40mm}
\\
\hline

$i_S$
&
\textbf{ON:}
$$i_S = i_L$$
\textbf{OFF:}
$$i_S = 0$$
\vspace{40mm}
&
\vspace{40mm}
&
\vspace{40mm}
\\
\hline

$v_D$
&
\textbf{ON:}
$$v_D = 0 - V_i = -V_i$$
\textbf{OFF:}
$$v_D = 0$$
\vspace{40mm}
&
\vspace{40mm}
&
\vspace{40mm}
\\
\hline

$i_D$
&
\textbf{ON:}
$$i_D = 0$$
\textbf{OFF:}
$$i_S = i_L$$
\vspace{40mm}
&
\vspace{40mm}
&
\vspace{40mm}
\\
\hline

$i_C$
&
$$i_C(t) = i_L(t) - I_o$$
$$I_1 = + \frac{1}{2} \Delta i_L$$
$$I_2 = - \frac{1}{2} \Delta i_L$$
\textbf{Waveform:}
\vspace{40mm}
&
\vspace{40mm}
&
\vspace{40mm}
\\

\end{longtabu}

\newpage

Isolated DC to DC Converters

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

\hline
What & Forward & Flyback \\
\hline

Circuit Diagram
&
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	% --- left side of the transformer ---
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,4) %battery
	(0,0) node[ground](){}
	(0,4) to[short, i^>=$i$](2,4) %left side upper node
	(2,4) to[short, i^>=$i_1$](4,4)
	(4,4) to[L, v_<=$v_1$](4,2) %First transformer winding
	(4,2) to[opening switch](4,0) %switching MOSFET
	(0,0) to[short](4,0) %lower node, ground
	(2,4) to[L, v_<=$v_{LM}$, i^>=$i_{LM}$](2,2) %transformer magnetizing inductance
	(2,2) to[short](4,2)
	% --- third winding ---
	(0,4) to[short](0,5)
	(0,5) to[short](5,5)
	(5,5) to[short](5,4)
	(5,4) to[L, v_>=$v_3$](5,2) %third transformer winding
	(5,0) to[diode, i>^=$i_{D3}$, v_<=$v_{D3}$](5,2) 
	(5,0) node[ground](){}
	% --- right side of the transformer ---
	(6,2) to[L, v^>=$v_2$](6,4) %second transformer winding
	(6,4) to[diode, i>^=$i_{D1}$, v_<=$v_{D1}$](8,4)
	(6,2) to[short](8,2)
	(8,2) to[diode, i>^=$i_{D2}$, v_<=$v_{D2}$](8,4)
	(8,2) to[short](10,2)
	(8,4) to[L, v^<=$v_L$, i_>=$i_L$](10,4)
	(10,4) to[C, i^>=$i_C$](10,2)
	(10,4) to[short, i^>=$i_o$](12,4)
	(10,2) to[short](12,2)
	(12,4) to[R, v^<=$v_o$](12,2)
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	% --- left side of the transformer ---
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,4) %battery
	(0,0) node[ground](){}
	(0,4) to[short](4,4) %left side upper node
	(4,4) to[L, v_<=$v_1$, i>^=$~$](4,2) %First transformer winding
	(4,2) to[opening switch, v_<=$v_S$, i^>=$i_S$](4,0)
	(0,0) to[short](4,0) %lower node, ground
	(2,4) to[L, v_<=$v_L$, i^>=$i_L$](2,2) %transformer magnetizing inductance
	(2,2) to[short](4,2)
	% --- right side of the transformer ---
	(5,2) to[L, v^<=$v_2$, i>^=$~$](5,4) %Second transformer winding
	(5,4) to[diode, i>^=$i_D$, v_<=$v_D$](7,4)
	(5,2) to[short](7,2)
	(7,4) to[C, i^>=$i_C$](7,2)
	(7,2) to[short](9,2)
	(7,4) to[short, i^>=$i_o$](9,4)
	(9,4) to[R, v^<=$v_o$](9,2)
	;
\end{circuitikz}
\\
\hline

ON Circuit
&
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	% --- left side of the transformer ---
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,4) %battery
	(0,0) node[ground](){}
	(0,4) to[short](4,4) %left side upper node
	(4,4) to[L, v_<=$v_1$](4,2) %First transformer winding
	(4,2) to[short, -*](4,1.33)
	(4,0) to[short, -*](4,0.66)
	(4,1.33) to[short](4,0.66)
	(0,0) to[short](4,0) %lower node, ground
	(2,4) to[L, v_<=$v_{LM}$, i^>=$i_{LM}$](2,2) %transformer magnetizing inductance
	(2,2) to[short](4,2)
	% --- third winding ---
	(0,4) to[short](0,5)
	(0,5) to[short](5,5)
	(5,5) to[short](5,4)
	(5,4) to[L, v_>=$v_3$](5,2) %third transformer winding
	(5,0) to[short, -*](5,0.66)
	(5,1.33) to[short, *-](5,2)
	(5,0.66) to[open](5,1.33)
	(5,0) node[ground](){}
	% --- right side of the transformer ---
	(6,2) to[L, v^>=$v_2$](6,4) %second transformer winding
	(6,4) to[short, -*](6.66,4)
	(7.33,4) to[short, *-](8,4)
	(6.66,4) to[short](7.33,4)
	(6,2) to[short](8,2)
	(8,2) to[short, -*](8,2.66)
	(8,3.33) to[short, *-](8,4)
	(8,2.66) to[open](8,3.33)
	(8,2) to[short](10,2)
	(8,4) to[L, v^<=$v_L$, i_>=$i_L$](10,4)
	(10,4) to[C, i^>=$i_C$](10,2)
	(10,4) to[short](12,4)
	(10,2) to[short](12,2)
	(12,4) to[R, v^<=$v_o$](12,2)
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	% --- left side of the transformer ---
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,4) %battery
	(0,0) node[ground](){}
	(0,4) to[short](4,4) %left side upper node
	(4,4) to[L, v_<=$v_1$, i>^=$~$](4,2) %First transformer winding
	(4,2) to[short, -*](4,1.33)
	(4,0) to[short, -*](4,0.66)
	(4,1.33) to[short](4,0.66)
	(0,0) to[short](4,0) %lower node, ground
	(2,4) to[L, v_<=$v_L$, i^>=$i_L$](2,2) %transformer magnetizing inductance
	(2,2) to[short](4,2)
	% --- right side of the transformer ---
	(5,2) to[L, v^<=$v_2$, i>^=$~$](5,4) %Second transformer winding
	(5,4) to[short, -*](5.66,4)
	(6.33,4) to[short, *-](7,4)
	(5.66,4) to[open](6.33,4)
	(5,2) to[short](7,2)
	(7,4) to[C, i^>=$i_C$](7,2)
	(7,2) to[short](9,2)
	(7,4) to[short, i^>=$i_o$](9,4)
	(9,4) to[R, v^<=$v_o$](9,2)
	;
\end{circuitikz}
\\
\hline

OFF Circuit
&
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	% --- left side of the transformer ---
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,4) %battery
	(0,0) node[ground](){}
	(0,4) to[short](4,4) %left side upper node
	(4,4) to[L, v_<=$v_1$](4,2) %First transformer winding
	(4,2) to[short, -*](4,1.33)
	(4,0) to[short, -*](4,0.66)
	(4,1.33) to[open](4,0.66)
	(0,0) to[short](4,0) %lower node, ground
	(2,4) to[L, v_<=$v_{LM}$, i^>=$i_{LM}$](2,2) %transformer magnetizing inductance
	(2,2) to[short](4,2)
	% --- third winding ---
	(0,4) to[short](0,5)
	(0,5) to[short](5,5)
	(5,5) to[short](5,4)
	(5,4) to[L, v_>=$v_3$](5,2) %third transformer winding
	(5,0) to[short, -*](5,0.66)
	(5,1.33) to[short, *-](5,2)
	(5,0.66) to[short](5,1.33)
	(5,0) node[ground](){}
	% --- right side of the transformer ---
	(6,2) to[L, v^>=$v_2$](6,4) %second transformer winding
	(6,4) to[short, -*](6.66,4)
	(7.33,4) to[short, *-](8,4)
	(6.66,4) to[open](7.33,4)
	(6,2) to[short](8,2)
	(8,2) to[short, -*](8,2.66)
	(8,3.33) to[short, *-](8,4)
	(8,2.66) to[short](8,3.33)
	(8,2) to[short](10,2)
	(8,4) to[L, v^<=$v_L$, i_>=$i_L$](10,4)
	(10,4) to[C, i^>=$i_C$](10,2)
	(10,4) to[short](12,4)
	(10,2) to[short](12,2)
	(12,4) to[R, v^<=$v_o$](12,2)
	;
\end{circuitikz}
&
\begin{circuitikz}[scale = 0.5, transform shape]
	\draw
	% --- left side of the transformer ---
	(0,0) to[battery1, v^>=$V_i$, i^>=$i_i$](0,4) %battery
	(0,0) node[ground](){}
	(0,4) to[short](4,4) %left side upper node
	(4,4) to[L, v_<=$v_1$, i>^=$~$](4,2) %First transformer winding
	(4,2) to[short, -*](4,1.33)
	(4,0) to[short, -*](4,0.66)
	(4,1.33) to[open](4,0.66)
	(0,0) to[short](4,0) %lower node, ground
	(2,4) to[L, v_<=$v_L$, i^>=$i_L$](2,2) %transformer magnetizing inductance
	(2,2) to[short](4,2)
	% --- right side of the transformer ---
	(5,2) to[L, v^<=$v_2$, i>^=$~$](5,4) %Second transformer winding
	(5,4) to[short, -*](5.66,4)
	(6.33,4) to[short, *-](7,4)
	(5.66,4) to[short](6.33,4)
	(5,2) to[short](7,2)
	(5,2) to[short](7,2)
	(7,4) to[C, i^>=$i_C$](7,2)
	(7,2) to[short](9,2)
	(7,4) to[short, i^>=$i_o$](9,4)
	(9,4) to[R, v^<=$v_o$](9,2)
	;
\end{circuitikz}
\\
\hline

$v_o$ CCM
&
$$V_o = \frac{N_2}{N_1}D V_i$$
&
$$ V_o = \frac{N_2}{N_1} \frac{D}{1-D} V_i $$
\\
\hline

$D$ CCM
&
$$D = \frac{V_o}{V_i} \frac{N_1}{N_2}$$
&
\vspace{10mm}
\\
\hline

$v_L$
&
\textbf{ON:}
$$v_L = v_2 - V_o$$
$$v_L = \frac{N_2}{N_1}v_1 - V_o$$
$$v_L = \frac{N_2}{N_1}V_i - V_o$$
\textbf{OFF:}
$$v_L = - V_o$$
\textbf{Waveform:}
\vspace{40mm}
&
\textbf{ON:}
$$v_L = V_i$$
\textbf{OFF:}
$$v_L = v_1$$
$$v_L = \frac{N_1}{N_2} v_2$$
$$v_L = -\frac{N_1}{N_2} V_o$$
\textbf{Waveform:}
\vspace{40mm}
\\
\hline

$$i_L$$
&
\vspace{50mm}
&
\vspace{50mm}
\\
\hline

$$v_{LM}$$
&
\vspace{50mm}
&
No
\\
\hline

$$v_3$$
&
\textbf{ON:}
$$v_3 = \frac{N_3}{N_1} v_1$$
$$v_3 = \frac{N_3}{N_1} V_i$$
\textbf{OFF:}
$$v_3 = -V_i$$
\textbf{Waveform:}
\vspace{40mm}
&
No
\\
\hline

$$v_S$$
&
\vspace{50mm}
&
\vspace{50mm}
\\
\hline

$$v_D$$
&
\vspace{50mm}
&
\vspace{50mm}
\\
\hline

$$i_S$$
&
\vspace{50mm}
&
\vspace{50mm}
\\
\hline

$$i_D$$
&
\vspace{50mm}
&
\vspace{50mm}
\\

\end{longtabu}

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