Added content on power and waveforms

acdcconvtablesMC.mdown

@@ -36,13 +36,13 @@
   (0,4) to[short](2,4)
   (2,4) node[circ] {}
   %Rectifier branch left
-  (2,0) to[diode, l^=$D3$](2,2)
+  (2,0) to[thyristor, l^=$T3$](2,2)
   (2,2) to[short](2,4)
-  (2,4) to[diode, l^=$D1$](2,6)
+  (2,4) to[thyristor, l^=$T1$](2,6)
   %Rectifier branch right
-  (4,0) to[diode, l^=$D4$](4,2)
+  (4,0) to[thyristor, l^=$T4$](4,2)
   (4,2) to[short](4,4)
-  (4,4) to[diode, l^=$D2$](4,6)
+  (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
@@ -61,17 +61,18 @@
   (0,4) to[short](2,4)
   (2,4) node[circ] {}
   %Rectifier branch left
-  (2,0) to[diode, l^=$D3$](2,2)
+  (2,0) to[thyristor, l^=$T3$](2,2)
   (2,2) to[short](2,4)
-  (2,4) to[diode, l^=$D1$](2,6)
+  (2,4) to[thyristor, l^=$T1$](2,6)
   %Rectifier branch right
-  (4,0) to[diode, l^=$D4$](4,2)
+  (4,0) to[thyristor, l^=$T4$](4,2)
   (4,2) to[short](4,4)
-  (4,4) to[diode, l^=$D2$](4,6)
+  (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
+  (8,6) to[L](8,3) %load
+  (8,0) to[R](8,3)
   ;
  \end{circuitikz}
  $$
@@ -194,8 +195,7 @@
   ]
   \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=0:4*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}
  \\
@@ -260,18 +260,34 @@
   ]
   \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=0:4*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
 
  $\bar{i_o}$
  &
- \vspace{20mm}
+ \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}
+ $$\bar{i_o} = \frac{\bar{v_o}}{R} = \frac{\frac{V_i}{\pi} ( \cos{\alpha} + 1 )}{R}$$
  &
- \vspace{20mm}
+ \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
 
@@ -295,6 +311,14 @@
   ]
   \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}
  &
@@ -316,8 +340,11 @@
   ]
   \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=0:0.53,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}
  \\
@@ -364,19 +391,33 @@
   ]
   \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))};
   \end{axis}
  \end{tikzpicture}
  \\
  \hline
 
- Power Factor
+ 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}