.MCAD 304020000 1 74 207 0
.CMD PLOTFORMAT
0 0 1 1 1 0 0 1 1 
0 0 1 1 1 0 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 15 0 0 3 
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.200000 1.216667 1.200000 1.200000 0
.CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty*
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.CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 colrid=-1
.CMD DEFAULT_TEXT_PARPROPS 0 0 0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
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.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2
.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3
.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4
.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5
.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6
.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7
.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=14 bold=0 italic=0 underline=0 colrid=-1
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.CMD UNITS U=1
.CMD DIMENSIONS_ANALYSIS 0 0
.CMD COLORTAB_ENTRY 0 0 0
.CMD COLORTAB_ENTRY 128 0 0
.CMD COLORTAB_ENTRY 0 128 0
.CMD COLORTAB_ENTRY 128 128 0
.CMD COLORTAB_ENTRY 0 0 128
.CMD COLORTAB_ENTRY 128 0 128
.CMD COLORTAB_ENTRY 0 128 128
.CMD COLORTAB_ENTRY 128 128 128
.CMD COLORTAB_ENTRY 192 192 192
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.TXT 5 3 56 0 0
Cg a71.000000,71.000000,402
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}{\f1\fcharset2\fnil Symbol;}}\plain
\cf1\fs28 \pard SINGLE-PHASE SEMI-CONTROLLED BRIDGE RECTIFIER\par \par 
Given the ratio of wL/R, the plots of rms line current, the rms of 
fundamental of line current, the Total Harmonic Distortion in the line 
current, the averagebridge output voltage, the rms  bridge output 
voltage and the Ripple factor of the bridge output voltage are 
obtained as a \par function of firing angle, {\f1 a}.  The firing 
angle is varied from 0{\up o} to 171{\up o}.}
.EQN 27 1 199 0 0
{0:\t}NAME:2.0
.TXT 0 11 200 0 0
Cg a60.000000,60.000000,22
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard The ratio is specified
}
.EQN 7 -11 192 0 0
{0:\b}NAME:{0:atan}NAME({0:\t}NAME)
.EQN 8 0 193 0 0
{0:Z}NAME:\(1+({0:\t}NAME)^(2))
.TXT 0 16 194 0 0
Cg a59.000000,59.000000,45
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard Impedance is 
calculated, assuming that R = 1.}
.TXT 10 -17 197 0 0
Cg a71.000000,71.000000,109
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard The 
coefficient that is present in the expression for load current is 
computed\par as a function of firing angle.}
.EQN 12 0 198 0 0
{0:A}NAME({0:\a}NAME):(1)/({0:Z}NAME)*({0:sin}NAME({0:\p}NAME-{0:\b}NAME)*({0:e}NAME)^(-(({0:\a}NAME)/({0:\t}NAME)))-{0:sin}NAME({0:\a}NAME-{0:\b}NAME))/(1-({0:e}NAME)^(-(({0:\p}NAME)/({0:\t}NAME))))
.TXT 12 0 195 0 0
Cg a71.000000,71.000000,65
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}{\f1\fcharset2\fnil Symbol;}}\plain
\cf1\fs28 \pard Load current at wt = {\f1 p} is obtained as a function 
of firing angle.}
.EQN 11 0 196 0 0
{0:I\p}NAME({0:\a}NAME):(1)/({0:Z}NAME)*{0:sin}NAME({0:\p}NAME-{0:\b}NAME)+{0:A}NAME({0:\a}NAME)*({0:e}NAME)^(-(({0:\p}NAME-{0:\a}NAME)/({0:\t}NAME)))
.TXT 19 1 76 0 0
Cg a70.000000,70.000000,68
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard Next the rms 
line current is obtained as a function of firing angle.}
.EQN 12 0 166 0 0
{0:f1}NAME({0:\a}NAME):(1)/({0:\p}NAME)*(0&{0:\a}NAME`(({0:I\p}NAME({0:\a}NAME)*({0:e}NAME)^(-(({0:\q}NAME)/({0:\t}NAME)))))^(2)&{0:\q}NAME)
.EQN 14 0 167 0 0
{0:f2}NAME({0:\a}NAME):(1)/({0:\p}NAME)*({0:\a}NAME&{0:\p}NAME`(((1)/({0:Z}NAME)*{0:sin}NAME({0:\q}NAME-{0:\b}NAME)+{0:A}NAME({0:\a}NAME)*({0:e}NAME)^(-(({0:\q}NAME-{0:\a}NAME)/({0:\t}NAME)))))^(2)&{0:\q}NAME)
.EQN 17 0 171 0 0
{0:IT}NAME({0:\a}NAME):\({0:f1}NAME({0:\a}NAME)+{0:f2}NAME({0:\a}NAME))
.TXT 9 0 201 0 0
Cg a70.000000,70.000000,179
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard The 
trigonometric coefficients of the fundamental are obtained(Fourier 
series).  Since the line current has half-wave symmetry, the 
coefficients can be calculated as shown below. }
.EQN 18 1 174 0 0
{0:f3}NAME({0:\a}NAME):(2)/({0:\p}NAME)*({0:\p}NAME&{0:\p}NAME+{0:\a}NAME`{0:I\p}NAME({0:\a}NAME)*({0:e}NAME)^(-((({0:\q}NAME-{0:\p}NAME))/({0:\t}NAME)))*{0:cos}NAME({0:\q}NAME)&{0:\q}NAME)
.EQN 15 0 176 0 0
{0:f4}NAME({0:\a}NAME):(2)/({0:\p}NAME)*({0:\a}NAME&{0:\p}NAME`((1)/({0:Z}NAME)*{0:sin}NAME({0:\q}NAME-{0:\b}NAME)+{0:A}NAME({0:\a}NAME)*({0:e}NAME)^(-(({0:\q}NAME-{0:\a}NAME)/({0:\t}NAME))))*{0:cos}NAME({0:\q}NAME)&{0:\q}NAME)
.EQN 23 0 179 0 0
{0:IC}NAME({0:\a}NAME):{0:f3}NAME({0:\a}NAME)+{0:f4}NAME({0:\a}NAME)
.EQN 14 0 181 0 0
{0:f5}NAME({0:\a}NAME):(2)/({0:\p}NAME)*({0:\p}NAME&{0:\p}NAME+{0:\a}NAME`{0:I\p}NAME({0:\a}NAME)*({0:e}NAME)^(-((({0:\q}NAME-{0:\p}NAME))/({0:\t}NAME)))*{0:sin}NAME({0:\q}NAME)&{0:\q}NAME)
.EQN 15 0 183 0 0
{0:f6}NAME({0:\a}NAME):(2)/({0:\p}NAME)*({0:\a}NAME&{0:\p}NAME`((1)/({0:Z}NAME)*{0:sin}NAME({0:\q}NAME-{0:\b}NAME)+{0:A}NAME({0:\a}NAME)*({0:e}NAME)^(-(({0:\q}NAME-{0:\a}NAME)/({0:\t}NAME))))*{0:sin}NAME({0:\q}NAME)&{0:\q}NAME)
.EQN 11 0 184 0 0
{0:IS}NAME({0:\a}NAME):{0:f5}NAME({0:\a}NAME)+{0:f6}NAME({0:\a}NAME)
.EQN 13 0 185 0 0
{0:I1}NAME({0:\a}NAME):\((({0:IC}NAME({0:\a}NAME))^(2)+({0:IS}NAME({0:\a}NAME))^(2))/(2))
.TXT 13 -2 203 0 0
Cg a70.000000,70.000000,101
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard The function 
displayed above calculates the rms value of the \par fundamental 
component of line current. }
.TXT 32 1 204 0 0
Cg a70.000000,70.000000,79
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard Next the Total 
Harmonic Distortion is expressed as a function of \par firing angle.}
.EQN 15 1 151 0 0
{0:THD}NAME({0:\a}NAME):\(((({0:IT}NAME({0:\a}NAME))/({0:I1}NAME({0:\a}NAME))))^(2)-1)
.TXT 8 0 152 0 0
Cg a70.000000,70.000000,45
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard Next the range 
for firing angle is specified.}
.EQN 7 0 153 0 0
{0:\a}NAME:0,({0:\p}NAME)/(180);0.95*{0:\p}NAME
.EQN 9 -2 205 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:THD}NAME({0:\a}NAME)@1&0&(_n_u_l_l_&_n_u_l_l_)&({0:\a}NAME)/({0:\p}NAME)
0 1 1 1 0 5 0 1 1 
0 1 1 1 0 4 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 51 27 18 0 3 Total Harmonic Distortion
.TXT 45 2 155 0 0
Cg a70.000000,70.000000,187
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard In addition to 
the plot of Total Harmonic Distortion, the plots of rms \par line 
current and the rms value of fundmental component of line \par current 
are displayed as functions of firing angle.}
.EQN 30 -3 206 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:IT}NAME({0:\a}NAME)@1&0&(_n_u_l_l_&_n_u_l_l_)&({0:\a}NAME)/({0:\p}NAME)
0 1 1 1 0 5 0 1 1 
0 1 1 1 0 4 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 51 27 18 0 3 Line RMS Current(Total)
.EQN 43 1 207 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:I1}NAME({0:\a}NAME)@1&0&(_n_u_l_l_&_n_u_l_l_)&({0:\a}NAME)/({0:\p}NAME)
0 1 1 1 0 5 0 1 1 
0 1 1 1 0 4 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 51 25 18 0 3 Line rms Current(Fundamental)
.TXT 52 1 141 0 0
Cg a70.000000,70.000000,81
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard Next the 
average voltage of the bridge is obtained as a function of firing\par angle.}
.EQN 10 0 142 0 0
{0:Vavg}NAME({0:\a}NAME):(1)/({0:\p}NAME)*(1+{0:cos}NAME({0:\a}NAME))
.TXT 6 -3 143 0 0
Cg b73.000000,73.000000,89
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard       Next the 
rms voltage of the bridge is obtained as a function of firing\par       angle.
}
.EQN 15 3 144 0 0
{0:Vrms}NAME({0:\a}NAME):\((1)/({0:\p}NAME)*({0:\a}NAME&{0:\p}NAME`({0:sin}NAME({0:\q}NAME))^(2)&{0:\q}NAME))
.TXT 9 0 145 0 0
Cg a70.000000,70.000000,82
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue128;}{\fonttbl{\f0
\fcharset0\fnil Times New Roman;}}\plain\cf1\fs28 \pard The Ripple 
Factor of the bridge output voltage is obtained next as a firing\par angle.}
.EQN 11 0 146 0 0
{0:RF}NAME({0:\a}NAME):({0:\p}NAME)/(2)*\(({0:Vrms}NAME({0:\a}NAME))^(2)-({0:Vavg}NAME({0:\a}NAME))^(2))
.EQN 8 -1 189 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:RF}NAME({0:\a}NAME)@1&0&(_n_u_l_l_&_n_u_l_l_)&({0:\a}NAME)/({0:\p}NAME)
0 1 1 1 0 5 0 1 1 
0 1 1 1 0 4 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 46 21 18 0 3 Ripple Factor
.EQN 54 -1 188 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:Vrms}NAME({0:\a}NAME)@1&0&(_n_u_l_l_&_n_u_l_l_)&({0:\a}NAME)/({0:\p}NAME)
0 1 1 1 0 5 0 1 1 
0 1 1 1 0 4 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 47 23 18 0 3 RMS Output voltage
.EQN 42 1 187 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:Vavg}NAME({0:\a}NAME)@1&0&(_n_u_l_l_&_n_u_l_l_)&({0:\a}NAME)/({0:\p}NAME)
0 1 1 1 0 5 0 1 1 
0 1 1 1 0 4 0 1 1 
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 46 22 18 0 3 Average Output voltage