{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 4: Thyristors"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.10: EX4_10.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"clear\n",
"function [I_TAV]=theta(th)\n",
"    n=360/th;\n",
"    I=1;    //supposition\n",
"    I_av=I/n;\n",
"    I_rms=I/sqrt(n);\n",
"    FF=I_rms/I_av;\n",
"    I_rms=35;\n",
"    I_TAV=I_rms/FF;\n",
"endfunction\n",
"disp('when conduction angle=180');\n",
"th=180;\n",
"I_TAV=theta(th);\n",
"printf('avg on current rating=%.3f A',I_TAV);\n",
"disp('when conduction angle=90');\n",
"th=90;\n",
"I_TAV=theta(th);\n",
"printf('avg on current rating=%.1f A',I_TAV);\n",
"disp('when conduction angle=30');\n",
"th=30;\n",
"I_TAV=theta(th);\n",
"printf('avg on current rating=%.4f A',I_TAV);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.11: to_calculate_surge_current_rating_and_power_rating.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"f=50;    //Hz\n",
"I_sb=3000;\n",
"t=1/(4*f);\n",
"T=1/(2*f);\n",
"I=sqrt(I_sb^2*t/T);    printf('surge current rating=%.2f A',I);\n",
"r=(I_sb/sqrt(2))^2*T;    printf('\nI^2*t rating=%.0f A^2.s',r);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.12: to_find_maximum_value_of_the_remedial_parameter.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"V_s=300;//V\n",
"R=60;//ohm\n",
"L=2;//H\n",
"t=40*10^-6;//s\n",
"i_T=(V_s/R)*(1-exp(-R*t/L));\n",
"i=.036;//A\n",
"R1=V_s/(i-i_T);\n",
"printf('maximum value of remedial parameter=%.3f kilo-ohm',R1/1000);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.16: to_calculate_fault_clearance_time.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"V_p=230*sqrt(2);\n",
"R=1+((1)^-1+(10)^-1)^-1;\n",
"A=V_p/R;\n",
"s=1;    //s\n",
"t_c=20*A^-2*s;    printf('fault clearance time=%.4f ms',t_c*10^3);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.17: EX4_17.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"V_s=sqrt(2)*230;    //V\n",
"L=15*10^-6;    //H\n",
"I=V_s/L;    //I=(di/dt)_max\n",
"printf('(di/dt)_max=%.3f A/usec',I/10^6);\n",
"R_s=10;  //ohm\n",
"v=I*R_s;    //v=(dv/dt)_max\n",
"printf('\n(dv/dt)_max=%.2f V/usec',v/10^6);\n",
"\n",
"f=50;    //Hz\n",
"X_L=L*2*%pi*f;\n",
"R=2;\n",
"I_max=V_s/(R+X_L);    printf('\nI_rms=%.3f A',I_max);\n",
"disp('when conduction angle=90');\n",
"FF=%pi/sqrt(2);\n",
"I_TAV=I_max/FF;    printf('I_TAV=%.3f A',I_TAV);\n",
"disp('when conduction angle=30');\n",
"FF=3.98184;\n",
"I_TAV=I_max/FF;    printf('I_TAV=%.3f A',I_TAV);\n",
"\n",
"printf('\nvoltage rating=%.3f V',2.75*V_s);//rating is taken 2.75 times of peak working voltage unlike 2.5 to 3 times as mentioned int book."
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.19: EX4_19.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"T_jm=125;\n",
"th_jc=.15;    //degC/W\n",
"th_cs=0.075;    //degC/W\n",
"\n",
"dT=54;    //dT=T_s-T_a\n",
"P_av=120;\n",
"th_sa=dT/P_av;\n",
"T_a=40;    //ambient temp\n",
"P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs);\n",
"if((P_av-120)<1)\n",
"    disp('selection of heat sink is satisfactory');\n",
"end\n",
"dT=58;    //dT=T_s-T_a\n",
"P_av=120;\n",
"th_sa=dT/P_av;\n",
"T_a=40;    //ambient temp\n",
"P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs);\n",
"if((P_av-120)<1)\n",
"    disp('selection of heat sink is satisfactory');\n",
"end\n",
"\n",
"V_m=sqrt(2)*230;\n",
"R=2;\n",
"I_TAV=V_m/(R*%pi);\n",
"P_av=90;\n",
"th_sa=(T_jm-T_a)/P_av-(th_jc+th_cs);\n",
"dT=P_av*th_sa;\n",
"disp('for heat sink');    printf('T_s-T_a=%.2f degC',dT);    printf('\nP_av=%.0f W',P_av);\n",
"P=(V_m/2)^2/R;\n",
"eff=P/(P+P_av);    printf('\nckt efficiency=%.3f pu',eff);\n",
"\n",
"a=60;    //delay angle\n",
"I_TAV=(V_m/(2*%pi*R))*(1+cosd(a));\n",
"printf('\nI_TAV=%.2f A',I_TAV);\n",
"dT=46;\n",
"T_s=dT+T_a;\n",
"T_c=T_s+P_av*th_cs;    printf('\ncase temp=%.2f degC',T_c);\n",
"T_j=T_c+P_av*th_jc;    printf('\njunction temp=%.2f degC',T_j);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.20: to_find_total_avg_power_loss_and_percentage_inc_in_device_rating.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"T_j=125;    //degC\n",
"T_s=70;    //degC\n",
"th_jc=.16;    //degC/W\n",
"th_cs=.08;    //degC/W\n",
"P_av1=(T_j-T_s)/(th_jc+th_cs);    printf('total avg power loss in thristor sink combination=%.2f W',P_av1);\n",
"\n",
"T_s=60;    //degC\n",
"P_av2=(T_j-T_s)/(th_jc+th_cs);    \n",
"\n",
"inc=(sqrt(P_av2)-sqrt(P_av1))*100/sqrt(P_av1);    printf('\npercentage inc in rating=%.2f',inc);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.21: to_determine_voltage_across_each_SCR_and_discharge_current_across_each_capacitor.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"R=25000;\n",
"I_l1=.021;    //I_l=leakage current\n",
"I_l2=.025;\n",
"I_l3=.018;\n",
"I_l4=.016;\n",
"//V1=(I-I_l1)*R;\n",
"//V2=(I-I_l2)*R;\n",
"//V3=(I-I_l3)*R;\n",
"//V4=(I-I_l4)*R;\n",
"//V=V1+V2+V3+V4\n",
"V=10000;\n",
"I_l=I_l1+I_l2+I_l3+I_l4;\n",
"//after solving\n",
"I=((V/R)+I_l)/4;\n",
"R_c=40;\n",
"V1=(I-I_l1)*R;    printf('voltage across SCR1=%.0f V',V1);\n",
"V2=(I-I_l2)*R;    printf('\nvoltage across SCR2=%.0f V',V2);\n",
"V3=(I-I_l3)*R;    printf('\nvoltage across SCR3=%.0f V',V3);\n",
"V4=(I-I_l4)*R;    printf('\nvoltage across SCR4=%.0f V',V4);\n",
"\n",
"I1=V1/R_c;    printf('\ndischarge current through SCR1=%.3f A',I1);\n",
"I2=V2/R_c;    printf('\ndischarge current through SCR2=%.3f A',I2);\n",
"I3=V3/R_c;    printf('\ndischarge current through SCR3=%.3f A',I3);\n",
"I4=V4/R_c;    printf('\ndischarge current through SCR4=%.3f A',I4);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.22: to_calculate_number_of_series_and_parrallel_units_of_SCRs.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"V_r=1000;    //rating of SCR\n",
"I_r=200;    //rating of SCR\n",
"V_s=6000;    //rating of String\n",
"I_s=1000;    //rating of String\n",
"disp('when DRF=.1');\n",
"DRF=.1;\n",
"n_s=V_s/(V_r*(1-DRF));    printf('number of series units=%.0f',ceil(n_s));\n",
"n_p=I_s/(I_r*(1-DRF));    printf('\nnumber of parrallel units=%.0f',ceil(n_p));\n",
"disp('when DRF=.2');\n",
"DRF=.2;\n",
"n_s=V_s/(V_r*(1-DRF));    printf('number of series units=%.0f',ceil(n_s));\n",
"n_p=I_s/(I_r*(1-DRF));    printf('\nnumber of parrallel units=%.0f',ceil(n_p));"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.23: to_calculate_the_resistance.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"V1=1.6;    //on state voltage drop of SCR1\n",
"V2=1.2;    //on state voltage drop of SCR2\n",
"I1=250;    //current rating of SCR1\n",
"I2=350;    //current rating of SCR2\n",
"R1=V1/I1;\n",
"R2=V2/I2;\n",
"I=600;    //current to be shared\n",
"//for SCR1,     I*(R1+R)/(total resistance)=k*I1                    (1)\n",
"//for SCR2,     I*(R2+R)/(total resistance)=k*I2                    (2)\n",
"//(1)/(2)\n",
"R=(R2*I2-R1*I1)/(I1-I2);\n",
"printf('reqd value of resistance=%.3f ohm',R);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.25: to_compute_value_of_various_resistances.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"f=2000;    //Hz\n",
"C=0.04*10^-6;\n",
"n=.72;\n",
"R=1/(f*C*log(1/(1-n)));    printf('R=%.2f kilo-ohm',R/1000);\n",
"V_p=18;\n",
"V_BB=V_p/n;\n",
"R2=10^4/(n*V_BB);    printf('\nR2=%.2f ohm',R2);\n",
"I=4.2*10^-3;    //leakage current\n",
"R_BB=5000;\n",
"R1=(V_BB/I)-R2-R_BB;    printf('\nR1=%.0f ohm',R1);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.26: to_compute_max_and_min_values_of_R_and_the_corresponding_freq.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"V_p=18;\n",
"n=.72;\n",
"V_BB=V_p/n;\n",
"I_p=.6*10^-3;\n",
"I_v=2.5*10^-3;\n",
"V_v=1;\n",
"R_max=V_BB*(1-n)/I_p;    printf('R_max=%.2f kilo-ohm',R_max/1000);\n",
"R_min=(V_BB-V_v)/I_v;    printf('\nR_min=%.2f kilo-ohm',R_min/1000);\n",
"\n",
"C=.04*10^-6;\n",
"f_min=1/(R_max*C*log(1/(1-n)));    printf('\nf_min=%.3f kHz',f_min/1000);\n",
"f_max=1/(R_min*C*log(1/(1-n)));    printf('\nf_max=%.2f kHz',f_max/1000);\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.27: to_find_max_and_min_firing_angles_for_triac.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"R1=1000;\n",
"C=.5*10^-6;\n",
"f=50;\n",
"w=2*%pi*f;\n",
"V_s=230;\n",
"X_c=1/(w*C);\n",
"v_c=30;\n",
"R=0;\n",
"Z=sqrt((R+R1)^2+X_c^2);\n",
"phi=atand(X_c/(R+R1));\n",
"I1=V_s/(Z*complex(cosd(-phi),sind(-phi)));\n",
"V_c=I1*X_c*complex(cosd(-90),sind(-90));\n",
"a=abs(V_c);    //magnitude of V_c\n",
"b=-atand(imag(V_c)/real(V_c));    //argument of V_c\n",
"//v_c=sqrt(2)*a*sind(a1-b)\n",
"a1=asind(v_c/(sqrt(2)*a))+b;    printf('min angle=%.1f deg',a1);\n",
"\n",
"R=25000;\n",
"Z=sqrt((R+R1)^2+X_c^2);\n",
"phi=atand(X_c/(R+R1));\n",
"I1=V_s/(Z*complex(cosd(-phi),sind(-phi)));\n",
"V_c=I1*X_c*complex(cosd(-90),sind(-90));\n",
"a=abs(V_c);    //magnitude of V_c\n",
"b=-atand(imag(V_c)/real(V_c));    //argument of V_c\n",
"//v_c=sqrt(2)*a*sind(a2-b)\n",
"a2=asind(v_c/(sqrt(2)*a))+b;    printf('\nmax angle=%.2f deg',a2);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.2: EX4_2.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"P=.5;    //P=V_g*I_g\n",
"V=[0.01:0.01:.25];\n",
"plot2d(P./V);\n",
"xlabel('I_g in A');\n",
"ylabel('V_g in V');\n",
"\n",
"t=poly(0,'t');\n",
"P1=P*t/(2*t);\n",
"printf('average gate power dissipation(in watts)');\n",
"disp(P1);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.3: to_compute_gate_source_resistance.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"P=.5;    //P=V_g*I_g\n",
"s=130;    //s=V_g/I_g\n",
"I_g=sqrt(P/s);\n",
"V_g=s*I_g;\n",
"E=15;\n",
"R_s=(E-V_g)/I_g;    printf('gate source resistance=%.2f ohm',R_s);\n",
"//Answers have small variations from that in the book due to difference in the rounding off of digits."
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.4: to_compute_gate_source_resistance_trigger_voltage_and_trigger_current.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"R_s=120;    //slope of load line is -120V/A. This gives gate source resistance\n",
"printf('gate source resistance=%.0f ohm',R_s);\n",
"\n",
"P=.4;    //P=V_g*I_g\n",
"E_s=15;\n",
"//E_s=I_g*R_s+V_g,    after solving this\n",
"//120*I_g^2-15*I_g+0.4=0    so\n",
"a=120;    b=-15;    c=0.4;\n",
"D=sqrt((b^2)-4*a*c);\n",
"I_g=(-b+D)/(2*a);    V_g=P/I_g;\n",
"printf('\ntrigger current=%.2f mA',I_g*10^3);    printf('\nthen trigger voltage=%.3f V',V_g);\n",
"\n",
"I_g=(-b-D)/(2*a);    V_g=P/I_g;\n",
"printf('\ntrigger current=%.2f mA',I_g*10^3);    printf('\nthen trigger voltage=%.2f V',V_g);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.5: to_compute_1_resistance_2_triggering_freq_3_duty_cycle_of_the_triggering_pulse.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"//V_g=1+10*I_g\n",
"P_gm=5;    //P_gm=V_g*I_g\n",
"//after solving, eqn becomes 10*I_g^2+I_g-5=0\n",
"a=10;    b=1;    c=-5;\n",
"I_g=(-b+sqrt(b^2-4*a*c))/(2*a);\n",
"E_s=15;\n",
"//using E_s=R_s*I_g+V_g\n",
"R_s=(E_s-1)/I_g-10;    printf('reistance=%.3f ohm',R_s);\n",
"\n",
"P_gav=.3;    //W\n",
"T=20*10^-6;\n",
"f=P_gav/(P_gm*T);    printf('\ntriggering freq=%.0f kHz',f/1000);\n",
"\n",
"dl=f*T;    printf('\nduty cycle=%.2f',dl);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.6: to_compute_min_width_of_gate_pulse_current.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"I=.1;\n",
"E=200;\n",
"disp('in case load consists of (a)L=.2H');\n",
"L=.2;\n",
"t=I*L/E;    printf('min gate pulse width=%.0f us',t*10^6);\n",
"disp('(b)R=20ohm in series with L=.2H');\n",
"R=20;\n",
"t=(-L/R)*log(1-(R*I/E));    printf('min gate pulse width=%.3f us',t*10^6);\n",
"disp('(c)R=20ohm in series with L=2H');\n",
"L=2;\n",
"t=(-L/R)*log(1-(R*I/E));    printf('min gate pulse width=%.2f us',t*10^6);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.8: to_calculate_trigger_voltage_and_trigger_current.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"E_s=16;\n",
"R_s=128;\n",
"P=.5;\n",
"y=poly([P -E_s R_s],'i','coeff');\n",
"a=roots(y);\n",
"printf('trigger current=%.1f mA',a(1)*1000);\n",
"printf('\ntrigger voltage=%.0f V',P/a(1));"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 4.9: EX4_9.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear;\n",
"clc;\n",
"function [I_TAV]=theta(th)\n",
"    I_m=1;    //supposition\n",
"    I_av=(I_m/(2*%pi))*(1+cosd(th));\n",
"    I_rms=sqrt((I_m/(2*%pi))*((180-th)*%pi/360+.25*sind(2*th)));\n",
"    FF=I_rms/I_av;\n",
"    I_rms=35;\n",
"    I_TAV=I_rms/FF;\n",
"endfunction\n",
"disp('when conduction angle=180');\n",
"th=0;\n",
"I_TAV=theta(th);\n",
"printf('avg on current rating=%.3f A',I_TAV);\n",
"disp('when conduction angle=90');\n",
"th=90;\n",
"I_TAV=theta(th);\n",
"printf('avg on current rating=%.3f A',I_TAV);\n",
"disp('when conduction angle=30');\n",
"th=150;\n",
"I_TAV=theta(th);\n",
"printf('avg on current rating=%.3f A',I_TAV);"
   ]
   }
],
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		   "language": "scilab",
		   "name": "scilab"
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		  "language_info": {
		   "file_extension": ".sce",
		   "help_links": [
			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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