{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 2 - Power Switching Devices & Their Characteristics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.1 page 67"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"VA = 1.10 V\n"
]
}
],
"source": [
"V1=1 # V across SCR\n",
"IG=0 # A\n",
"Ih=2 # mA holding current\n",
"R=50 # ohm\n",
"\n",
"# Applying kirchoff law\n",
"#VA-(IAK*R)-V1=0\n",
"VA=(Ih*10**-3*R)+V1 # V (let IAK=Ih)\n",
"print 'VA = %.2f V'%(VA)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.2 page 67"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minimum duration of gating pulse = 10 us\n"
]
}
],
"source": [
"diBYdt=1000 # A/s (rate of rise of current)\n",
"il=10 # mA (latching current = diBYdt * tp)\n",
"tp=il*10**-3/diBYdt # s\n",
"print 'Minimum duration of gating pulse = %.f us'%(tp*10**6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.3 page 68"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Gate power dissipation = 4 W\n",
"\n",
" Resistance to be connected = 14 ohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"m=16 # V/A (gradient)\n",
"t_on=4 # us\n",
"IG=500 # mA\n",
"VS=15 # V\n",
"\n",
"VG=m*IG/1000 # V\n",
"#Load line equation\n",
"#VG=VS-IG*RS\n",
"RS=(VS-VG)/(IG/1000) # ohm\n",
"Pg=VS*(IG/1000)**2 # # W\n",
"print 'Gate power dissipation = %.f W'%(Pg)\n",
"print '\\n Resistance to be connected = %.f ohm'%(RS)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.4 page 68"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Value of resistance to be added in series = 44.11 ohm\n"
]
}
],
"source": [
"from numpy import roots\n",
"# VG=0.5+8*IG -- eqn(1)\n",
"f=400# # Hz\n",
"delta=0.1 # # (Duty Cycle)\n",
"P=0.5 # W\n",
"VS=12 # V\n",
"\n",
"Tp=1/f*10**6 # us\n",
"# P= VG*IG -- eqn(2)\n",
"# solving eqn 1 and 2\n",
"#8*IG*IG**2+0.5*IG-P=0\n",
"p=[8, 0.5, -P] # polynomial for IG\n",
"IG=roots(p) # A \n",
"IG=IG[1] # A (discarding -ve value)\n",
"VG=0.5+8*IG # V\n",
"# VS=VG+IG*RS\n",
"RS=(VS-VG)/IG\n",
"print 'Value of resistance to be added in series = %.2f ohm'%(RS)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.5 page 69"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Value of resistance to be connected in series = 6.97 ohm\n",
"\n",
" Triggering frequency = 5.00 kHz\n",
"\n",
" Duty Cycle = 0.1 \n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"# VG=10*IG -- eqn(1)\n",
"PGM=5 # W\n",
"PGav=.5 # W\n",
"VS=12 # V\n",
"Tp=20 # us\n",
"\n",
"# PGM = VG*IG where VG=10*IG\n",
"\n",
"IG=sqrt(PGM/10) # A\n",
"VG=10*IG # V\n",
"# During the application of pulse VS = VG+(IG*RS)\n",
"RS=(VS-VG)/IG # ohm\n",
"f=PGav/(PGM*Tp*10**-6)/1000 # kHz\n",
"delta=f*1000*Tp*10**-6 # Duty Cycle\n",
"print 'Value of resistance to be connected in series = %.2f ohm'%(RS)\n",
"print '\\n Triggering frequency = %.2f kHz'%(f)\n",
"print '\\n Duty Cycle = %.1f '%(delta)\n",
"# Note : ans in the textbook is not accurate."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.6 page 70"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Value of R = 31.25 kohm\n",
"\n",
" Value of C = 1.20e-07 F\n"
]
}
],
"source": [
"from __future__ import division\n",
"VS=3 # kV\n",
"IS=750 # A\n",
"\n",
"VD=800 # V\n",
"ID=175 # A\n",
"dr=30/100 # de-rating factor\n",
"IB=8 # mA\n",
"delQ=30 # u Coulomb\n",
"# dr = 1-IS/np*ID\n",
"np = round(IS/(1-dr)/(ID)) # # no. of parallel string\n",
"ns = round(VS*1000/(1-dr)/(VD)) # # no. of series string\n",
"R=(ns*VD-VS*1000)/(ns-1)/(IB/1000)/1000 # kohm\n",
"C=(ns-1)*delQ*10**-6/(ns*VD-VS*1000)\n",
"print 'Value of R = %.2f kohm'%(R)\n",
"print '\\n Value of C = %.2e F'%(C)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.7 page 71"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" no. of series connection = 7\n",
"\n",
" no. of parallel connection = 5\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import ceil\n",
"VS=4 # kV\n",
"IS=800 # A\n",
"\n",
"VD=800 # V\n",
"ID=200 # A\n",
"dr=20/100 # de-rating factor\n",
"# for series connection\n",
"ns = ceil(VS*1000/(1-dr)/(VD)) # # no. of series string\n",
"# for parallel connection\n",
"np = round(IS/(1-dr)/(ID)) # # no. of parallel string\n",
"print '\\n no. of series connection = %d'%(ns)\n",
"print '\\n no. of parallel connection = %d'%(np)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.8 page 72"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Series resistance = 0.007 ohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"IS1=100 # A\n",
"IS2=150 # A\n",
"vd1=2.1 # V\n",
"vd2=1.75 # V\n",
"I=250 # A\n",
"\n",
"rf1=vd1/IS1 # ohm\n",
"rf2=vd2/IS2 # ohm\n",
"# Equating voltage drops\n",
"# vd1+IS1*re = vd2+IS2*re\n",
"re=(vd1-vd2)/(IS2-IS1)\n",
"print ' Series resistance = %.3f ohm'%(re)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.9 page 72"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average power loss = 34.8 W\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"Vf1=1 # V\n",
"If1=0 # A\n",
"Vf2=1.9 # V\n",
"If2=60 # A\n",
"IT=20*pi # A\n",
"# PAV = 1/T*integrate(VT*IT,0,T)*dt = ITAV+0.015*IRMS**2\n",
"ITAV=IT/pi # A\n",
"ITRMS=IT/2 # A\n",
"dt=ITAV+0.015*ITRMS**2 # W\n",
"print 'Average power loss = %.1f W'%(dt)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.10 page 73"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minimum gate pulse width = 8.7 us\n"
]
}
],
"source": [
"from __future__ import division\n",
"R=10 # ohm\n",
"L=0.1 # H\n",
"delta_i=20/1000 # A\n",
"Vs=230 # V4\n",
"f=50 # Hz\n",
"theta=45 # degree\n",
"\n",
"delta_t = L*delta_i/Vs# # s\n",
"delta_t = delta_t*10**6 # us\n",
"print 'Minimum gate pulse width = %.1f us'%(delta_t)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.11 page 73"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gate source resistance = 2.0 kohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"m=3*10**3 # gradient (VG/IG)\n",
"VS=10 # V\n",
"PG=0.012 # W\n",
"# IG = VG/m & PG=VG*IG\n",
"VG=sqrt(PG*m)\n",
"IG=VG/m # # A\n",
"RS=(VS-VG)/IG/1000 # kohm\n",
"print 'gate source resistance = %.1f kohm'%(RS)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.12 page 74"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Value of resistance = 6.82 kohm\n"
]
}
],
"source": [
"from __future__ import division\n",
"VS=300 # V\n",
"delta_i = 50/1000 # A\n",
"R=60 # ohm\n",
"L=2 # H\n",
"TP=40*10**-6 # s\n",
"\n",
"I1=VS/L*TP # A (at the end of pulse)\n",
"# as I1 << delta_i\n",
"I2=delta_i # A (anode current with RL load)\n",
"\n",
"Rdash = VS/(I2-I1)/1000 # kohm\n",
"print 'Value of resistance = %.2f kohm'%(Rdash)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.13 page 74"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"For half sine wave current : \n",
"\n",
"(i) Average ON State current = 31.83 A\n",
"\n",
"(ii) Average ON State current = 22.51 A\n",
"\n",
"(iii) Average ON State current = 12.54 A\n",
"\n",
"\n",
" For rectangular wave current : \n",
"\n",
"(i) Average ON State current = 35.36 A\n",
"\n",
"(ii) Average ON State current = 25.00 A\n",
"\n",
"(i) Average ON State current = 14.43 A\n",
"\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,sqrt\n",
"Im=50 # A\n",
"\n",
"print 'For half sine wave current : \\n'\n",
"# theta=180 # degree\n",
"theta=180 # degree\n",
"Iav=Im/pi # A\n",
"Irms=Im/2 # A\n",
"FF=Irms/Iav # form factor\n",
"ITav=Im/FF # # A\n",
"print '(i) Average ON State current = %.2f A\\n'%(ITav) \n",
"\n",
"# theta=90 # degree\n",
"theta=90 # degree\n",
"Iav=Im/2/pi # A\n",
"Irms=Im/2/sqrt(2) # A\n",
"FF=Irms/Iav # form factor\n",
"ITav=Im/FF # # A\n",
"print '(ii) Average ON State current = %.2f A\\n'%(ITav) \n",
"\n",
"# theta=180 # degree\n",
"theta=180 # degree\n",
"Iav=Im*0.0213 # A\n",
"Irms=Im*0.0849 # A\n",
"FF=Irms/Iav # form factor\n",
"ITav=Im/FF # # A\n",
"print '(iii) Average ON State current = %.2f A\\n'%(ITav) \n",
"\n",
"print '\\n For rectangular wave current : \\n'\n",
"# theta=180 # degree\n",
"theta=180 # degree\n",
"Iav=Im/2 # A\n",
"Irms=Im/sqrt(2) # A\n",
"FF=Irms/Iav # form factor\n",
"ITav=Im/FF # # A\n",
"print '(i) Average ON State current = %.2f A\\n'%(ITav) \n",
"\n",
"# theta=90 # degree\n",
"theta=90 # degree\n",
"Iav=Im/4 # A\n",
"Irms=Im/2 # A\n",
"FF=Irms/Iav # form factor\n",
"ITav=Im/FF # # A\n",
"print '(ii) Average ON State current = %.2f A\\n'%(ITav) \n",
"\n",
"# theta=180 # degree\n",
"theta=180 # degree\n",
"Iav=Im/12 # A\n",
"Irms=Im/2/sqrt(3) # A\n",
"FF=Irms/Iav # form factor\n",
"ITav=Im/FF # # A\n",
"print '(i) Average ON State current = %.2f A\\n'%(ITav) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.14 page 76"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Value of L = 16.67 uH\n",
"\n",
" Value of R = 3.3 ohm\n",
"\n",
" Value of Ip = 175.0 A is greater than permissible peak current = 125.0 A\n",
" change the value of Rs\n",
"\n",
" Value of C = 0.78 uF\n"
]
}
],
"source": [
"from __future__ import division\n",
"VS=500 # V\n",
"IP=250 # A\n",
"diBYdt=60 # A/us\n",
"dvaBYdt=200 # V/us\n",
"RL=20 # ohm\n",
"r=0.65 # ohm\n",
"eps=0.65 # damping ratios\n",
"\n",
"F=2 # saftety factor\n",
"IP=IP/2 # A\n",
"diBYdt=60/2 # A/us\n",
"dvaBYdt=200/2 # V/us\n",
"L=VS/diBYdt # uH\n",
"R=L*10**6/VS*dvaBYdt/10**6 # ohm\n",
"print 'Value of L = %.2f uH'%(L)\n",
"print '\\n Value of R = %.1f ohm'%(R)\n",
"\n",
"Ip=VS/RL+VS/R # A\n",
"if Ip > IP :\n",
" print '\\n Value of Ip = %.1f A is greater than permissible peak current = %.1f A\\n change the value of Rs'%(Ip,IP)\n",
" Rs=6 # ohm\n",
"\n",
"Ip=VS/RL+VS/Rs # A\n",
"Cs=(2*eps/Rs)**2*L # uF\n",
"print '\\n Value of C = %.2f uF'%(Cs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 2.15 page 77"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"I2t rating = 45000 A**2/s\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import ceil,sqrt\n",
"Isb=3000 # A\n",
"f=50 # Hz\n",
"I=sqrt((Isb**2*1/2/f)*f) # A\n",
"I2t=I**2/2/f # A**2/s\n",
"print 'I2t rating = %d A**2/s'%(ceil(I2t))"
]
}
],
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