Chapter 2 - Power Switching Devices & Their Characteristics

Ex 2.1 page 67

In [1]:
V1=1    # V across SCR
IG=0    # A
Ih=2    # mA holding current
R=50    # ohm

# Applying kirchoff law
#VA-(IAK*R)-V1=0
VA=(Ih*10**-3*R)+V1    # V (let IAK=Ih)
print 'VA = %.2f V'%(VA)
VA = 1.10 V

Ex 2.2 page 67

In [2]:
diBYdt=1000    # A/s (rate of rise of current)
il=10    # mA (latching current = diBYdt * tp)
tp=il*10**-3/diBYdt    # s
print 'Minimum duration of gating pulse = %.f us'%(tp*10**6)
Minimum duration of gating pulse = 10 us

Ex 2.3 page 68

In [3]:
from __future__ import division
m=16    #  V/A (gradient)
t_on=4    #  us
IG=500    #  mA
VS=15    #  V

VG=m*IG/1000    #  V
#Load line equation
#VG=VS-IG*RS
RS=(VS-VG)/(IG/1000)     #  ohm
Pg=VS*(IG/1000)**2 # # W
print 'Gate power dissipation = %.f W'%(Pg)
print '\n Resistance to be connected = %.f ohm'%(RS)
Gate power dissipation = 4 W

 Resistance to be connected = 14 ohm

Ex 2.4 page 68

In [4]:
from numpy import roots
# VG=0.5+8*IG -- eqn(1)
f=400# # Hz
delta=0.1 # # (Duty Cycle)
P=0.5    # W
VS=12    #  V

Tp=1/f*10**6    #  us
# P= VG*IG -- eqn(2)
# solving eqn  1 and 2
#8*IG*IG**2+0.5*IG-P=0
p=[8, 0.5, -P] # polynomial for IG
IG=roots(p)     #  A 
IG=IG[1]     #  A (discarding -ve value)
VG=0.5+8*IG    #  V
# VS=VG+IG*RS
RS=(VS-VG)/IG
print 'Value of resistance to be added in series = %.2f ohm'%(RS)
Value of resistance to be added in series = 44.11 ohm

Ex 2.5 page 69

In [5]:
from __future__ import division
from math import sqrt
# VG=10*IG -- eqn(1)
PGM=5    #  W
PGav=.5    #  W
VS=12    #  V
Tp=20    #  us

# PGM = VG*IG where VG=10*IG

IG=sqrt(PGM/10)    #  A
VG=10*IG    #  V
# During the application of pulse VS = VG+(IG*RS)
RS=(VS-VG)/IG     #  ohm
f=PGav/(PGM*Tp*10**-6)/1000    #  kHz
delta=f*1000*Tp*10**-6    #  Duty Cycle
print 'Value of resistance to be connected in series = %.2f ohm'%(RS)
print '\n Triggering frequency = %.2f kHz'%(f)
print '\n Duty Cycle = %.1f '%(delta)
# Note : ans in the textbook is not accurate.
Value of resistance to be connected in series = 6.97 ohm

 Triggering frequency = 5.00 kHz

 Duty Cycle = 0.1 

Ex 2.6 page 70

In [6]:
from __future__ import division
VS=3    #  kV
IS=750    #  A

VD=800    #  V
ID=175    #  A
dr=30/100    #  de-rating factor
IB=8    # mA
delQ=30    #  u Coulomb
# dr = 1-IS/np*ID
np = round(IS/(1-dr)/(ID)) # # no. of parallel string
ns = round(VS*1000/(1-dr)/(VD)) # # no. of series string
R=(ns*VD-VS*1000)/(ns-1)/(IB/1000)/1000    # kohm
C=(ns-1)*delQ*10**-6/(ns*VD-VS*1000)
print 'Value of R = %.2f kohm'%(R)
print '\n Value of C = %.2e F'%(C)
Value of R = 31.25 kohm

 Value of C = 1.20e-07 F

Ex 2.7 page 71

In [7]:
from __future__ import division
from math import ceil
VS=4    #  kV
IS=800    #  A

VD=800    #  V
ID=200    #  A
dr=20/100    #  de-rating factor
# for series connection
ns = ceil(VS*1000/(1-dr)/(VD)) # # no. of series string
# for parallel connection
np = round(IS/(1-dr)/(ID)) # # no. of parallel string
print '\n no. of series connection = %d'%(ns)
print '\n no. of parallel connection = %d'%(np)
 no. of series connection = 7

 no. of parallel connection = 5

Ex 2.8 page 72

In [8]:
from __future__ import division
IS1=100    #  A
IS2=150    #  A
vd1=2.1    #  V
vd2=1.75    #  V
I=250    #  A

rf1=vd1/IS1    #  ohm
rf2=vd2/IS2    #  ohm
# Equating voltage drops
# vd1+IS1*re = vd2+IS2*re
re=(vd1-vd2)/(IS2-IS1)
print ' Series resistance = %.3f ohm'%(re)
 Series resistance = 0.007 ohm

Ex 2.9 page 72

In [9]:
from __future__ import division
from math import pi
Vf1=1    #  V
If1=0    # A
Vf2=1.9    #  V
If2=60    # A
IT=20*pi    #  A
# PAV = 1/T*integrate(VT*IT,0,T)*dt = ITAV+0.015*IRMS**2
ITAV=IT/pi    # A
ITRMS=IT/2    #  A
dt=ITAV+0.015*ITRMS**2    #  W
print 'Average power loss = %.1f W'%(dt)
Average power loss = 34.8 W

Ex 2.10 page 73

In [10]:
from __future__ import division
R=10    #  ohm
L=0.1    #  H
delta_i=20/1000    #  A
Vs=230    #  V4
f=50    #  Hz
theta=45    # degree

delta_t = L*delta_i/Vs# # s
delta_t = delta_t*10**6    #  us
print 'Minimum gate pulse width = %.1f us'%(delta_t)
Minimum gate pulse width = 8.7 us

Ex 2.11 page 73

In [11]:
from __future__ import division
from math import sqrt
m=3*10**3    #  gradient (VG/IG)
VS=10    #  V
PG=0.012    #  W
# IG = VG/m & PG=VG*IG
VG=sqrt(PG*m)
IG=VG/m # # A
RS=(VS-VG)/IG/1000    #  kohm
print 'gate source resistance = %.1f kohm'%(RS)
gate source resistance = 2.0 kohm

Ex 2.12 page 74

In [12]:
from __future__ import division
VS=300    #  V
delta_i = 50/1000    #  A
R=60    #  ohm
L=2    #  H
TP=40*10**-6    #  s

I1=VS/L*TP    #  A (at the end of pulse)
# as I1 << delta_i
I2=delta_i    #  A (anode current with RL load)

Rdash = VS/(I2-I1)/1000    #  kohm
print 'Value of resistance = %.2f kohm'%(Rdash)
Value of resistance = 6.82 kohm

Ex 2.13 page 74

In [13]:
from __future__ import division
from math import pi,sqrt
Im=50    #  A

print 'For half sine wave current : \n'
# theta=180    #  degree
theta=180    #  degree
Iav=Im/pi    #  A
Irms=Im/2    #  A
FF=Irms/Iav    #  form factor
ITav=Im/FF # # A
print '(i) Average ON State current  = %.2f A\n'%(ITav)    

# theta=90    #  degree
theta=90    #  degree
Iav=Im/2/pi    #  A
Irms=Im/2/sqrt(2)    #  A
FF=Irms/Iav    #  form factor
ITav=Im/FF # # A
print '(ii) Average ON State current  = %.2f A\n'%(ITav)    

# theta=180    #  degree
theta=180    #  degree
Iav=Im*0.0213    #  A
Irms=Im*0.0849    #  A
FF=Irms/Iav    #  form factor
ITav=Im/FF # # A
print '(iii) Average ON State current  = %.2f A\n'%(ITav)    

print '\n For rectangular wave current : \n'
# theta=180    #  degree
theta=180    #  degree
Iav=Im/2    #  A
Irms=Im/sqrt(2)    #  A
FF=Irms/Iav    #  form factor
ITav=Im/FF # # A
print '(i) Average ON State current  = %.2f A\n'%(ITav)    

# theta=90    #  degree
theta=90    #  degree
Iav=Im/4    #  A
Irms=Im/2    #  A
FF=Irms/Iav    #  form factor
ITav=Im/FF # # A
print '(ii) Average ON State current  = %.2f A\n'%(ITav)    

# theta=180    #  degree
theta=180    #  degree
Iav=Im/12    #  A
Irms=Im/2/sqrt(3)    #  A
FF=Irms/Iav    #  form factor
ITav=Im/FF # # A
print '(i) Average ON State current  = %.2f A\n'%(ITav)    
For half sine wave current : 

(i) Average ON State current  = 31.83 A

(ii) Average ON State current  = 22.51 A

(iii) Average ON State current  = 12.54 A


 For rectangular wave current : 

(i) Average ON State current  = 35.36 A

(ii) Average ON State current  = 25.00 A

(i) Average ON State current  = 14.43 A

Ex 2.14 page 76

In [14]:
from __future__ import division
VS=500    #  V
IP=250    #  A
diBYdt=60    #  A/us
dvaBYdt=200    #  V/us
RL=20    #  ohm
r=0.65    #  ohm
eps=0.65     #  damping ratios

F=2    #  saftety factor
IP=IP/2    #  A
diBYdt=60/2    #  A/us
dvaBYdt=200/2    #  V/us
L=VS/diBYdt    #  uH
R=L*10**6/VS*dvaBYdt/10**6    #  ohm
print 'Value of L = %.2f uH'%(L)
print '\n Value of R = %.1f ohm'%(R)

Ip=VS/RL+VS/R    #  A
if Ip > IP :
    print '\n Value of Ip = %.1f A is greater than permissible peak current = %.1f A\n change the value of Rs'%(Ip,IP)
    Rs=6    # ohm

Ip=VS/RL+VS/Rs    #  A
Cs=(2*eps/Rs)**2*L    #  uF
print '\n Value of C = %.2f uF'%(Cs)
Value of L = 16.67 uH

 Value of R = 3.3 ohm

 Value of Ip = 175.0 A is greater than permissible peak current = 125.0 A
 change the value of Rs

 Value of C = 0.78 uF

Ex 2.15 page 77

In [15]:
from __future__ import division
from math import ceil,sqrt
Isb=3000    #  A
f=50    #  Hz
I=sqrt((Isb**2*1/2/f)*f)     #  A
I2t=I**2/2/f    #  A**2/s
print 'I2t rating = %d A**2/s'%(ceil(I2t))
I2t rating = 45000 A**2/s