Chapter 04 : Thyristors

Example 4.3, Page No 149

In [1]:
import math
#initialisation of variables
P=.5    #P=V_g*I_g
s=130    #s=V_g/I_g

#Calculations
I_g=math.sqrt(P/s)
V_g=s*I_g
E=15
R_s=(E-V_g)/I_g    

#Results
print("Gate source resistance=%.2f ohm" %R_s)
#Answers have small variations from that in the book due to difference in the rounding off of digits.

Gate source resistance=111.87 ohm

Example 4.4, Page No 149

In [2]:
import math

#initialisation of variables

R_s=120     #slope of load line is -120V/A. This gives gate source resistance
print("gate source resistance=%.0f ohm" %R_s)

P=.4     #P=V_g*I_g
E_s=15

#Calculations
 #E_s=I_g*R_s+V_g %    after solving this
 #120*I_g**2-15*I_g+0.4=0    so
a=120   
b=-15
c=0.4
D=math.sqrt((b**2)-4*a*c)
I_g=(-b+D)/(2*a)   
V_g=P/I_g

#Results
print("\ntrigger current=%.2f mA" %(I_g*10**3))    
print("\nthen trigger voltage=%.3f V" %V_g)
I_g=(-b-D)/(2*a)   
V_g=P/I_g
print("\ntrigger current=%.2f mA" %(I_g*10**3))    
print("\nthen trigger voltage=%.2f V" %V_g)

gate source resistance=120 ohm

trigger current=86.44 mA

then trigger voltage=4.628 V

trigger current=38.56 mA

then trigger voltage=10.37 V

Example 4.5 Page No 150

In [3]:
import math

#initialisation of variables

#V_g=1+10*I_g
P_gm=5     #P_gm=V_g*I_g
#after solving % eqn becomes 10*I_g**2+I_g-5=0
a=10.0    
b=1.0    
c=-5

#Calculations
I_g=(-b+math.sqrt(b**2-4*a*c))/(2*a)
E_s=15
#using E_s=R_s*I_g+V_g
R_s=(E_s-1)/I_g-10   
P_gav=.3     #W
T=20*10**-6
f=P_gav/(P_gm*T)
dl=f*T

#Results
print("Reistance=%.3f ohm" %R_s)
print("Triggering freq=%.0f kHz" %(f/1000))
print("Tduty cycle=%.2f" %dl)

Reistance=11.248 ohm
Triggering freq=3 kHz
Tduty cycle=0.06

Example 4.6, Page No 151

In [4]:
import math
#initialisation of variables
I=.1
E=200.0
L=0.2

#Calculations
t=I*L/E   
R=20.0
t1=(-L/R)*math.log(1-(R*I/E))    
L=2.0
t2=(-L/R)*math.log(1-(R*I/E))   

#Results
print("in case load consists of (a)L=.2H")
print("min gate pulse width=%.0f us" %(t*10**6))
print("(b)R=20ohm in series with L=.2H")
print("min gate pulse width=%.3f us" %(t1*10**6))
print("(c)R=20ohm in series with L=2H")
print("min gate pulse width=%.2f us" %(t2*10**6))

in case load consists of (a)L=.2H
min gate pulse width=100 us
(b)R=20ohm in series with L=.2H
min gate pulse width=100.503 us
(c)R=20ohm in series with L=2H
min gate pulse width=1005.03 us

Example 4.9 Page No 163

In [5]:
import math

#initialisation of variables

def theta(th):
    I_m=1     #supposition
    I_av=(I_m/(2*math.pi))*(1+math.cos(math.radians(th)))
    I_rms=math.sqrt((I_m/(2*math.pi))*((180-th)*math.pi/360+.25*math.sin(math.radians(2*th))))
    FF=I_rms/I_av
    I_rms=35
    I_TAV=I_rms/FF
    return I_TAV

#Calculations
print("when conduction angle=180")
th=0
I_TAV=theta(th)
print("avg on current rating=%.3f A" %I_TAV)
print("when conduction angle=90")
th=90
I_TAV=theta(th)

#Results
print("avg on current rating=%.3f A" %I_TAV)
print("when conduction angle=30")
th=150
I_TAV=theta(th)
print("avg on current rating=%.3f A" %I_TAV)

when conduction angle=180
avg on current rating=22.282 A
when conduction angle=90
avg on current rating=15.756 A
when conduction angle=30
avg on current rating=8.790 A

Example 4.10, Page No 164

In [6]:
import math
#initialisation of variables

def theta(th):
    n=360.0/th
    I=1.0     #supposition
    I_av=I/n
    I_rms=I/math.sqrt(n)
    FF=I_rms/I_av
    I_rms=35
    I_TAV=I_rms/FF
    return I_TAV

#Calculations
th=180.0
I_TAV1=theta(th)
th=90.0
I_TAV2=theta(th)
th=30.0
I_TAV3=theta(th)

#Results
print("when conduction angle=180")
print("avg on current rating=%.3f A" %I_TAV)
print("when conduction angle=90")
print("avg on current rating=%.1f A" %I_TAV2)
print("when conduction angle=30")
print("avg on current rating=%.4f A" %I_TAV3)

when conduction angle=180
avg on current rating=8.790 A
when conduction angle=90
avg on current rating=17.5 A
when conduction angle=30
avg on current rating=10.1036 A

Example 4.11 Page No 165

In [7]:
import math 

#initialisation of variables
f=50.0     #Hz

#Calculations
I_sb=3000.0
t=1/(4*f)
T=1/(2*f)
I=math.sqrt(I_sb**2*t/T)    
r=(I_sb/math.sqrt(2))**2*T   

#Results
print("surge current rating=%.2f A" %I)
print("\nI**2*t rating=%.0f A^2.s" %r)

surge current rating=2121.32 A

I**2*t rating=45000 A^2.s

Example 4.12 Page No 165

In [8]:
import math
#initialisation of variables

V_s=300.0 #V
R=60.0 #ohm
L=2.0 #H

#Calculations
t=40*10**-6 #s
i_T=(V_s/R)*(1-math.exp(-R*t/L))
i=.036 #A
R1=V_s/(i-i_T)

#Results
print("maximum value of remedial parameter=%.3f kilo-ohm" %(R1/1000))

maximum value of remedial parameter=9.999 kilo-ohm

Example 4.16 Page No 172

In [9]:
import math

#initialisation of variables
V_p=230.0*math.sqrt(2)

#Calculations
R=1+((1)**-1+(10)**-1)**-1
A=V_p/R
s=1     #s
t_c=20*A**-2*s

#Results
print("fault clearance time=%.4f ms" %(t_c*10**3))

fault clearance time=0.6890 ms

Example 4.17, Page No 176

In [10]:
import math

#initialisation of variables

V_s=math.sqrt(2)*230     #V
L=15*10**-6     #H
I=V_s/L     #I=(di/dt)_max
R_s=10   #ohm
v=I*R_s     #v=(dv/dt)_max

#Calculations
f=50     #Hz
X_L=L*2*math.pi*f
R=2
I_max=V_s/(R+X_L)    
FF=math.pi/math.sqrt(2)
I_TAV1=I_max/FF    
FF=3.98184
I_TAV2=I_max/FF    


#RESULTS
print("(di/dt)_max=%.3f A/usec" %(I/10**6))
print("\n(dv/dt)_max=%.2f V/usec" %(v/10**6))
print("\nI_rms=%.3f A" %I_max)
print("when conduction angle=90")
print("I_TAV=%.3f A" %I_TAV1)
print("when conduction angle=30")
print("I_TAV=%.3f A" %I_TAV2)
print("\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.

(di/dt)_max=21.685 A/usec

(dv/dt)_max=216.85 V/usec

I_rms=162.252 A
when conduction angle=90
I_TAV=73.039 A
when conduction angle=30
I_TAV=40.748 A

voltage rating=894.490 V

Example 4.19, Page No 186

In [11]:
import math
#initialisation of variables

T_jm=125
th_jc=.15     #degC/W
th_cs=0.075     #degC/W


#Calculations
dT=54     #dT=T_s-T_a
P_av=120
th_sa=dT/P_av
T_a=40     #ambient temp
P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)
if (P_av-120)<1 :
    print("selection of heat sink is satisfactory")

dT=58     #dT=T_s-T_a
P_av=120
th_sa=dT/P_av
T_a=40     #ambient temp
P_av=(T_jm-T_a)/(th_sa+th_jc+th_cs)
if (P_av-120)<1 :
    print("selection of heat sink is satisfactory")

V_m=math.sqrt(2)*230
R=2
I_TAV=V_m/(R*math.pi)
P_av=90
th_sa=(T_jm-T_a)/P_av-(th_jc+th_cs)
dT=P_av*th_sa
print("for heat sink")    
print("T_s-T_a=%.2f degC" %dT)   
print("\nP_av=%.0f W" %P_av)
P=(V_m/2)**2/R
eff=P/(P+P_av)   
print("\nckt efficiency=%.3f pu" %eff)
a=60     #delay angle
I_TAV=(V_m/(2*math.pi*R))*(1+math.cos(math.radians(a)))
print("\nI_TAV=%.2f A" %I_TAV)
dT=46
T_s=dT+T_a
T_c=T_s+P_av*th_cs    
T_j=T_c+P_av*th_jc    

#Results
print("\ncase temp=%.2f degC" %T_c)
print("\njunction temp=%.2f degC" %T_j)

for heat sink
T_s-T_a=-20.25 degC

P_av=90 W

ckt efficiency=0.993 pu

I_TAV=38.83 A

case temp=92.75 degC

junction temp=106.25 degC

Example 4.20, Page No 187

In [12]:
import math
#initialisation of variables
T_j=125.0     #degC
T_s=70.0     #degC
th_jc=.16     #degC/W
th_cs=.08     #degC/W

#Calculations
P_av1=(T_j-T_s)/(th_jc+th_cs)    

T_s=60     #degC
P_av2=(T_j-T_s)/(th_jc+th_cs)    
inc=(math.sqrt(P_av2)-math.sqrt(P_av1))*100/math.sqrt(P_av1)    

#Results
print("Total avg power loss in thristor sink combination=%.2f W" %P_av1)
print("Percentage inc in rating=%.2f" %inc)

Total avg power loss in thristor sink combination=229.17 W
Percentage inc in rating=8.71

Example 4.21, Page No 197

In [13]:
import math
#initialisation of variables

R=25000.0
I_l1=.021     #I_l=leakage current
I_l2=.025
I_l3=.018
I_l4=.016
 #V1=(I-I_l1)*R
 #V2=(I-I_l2)*R
 #V3=(I-I_l3)*R
 #V4=(I-I_l4)*R
 #V=V1+V2+V3+V4
    
#Calculations
V=10000.0
I_l=I_l1+I_l2+I_l3+I_l4
 #after solving
I=((V/R)+I_l)/4
R_c=40.0
V1=(I-I_l1)*R    

#Resluts
print("voltage across SCR1=%.0f V" %V1)
V2=(I-I_l2)*R    
print("\nvoltage across SCR2=%.0f V" %V2)
V3=(I-I_l3)*R    
print("\nvoltage across SCR3=%.0f V" %V3)
V4=(I-I_l4)*R    
print("\nvoltage across SCR4=%.0f V" %V4)

I1=V1/R_c    
print("\ndischarge current through SCR1=%.3f A" %I1)
I2=V2/R_c   
print("\ndischarge current through SCR2=%.3f A" %I2)
I3=V3/R_c    
print("\ndischarge current through SCR3=%.3f A" %I3)
I4=V4/R_c    
print("\ndischarge current through SCR4=%.3f A" %I4)

voltage across SCR1=2475 V

voltage across SCR2=2375 V

voltage across SCR3=2550 V

voltage across SCR4=2600 V

discharge current through SCR1=61.875 A

discharge current through SCR2=59.375 A

discharge current through SCR3=63.750 A

discharge current through SCR4=65.000 A

Example 4.22, Page No 198

In [14]:
import math
#initialisation of variables
V_r=1000     #rating of SCR
I_r=200     #rating of SCR
V_s=6000     #rating of String
I_s=1000     #rating of String

#Calculations
print("when DRF=.1")
DRF=.1
n_s=V_s/(V_r*(1-DRF))    
print("number of series units=%.0f" %math.ceil(n_s))
n_p=I_s/(I_r*(1-DRF))    
print("\nnumber of parrallel units=%.0f" %math.ceil(n_p))
print("when DRF=.2")
DRF=.2

#Results
n_s=V_s/(V_r*(1-DRF))   
print("number of series units=%.0f" %math.ceil(n_s))
n_p=I_s/(I_r*(1-DRF))    
print("\nnumber of parrallel units=%.0f" %math.ceil(n_p))

when DRF=.1
number of series units=7

number of parrallel units=6
when DRF=.2
number of series units=8

number of parrallel units=7

Example 4.23, Page No 198

In [15]:
import math
#initialisation of variables
V1=1.6     #on state voltage drop of SCR1
V2=1.2     #on state voltage drop of SCR2
I1=250.0     #current rating of SCR1
I2=350.0     #current rating of SCR2

#Calculations
R1=V1/I1
R2=V2/I2
I=600.0     #current to be shared
 #for SCR1 %     I*(R1+R)/(total resistance)=k*I1                    (1)
 #for SCR2 %     I*(R2+R)/(total resistance)=k*I2                    (2)
 #(1)/(2)
R=(R2*I2-R1*I1)/(I1-I2)


#Results
print("RSequired value of resistance=%.3f ohm" %R)

RSequired value of resistance=0.004 ohm

Example 4.25, Page No 223

In [16]:
import math
#initialisation of variables
f=2000.0     #Hz
C=0.04*10**-6
n=.72

#Calculations
R=1/(f*C*math.log(1/(1-n)))    
V_p=18
V_BB=V_p/n
R2=10**4/(n*V_BB)    
I=4.2*10**-3     #leakage current
R_BB=5000
R1=(V_BB/I)-R2-R_BB

#Results
print("R=%.2f kilo-ohm" %(R/1000))
print("\nR2=%.2f ohm" %R2)
print("\nR1=%.0f ohm" %R1)

R=9.82 kilo-ohm

R2=555.56 ohm

R1=397 ohm

Example 4.26, Page No 223

In [17]:
import math
#initialisation of variables

V_p=18.0
n=.72
V_BB=V_p/n
I_p=.6*10**-3
I_v=2.5*10**-3
V_v=1

#Calculations
R_max=V_BB*(1-n)/I_p    
print("R_max=%.2f kilo-ohm" %(R_max/1000))
R_min=(V_BB-V_v)/I_v    
print("\nR_min=%.2f kilo-ohm" %(R_min/1000))

C=.04*10**-6
f_min=1/(R_max*C*math.log(1/(1-n)))    
print("\nf_min=%.3f kHz" %(f_min/1000))
f_max=1/(R_min*C*math.log(1/(1-n)))    
print("\nf_max=%.2f kHz" %(f_max/1000))

R_max=11.67 kilo-ohm

R_min=9.60 kilo-ohm

f_min=1.683 kHz

f_max=2.05 kHz