Chapter 9 : Optical Fiber System-I

Example 1: PgNo-424

In [31]:
import math

# Initialisation of variables
e_c=550.0 # number of electron collected
p=800.0 # number of photon incident
n=e_c/p # quantum efficiency
eq=1.602*math.pow(10,-19)# charge
h=6.626*math.pow(10,-34)# plank constant
c=3*math.pow(10,8)# speed of light in m/s
y=1.3*math.pow(10,-6) #wavelength in m
R=(n*eq*y)/(h*c)# responsivity in A/W

# Results
print ('%s %.2f %s' %(" The responsivity = ",R,"Amp/Watt"))

 The responsivity =  0.72 Amp/Watt

Example 2: PgNo-427

In [32]:
import math

# Variable initialisation
eq=1.602*math.pow(10,-19)# charge
h=6.626*math.pow(10,-34)# plank constant
c=3*math.pow(10,8)# speed of light in m/s
y=0.85*math.pow(10,-6) # wavelength in m
R=0.274 # responsivity in A/W
n=(R*h*c)/(eq*y) # quantum efficiency
n1=n*100 # % of quantum efficiency
# Results
print ('%s %.2f %s' %(" The quantum efficiency = ",n1,"%"))

 The quantum efficiency =  40.00 %

Example 3: PgNo-429

In [33]:
import math

# Variable declaration
e_c=1.0  # number of electron collected
p=3.0    # number of photon incident
n=e_c/p # quantum efficiency
eq=1.602*math.pow(10,-19) # charge
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # speed of light in m/s
y=0.8*math.pow(10,-6) # wavelength in m
Eg=(h*c)/y # band gap energy in J
R=(n*eq*y)/(h*c)# responsivity in A/W
Po=math.pow(10,-7) # in W
Ip=R*Po # output photo current

# Results
print ('%s %.2f %s' %(" The quantum efficiency = ",n*100,"%"))
print ('%s %.2f %s' %("\n band gap energy = ",Eg*pow(10,20),"*10^-20 J"))
print ('%s %.2f %s' %("\n The output photo current = ",Ip*pow(10,9),"nA"))

 The quantum efficiency =  33.33 %

 band gap energy =  24.85 *10^-20 J

 The output photo current =  21.49 nA

Example 4: PgNo-432

In [34]:
import math

# Variable initialisation
n=0.50 # quantum efficiency
eq=1.602*math.pow(10,-19)# charge
h=6.626*math.pow(10,-34)# plank constant
c=3*math.pow(10,8)# speed of light in m/s
y=0.85*math.pow(10,-6) # wavelength in m
R=(n*eq*y)/(h*c)# responsivity in A/W
Ip=math.pow(10,-6)# mean photo current
Po=Ip/R  # received optical power in W
f=c/y
re=(n*Po)/(h*f)
rp=re/n # number of received photons

# Results
print ('%s %.2f %s' %(" The responsivity = ",R,"A/W"))
print ('%s %.2f %s' %("\n The received optical power = ",Po*pow(10,6),"uW"))
print ('%s %.2f %s' %("\n The number of received photons = ",rp/pow(10,13),"*10^13 photons/sec"))

 The responsivity =  0.34 A/W

 The received optical power =  2.92 uW

 The number of received photons =  1.25 *10^13 photons/sec

Example 5: PgNo-435

In [35]:
import math

# Variable initialisation
h=6.626*math.pow(10,-34)# plank constant
c=3*math.pow(10,8)   # speed of light in m/s
Eg=1.43         # in eV
Eg1=Eg*1.602*math.pow(10,-19) # in J
y=(h*c)/Eg1    # cut off wavelength in m
# Results
print ('%s %.2f %s' %(" The cut off wavelength = ",y*pow(10,6),"um"))

 The cut off wavelength =  0.87 um

Example 6: PgNo-437

In [36]:
import math

# Initialisation of variables
vd=2.5*math.pow(10,4)# carrier velocity in m/s
w=30*math.pow(10,-6)# width in m
Bm=vd/(2*math.pi*w)
Tm=1/Bm # max response time in sec
Tm1=Tm*math.pow(10,9) # max response time in ns
# Results
print ('%s %.2f %s' %(" The max response time = ",Tm1,"ns"))

 The max response time =  7.54 ns

Example 7: PgNo-440

In [37]:
import math

# Variable initialisation
n=0.65  # quantum efficiency
eq=1.602*math.pow(10,-19) # charge
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # speed of light in m/s
y=0.85*math.pow(10,-6)# wavelength in m
R=(n*eq*y)/(h*c)# responsivity in A/W
Po=0.35*math.pow(10,-6) # in W
Ip=R*Po # output photo current
I=9*math.pow(10,-6) # output current in A
M=I/Ip # multiplication factor
M1=math.ceil(M)
# Results
print " The multiplication factor = ",int(M1)

 The multiplication factor =  58

Example 8: PgNo-442

In [38]:
import math

# Variable declaration
n=0.50  # quantum efficiency
eq=1.602*math.pow(10,-19) # charge
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # speed of light in m/s
Eg=1.5*math.pow(10,-19) # in J
y=(h*c)/Eg # cut off wavelength in m
f=c/y
R=(n*eq)/(h*f) # responsivity in A/W
Ip=2.7*math.pow(10,-6) # photo current in A
Po=Ip/R # incident optical power in W
Po1=Po*math.pow(10,6) # incident optical power in uW

# results
print ('%s %.2f %s' %( " The cut off wavelength = ",y*pow(10,6),"um"))
print ('%s %.2f %s' %("\n The responsivity = ",R,"A/W "))
print ('%s %.2f %s' %("\n The incident optical power = ",Po1,"uW"))

 The cut off wavelength =  1.33 um

 The responsivity =  0.53 A/W 

 The incident optical power =  5.06 uW

Example 9: PgNo-445

In [39]:
import math

#Variable declaration
n=0.15 # quantum efficiency
eq=1.6*math.pow(10,-19) # charge
h=6.63*math.pow(10,-34)# plank constant
c=3*math.pow(10,8) # speed of light in m/s
y=0.85*math.pow(10,-6) # cut off wavelength in m
f=c/y # frequency in Hz
R=(n*eq)/(h*f) # responsivity in A/W
# Results
print ('%s %.3f %s' %(" The responsivity = ",R,"A/W"))

 The responsivity =  0.103 A/W

Example 10: PgNo-448

In [40]:
import math

# Variable initialisation
Iph=75*math.pow(10,-6) # output photocurrent in A
y=0.85 # operating wavelength in um
Pie=750*math.pow(10,-6) # incident optical power in uW
R=Iph/Pie # responsivity in A/W
n=1.24*R/y # external quantum efficiency
n1=n*100  # percentage of external quantum efficiency

# Results
print ('%s %.2f %s' %(" The responsivity = ",R,"A/W"))
print ('%s %.2f %s' %("\n The external quantum efficiency = ",n1,"%"))

 The responsivity =  0.10 A/W

 The external quantum efficiency =  14.59 %

Example 11: PgNo-451

In [41]:
import math

# Variable initialisation
Vs=math.pow(10,5) # saturation in m/s
W=7*math.pow(10,-6) # depletion layer width in m
tr=W/Vs # transit time in sec

# Results
print ('%s %.1f %s' %(" The transit time = ",tr*pow(10,12),"ps"))

 The transit time =  70.0 ps

Example 12: PgNo-454

In [42]:
import math

# Variable initialisation
Vs=3*math.pow(10,4)# saturation in m/s
W=25*math.pow(10,-6) # depletion layer width in m
tr=W/Vs # transit time in sec
f=0.35/tr # max 3 dB bandwidth Hz
f1=f/math.pow(10,6) # max 3 dB bandwidth Hz

# results
print ('%s %.f %s' %(" The max 3 dB bandwidth = ",f1,"MHz"))
print ("\n The answer is wrong in the textbook ")

 The max 3 dB bandwidth =  420 MHz

 The answer is wrong in the textbook

Example 13: PgNo-456

In [43]:
import math

# variable initialisation
Vs=3*math.pow(10,4) # saturation in m/s
W=25*math.pow(10,-6) # depletion layer width in m
E=10.5*math.pow(10,-11) # in F/m
RL=15*math.pow(10,6) # load resister in ohm
A=0.25*math.pow(10,-6) # area in m^2
tr=W/Vs # transit time in sec
Cj=E*A/W # junction capacitance in F
t=RL*Cj # time constant in sec

# Results
print ('%s %.3f %s' %(" The transit time = ",tr*pow(10,9),"ns"))
print ('%s %.2f %s' %("\n The junction capacitance = ",Cj*pow(10,12),"pF"))
print ('%s %.2f %s' %("\n The time constant = ",t*pow(10,6),"us"))

 The transit time =  0.833 ns

 The junction capacitance =  1.05 pF

 The time constant =  15.75 us

Example 14: PgNo-459

In [44]:
import math

# Initialisation of variables
Eg1=1.12    # band gap for Si in eV
Eg2=0.667   # band gap for Ge in eV
y_si=1.24/Eg1 # cut off wavelength for Si in um
y_he=1.24/Eg2 # cut off wavelength for Ge in um

# Results
print ('%s %.3f %s' %(" The cut off wavelength for Si  = ",y_si,"um"))
print ('%s %.3f %s' %("\n The cut off wavelength for Ge = ",y_he,"um"))

 The cut off wavelength for Si  =  1.107 um

 The cut off wavelength for Ge =  1.859 um

Example 15: PgNo-463

In [45]:
import math

# variable declaration
n=0.50  # quantum efficiency
eq=1.6*math.pow(10,-19)# charge
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # speed of light in m/s
y=0.9*math.pow(10,-6) # wavelength in m
R=(n*eq*y)/(h*c) # responsivity in A/W
Ip=math.pow(10,-6) # mean photo current
Po=Ip/R # received optical power in W
f=c/y
re=(n*Po)/(h*f)
rp=re/n # number of received photons

# Results
print ('%s %.2f %s' %(" The responsivity = ",R,"A/W"))
print ('%s %.2f %s' %("\n The received optical power = ",Po*pow(10,6),"uW"))
print ('%s %.2f %s' %("\n The number of received photons = ",rp/pow(10,13),"*10^13 photons/sec"))

 The responsivity =  0.36 A/W

 The received optical power =  2.76 uW

 The number of received photons =  1.25 *10^13 photons/sec

Example 16: PgNo-466

In [46]:
import math

# Initialisation of variables
R=0.40 # Responsivity in A/W
m=100*math.pow(10,-6) # incident flux in W/m-m
A=2  # area in m-m
Po=m*A # incident power in W
Ip=R*Po # photon current in A

# Results
print ('%s %.f %s' %(" The photon current = ",Ip*math.pow(10,6),"uA"))

 The photon current =  80 uA

Example 17: PgNo-470

In [47]:
import math

# Variable declaration
n=0.65      # quantum efficiency
eq=1.602*math.pow(10,-19) # charge
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8)  # speed of light in m/s
Eg=1.5*math.pow(10,-19) # in J
y=(h*c)/Eg   # cut off wavelength in m
f=c/y
R=(n*eq)/(h*f)  # responsivity in A/W
Ip=2.5*math.pow(10,-6) # photo current in A
Po=Ip/R    # incident optical power in W
Po1=Po*math.pow(10,6) # incident optical power in uW

# Results
print ('%s %.2f %s' %(" The cut off wavelength = ",y*math.pow(10,6),"um"))
print ('%s %.2f %s' %("\n The responsivity = ",R,"A/W"))
print ('%s %.2f %s' %("\n The incident optical power = ",Po1,"uW"))

 The cut off wavelength =  1.33 um

 The responsivity =  0.69 A/W

 The incident optical power =  3.60 uW

Example 18: PgNo-472

In [48]:
import math

# Variable declaration
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # speed of light in m/s
Eg=1.43 # in eV
Eg1=Eg*1.602*math.pow(10,-19) # in J
y=(h*c)/Eg1 # cut off wavelength in m

# Results
print ('%s %.3f %s' %(" The cut off wavelength = ",y*math.pow(10,6),"um"))

 The cut off wavelength =  0.868 um

Example 19: PgNo-474

In [49]:
import math

# Variable declaration
n=0.45  # quantum efficiency
h=6.62*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # speed of light in m/s
y=1.2*math.pow(10,-6) # cut off wavelength in m
Ic=20*math.pow(10,-6) # collector current in A
Po=120*math.pow(10,-6)# incident optical power in W
eq=1.602*math.pow(10,-19)# charge
Go=(h*c*Ic)/(y*Po*eq) # optical gain
h_e=Go/n # common emitter gain

# Results
print ('%s %.3f ' %(" The optical gain = ",Go))
print ('%s %.3f ' %("\n The common emitter gain = ",h_e))

 The optical gain =  0.172 

 The common emitter gain =  0.383

Example 20: PgNo-477

In [50]:
import math

# Initialisation of variables
n=0.5   # quantum efficiency
eq=1.602*math.pow(10,-19) # charge
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # speed of light in m/s
y=1.3*math.pow(10,-6) # wavelength in m
R=(n*eq*y)/(h*c)# responsivity in A/W
Po=0.4*math.pow(10,-6) # in W
Ip=R*Po # output photo current
I=8*math.pow(10,-6) # output current in A
M=I/Ip # multiplication factor

# Results
print " The multiplication factor = ",int(M)

 The multiplication factor =  38

Example 21: PgNo-481

In [51]:
import math

# Initialisation of variables
n=0.85  # quantum efficiency
eq=1.6*math.pow(10,-19) # charge
h=6.625*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # speed of light in m/s
y=0.9*math.pow(10,-6) # wavelength in m
R=(n*eq*y)/(h*c)# responsivity in A/W
Po=0.6*math.pow(10,-6) # in W
Ip=R*Po # output photo current
I=10*math.pow(10,-6) # output current in A
M=I/Ip # multiplication factor

# Results
print " The multiplication factor = ",int(M)

 The multiplication factor =  27

Example 22: PgNo-483

In [52]:
import math

# Variable initialisation
e_c=1.2*math.pow(10,11) # number of electron collected
p=2*math.pow(10,11) # number of photon incident
n=e_c/p  # quantum efficiency
eq=1.602*math.pow(10,-19) # charge
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8)    # speed of light in m/s
E=1.5*math.pow(10,-19) # energy in J

# Calculations
y=(h*c)/E  # wavelength in m
R=(n*eq*y)/(h*c)  # responsivity in A/W
Ip=2.6*math.pow(10,-6) # photocurrent in A
Po=Ip/R     # incident optical power in W

# Results
print ('%s %.2f %s' %(" The quantum efficiency = ",n*100,"%"))
print ('%s %.2f %s' %("\n The wavelength = ",y*pow(10,6),"um"))
print ('%s %.2f %s' %("\n The responsivity = ",R,"Amp/Watt"))
print ('%s %.2f %s' %("\n The incident optical power = ",Po*math.pow(10,6),"uW"))

 The quantum efficiency =  60.00 %

 The wavelength =  1.33 um

 The responsivity =  0.64 Amp/Watt

 The incident optical power =  4.06 uW

Example 23: PgNo-485

In [53]:
import math

# Variable initialisation
n=0.40  # quantum efficiency
eq=1.602*math.pow(10,-19) # charge
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # speed of light in m/s
y=1.35*math.pow(10,-6) # wavelength in m
R=(n*eq*y)/(h*c) # responsivity in A/W
Po=0.2*math.pow(10,-6) # in W
Ip=R*Po     # output photo current
I=4.9*math.pow(10,-6) # output current in A
M=I/Ip    # multiplication factor

# Results
print " The multiplication factor = ",int(M)

 The multiplication factor =  56

Example 24: PgNo-489

In [54]:
import math

# Variable initialisation
n=0.55      # quantum efficiency
eq=1.6*math.pow(10,-19) # charge
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # speed of light in m/s
y=0.85*math.pow(10,-6) # wavelength in m
R=(n*eq*y)/(h*c) # responsivity in A/W
Ip=2*math.pow(10,-6) # mean photo current
Po=Ip/R   # received optical power in W
re=(n*Po*y)/(h*c)  # number of received photons

# Results
print ('%s %.3f %s' %(" The responsivity = ",R,"A/W"))
print ('%s %.3f %s' %("\n The received optical power = ",Po*math.pow(10,6),"uW"))
print ('%s %.2f %s' %("\n The number of received photons = ",re/math.pow(10,13),"*10^13 photons/sec"))

 The responsivity =  0.376 A/W

 The received optical power =  5.315 uW

 The number of received photons =  1.25 *10^13 photons/sec

Example 25: PgNo-494

In [55]:
import math

# Variable declaration
h=6.625*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # speed of light in m/s
n=1      # quantum efficiency
eq=1.602*math.pow(10,-19) # charge
E=1.3*math.pow(10,-19) # energy in J
y=(h*c)/E # wavelength in m
M=18      # multiplication factor
rp=math.pow(10,13) # no. of photon per sec
Po=rp*E   # output power in w
Ip=(n*Po*eq)/E   # output photocurrent in A
I=M*Ip     # photocurrent in A

# Results
print ('%s %.3f %s' %(" The wavelength = ",y*math.pow(10,6),"um"))
print ('%s %.1f %s' %("\n The output power = ",Po*math.pow(10,6),"uW"))
print ('%s %.3f %s' %("\n The photocurrent = ",I*math.pow(10,6),"uA"))

 The wavelength =  1.529 um

 The output power =  1.3 uW

 The photocurrent =  28.836 uA

Example 26: PgNo-497

In [56]:
import math

# Variable declaration
e_c=2*math.pow(10,10) # number of electron collected
p=5*math.pow(10,10)  # number of photon incident
n=e_c/p   # quantum efficiency
eq=1.602*math.pow(10,-19) # charge
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8)# speed of light in m/s
y=0.85*math.pow(10,-6) # wavelength in m
y1=0.85     # wavelength in um
Eg=(h*c)/y  #  bandgap energy in J
Eg1=1.24/y1 # bandgap energy in terms of eV
Po=10*math.pow(10,-6) # incident power in W
Ip=(n*eq*Po)/Eg   # mean output photocurrent in A

# Results
print ('%s %.2f %s' %(" The quantum efficiency = ",n*100,"%"))
print ('%s %.3f %s' %("\n The bandgap energy = ",Eg*math.pow(10,19),"*10^-19 J"))
print ('%s %.2f %s' %("\n The bandgap energy = ",Eg1,"eV"))
print ('%s %.3f %s' %("\n The mean output photocurrent = ",Ip*math.pow(10,6),"uA"))

 The quantum efficiency =  40.00 %

 The bandgap energy =  2.339 *10^-19 J

 The bandgap energy =  1.46 eV

 The mean output photocurrent =  2.740 uA