Chapter02: Optical Fiber for Telecommunication

Ex2.2.1:Pg-2.4

In [4]:
#  Given
import math

alpha= 3     #  average loss     Power decreases by 50% so P(0)/P(z)= 0.5
lamda= 900*10**-9     # wavelength
z= 10*math.log10(0.5)/alpha     # z is the length
z= z*-1 
print " The length over which power decreases by 50% in Kms= ",round(z,2) 

z1= 10*math.log10(0.25)/alpha       # Power decreases by 75% so P(0)/P(z)= 0.25
z1=z1*-1     # as distance cannot be negative...
print " \n\nThe length over which power decreases by 75% in Kms= ",round(z1,2) 

 The length over which power decreases by 50% in Kms=  1.0
 

The length over which power decreases by 75% in Kms=  2.01

Ex2.2.2:Pg-2.5

In [7]:
# Given

z=30.0     # Length of the fibre in kms
alpha= 0.8    # in dB
P0= 200.0      # Power launched in uW
pz= P0/10**(alpha*z/10)      
print " The output power in  uW =",round(pz,4) 

 The output power in  uW = 0.7962

Ex2.2.3:Pg-2.6

In [9]:
# Given
import math 

z=8.0      # fibre length
p0= 120*10**-6    # power launched
pz= 3*10**-6 
alpha= 10*math.log10(p0/pz)   #  overall attenuation
print " The overall attenuation in dB =",round(alpha,2) 
alpha = alpha/z      #  attenuation per km
alpha_new= alpha *10     #  attenuation for 10kms
total_attenuation = alpha_new + 9    # 9dB because of splices
print " \n\nThe total attenuation in dB =",int(total_attenuation) 

 The overall attenuation in dB = 16.02
 

The total attenuation in dB = 29

Ex2.2.4:Pg-2.6

In [16]:
 # Given
 
z=12.0     # fibre length
alpha = 1.5 
p0= 0.3 
pz= p0/10**(alpha*z/10) 
pz=pz*1000    # formatting pz in nano watts...
print " The power at the output of the cable in W = ",round(pz,2),"x 10^-9" 
alpha_new= 2.5 
pz=pz/1000   # pz in uWatts...
p0_new= 10**(alpha_new*z/10)*pz 
print " \n\nThe Input power in uW= ",round(p0_new,2) 

 The power at the output of the cable in W =  4.75 x 10^-9
 

The Input power in uW=  4.75

Ex2.2.5:Pg-2.7

In [18]:
# Given
import math

p0=150*10**-6      # power input
z= 10.0    # fibre length in km
pz= -38.2   #  in dBm...
pz= 10**(pz/10)*1*10**-3 
alpha_1= 10/z *math.log10(p0/pz)          # attenuation in 1st window
print " Attenuation is 1st window in dB/Km =",round(alpha_1,2) 
alpha_2= 10/z *math.log10(p0/(47.5*10**-6))          # attenuation in 2nd window
print " \n\nAttenuation is 2nd window in dB/Km =",round(alpha_2,2) 
alpha_3= 10/z *math.log10(p0/(75*10**-6))          # attenuation in 3rd window
print " \n\nAttenuation is 3rd window in dB/Km =",round(alpha_3,2) 

 Attenuation is 1st window in dB/Km = 3.0
 

Attenuation is 2nd window in dB/Km = 0.5
 

Attenuation is 3rd window in dB/Km = 0.3

Ex2.2.6:Pg-2.8

In [20]:
#Given
import math
p0=3*10**-3 
pz=3*10**-6 
alpha= 0.5 
z= math.log10(p0/pz)/(alpha/10) 
print " The Length of the fibre in Km =",int(z)

 The Length of the fibre in Km = 60

Ex2.2.7:Pg-2.9

In [22]:
#Given
import math

z= 10.0 
p0= 100*10**-6    #  input power
pz=5*10**-6       # output power
alpha = 10*math.log10(p0/pz)      # total attenuation
print " The overall signal attenuation in dB = ",round(alpha,2) 
alpha = alpha/z      #  attenuation per km
print " \n\nThe attenuation per Km in dB/Km = ",round(alpha,2)
z_new = 12.0 
splice_attenuation = 11*0.5 
cable_attenuation = alpha*z_new 
total_attenuation = splice_attenuation+cable_attenuation 
print " \n\nThe overall signal attenuation for 12Kms in dB = ",round(total_attenuation,1) 

 The overall signal attenuation in dB =  13.01
 

The attenuation per Km in dB/Km =  1.3
 

The overall signal attenuation for 12Kms in dB =  21.1

Ex2.2.8:Pg-2.15

In [25]:
#Given
import math
Tf = 1400.0     # fictive temperature
BETA = 7*10**-11 
n= 1.46         # RI 
p= 0.286     # photo elastic constant
Kb = 1.381*10**-23       # Boltzmann's constant
lamda = 850*10**-9    # wavelength
alpha_scat = 8*math.pi**3*n**8*p**2*Kb*Tf*BETA/(3*lamda**4) 
l= 1000      # fibre length
TL = exp(-alpha_scat*l)    # transmission loss
attenuation = 10*math.log10(1/TL) 
print " The attenuation in dB/Km =",round(attenuation,3)

 The attenuation in dB/Km = 1.572

Ex2.3.1:Pg-2.20

In [28]:
#Given
import math
alpha = 2 
n1= 1.5  
a= 25*10**-6 
lamda= 1.3*10**-6 
M= 0.5 
NA= math.sqrt(0.5*2*1.3**2/(math.pi**2*25**2)) 
Rc= 3*n1**2*lamda/(4*math.pi*NA**3) 
Rc=Rc*1000   #  converting into um.....
print " The radius of curvature in um =",round(Rc,2) 

 The radius of curvature in um = 153.98

Ex2.5.1:Pg-2.25

In [30]:
#Given
lamda = 850 *10**-9 
sigma= 45*10**-9 
L= 1 
M= 0.025/(3*10**5*lamda) 
sigma_m= sigma*L*M 
sigma_m= sigma_m*10**9   #  formatting in ns/km....
print " The Pulse spreading in ns/Km =",round(sigma_m,2) 
print " \n\nNOTE*** - The answer in text book is wrongly calculated.." 

 The Pulse spreading in ns/Km = 4.41
 

NOTE*** - The answer in text book is wrongly calculated..

Ex2.5.2:Pg-2.26

In [31]:
#Given

lamda= 2*10**-9 
sigma = 75 
D_mat= 0.03/(3*10**5*2) 
sigma_m= 2*1*D_mat 
sigma_m=sigma_m*10**9   # Fornamtting in ns/Km
print " The Pulse spreading in ns/Km =",int(sigma_m)
D_mat_led= 0.025/(3*10**5*1550) 
sigma_m_led = 75*1*D_mat_led*10**9   # in ns/Km
print " \n\nThe Pulse spreading foe LED is ns/Km =",round(sigma_m_led,2) 

 The Pulse spreading in ns/Km = 100
 

The Pulse spreading foe LED is ns/Km = 4.03

Ex2.5.3:Pg-2.26

In [34]:
#Given

lamda = 850 
sigma= 20 
D_mat = 0.055/(3*10**5*lamda) 
sigma_m= sigma*1*D_mat 
D_mat=D_mat*10**12   #  in Ps...
sigma_m=sigma_m*10**9   # in ns #  # 
print " The material Dispersion in Ps/nm-Km =",round(D_mat,2) 
print " \n\nThe Pulse spreading in ns/Km =",round(sigma_m,4) 

 The material Dispersion in Ps/nm-Km = 215.69
 

The Pulse spreading in ns/Km = 4.3137

Ex2.5.4:Pg-2.30

In [37]:
#Given
n2= 1.48  
dele = 0.2 
lamda = 1320 
Dw = -n2*dele*0.26/(3*10**5*lamda) 
Dw=Dw*10**10   # converting in math.picosecs....
print " The waveguide dispersion in math.picosec/nm.Km =",round(Dw,3) 

 The waveguide dispersion in math.picosec/nm.Km = -1.943

Ex2.6.1:Pg-2.34

In [38]:
#Given
t= 0.1*10**-6 
L= 12 
B_opt= 1/(2*t) 
B_opt=B_opt/1000000   # converting from Hz to MHz
print " The maximum optical bandwidth in MHz. =",int(B_opt) 
dele= t/L     # Pulse broadening
dele=dele*10**9   #  converting in ns...
print " \n\nThe pulse broadening per unit length in ns/Km =",round(dele,2) 
BLP= B_opt*L   # BW length product
print " \n\nThe Bandwidth-Length Product in MHz.Km =",int(BLP) 

 The maximum optical bandwidth in MHz. = 5
 

The pulse broadening per unit length in ns/Km = 8.33
 

The Bandwidth-Length Product in MHz.Km = 60

Ex2.6.2:Pg-2.34

In [40]:
#Given
t= 0.1*10**-6 
L= 10.0 
B_opt= 1/(2*t) 
B_opt=B_opt/1000000   # converting from Hz to MHz
print " The maximum optical bandwidth in MHz. =",int(B_opt) 
dele= t/L 
dele=dele/10**-6   # converting in us...
print " \n\nThe dispersion per unit length in us/Km =",round(dele,2) 
BLP= B_opt*L 
print " \n\nThe Bandwidth-Length product in MHz.Km =",int(BLP) 

 The maximum optical bandwidth in MHz. = 5
 

The dispersion per unit length in us/Km = 0.01
 

The Bandwidth-Length product in MHz.Km = 50

Ex2.6.3:Pg-2.35

In [42]:
#Given
t= 0.1*10**-6 
L=15 
B_opt= 1/(2*t) 
B_opt=B_opt/1000000   # converting from Hz to MHz
print " The maximum optical bandwidth in MHz. =",int(B_opt) 
dele= t/L*10**9   # in ns...
print " \n\nThe dispersion per unit length in ns/Km =",round(dele,2) 

 The maximum optical bandwidth in MHz. = 5
 

The dispersion per unit length in ns/Km = 6.67

Ex2.6.4:Pg-2.35

In [43]:
#Given
lamda = 0.85*10**-6 
rms_spect_width = 0.0012*lamda 
sigma_m= rms_spect_width*1*98.1*10**-3 
sigma_m=sigma_m*10**9   #  converting in ns...
print " The Pulse Broadening due to material dispersion in ns/Km =",round(sigma_m,2) 

 The Pulse Broadening due to material dispersion in ns/Km = 0.1

Ex2.6.5:Pg-2.35

In [47]:
#Given
import math

L= 5.0   # in KM
n1= 1.5 
dele= 0.01 
c= 3*10**8   #  in m/s
delta_t = (L*n1*dele)/c 
delta_t=delta_t*10**12   # convertin to nano secs...
print " The delay difference in ns =",round(delta_t,1)
sigma= L*n1*dele/(2*math.sqrt(3)*c) 
sigma=sigma*10**12   # convertin to nano secs...
print " \n\nThe r.m.s pulse broadening in ns =",round(sigma,2) 
B= 0.2/sigma*1000   # in Mz
print " \n\nThe maximum bit rate in MBits/sec =",round(B,2) 
BLP = B*5 
print " \n\nThe Bandwidth-Length in MHz.Km =",round(BLP,2) 

 The delay difference in ns = 250.0
 

The r.m.s pulse broadening in ns = 72.17
 

The maximum bit rate in MBits/sec = 2.77
 

The Bandwidth-Length in MHz.Km = 13.86

Ex2.6.6:Pg-2.36

In [49]:
#Given
import math
del_t_inter = 5*1 
del_t_intra = 50*80*1 
total_dispersion = math.sqrt(5**2 + 0.4**2) 
print " Total dispersion in ns =",round(total_dispersion,3) 

 Total dispersion in ns = 5.016

Ex2.7.1:Pg-2.37

In [51]:
#Given
t= 0.1*10**-6 
L=15 
dele= t/L*10**9    # convertin to nano secs...
print " The Pulse Dispersion in ns =",round(dele,2) 
B_opt= 1/(2*t)/10**6   # convertin to nano secs...
print " \n\n The maximum possible Bandwidth in MHz =",int(B_opt) 
BLP = B_opt*L 
print " \n\nThe BandwidthLength product in MHz.Km =",int(BLP) 

 The Pulse Dispersion in ns = 6.67
 

 The maximum possible Bandwidth in MHz = 5
 

The BandwidthLength product in MHz.Km = 75

Ex2.7.2:Pg-2.38

In [52]:
#Given
L= 6 
n1= 1.5 
delt= 0.01 
delta_t = L*n1*delt/(3*10**8)*10**12   # convertin to nano secs...
print " The delay difference in ns =",int(delta_t) 

 The delay difference in ns = 300

Ex2.7.3:Pg-2.39

In [53]:
#Given
import math
Lb= 0.09 
lamda= 1.55*10**-6 
delta_lamda = 1*10**-9 
Bf= lamda/Lb 
Lbc= lamda**2/(Bf*delta_lamda) 
print " The modal Bifriengence in meters  =",round(Lbc,2) 
beta_xy= 2*math.pi/Lb 
print " \n\nThe difference between propogation constants  =",round(beta_xy,2) 

 The modal Bifriengence in meters  = 139.5
 

The difference between propogation constants  = 69.81

Ex2.7.4:Pg-2.39

In [54]:
#Given

t= 0.1*10**-6 
B_opt= 1/(2*t)/1000000 
print " The maximum possible Bandwidth in MHz =",int(B_opt) 

 The maximum possible Bandwidth in MHz = 5

Ex2.7.5:Pg-2.40

In [55]:
#Given

t= 0.1*10**-6 
B_opt= 1/(2*t)/1000000 
print " The maximum possible Bandwidth in MHz =",int(B_opt) 

 The maximum possible Bandwidth in MHz = 5