# Chapter 12 :- Optical fiber systems 1: Intensity modulation/direct detection¶

## Example 12.1, page 706¶

In [1]:
#Variable declaration
n=8                             #bits in a time slot
t=32                            #bits in a frame
f=8*10**3                       #frequency
m=16                            #bits in a multiframe

#Calculation
nb=n*t                          #number of bits in a frame
fr=nb*f                         #transmission rate
tr=fr**-1                       #bit duration
ts=tr*n                         #duration of a time slot
tf=ts*t                         #duration of a frame
tm=tf*m                         #duration of a multiframe

#Result
print'(a) Bit rate for the system = %.3f Mbit s^-1'%(fr*10**-6)
print'(b) Duration of the time slot = %.1f μs'%(ts*10**6)
print'(c) Duration of a frame = %d μs' %(tf*10**6)
print'Duration of a multiframe = %d ms' %(tm*10**3)

(a) Bit rate for the system = 2.048 Mbit s^-1
(b) Duration of the time slot = 3.9 μs
(c) Duration of a frame = 125 μs
Duration of a multiframe = 2 ms


## Example 12.2, page 720¶

In [2]:
import math

#Variable declaration
m=4.24                                  #erfc = 2*10^9
a=2*math.sqrt(2)

#Calculation
sn=m*a                                 #root of S/N = optical
sn1=10*math.log10(sn)                  #in dB
isq=sn**2                              #S/N = electrical
isq1=10*math.log10(isq)                #in dB
#Result
print'Optical SNR = %.1f'%sn
print'            = %.1f dB'%sn1
print'Electrical SNR = %.1f'%round(isq)
print'               = %.1f dB'%isq1

Optical SNR = 12.0
= 10.8 dB
Electrical SNR = 144.0
= 21.6 dB


## Example 12.3, page 723¶

In [3]:
import math

#Variable declaration
m=100                             #multiplication factor
k=0.02                            #ratio of carrier ionization rates
sn=144                            #electrical SNR
n=0.8                             #quantum efficiency
B=0.6

#Calculation
fm=(k*m)+(2-(1/m))*(1-k)                 #avalanche noise factor
zm=2*B*round(fm)*sn/n                    #average number of photons

#Result
print'Average no of photons = %d photons'%round(zm)

Average no of photons = 864 photons


## Example 12.4, page 724¶

In [4]:
import math

#Variable declaration
zm=864                                       #average no of photons
h=6.626*10**-34                             #plancks constant
c=2.998*10**8                               #velocity of light
l1=10**-6                                   #wavelength
l2=10**-14                                  #wavelength
bt=10**7
n=14

#Calculation
po1=(zm*h*c*bt)/(2*l1)                        #At 10 Mbit s^-1
po2=(zm*h*c*n*bt)/(2*l2)                      #At 140 Mbit s^-1

#Result
print'Incident optical power (10 Mbit s^-l) = %.1f pW'%(po1*10**12)
print'Incident optical power (140 Mbit s^-l) = %.3f W'%po2                 #value given in a textbook is incorrect

Incident optical power (10 Mbit s^-l) = 858.2 pW
Incident optical power (140 Mbit s^-l) = 1.201 W


## Example 12.5, page 726¶

In [5]:
#Variable declaration
afc=5                                    #fibre cable attenuation
ai=2                                     #splice losses
l=4                                      #length in Km
af=3.5+2.5                               #connector losses at source and detector resp

#Calculation
Cl=(afc+ai)*l+af                          #total channel loss

#Result
print'Total channel loss = %d dB'%Cl

Total channel loss = 34 dB


## Example 12.6, page 727¶

In [6]:
import math

#Variable declaration
L=8                                               #length in km
bt=25*10**6                                       #bit rates
bt1=150*10**6                                     #bit rates

#Calculation
dl1=2*(2*st*bt*math.sqrt(2))**4                   #without mode coupling
dl2=2*(2*st1*bt*math.sqrt(2))**4                  #with mode coupling
dl3=2*(2*st*bt1*math.sqrt(2))**4                  #without mode coupling
dl4=2*(2*st1*bt1*math.sqrt(2))**4                 #with mode coupling

#Result
print'(a) For 25 Mbit per sec'
print'dispersion–equalization penalty (without mode coupling) = %.2f dB'%dl1
print'dispersion–equalization penalty (with mode coupling) = %.2f x 10^-4 dB\n'%(dl2*10**4)
print'(b) For 150 Mbit per sec'
print'dispersion–equalization penalty (without mode coupling) = %.2f dB'%dl3
print'dispersion–equalization penalty (with mode coupling) = %.2f dB'%dl4

(a) For 25 Mbit per sec
dispersion–equalization penalty (without mode coupling) = 0.03 dB
dispersion–equalization penalty (with mode coupling) = 4.15 x 10^-4 dB

(b) For 150 Mbit per sec
dispersion–equalization penalty (without mode coupling) = 34.40 dB
dispersion–equalization penalty (with mode coupling) = 0.54 dB


## Example 12.7, page 731¶

In [7]:
import math

#Variable declaration
ts=8                                    #rise time for source in ns
tn=5*ts                                 #for fiber intermodal
td=6                                    #for detector

#Calculation
tsys=1.1*(ts**2+tn**2+tc**2+td**2)**0.5             #total system rise time
Bt=0.7/(tsys*10**-9)                                #max bit rate

#Result
print'Bt (Max) = %.1f Mbit per sec'%(Bt/10**6)

Bt (Max) = 15.2 Mbit per sec


## Example 12.8, page 732¶

In [8]:
import math

#Variable declaration
po=-55                          #mean power required at the APD receiver at 35 Mbit s^-1
po1=-44                         #mean power required at the APD receiver at 400 Mbit s^-1
pi=-3                           #mean power launched from the laser transmitter
l1=0.4                         #cable fiber loss
l2=0.1                         #splice losses
l3=1                            #connector loss
ma=7                            #safety margin
a=0.5
acr=2
dl=1.5

#Calculation
L1=(pi-po-acr-ma)/a                          #for 35 Mbit s^-1
L2=(pi-po1-acr-ma)/a                         #for 400 Mbit s^-1
L3=(pi-po1-acr-dl-ma)/a                      #reduction in the maximum possible link

#Result
print'(a) Maximum possible link length (operating at 35 Mbit s^-1) = %d km'%L1
print'(b) Maximum possible link length (operating at 400 Mbit s^-1) = %d km'%L2
print'(c) Reduction in the maximum possible link length = %d km'%L3

(a) Maximum possible link length (operating at 35 Mbit s^-1) = 86 km
(b) Maximum possible link length (operating at 400 Mbit s^-1) = 64 km
(c) Reduction in the maximum possible link length = 61 km


## Example 12.9, page 734¶

In [9]:
import math

#Variable declaration
po=-10                          #mean optical power launched into the fiber from the transmitter (100 μm)
rs=-41                          #receiver sensitivity at 20 Mbit s^-1
l1=7*2.6                        #cabled fiber loss
l2=6*0.5                        #splice losses
l3=1*1.5                        #connector loss
ms=6                            #safety margin

#Calculation
ts=po-rs                             #Total system margin
tsl=l1+l2+l3+ms                      #Total system loss
pm=ts-tsl                            #Excess power margin

#Result
print'Total system margin = %d dB'%ts
print'Total system loss = %.1f dB'%tsl
print'Excess power margin = %.1f dB'%pm

Total system margin = 31 dB
Total system loss = 28.7 dB
Excess power margin = 2.3 dB


## Example 12.10, page 740¶

In [10]:
import math

#Variable declaration
v=5                                         #output voltage
h=6.626*10**-34                             #plancks constant
c=2.998*10**8                               #velocity of light
k=1.385*10**-23                             #boltzman constant
t=290                                       #tempreture in kelvin
zo=100                                      #cable impedance
n=0.7                                       #quantum efficiency
pi=10**-3                                   #optical power
lam=0.85*10**-6                             #wavelength

#Calculation
ratio=(v**2*h*c)/(2*k*t*zo*n*pi*lam)        #ratio
ratio1=10*math.log10(ratio)                 #ration in dB

#Result
print'Ratio = %d dB'%ratio1

Ratio = 40 dB


## Example 12.11, page 744¶

In [11]:
import math

#Variable declaration
ma=0.8                                      #modulation index
R=0.5                                       #responsivity
b=0.7                                       #ratio of luminance to composite video
snr=3.162*10**5                             #SNR
e=1.602*10**-19                             #electron volt
B=5*10**6                                   #bandwidth
K=1.385*10**-23                             #boltzman constant
T=293                                       #tempreture in kelvin
Fn=1.413
Rl=10**6

#Calculation
a=(2*ma*R*b)**2
c=snr*2*e*B*R
d=snr*4*K*T*B*Fn/Rl
f = (c**2)+(4*a*d)
po=(c+math.sqrt(f))/(2*a)                  #average incident optical power
po1=10*math.log10(po*1000)                 #in dB

#Result
print'Average incident optical power = %.2f uW'%(po*10**6)
print'                               = %.1f dB m'%po1

Average incident optical power = 0.93 uW
= -30.3 dB m


## Example 12.12, page 747¶

In [12]:
import math

#Variable declaration
h=6.626*10**-34                             #plancks constant
c=2.998*10**8                               #velocity of light
e=1.602*10**-19                             #1 electron volt
n=0.6                                       #p–i–n photodiode quantum efficiency
ma=0.5                                      #modulation index
lam=10**-6                                  #wavelength
k=1.385*10**-23                             #boltzman constant
t=300                                       #tempreture in kelvin
f=4                                         #amplifier noise figure
sn=3.162*10**4                              #signal to noise ratio
B=10**7                                     #bandwidth

#Calculation
a=h*c/(e*n*ma**2*lam)
b=math.sqrt((8*k*t*f)/rl)
c=math.sqrt(sn*B)
po=a*b*c                                     #optical power
po1=10*math.log10(po*1000)                   #optical power in dB

#Result
print'Optical power, Po = %.2f uW'%(po*10**6)
print'                  = %.1f dBm'%po1

Optical power, Po = 7.58 uW
= -21.2 dBm


## Example 12.13, page 748¶

In [13]:
import math

#Variable declaration
po=-10                          #mean optical power launched into the fiber from the transmitter (100 μm)
l1=2*3.5                        #cable fiber loss
l2=2*0.7                        #splice losses
l3=1.6                          #connector loss
ms=4.0                           #safety margin
afc=3.5
ai=0.7
acr=1.6
ma=7

#Calculation
ts=po-rs                             #Total system margi
tsl=l1+l2+l3+ms                      #Total system loss
pm=ts-tsl                            #Excess power margin
L=((0-rs)-(acr+ma))/(afc+ai)

#Result
print'(a) Total system margin = %d dB'%ts
print'    Total system loss = %.1f dB'%tsl
print'    Excess power margin = %.1f dB'%pm
print'\n(b) Increase in link length = %.1f Km'%(L)

(a) Total system margin = 15 dB
Total system loss = 14.0 dB
Excess power margin = 1.0 dB

(b) Increase in link length = 3.9 Km


## Example 12.14, page 750¶

In [14]:
#Variable declaration
Bop=6*10**6
ts=10                                   #rise time for source in ns
tn=5*9                                 #for fiber intermodal
td=3                                    #for detector

#Calculation
tsys=0.35/Bop
tsys1=1.1*(ts**2+tn**2+tc**2+td**2)**0.5             #total system rise time

#Result
print'Maximum permitted system rise time = %.1f ns'%(tsys*10**9)
print'Total system rise time = %.1f ns'%(tsys1)

Maximum permitted system rise time = 58.3 ns
Total system rise time = 52.0 ns


## Example 12.15, page 755¶

In [15]:
import math

#Variable declaration
fd=400*10**3                                      #peak frequency deviation
Ba=4*10**3                                        #bandwidth

#Calculation
Df=fd/Ba                                            #frequency deviation ratio
snr=1.76+(20*math.log10(Df))                        #SNR improvement
Bm=2*(Df+1)*Ba                                      #bandwidth of the FM–IM signal

#Result
print'(a) SNR improvement = %.2f dB'%snr
print'(b) Frequency deviation ratio = %d'%Df
print'    Bandwidth of FM-IM signal = %d kHz'%(Bm/1000)

(a) SNR improvement = 41.76 dB
(b) Frequency deviation ratio = 100
Bandwidth of FM-IM signal = 808 kHz


## Example 12.16, page 757¶

In [16]:
import math

#Variable declaration
fm=3                                    #output FM ratio
pm=1                                    #output PM ratio

#Calculation
ratio=fm/pm                              #SNR ratio
ratio1=10*math.log10(ratio)              #SNR ratio in dB

#Result
print'Ratio of output SNR = %.2f dB'%(ratio1)

Ratio of output SNR = 4.77 dB


## Example 12.17, page 759¶

In [17]:
import math

#Variable declaration
to=5*10**-8                          #nominal pulse period
fd=5*10**6                           #Peak-to-peak frequency deviation
M=60                                 #A PD multiplication factor
R=0.7                                #A PD responsivity
po=10**-7                            #peak optical power at receiver
tr=12*10**-9                         #Total system 10–90% rise time
B=6*10**6                            #baseband noise bandwidth
i=10**-17                            #Receiver mean square noise current

#Calculation
snp=(3*(to*fd*M*R*po)**2)/(i*(2*math.pi*tr*B)**2)          #peak-to-peak signal to rms noise ratio
snp1=10*math.log10(snp)                                    #in dB

#Result
print'Peak-to-peak signal to rms noise ratio = %.1f dB'%snp1

Peak-to-peak signal to rms noise ratio = 62.1 dB


## Example 12.18, page 763¶

In [11]:
%matplotlib inline
import math
from pylab import *
from numpy import *

#Variable declaration
acr=1                                     #connector loss in dB
afc=5                                     #loss per kilometer in dB
Lbu=0.1                                   #fiber length between each of the access couplers
Lac=1                                     #insertion loss
Ltr=10                                    #loss due to the tap ratio
Lsp=3                                     #splitting loss

#Calculating, we get two equation in terms of N, no of nodes, i.e C(1,N-1)=(3.5*N)+8.5 and C(star)=4.5+(10*log10(N))

#For Bus distribution system

for N in range(1,13,1):
C=(3.5*N)+8.5;
a=plot(N,C,'.r')

#for Star distribution system

for N in range(1,30,1):
C1=4.5+(10*log10(N));
b=plot(N,C1,'.g')

#To show plot in same graph
#Graphical comparison showing total channel loss against number of nodes

plt.annotate('Linear Bus',xy=(10, 43.5), xytext=(11, 40))
plt.annotate('Star',xy=(16, 15), xytext=(17, 13))
xlabel("Number of nodes $N$")
ylabel("Total channel loss $CL$ (dB)")
title("Characteristics showing the total channel loss against the number of nodes")
grid()
show(a)
show(b)

Populating the interactive namespace from numpy and matplotlib


## Example 12.19, page 782¶

In [19]:
#Variable declaration
h=6.626*10**-34                             #plancks constant
c=2.998*10**8                               #velocity of light
lam=1.55*10**-6                             #wavelength
L=100*10**3                                 #length
K=4
B=1.2*10**9                                 #bandwidth
snr=50                                      #SNR
a=10**-2.5
pi=10**-3

#Calculation

#Result
print'Maximum system length = %d x 10^4 km'%(Lt/10**7)

Maximum system length = 1 x 10^4 km


## Example 12.21, page 791¶

In [20]:
import math

#Variable declaration
b=17                                     #second-order dispersion coefficient for the latter path
L2=20                                    #path length in km
L1=160.00                                   #path length in km
s1=-0.075                                #dispersion slope

#Calculation
a=-b*L2
G=a/L1                                   #second-order dispersion coefficient
s2=s1*L1/L2                              #chromatic dispersion slope

#Result
print'(a) Second-order dispersion coefficient = %.3f ps nm^-1 km^-1'%G
print'(b) chromatic dispersion slope = %.1f ps nm^-2 km^-1'%s2

(a) Second-order dispersion coefficient = -2.125 ps nm^-1 km^-1
(b) chromatic dispersion slope = -0.6 ps nm^-2 km^-1


## Example 12.22, page 798¶

In [21]:
import math

#Variable declaration
to=70*10**-12                                       #bit period
t=6*10**-12                                         #RZ pulse width
B2=50*10**-12*10**-12*10**-3                        #second-order dispersion coefficient
L=50*10**3                                          #amplifier spacing

#Calculation
qo=0.5*to/t                                          #separation of the soliton pulses
Bt=(2*qo*math.sqrt(B2*L))**-1                        #transmission bit rate

#Result
print'(a) Separation = %.1f'%qo
print'(b) Transmission bit rate = %.2f x 10^9'%(Bt*10**-8)

(a) Separation = 5.8
(b) Transmission bit rate = 17.14 x 10^9


## Example 12.23, page 799¶

In [22]:
import math

#Variable declaration
to=40*10**-12                             #bit period
t=4*10**-12                               #RZ pulse width
a=0.2*10**-3                              #attenuation coefficient
B2=1.25*10**-12*10**-12*10**-3            #second-order dispersion coefficient

#Calculation
qo=0.5*to/t                            #separation of the soliton pulses
b=1/(2*qo)
c=math.sqrt(a/B2)
Bt=b*c                                  #transmission bit rate

#Result
print'(a) Separation = %.1f'%qo
print'(b) Transmission bit rate = %.2f x 10^10 bit s^-1'%(Bt*10**-10)

(a) Separation = 5.0
(b) Transmission bit rate = 4.00 x 10^10 bit s^-1