Chapter 09:Channel Multiplexing Techniques

Ex9.1:pg-392

In [3]:
# Example 9.1
# Calculation of the (a) the channel spacing, (b) the signal bandwidth in a channel and cther total bandwidth of the WDM signal, and (c) the total data rate.
# Page no 392

import math

#Given data
Bs=10*10**12;               # Symbol rate
n=6;                      # Spectral efficiency
Fs=10*10**12;              # Symbol rate
N=12;                    # No of channels



# (a) Channel spacing
B=Bs*math.log(64,2);
f=B/n;

# (b) Total bandwidth of the WDM signal
T1=(N-1)*f+(2*Fs)/2; 
T1=T1*10**-12;
# (c) Total data rate
T2=N*B;
T2=T2*10**-12;

# Displaying results in the command window            
print "\n Channel spacing = ",round(f*10**-12)," GHz "

print "\n Total bandwidth of the WDM signal = ",T1," GHz "
print "\n Total data rate = ",T2," Gb/s "
 Channel spacing =  10.0  GHz 

 Total bandwidth of the WDM signal =  120.0  GHz 

 Total data rate =  720.0  Gb/s 

Ex9.2:pg-393

In [4]:
# Example 9.2
# Calculation of the total power at the fiber output.
# Page no 393

import math

#Given data

p=0;                # Power per channel
fl=0.2;             # Fiber loss
f=50;               # Wavelength


# The total power at the fiber output.
pc=10**(0.1*p);
tp=pc*11;
tp1=10*math.log10(tp);
tfl=fl*f;
to=tp1-tfl;




#Displaying results in the command window            
print "\n The total power at the fiber output = ",round(to,3)," dBm "
 The total power at the fiber output =  0.414  dBm 

Ex9.3:pg-400

In [5]:
# Example 9.3
# Calculation of a) The lengths of the adjacent waveguides and b) phase shift phi1 and phi2.
# Page no 400


import math

#Given data

p=0;                     # Power per channel
fl=0.2;                  # Fiber loss
m1=100;                  # Wavelength
m2=110;
lambdaa1=1550*10**-9;
lambdaa2=1550.8*10**-9;
c=3*10**8;               # Velocity of light
b0=5.87*10**6;
b1=4.86*10**-9;

# a) The lengths of the adjacent waveguides
l1=(2*math.pi*m1)/b0;
l2=(2*math.pi*m2)/b0;


# b) Phase shift phi1 and phi2.
dfdl=-(c/lambdaa1**2);
dbdl=2*math.pi*b1*dfdl;
phi1=2*math.pi*m1+(lambdaa2-lambdaa1)*l1*dbdl;
phi2=2*math.pi*m2+(lambdaa2-lambdaa1)*l2*dbdl;

#Displaying results in the command window            
print "\n The lengths of the adjacent waveguides  = ",round(l1*10**6,2)," micrometer "
print "\n The lengths of the adjacent waveguides  = ",round(l2*10**6,2)," micrometer"
print "\n Phase shift phi1   = ",round(phi1*10**-2,2)," x 10**2 rad "
print "\n Phase shift phi2 = ",round(phi2*10**-2,2),"  x 10**2 rad"

# The answers vary due to round off error
 The lengths of the adjacent waveguides  =  107.04  micrometer 

 The lengths of the adjacent waveguides  =  117.74  micrometer

 Phase shift phi1   =  6.28  x 10**2 rad 

 Phase shift phi2 =  6.91   x 10**2 rad

Ex9.4:pg-408

In [13]:
# Example 9.4
# Calculation of the maximum reach up to which the carrier orthogonality is preserved.
# Page no 408

import math

#Given data
b=22*10**-27;                 # Power launched in port 1
T=1.28*10**-9;                # Guard interval
N=128;                       #  Subcarriers
f=78.125*10**6;               # Frequency spacing between subcarriers

# Bit rate of communication system
I=T/(b*2*math.pi*N*f);
I=I*10**-3;



#Displaying results in the command window            
print "\n The maximum reach up to which the carrier orthogonality is preserved = ",round(I)," km "

# The answers vary due to round off error
 The maximum reach up to which the carrier orthogonality is preserved =  926.0  km 

Ex9.5:pg-410

In [6]:
# Example 9.5
# Calculation of the maximum reach up to which the carrier orthogonality is preserved.
# Page no 410

import math


#Given data
d=30*10**-12;          # Delay
b=0.5*10**-8;          

# The maximum reach up to which the carrier orthogonality is preserved
L=d/b;
L=L*10**3;



#Displaying results in the command window            
print "\n The maximum reach up to which the carrier orthogonality is preserved = ",round(L,3)," mm "

# The answers vary due to round off error
 The maximum reach up to which the carrier orthogonality is preserved =  6.0  mm 

Ex9.6:pg-411

In [7]:
# Example 9.6
# Calculation of the ODTM to multiplex data.
# Page no 411

import math

#Given data
f1=10*10**9;
f2=40*10**9;


# The ODTM to multiplex data
b1=1.0/(f1);
b2=1.0/(f2);
b1=b1*10**12;
b2=b2*10**12;

#Displaying results in the command window            
print "\n Bit interval for 10 Gb/s signal is  =",round(b1)," ps "
print "\n Bit interval for 40 Gb/s signal is = ",round(b2),"ps "

# The answers vary due to round off error
 Bit interval for 10 Gb/s signal is  = 100.0  ps 

 Bit interval for 40 Gb/s signal is =  25.0 ps 

Ex9.7:pg-413

In [22]:
# Example 9.7
# Calculation of the (a) the total data rate and (b) the spectral efficiency.
# Page no 413

import math

#Given data
M=16;
np=2;              # No of polarization
nc=24;             # No of channels
bs=28*10**9;      # Symbol rate per polarization

# (a) The total data rate
B=bs*math.log(M,2);
T=B*np*nc;


# (b) The spectral efficiency
N=bs*nc;
s=T/N;

#Displaying results in the command window            
print "\n The total data rate  = ",round(T*10**-12,3)," Tb/s "

print "\n The spectral efficiency = ",round(s,1)," b/s/Hz "
 The total data rate  =  5.376  Tb/s 

 The spectral efficiency =  8.0  b/s/Hz 

Ex9.8:pg-413

In [23]:
# Example 9.8
# Calculation of the number of subcarriers required to transmit information.
# Page no 413

import math

#Given data
M=4;
np=2;              # No of polarization
nc=24;            # No of channels
bs=10*10**9;      # Symbol rate per polarization
d=5000*10**3;     # Transmission distance
b=22*10**-27;
ts= 49.3*10**-9;

# The total data rate
B=bs*math.log(M,2);
T=d*b*math.pi*bs;
#L=T/(b*2*math.pi*N*bs);
N=(bs*ts)/2;


#Displaying results in the command window            
print "\n The number of subcarriers required to transmit information = ",round(N)," "

# The answers vary due to round off error
 The number of subcarriers required to transmit information =  247.0  

Ex9.9:pg-414

In [24]:
# Example 9.9
# Calculation of the (a) the signal power/subcarrier/polarization at the fiber output, (b) the data rate and (c) the spectral efficiency
# Page no 414

import math

#Given data
fl=0.19;            # Fiber loss
fg=70;              # Fiber length
nc=24;             # No of channels
ip=2;
bs=10*10**9;        # Symbol rate per polarization
ts= 12.8*10**-9;    # Symbol period
n=64;              # No of subcarriers
np=2;              # Launch power to the fiber


# (a) The signal power/subcarrier/polarization at the fiber output
T=fl*fg;
p=ip-T;
p1=10**(p/10);
s=p1/(np*n);
#s=s*10**4;

# (b) The data rate
bs=1/ts;
B=math.log(n,2)*bs;
bt=B*2*n;

# (c) the spectral efficiency
Tb=n*bs;
se=bt/Tb;




#Displaying results in the command window            
print "\n The signal power/subcarrier/polarization at the fiber output = ",round(s*10**4,3)," x 10**-4 mW "

print "\n The data rate = ",bt*10**-9,"Gb/s "

print "\n The spectral efficiency = ",se," b/s/Hz "

# The answers vary due to round off error
 The signal power/subcarrier/polarization at the fiber output =  5.791  x 10**-4 mW 

 The data rate =  60.0 Gb/s 

 The spectral efficiency =  12.0  b/s/Hz