# Chapter 13 : Performance of Modulation systems with noise¶

## Example 13.1 Page No : 442¶

In [3]:
import math

# Variables
Gb = 1.;
print 'a) SSB:  Gb = %i  '%(Gb);
print '   GbdB = %i  dB'%(10*math.log10(Gb));
print 'b) DSB:  Gb = %i  '%(Gb);
print '   GbdB = %i  dB'%(10*math.log10(Gb));
m = 0.5;
Gb = m**2/(2+m**2);
print 'c) AMm = .5):  Gb = %.3f  '%(Gb);
print '   GbdB = %.3f  dB'%(10*math.log10(Gb));
m = 1.;
Gb = m**2/(2+m**2);
print 'd) AMm = 1):  Gb = %.3f  '%(Gb);
print '   GbdB = %.3f  dB'%(10*math.log10(Gb));
delta_phi = 5.;
Gb = delta_phi**2/2;
print 'e) FMdelta phi = 5)):  Gb = %.1f  '%(Gb);
print '   GbdB = %.3f  dB'%(10*math.log10(Gb));
D = 5.;
Gb = 3.*D**2/2;
print 'f) FMD = 5):  Gb = %.1f  '%(Gb);
print '   GbdB = %.3f  dB'%(10*math.log10(Gb));
Wf1 = 7.07;
Gb = 3./2*D**2*math.pi/6*Wf1;
print 'g) FMD = 5, W/f1 = 7.07):  Gb = %.1f  '%(Gb);
print '   GbdB = %.2f  dB'%(10*math.log10(Gb));
a) SSB:  Gb = 1
GbdB = 0  dB
b) DSB:  Gb = 1
GbdB = 0  dB
c) AMm = .5):  Gb = 0.111
GbdB = -9.542  dB
d) AMm = 1):  Gb = 0.333
GbdB = -4.771  dB
e) FMdelta phi = 5)):  Gb = 12.5
GbdB = 10.969  dB
f) FMD = 5):  Gb = 37.5
GbdB = 15.740  dB
g) FMD = 5, W/f1 = 7.07):  Gb = 138.8
GbdB = 21.42  dB

## Example 13.2 Page No : 443¶

In [6]:
import math

# Calculations and Results
GR = 1.;
print 'a) SSB:  GR = %i  '%(GR);
print '   GRdB = %i  dB'%(10*math.log10(GR));
GR = 2.;
print 'b) DSB:  GR = %i  '%(GR);
print '   GRdB = %.2f  dB'%(10*math.log10(GR));
m = 0.5;
GR = 2*m**2/(2+m**2);
print 'c) AMm = .5):  GR = %.4f  '%(GR);
print '   GRdB = %.3f  dB'%(10*math.log10(GR));
m = 1.;
GR = 2*m**2/(2+m**2);
print 'd) AMm = 1):  GR = %.3f  '%(GR);
print '   GRdB = %.2f  dB'%(10*math.log10(GR));
delta_phi = 5.;
GR = (1+delta_phi)*delta_phi**2;
print 'e) FMdelta phi = 5)):  GR = %.1f  '%(GR);
print '   GRdB = %.3f  dB'%(10*math.log10(GR));
D = 5.;
GR = 3*D**2*(1+D);
print 'f) FMD = 5):  GR = %.1f  '%(GR);
print '   GRdB = %.3f  dB'%(10*math.log10(GR));
Wf1 = 7.07;
GR = 3*(1+D)*D**2*math.pi/6*Wf1;
print 'g) FMD = 5, W/f1 = 7.07):  GR = %.1f  '%(GR);
print '   GRdB = %.2f  dB'%(10*math.log10(GR));
a) SSB:  GR = 1
GRdB = 0  dB
b) DSB:  GR = 2
GRdB = 3.01  dB
c) AMm = .5):  GR = 0.2222
GRdB = -6.532  dB
d) AMm = 1):  GR = 0.667
GRdB = -1.76  dB
e) FMdelta phi = 5)):  GR = 150.0
GRdB = 21.761  dB
f) FMD = 5):  GR = 450.0
GRdB = 26.532  dB
g) FMD = 5, W/f1 = 7.07):  GR = 1665.8
GRdB = 32.22  dB

## Example 13.3 Page No : 447¶

In [7]:
import math

# Variables
k = 1.38*10**-23;   #Boltzmann's const
#Temperatures in K
Ti = 150.;
Te = 325.;

# Calculations and Results
Tsys = Ti+Te;
print ' Tsys = %i K '%(Tsys);
D = 5;
W = 15;   #kHz
B = 2*(1+D)*W;
print '  B = %i  kHz'%(B);
Nsys = k*Tsys*B*10**3;   #W
print '  Nsys = %.3f fW'%(Nsys*10**15);
PR = 50*10**-12;   #W
SNsys = PR/Nsys;
print '  S/N)sys = %i  '%(SNsys);
GR = 3*(1+D)*D**2
print '  GR = %.0f  '%(GR);
SNoutput = GR*SNsys;
print '  S/N)output = %.0f  '%(SNoutput);
print '  S/N)out,dB = %.2f  dB'%(10*math.log10(SNoutput));
print '  S/N)sys, dB = %.2f  dB'%(10*math.log10(SNsys));
GRdb = 10*math.log10(GR);
print '  GR, dB = %.2f dB '%(GRdb);
print '  S/N)output ,dB = %.2f  dB'%(10*math.log10(SNoutput));
Tsys = 475 K
B = 180  kHz
Nsys = 1.180 fW
S/N)sys = 42376
GR = 450
S/N)output = 19069413
S/N)out,dB = 72.80  dB
S/N)sys, dB = 46.27  dB
GR, dB = 26.53 dB
S/N)output ,dB = 72.80  dB

## Example 13.4 Page No : 450¶

In [8]:
# Variables
N = 16;  #bit

# Calculations
SNoutdB = 1.76+6.02*N;

# Results
print ' (S/N)output, dB = %.2f dB '%(SNoutdB);
(S/N)output, dB = 98.08 dB

## Example 13.5 Page No : 450¶

In [9]:
# Variables
SNoutdB = 53;

# Calculations and Results
N = (SNoutdB-1.76)/6.02;
print ' N = %.2f bits '%(N);
N = 9;   #roundup
print ' N = %i bits '%(N);
N = 8.51 bits
N = 9 bits

## Example 13.6 Page No : 453¶

In [11]:
import math

# Variables
N = 6.;   #bits per word

# Calculations and Results
M = 2**N;
print ' M = %i  '%(M);
Pr = 200.*10**-15;   #W
R = 2.*10**6;   #bits/s
Eb = Pr/R;
print ' Bit energy ,Eb = %.0f*10**-21  '%(Eb*10**21);
k = 1.38*10**-23;   #Boltzmann cons
Ti = 300.;  #K
Te = 425.;  #K
Tsys = Ti+Te;
nsys = k*Tsys;
print '  Noise power spectral density ,nsys = %.0f*10**-20 W/Hz '%(nsys*10**20);
rho = Eb/nsys;
print ' Bit energy , rho = %.0f  '%(rho);
rhodB = 10*math.log10(rho);
print ' Bit energy in db, rho,dB = %.0f dB '%(rhodB);
#part a
Pe = 4*10**-6;
SNout = 1.5*M**2/(1+4*M**2*Pe);
print ' a) S/N)output = %.0f or %0.2f  dB) '%(SNout,10*math.log10(SNout));
#part b
Pe = 2.3*10**-5;
SNout = 1.5*M**2/(1+4*M**2*Pe);
print ' b) S/N)output = %.0f or %0.2f  dB) '%(SNout,10*math.log10(SNout));
#part c
Pe = 8*10**-4;
SNout = 1.5*M**2/(1+4*M**2*Pe);
print ' c) S/N)output = %.1f or %0.2f  dB) '%(SNout,10*math.log10(SNout));
#part d
Pe = 3.5*10**-3;
SNout = 1.5*M**2/(1+4*M**2*Pe);
print ' d) S/N)output = %.1f or %0.2f  dB) '%(SNout,10*math.log10(SNout));
M = 64
Bit energy ,Eb = 100*10**-21
Noise power spectral density ,nsys = 1*10**-20 W/Hz
Bit energy , rho = 10
Bit energy in db, rho,dB = 10 dB
a) S/N)output = 5766 or 37.61  dB)
b) S/N)output = 4462 or 36.50  dB)
c) S/N)output = 435.5 or 26.39  dB)
d) S/N)output = 105.3 or 20.22  dB)

## Example 13.7 Page No : 455¶

In [13]:
import math

# Variables
#data from ex 13.6
M = 2.**6;
Pr = 200.*10**-15;   #W
R = 8.*10**6;   #bits/s    (changed)
Eb = Pr/R;

# Calculations and Results
k = 1.38*10**-23;   #Boltzmann cons
Ti = 300;  #K
Te = 425;  #K
Tsys = Ti+Te;
nsys = k*Tsys;
#print '  Noise power spectral density %(nsys = %.0f*10**-20 W/Hz '%(nsys*10**20);
rho = Eb/nsys;
print ' Bit energy , rho = %.1f  '%(rho);
rhodB = 10*math.log10(rho);
print ' Bit energy in db, rho,dB = %.2f dB '%(rhodB);

Pe = 1.3*10**-2;
SNout = 1.5*M**2/(1+4*M**2*Pe);
print '  S/N)output = %.2f or %0.2f  dB) '%(SNout,10*math.log10(SNout));
Bit energy , rho = 2.5
Bit energy in db, rho,dB = 3.98 dB
S/N)output = 28.71 or 14.58  dB)

## Example 13.8 Page No : 455¶

In [14]:
import math

# Variables
Pe = 10.**-5;
R = 1*10**6;  #bits/s
k = 1.38*10**-23;   #Boltzmann cons
Ti = 475.;  #K
Te = 250.;  #K
Tsys = Ti+Te;
nsys = k*Tsys;  #W/Hz

# Calculations
def E(rhodb):    #function for Eb
rho = 10**(rhodb/10);
return nsys*rho;

def P(E):      #function for Pr
return R*Eb;

def lay(rhodb,pt):
Eb = E(rhodb);
print P(E);
print '%c)Bit energy , Eb = %.2f*10**-21 J '%(pt,Eb*10**21);
print ' Required reciver carrier power , Pr = %.2f fW '%(Pr*10**15);

#Part a
rhodb = 9.6;
lay(rhodb,'a');

#Part b
rhodb = 10.3;
lay(rhodb,'b');

#Part c
rhodb = 12.6;
lay(rhodb,'c');

#Part d
rhodb = 13.4;
lay(rhodb,'d');
2.5e-14
a)Bit energy , Eb = 91.25*10**-21 J
Required reciver carrier power , Pr = 200.00 fW
2.5e-14
b)Bit energy , Eb = 107.21*10**-21 J
Required reciver carrier power , Pr = 200.00 fW
2.5e-14
c)Bit energy , Eb = 182.06*10**-21 J
Required reciver carrier power , Pr = 200.00 fW
2.5e-14
d)Bit energy , Eb = 218.89*10**-21 J
Required reciver carrier power , Pr = 200.00 fW

## Example 13.9 Page No : 456¶

In [15]:
import math

#Data form ex13.8

# Variables
Pe = 10**-5;
R = 2*10**6;  #bits/s  (changed)
k = 1.38*10**-23;   #Boltzmann cons
Ti = 475;  #K
Te = 250;  #K
Tsys = Ti+Te;
nsys = k*Tsys;  #W/Hz

# Calculations
def E(rhodb):    #function for Eb
rho = 10**(rhodb/10);
return nsys*rho;

def P(E):      #function for Pr
return R*Eb;

rhodb = 9.6;
Eb = E(rhodb);
Pr = P(E);

# Results
print 'Bit energy , Eb = %.2f*10**-21 J '%(Eb*10**21);
print ' Required reciver carrier power , Pr = %.2f fW '%(Pr*10**15);
Bit energy , Eb = 91.25*10**-21 J
Required reciver carrier power , Pr = 182.49 fW