# Chapter 12 : Noise in Communication systems¶

## Example 12.1 Page No : 400¶

In [1]:
import math
from numpy import array

# Variables
B = 10**6;  #Hz
R = array([1, 100, 10000])*10**3  #ohm

# Calculations and Resultsc
Vrms = (16*10**-21*B*R)**0.5;  #volts
print ' R K-ohm   Vrms micro-V';
out = [R*10**-3, Vrms*10**6];
print (out);

 R K-ohm   Vrms micro-V
[array([  1.00000000e+00,   1.00000000e+02,   1.00000000e+04]), array([   4.,   40.,  400.])]


## Example 12.2 Page No : 401¶

In [2]:
# Variables
B = 10.**6;  #Hz
R = 10**7 ; #ohm

# Calculations
Vrms = (16*10**-21*B*R)**0.5;  #volts
G = 5000;  #gain
vorms = Vrms*G;

# Results
print 'vorms = %.1f V'%(vorms);

vorms = 2.0 V


## Example 12.3 Page No : 403¶

In [3]:
# Variables
B = 2*10**6;  #Hz
Req = 6*10**6 ; #ohm

# Calculations
Vrms = (16*10**-21*B*Req)**0.5;  #volts

# Results
print 'vrms = %.1f micro-V'%(Vrms*10**6);

vrms = 438.2 micro-V


## Example 12.4 Page No : 405¶

In [4]:
# Variables
B = 2*10**6;  #Hz
R = 50 ; #ohm
kT0 = 4*10**-21;

# Calculations
Nav = kT0*B;

# Results
print 'Noise power = %.0f fW'%(Nav*10**15);

Noise power = 8 fW


## Example 12.5 Page No : 406¶

In [5]:
# Variables
B = 2*10**6;  #Hz
R = 50 ; #ohm
G = 10**6;  #gain
kT0 = 4*10**-21;

# Calculations
Nav = kT0*B;
No = G*Nav;

# Results
print 'output Noise power = %.0f nW'%(No*10**9);

output Noise power = 8 nW


## Example 12.6 Page No : 406¶

In [6]:
# Variables
#data from ex 12.5
B = 2*10**6;  #Hz
R = 50 ; #ohm
G = 10**6;  #gain
kT0 = 4*10**-21;

# Calculations
Nav = kT0*B;
No = G*Nav;
#ex12.6
Vrms = (No*50)**0.5;

# Results
print 'Vrms = %.1f micro-V'%(Vrms*10**6);

Vrms = 632.5 micro-V


## Example 12.7 Page No : 408¶

In [7]:
# Variables
R = 50 ; #ohm
G = 10**8;  #gain
kT0 = 4*10**-21;

# Calculations
So = G*kT0;

# Results
print 'Output spectral density Sof) = %.0f fW/Hz'%(So*10**15);

Output spectral density Sof) = 400 fW/Hz


## Example 12.8 Page No : 409¶

In [9]:
# Variables
ns = 6*10**-18;   #W/Hz
k = 1.38*10**-23;

# Calculations and Results
Ts = ns/k;
print 'a) Equilant source temperature is Ts = %.0f K'%(Ts);
Gdb = 43;  #gain in dB
G = 10**(Gdb/10);
print ' b) Absolute gain G = %.3f'%(G);
G = 20*10**3;   #Approximate
Si = ns;
So = G*Si;
print 'Output spectral density Sof) = %.0f fW/Hz'%(So*10**15);
B = 12*10**6;   #Hz
no = So;
No = no*B;
print ' c)Total Output Noise power ,No = %.3f micro-W'%(No*10**6);

a) Equilant source temperature is Ts = 434783 K
b) Absolute gain G = 10000.000
Output spectral density Sof) = 120 fW/Hz
c)Total Output Noise power ,No = 1.440 micro-W


## Example 12.9 Page No : 409¶

In [11]:
# Variables
Gdb1 = 10.;
Gdb2 = 15.;
Gdb3 = 25.;

# Calculations and Results
Gdb = Gdb1+Gdb2+Gdb3;  # net gain in dB
G = 10**(Gdb/10);
print 'Absolute gain G = %i'%(G);
B = 10**4;   #Hz
ni = 10**-12;  #pW/Hz
No = ni*G*B;
print ' Output Noise power ,No = %i mW'%(No*10**3);

Absolute gain G = 100000
Output Noise power ,No = 1 mW


## Example 12.10 Page No : 412¶

In [12]:
# Variables
Te = 50.;   #K
T0 = 290.;   #K

# Calculations and Results
F = 1+Te/T0;
print 'a) Noise figure, F = %.3f'%(F);
Fdb = 10*math.log10(F);
print ' b) Decibel value , Fdb = %.3f dB '%(Fdb);

a) Noise figure, F = 1.172
b) Decibel value , Fdb = 0.691 dB


## Example 12.11 Page No : 412¶

In [13]:
# Variables
Fdb = 5.;
T0 = 290.;  #K

# Calculations and Results
F = 10**(Fdb/10);
print 'Noise figure, F = %.3f'%(F);
Te = (F-1)*T0;
print ' Noise Temperature , Te = %i K '%(Te);

Noise figure, F = 3.162
Noise Temperature , Te = 627 K


## Example 12.12 Page No : 413¶

In [14]:
import math

# Variables
T0 = 290.;  #K
Fdb = 9.;

# Calculations and Results
F = 10**(Fdb/10);
print 'Absolute Noise figure, F = %.3f = 8Approx)'%(F);
F = 8;   #Approximate
Te = (F-1)*T0;
print ' Noise Temperature, Te = %i K '%(Te);
Ti = T0;
k = 1.38*10**-23;   #Boltzmann's Consmath.tant
B = 2*10**6;  #Hz
Ni = k*Ti*B;  #W
print ' a) Input source Noise ratio, Ni = %i fW '%(Ni*10**15);
Pi = 8*10**-12;   #W
SNinput = Pi/Ni;
print 'b) Input source signal to noise ratio S:Ninput = %.0f'%(SNinput);
print '  Corresponding dB value SNinputdb) = %.0f dB'%(10*math.log10(SNinput));
Gdb = 50;
G = 10**(Gdb/10);
Po = G*Pi;  #W
print 'c) The output signal power, Po = %i nW'%(Po*10**9);
Tsys = Ti+Te;
No = G*k*Tsys*B;  #W
print 'd) output noise power No = %.2f nw'%(No*10**9);
SNoutput = Po/No;
print 'e) Output signal to noise ratio S:Noutput = %.0f'%(SNoutput);
print '  Corresponding dB value S;Noutputdb) = %.0f dB'%(10*math.log10(SNoutput));

Absolute Noise figure, F = 7.943 = 8Approx)
Noise Temperature, Te = 2030 K
a) Input source Noise ratio, Ni = 8 fW
b) Input source signal to noise ratio S:Ninput = 1000
Corresponding dB value SNinputdb) = 30 dB
c) The output signal power, Po = 800 nW
d) output noise power No = 6.40 nw
e) Output signal to noise ratio S:Noutput = 125
Corresponding dB value S;Noutputdb) = 21 dB


## Example 12.13 Page No : 414¶

In [15]:
import math

# Variables
#Data from ex-12
T0 = 290.;  #K
Fdb = 9.;
F = 10**(Fdb/10);
F = 8;   #Approximate
Te = (F-1)*T0;
Ti = T0;

# Calculations
k = 1.38*10**-23;   #Boltzmann's Consmath.tant
B = 2*10**6;  #Hz
Ni = k*Ti*B;  #W
Pi = 8*10**-12;   #W
SNinput = Pi/Ni;
SNinputdb = 10*math.log10(SNinput);
#Ex13 calculation
SNoutputdB = SNinputdb-Fdb;

# Results
print '  S:Noutputdb) = %.0f dB'%(SNoutputdB);

  S:Noutputdb) = 21 dB


## Example 12.14 Page No : 418¶

In [17]:
# Variables
#Absolute gains
G1 = 20.;
G2 = 15.;
G3 = 12.;
#Temp in K
Te1 = 100.;
Te2 = 200.;
Te3 = 300.;

# Calculations
Te = Te1+Te2/G1+Te3/G1/G2

# Results
print 'Noise Temperature ,Te = %.0f K'%(Te);

Noise Temperature ,Te = 111 K


## Example 12.15 Page No : 418¶

In [19]:
# Variables
#Absolute gains
G1 = 20.;
G2 = 15.;
G3 = 12.;
#Temp in K
Te1 = 100.;
Te2 = 200.;
Te3 = 300.;

# Calculations
#Noise figures
F1 = 1+Te1/290;
F2 = 1+Te2/290;
F3 = 1+Te3/290;
F = F1+(F2-1)/G1+(F3-1)/G1/G2;

# Results
print 'Noise figure ,F = %.4f'%(F);
Te = (F-1)*290;

print 'Noise Temperature ,Te = %.0f K'%(Te);

Noise figure ,F = 1.3828
Noise Temperature ,Te = 111 K


## Example 12.16 Page No : 419¶

In [22]:
# Variables
Ldb = 6.02;  #db

# Calculations and Results
L = 10**(Ldb/10);
print 'Absloute loss ,L = %.0f'%(L);
Tp = 290;  #K
#Noise temp  (K)
TeL = (L-1)*Tp;
Tepre = 50.;
Terec = 200.;
Gpre = 10**(20./10);
Te = TeL+L*Tepre+L*Terec/Gpre;
print 'Noise Temperature ,Te = %.0f K'%(Te);

#Noise figures
F = 1+Te/290;
print 'Noise figure ,F = %.4f'%(F);
print 'Noise figure ,(FdB) = %.3f  dB'%(10*math.log10(F));

Absloute loss ,L = 4
Noise Temperature ,Te = 1078 K
Noise figure ,F = 4.7166
Noise figure ,(FdB) = 6.736  dB


## Example 12.17 Page No : 419¶

In [25]:
import math

# Variables
Ldb = 6.02;  #db

# Calculations and Results
L = 10**(Ldb/10);
print 'Absloute loss ,L = %.0f'%(L);
Tp = 290.;  #K
#Noise temp  (K)
TeL = (L-1)*Tp;
Tepre = 50.;
Terec = 200.;
Gpre = 10**(20./10);
Te = Tepre+TeL/Gpre+L*Terec/Gpre;
print ' a) Noise Temperature ,Te = %.1f K'%(Te);

#Noise figures
F = 1+Te/290.;
print ' b) Noise figure ,F = %.2f'%(F);
print 'Noise figure ,(FdB) = %.3f  dB'%(10*math.log10(F));

Absloute loss ,L = 4
a) Noise Temperature ,Te = 66.7 K
b) Noise figure ,F = 1.23
Noise figure ,(FdB) = 0.899  dB