Chapter 7 : Noise

Example7.2, page no 276

In [1]:
from numpy import sqrt,pi
from mpmath  import quad
#Given
mue=25#
rp=5e3
Rl=10e3
C=1e-9
gm=mue/rp
Req=2.5/gm

k=1.381e-23
T=293
R1=1e5
# Power density spectrum for respective res
d1=2*k*T*R1
d2=2*k*T*Req
d3=2*k*T*Rl
xo=0
x1=1e14
#w=0:inf
#H1(w)=(-gm*rp*Rl)/(rp+Rl+(1J*w*rp*Rl*C))
Vo=sqrt((20231.65e2/pi)*quad(lambda w:1/(((3e9)**2)+(w**2)),[xo,x1]))
print 'The mean square noise voltage is: %0.3f mV'%(Vo*1e3)

The mean square noise voltage is: 18.363 mV

Example7.3, page no 279

In [2]:
from numpy import sqrt,pi
from mpmath  import quad

#Given
mue=25
rp=5e3
Rs=1e3#input resistance
#Coupling Capacitors are assumed as short circuit
Rg=1e5
gm=25/5e3
Req=2.5/gm
F=1+((((Req*(Rs+Rg)**2)+(Rg*Rs**2))/(Rs*Rg**2)))
xo=0
x1=1e10
#w=0:inf

vo=sqrt((30145e-8/pi)*quad(lambda w:1/(((3e5)**2)+(w**2)),[xo,x1]))
print 'The mean square noise voltage is: %.3f uV'%(vo*1e6)

The mean square noise voltage is: 22.414 uV

Example7.4, page no 283

In [3]:
from __future__ import division
#Given
Ap1=10
Ap2=10
Ap3=10#  # Gain of each states
F_1=6
F_2=6
F_3=6#   #Noise figure of each state
F1= round(10**(F_1/10))
F2= round(10**(F_2/10))
F3= round(10**(F_3/10))#   # approximating the values

F=F1+((F2-1)/Ap1)+((F3-1)/(Ap1*Ap2))
print 'overall noise Figure is: %.2f'%(F)

overall noise Figure is: 4.33

Example7.5, page no 283

In [4]:
from __future__ import division
#Given
Fif=15# Noise figure of IF amplifier
Ap1=10# Gain of Preamplifier
Fpa=6#Noise figure of preamplifier
F2=10**(Fif/10)
F1=10**(Fpa/10)

F=F1+((F2-1)/Ap1)#overall noise figure
print 'The overall noise figure is: %.2f'%(F)

The overall noise figure is: 7.04

Example7.6, page no 284

In [5]:
from __future__ import division
#Given
mue=25# tube parameters
rp=10e3# tube parameters
gm=2.5e-3# transconductance
Req=2.5/gm# equivalent resistance
Rs=1000
Rg=1e5
F1=1+(((Req*((Rs+Rg)**2))+Rg*Rs**2)/(Rs*(Rg**2)))#noise figure of the first stage
Rg2=9.1e3
Rs2=10e3
Es=1# assuming Es=1 for ease of calculation
Pi=((Es/2e3)**2)*1e3
Po=1.532e-2*Es**2
Ap1=Po/Pi
F2=1+(((Req*((Rs2+Rg2)**2))+Rg2*Rs2**2)/(Rs2*(Rg2**2)))# noise figure of the second stage
F=(F1)+((F2-1)/Ap1)
print 'Overall Noise figure is: %.3f'%(F)

Overall Noise figure is: 2.055

Example7.8, page no 285

In [6]:
from __future__ import division
#Given
g01=30# gain of 1st stage
g02=20#gain of 2nd stage
g03=40#gain of 3rd stage
F2=6# Noise factor of stage 2
F3=12# Noise factor of stage 3
Te1=4# Eq noise temp of stage 1
T=290# Room 
G01=round(10**(g01/10))
G02=round(10**(g02/10))
G03=round(10**(g03/10))
F_2=round(10**(F2/10))
F_3=round(10**(F3/10))
Te2=round((F_2-1))*T
Te3=round((F_3-1))*T
Te=Te1+(Te2/G01)+(Te3/(G01*G02))# Eq overall noise temp
print 'The equivalent noise temp is: %.3f K'%(Te)

The equivalent noise temp is: 4.913 K

Example7.9, page no 286

In [7]:
from __future__ import division
#Given
g01=round(10**(25/10))#low noise amplifier gain
Te1=4#low noise amplifier noise temp
g02=round(10**(1.7))#preamplifier gain
F2=round(10**0.6)#preamplifier noise figure
F3=round(10**1.2)#preamplifier noise figure
T=290# room temp
Te2=round((F2-1)*T)
Te3=round((F3-1)*T)
Te=Te1+(Te2/g01)+(Te3/(g01*g02))#Overall noise Temperature
print 'Equivalent noise temperature is %.3f K'%(Te)

Equivalent noise temperature is 7.028 K

Example7.10, page no 286

In [8]:
from __future__ import division
from math import log10
#Given
SNRam=25# Signal to noise ratio of AM
PcFM_AM=0.9#
mf=5
SNRfm=(10*log10(3*(mf**2)*(PcFM_AM)))+SNRam
print 'S/N ratio for FM is %.2f dBs'%(SNRfm)
# Note :  There are some calculation errors in the solution presented in the book

S/N ratio for FM is 43.29 dBs

Example7.11, page no 287

In [9]:
from __future__ import division
from math import log10
#Given
ma=0.3
SNR=20# s/n ratio
SNR1=10**(0.1*SNR)
SNR_new=SNR+3
ma2=0.6# increased new depth of modulation
Pt_Ni=SNR1*((1+(ma**2))/(ma**2))
SNR2=10*log10(Pt_Ni*((ma2**2)/(1+((ma2**2)/2))))

print 'a)\n  New SNR for 3dB increase in input s/g is %d dBs\nb)  When Modulation depth is increased to 60%%\n SNR becomes %f dBs'%(SNR_new,(SNR2))

a)
  New SNR for 3dB increase in input s/g is 23 dBs
b)  When Modulation depth is increased to 60%
 SNR becomes 25.676045 dBs

Example7.12, page no 287

In [10]:
from __future__ import division
from math import log
#Given
fmax=5e3#max s/g freq
S_fmin=2*fmax# Min sampling freq
B_S=6#Binary bits sent per sample
BTR=B_S*S_fmin#Bit Transmission rate
Q=2**B_S#No of Quantizable levels
MQN=0.5/Q#Max Quantization noise
S_QNR=MQN**-1# Signal to Quantization noise ratio
#b
S_QNRreq=0.5*S_QNR# Signal to Quantization noise ratio
Qreq=0.5*S_QNRreq#No of Quantizable levels
B_Sreq=log(Qreq,2)#Binary bits sent per sample
print 'a)  Bit Transmission rate: %d kbits/s\n    Signal to Quantization noise ratio %d \nb)\n  Bit Transmission rate: %d kbits/sample\n    Signal to Quantization noise ratio: %d'%(BTR/1000,S_QNR,B_Sreq,S_QNRreq)

a)  Bit Transmission rate: 60 kbits/s
    Signal to Quantization noise ratio 128 
b)
  Bit Transmission rate: 5 kbits/sample
    Signal to Quantization noise ratio: 64