Chapter 7 : Noise

Example 7.1, Page 317

In [1]:
import math

#Calculation

def calc(fL,fH,enw,fce):
    En=enw*math.sqrt((fce*math.log(fH/fL))+fH-fL)
    return En

#answer

print "a)\n  Estimated RMS input voltage =",round(calc(0.1,100.0,20*10**(-9),200.0)*10**6,2),"micro volt"
print "b)\n  Estimated RMS input voltage =",round(calc(20.0,20*10**3,20*10**(-9),200.0)*10**6,2),"micro volt"
print "c)\n  Estimated RMS input voltage =",round(calc(0.1,1*10**6,20*10**(-9),200.0)*10**6,1),"micro volt"

a)
  Estimated RMS input voltage = 0.77 micro volt
b)
  Estimated RMS input voltage = 2.92 micro volt
c)
  Estimated RMS input voltage = 20.0 micro volt

Example 7.3, Page 320

In [2]:
from sympy import Symbol,integrate
import math

#Variable Declaration

fL1=1.0                # Hz
fH1=1*10**3            # Hz
fL2=fH1
fH2=10*10**3           # Hz
fL3=fH2

#Calculation

#fH3=infinity
enw=20*10**(-9)
fce=100.0             # Hz
Eno1=enw*math.sqrt((fce*math.log(fH1/fL1))+fH1-fL1)
eno=float(enw)/fL2
f=Symbol('f')
Eno2=eno*math.sqrt(integrate(f**2,(f,fL2,fH2)))      # Integrating
f0=100*10**3            # Hz
enw3=200*10**(-9)
Eno3=enw3*math.sqrt((1.57*f0)-fL3)
Eno=math.sqrt((Eno1**2)+(Eno2**2)+(Eno3**2))

#answer

print "Estimated rms noise voltage =",round(Eno*10**6,1),"micro volt"

Estimated rms noise voltage = 77.5 micro volt

Example 7.4, Page 323

In [3]:
import math

#Variable Declaration

R=10*10**3                  # ohm

#Calculation

k=1.38*10**(-23)
T=25+273            # Room Temperature in Kelvin
eR=math.sqrt(4*k*T*R)
iR=eR/R
fH=20*10**3           # Hz
fL=20                 # Hz
ER=eR*math.sqrt(fH-fL)

#answer

print "a)\n  Noise Voltage (eR) =",round(eR*10**9,1),"nV/(Hz)^0.5"
print "b)\n  Noise Current (iR) =",round(iR*10**12,2),"pA/(Hz)^0.5"
print "c)\n  Rms noise voltage over audio range =",round(ER*10**6,2),"micro volt"

a)
  Noise Voltage (eR) = 12.8 nV/(Hz)^0.5
b)
  Noise Current (iR) = 1.28 pA/(Hz)^0.5
c)
  Rms noise voltage over audio range = 1.81 micro volt

Example 7.5, Page 323

In [4]:
import math

#Variable Declaration

fH=1*10**6             # Hz
q=1.602*10**(-19)

#Calculation

def calc(ID):
    global fH,q
    In=math.sqrt(2*q*ID*fH)
    SNR=20*math.log10(ID/In)
    return SNR

#answer

print "a)\n  Signal to Noise Ratio =",round(calc(1*10**(-6)),1),"dB"
print "b)\n  Signal to Noise Ratio =",round(calc(1*10**(-9)),1),"dB"

a)
  Signal to Noise Ratio = 64.9 dB
b)
  Signal to Noise Ratio = 34.9 dB

Example 7.7, Page 331

In [5]:
import math

#Variable Declaration

R1=100*10**3           # ohm
R2=200*10**3           # ohm
R3=68*10**3            # ohm
enw=20*10**(-9)        # V/(Hz)^0.5
fce=200.0              # Hz
ft=1*10**6             # Hz
inw=0.5*10**(-12)      # A/(Hz)^0.5
fci=2*10**3            # Hz

#Calculation

Rp=(R1*R2)/(R1+R2)
Ano=1+(R2/R1)
fB=ft/Ano
fL=0.1
Enoe=Ano*enw*math.sqrt((fce*math.log(fB/fL))+(1.57*fB)-fL)
Enoi=Ano*math.sqrt((R3**2)+(Rp**2))*inw*math.sqrt((fci*math.log(fB/ fL))+(1.57*fB))
k=1.38*10**(-23)
T=25+273                  #Room temperature in Kelvin 
EnoR=Ano*math.sqrt((4*k*T)*(R3+Rp)*1.57*fB)
Eno=math.sqrt((Enoe**2)+(Enoi**2)+(EnoR**2))

#answer

print "a)\n  RMS Output Noise Voltage =",round(Eno*10**6),"micro volt"
print "  Peak to Peak Noise Voltage =",round(6.6* Eno*10**3,2),"mV"        # answer in book differs due to precision error

a)
  RMS Output Noise Voltage = 154.0 micro volt
  Peak to Peak Noise Voltage = 1.01 mV

Example 7.8, Page 333

In [6]:
from sympy.solvers import solve
from sympy import Symbol
import math

#Variable Declaration

R1=100*10**3         # ohm
R2=200*10**3         # ohm
R3=68*10**3          # ohm
enw=20*10**(-9)      # V/(Hz)^0.5
fce=200.0            # Hz
ft=1*10**6           # Hz
inw=0.5*10**(-12)    # A/(Hz)^0.5
fci=2*10**3          # Hz

#Calculation

Rp=(R1*R2)/(R1+R2)
Ano=1+(R2/R1)
fB=ft/Ano
fL=0.1
Enoeold=Ano*enw*math.sqrt((fce*math.log(fB/fL))+(1.57*fB)-fL )
Enoiold=Ano*math.sqrt((R3**2)+(Rp**2))*inw*math.sqrt((fci*math.log(fB/fL))+(1.57*fB))
k=1.38*10**(-23)
T=25+273             #Room temperature in Kelvin
EnoRold=Ano*math.sqrt((4*k*T)*(R3+Rp)*1.57*fB)
Enoold=math.sqrt((Enoeold**2)+(Enoiold**2)+(EnoRold**2))
Enonew=50*10**(-6)          #New Value of Eno mentioned in problem 
Enoisum=(Enonew**2)-(Enoeold**2)                #sum of ( Enoi ˆ2) and (EnoRˆ2) 
Enoinewsq=(Ano**2)*(inw**2)*((fci*math.log(fB/fL))+(1.57*fB ))  #( Enoinew ˆ2) /(Rˆ2)
EnoRnewsq=(Ano**2)*((4*k*T)*1.57*fB)
x=Symbol('x')
r1=solve((Enoinewsq*(x**2))+(EnoRnewsq*x)-Enoisum,x)
R=r1[1]
R3new=R/2
R1new=(3*R3new)/2
R2new=2*R1new

#answer

print "Resistances after scaling are : "
print "R1 =",round(R1new*10**(-3),2),"kilo ohm"       # answer in book wrong due to precision error
print "R2 =",round(R2new*10**(-3),1),"kilo ohm"
print "R3 =",round(R3new*10**(-3),1),"kilo ohm"

Resistances after scaling are : 
R1 = 5.26 kilo ohm
R2 = 10.5 kilo ohm
R3 = 3.5 kilo ohm

Example 7.9, Page 334

In [7]:
import math

#Variable Declaration

R1=100*10**3       #ohm, From Example 7.7( a) 
R2=200*10**3       #ohm, From Example 7.7( a)
Eno=154*10**(-6)   # V, From Example 7.9 

#Calculation

Aso=-(R2/R1)
Eni=Eno/abs(Aso)
Vipa=0.5            #Peak amplitude of input ac signal
Virms=Vipa/math.sqrt(2)
SNR=20*math.log10(Virms/Eni)

#answer

print "SNR of the c irc uit of Example 7.7 =",round(SNR,1),"dB"

SNR of the c irc uit of Example 7.7 = 73.2 dB

Example 7.10, Page 334

In [8]:
import math

#Variable Declaration

z0=710*10**3           # ohm
fb=350*10**3           # Hz
rn=50.0                # ohm
enw=2.4*10**(-9)       # V/(Hz)^0.5
fce=50*10**3           # Hz
inpw=3.8*10**(-12)     # A/(Hz)^0.5
fcip=100*10**3         # Hz
innw=20*10**(-12)      # A/(Hz)^0.5
fcin=100*10**3         # Hz
R1=166.7               # ohm
R2=1.5*10**3           # ohm

#Calculation

R3=100        # internal resistance 
fL=0.1
Rp=(R1*R2)/(R1+R2)
ft=(z0*fb)/R2
fB=ft/(1+(rn/((R1*R2)/(R1+R2))))
Ano=1+(R2/R1)
Enoe=enw*math.sqrt((fce*math.log(fB/fL))+(1.57*fB)-fL)
Enoi=R3*inpw*math.sqrt(((fcip*math.log(fB/fL))+(1.57*fB)-fL))
Enop=Rp*innw*math.sqrt((fcin*math.log(fB/fL))+(1.57*fB)-fL)
k=1.38*10**(-23)
T=25+273                #/Room temperature in Kelvin
EnoR=math.sqrt((4*k*T)*(R3+Rp)*((1.57*fB)-fL))
Eno=Ano*math.sqrt((Enoe**2)+(Enoi**2)+(EnoR**2)+(Enop**2))
c=6.6*10**3                     # F
Eno1=Eno*c

#answer

print "RMS Noise Voltage (Eno) =",round(Eno*10**6,2),"micro volt"    #answer in textbook is wrong
print "Peak to Peak Noise Voltage (Eno) =",round(Eno1,2),"mV"        #answer in textbook is wrong

RMS Noise Voltage (Eno) = 611.1 micro volt
Peak to Peak Noise Voltage (Eno) = 4.03 mV

Example 7.11, 337

In [9]:
import math
import numpy as np

#Variable Declaration

ft=16*10**6         # Hz
enw=4.5*10**(-9)    # V/(Hz)^0.5
fce=100.0           # Hz
IB=1*10**(-12)      # A
fL=0.01             # Hz
R1=100*10**(9)      # ohm
C1=45*10**(-12)     # F
R2=10*10**6         # ohm
C2=0.5*10**(-12)    # F

#Calculation

b0rec=1.0
binfrec=91.0
fz=350.0                  # Hz
fp=31.8*10**3             # Hz
fx=176*10**3              # Hz
k=1.38*10**(-23)
T=25+273
iR2=math.sqrt((4*k*T)/R2)
q=1.602*10**(-19)
In=math.sqrt(2*q*IB)
Enoe=binfrec*enw*math.sqrt(((np.pi/2)*fx)-fp)
EnoR=R2*iR2*math.sqrt((np.pi/2)*fp)
Eno=math.sqrt((Enoe**2)+(EnoR**2))

#answer

print "Total Output Noise =",round(Eno*10**6),"micro Volt"

Total Output Noise = 222.0 micro Volt

Example 7.12, Page 338

In [10]:
import math

#Variable Declaration

ft=16*10**6          # Hz
enw=4.5*10**(-9)     # V/(Hz)^0.5
fce=100.0            # Hz
IB=1*10**(-12)       # A
fL=0.01              # Hz
R1=100*10**(9)       # ohm
C1=45*10**(-12)      # F
R2=10*10**6          # ohm
C2=0.5*10**(-12)     # F

#Calculation

b0rec=1.0
binfrec=91.0
fz=350.0              # Hz
fp=31.8*10**3         # Hz
fx=176*10**3          # Hz
k=1.38*10**(-23)
T=25+273
Cc=0.5*10**(-12)       # Assumed
C2=Cc
C3=10*10**(-9)
R3=(R2*Cc)/C3

#answer

print "Cc = C2 =",round(Cc*10**(12),2),"pF"
print "R3 =",round(R3,2),"ohm"
print "C3 =",round(C3*10**(9),2),"nF"

Cc = C2 = 0.5 pF
R3 = 500.0 ohm
C3 = 10.0 nF

Example 7.13, Page 339

In [11]:
import math
import numpy as np

#Variable Declaration

C1=2*10**(-9)          # F
binfrec=4000.0         # V/V
T=1*10**(9)            # V/A

#Calculation

inw=0.566*10**(-15)     
ft=16*10**6          # Hz
R1=100*10**(9)      #ohm
C2=0.5*10**(-12)    #F
fx=(1.0/binfrec)*ft
enw=4.5*10**(-9)
Enoe=binfrec*enw*math.sqrt((np.pi*fx)/2)
EnoRmax=Enoe/3
k=1.38*10**(-23)
Temp=25+273
ex=((EnoRmax**2)*C2)/(k*Temp)
R2=T/ex
R3=1*10**3       # Assumed
R4=(ex-1)*R3
fp=1/(2*np.pi*ex*R2*C2)
fB=fp
Rp=(R1*R2)/(R1+R2)
Enoi=math.sqrt(1.57*fB)*inw
Eno=math.sqrt((Enoe**2)+(Enoi**2)+(EnoRmax**2))

#answer

print "a) Designed T Network : "
print "  R1 =",round(R1*10**(-9)),"giga ohm"
print "  R2 =",round(R2*10**(-6)),"mega ohm"          # precision error in book
print "  R3 =",round(R3*10**(-3)),"kilo ohm"
print "  R4 =",round(R4*10**(-3),1),"kilo ohm"        # precision error in book
print "  C1 =",round(C1*10**9),"nF"
print "  C2 =",round(C2*10**12),"pF"
print "b)\n  Total rms Output Noise =",round(Eno*10**3,2),"mV"
print "  Bandwidth (fB) =",round(fB),"Hz"

a) Designed T Network : 
  R1 = 100.0 giga ohm
  R2 = 36.0 mega ohm
  R3 = 1.0 kilo ohm
  R4 = 26.5 kilo ohm
  C1 = 2.0 nF
  C2 = 1.0 pF
b)
  Total rms Output Noise = 1.5 mV
  Bandwidth (fB) = 318.0 Hz