Chapter 6 - Noise

Example 1 - pg 281

In [1]:
#calculate the RMS noise voltage
import math
#given
R = 10.*10**3#resistance of amplifier in ohms
T = 273.+27#temperature in kelvin
B = (20.-18)*10**6#bandwidth
k = 1.38*10**-23#boltzman's constant

#calculations
V_n = math.sqrt(4*R*k*T*B)*10**6;#rms noise voltage

#result
print "Rms noise voltage (muV) = ",round(V_n,2)

Rms noise voltage (muV) =  18.2

Example 2 - pg 281

In [2]:
#calculate the RMS noise voltage
import math
#given
R_1  = 300.#equivalent noise resistance
R_2 = 400.#input resistance
T = 273+27.#temperature in kelvin
B = 7.*10**6#bandwidth
k = 1.38*10**-23#boltzman's constant

#calculations
R_s = R_1 +R_2#effective resistance in series
V_nr = math.sqrt(4*k*T*B*R_s)*10**6#rms noise voltage

#result 
print "Rms noise voltage (muV) = ",round(V_nr,0)

Rms noise voltage (muV) =  9.0

Example 3 - pg 282

In [3]:
#calculate the Noise voltage in all cases
import math
from math import sqrt
#given
R_1 = 20*10**3#resistance one
R_2 = 50*10**3#resistance two
T = 273+15#temperature in kelvin
B = 100*10**3#bandwidth
k = 1.38*10**-23#boltzman's constant

#calculations
R_s = R_1 +R_2#series effective resistance
R_p = (R_1*R_2)/(R_1 + R_2)#parallel effective resistance
V_1 = sqrt(4*k*T*R_1*B)*10**6#noise voltage in R_1
V_2 = sqrt(4*k*T*R_1*B)*10**6#noise voltage in R_2
V_s = sqrt(4*k*T*R_s*B)*10**6#noise voltage when resistance connected in series
V_p = sqrt(4*k*T*R_p*B)*10**6#noise voltage when resistance connected in parallel

#results
print "i.Noise voltage due to R_1 (muV) = ",round(V_1,2)
print "ii.Noise voltage due to R_2 (muV) = ",round(V_2,2)
print "iii.Noise voltage due to two resistance in series (muV) = ",round(V_s,2)
print "iv.Noise voltage due to two resistance in parallel (muV) = ",round(V_p,2)

i.Noise voltage due to R_1 (muV) =  5.64
ii.Noise voltage due to R_2 (muV) =  5.64
iii.Noise voltage due to two resistance in series (muV) =  10.55
iv.Noise voltage due to two resistance in parallel (muV) =  4.77

Example 4 - pg 283

In [4]:
#calculate the Equivalent input noise resistance

#given
A_1 = 10.#voltage gain for first stage
A_2 = 25.#volatage gain for second stage
R_i1 = 600.#input resistance for first stage in ohms
R_eq1 = 1600.#equivalent noise resistance for first stage 
R_01 = 27.*10**3#Output resistance for first stage 
R_i2 = 81.*10**3#input resistance for second stage
R_eq2 = 10.*10**3#Equivalent noise resistance for second stage 
R_02 = 1.*10**6#putput resistance for second case

#calculations
R_1 = R_i1 + R_eq1
R_2 = ((R_01*R_i2)/(R_01+R_i2)) + R_eq2
R_3 = R_02
R_eq = R_1 + (R_2/A_1**2) + R_3/(A_1**2 *A_2**2);

#results
print "Equivalent input noise resistance (Ohms) = ",round(R_eq,0)

Equivalent input noise resistance (Ohms) =  2519.0

Example 7 - pg 295

In [5]:
#calculate the output voltage
import math
#given
T = 273. + 17#temperature in kelvin
Q = 10.#quality factor
c  = 10.*10**-12#capacitance
f_r = 100.*10**6#resonate frequency
k = 1.38*10**-23#boltzman's constant

#calculations
delta_f = f_r/Q#bandwidth of the tuned circuit
w = 2*math.pi*f_r;#angular frequency
R = 1/(Q*w*c);#resistance
V_no = math.sqrt(4*k*Q**2*T*delta_f*R)*10**6 #output voltage

#results
print "Output voltge (V) = ",round(V_no,0)

Output voltge (V) =  16.0

Example 8 - pg 297

In [6]:
#calculate the Noise figure and Equivalent temperature
import math
#given
R_a = 50.#antenna resistance
R_eq = 30.#equivalent noise resistance of receiver
T_0 = 290.#initial temperature in degree kelvin
#calculations
F = 1+(R_eq/R_a);#noise figure
F_dB = 10*math.log10(F)#noise figure in decibels
T_eq = T_0*(F-1)#equivalent temperature

#results
print "i.Noise figure in decibels (dB) = ",round(F_dB,2)
print "ii.Equivalent temperature (degree kelvin) = ",T_eq

i.Noise figure in decibels (dB) =  2.04
ii.Equivalent temperature (degree kelvin) =  174.0

Example 9 - pg 302

In [7]:
#calculate the Noise figure
import math
#given
R_eq = 2518.#equivalent resistance in ohms
R_t = 600.#input impedence in ohms
R_a= 50.#output impedencre in ohms

#calculations
R_eq1 = R_eq - R_t;
F = 1 + (R_eq1/R_a) #noise figure
F_dB = 10*math.log10(F)#noise figure in dB

#results
print "Noise figure in dB = ",round(F_dB,2)
print "Note:Calculation mistake is their in text book in finding noise figure in dB"

Noise figure in dB =  15.95
Note:Calculation mistake is their in text book in finding noise figure in dB

Example 10 - pg 305

In [9]:
#calculate the Overall noise figure
import math
from math import exp, log10,log
#given
F_1 = 2.#noise figure of first stage in dB
A_1 = 12.#gain in first stage in dB
F_2 = 6.#noise figure of second stage in dB
A_2 = 10.#gain in first second in dB 


#calculations
F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio 
F_2ratio = exp((F_2/10)*log(10));#noise figure of second stage in ratio 
A_1ratio = exp((A_1/10)*log(10));#gain of first stage in ratio
A_2ratio = exp((A_2/10)*log(10));#gain of second stage in ratio
F = F_1ratio + ((F_2ratio - 1)/(A_1ratio));#Overall noise figure 
F_dB = 10*log10(F);#Overall noise figure  in dB

#results
print "Overall noise figure (dB) = ",round(F_dB ,1)

Overall noise figure (dB) =  2.5

Example 11 - pg 306

In [10]:
#calculate the Overall noise figure
import math
from math import exp, log10,log
#given
F_1 = 9.#noise figure for first stage in dB
F_2 = 20.#noise figure for second stage in dB
A_1 = 15.#gain in first stage in dB

#calculations
F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio 
F_2ratio = exp((F_2/10)*log(10));#noise figure of second stage in ratio  
A_1ratio = exp((A_1/10)*log(10));#gain of first stage in ratio
F = F_1ratio + ((F_2ratio - 1)/(A_1ratio));
F_dB = 10*log10(F);
 
#results
print "Overall noise figure (dB) = ", round(F_dB,2)

Overall noise figure (dB) =  10.44

Example 12 - pg 307

In [11]:
#calculate the rms noise voltage
import math
#given
f_1 = 18.*10**6#lower operating frequency in Hz
f_2 = 20.*10**6#lower operating frequency in Hz
T = 273. + 17#temperature in kelvin
R = 10.*10**3#input resistance
k = 1.38*10**-23#boltzman's constant

#calculations
B = f_2 - f_1#bandwidth in Hz
V_n = math.sqrt(4*k*B*R*T)*10**6;#rms noise voltage

#results
print "rms noise voltage (muV) = ",round(V_n,1)

rms noise voltage (muV) =  17.9

Example 14 - pg 308

In [12]:
#calculate the Meter reading, resistance

#given
A = 60.#gain of noiseless amplifier
V_n1 = 1.*10**-3#output of the amplifier
B = 20.*10**3#initial bandwidth
B1 = 5.*10**3#change in bandwidth
k = 1.38*10**-23#boltzman's constant
T = 273. + 80#temperature in degree kelvin

#calculaitons
#since the bandwidth is reesuced to 1/4th of its value,therefore the noise voltage 
#will be V_n proportional to sqrt(B)
#Hence, the noise voltage at 5KHz will become half its value at 20KHz bandwidth i.e,
V_n = .5*10**-3#noise voltage in volts
V_no = V_n1/A;#noise ouput voltage 
R = (V_no**2/(4*k * T * B ));#resistance at 80degree celcius

#results
print "i.Meter reading in volts (V) = ",V_n
print "ii.Resistance at 80 degree celcius (kohms) = ",round(R/1000.,0)
print "Note: There is calculation mistake in textbook in the measurement of resistance they took constant in formula as 1 instead of 4"

i.Meter reading in volts (V) =  0.0005
ii.Resistance at 80 degree celcius (kohms) =  713.0
Note: There is calculation mistake in textbook in the measurement of resistance they took constant in formula as 1 instead of 4

Example 16 - pg 309

In [13]:
#calculate the Overall noise figure
import math
from math import exp, log10,log
#given
A_1 = 10.#gain in first stage in dB
A_2 = 10.#gain in second stage in dB
A_3 = 10.#gain in third stage in dB
F_1 = 6.#noise figure for first stage in dB
F_2 = 6.#noise figure for second stage in dB
F_3 = 6.#noise figure for third stage in dB

#calculations
F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio 
F_2ratio = exp((F_2/10)*log(10));#noise figure of second stage in ratio 
F_3ratio = exp((F_3/10)*log(10));#noise figure in third stage in ratio 
A_1ratio = exp((A_1/10)*log(10));#gain of first stage in ratio
A_2ratio = exp((A_2/10)*log(10));#gain of second stage in ratio
A_3ratio = exp((A_3/10)*log(10));#gain of third stage in ratio
F = F_1ratio + ((F_2ratio - 1)/(A_1ratio)) + ((F_3ratio - 1)/(A_2ratio*A_1ratio));#Overall noise figure

#results
print "Overall noise figure of three stage cascaded amplifier = ",round(F,2)

Overall noise figure of three stage cascaded amplifier =  4.31

Example 17 - pg 310

In [14]:
#calculate the Overall noise figure
import math
from math import exp, log10,log
#given
G_1 = 10.#gain in first stage in dB
#noise figure for both the stages are same
F_1 = 10.#noise figure for first stage in dB
F_2 = 10.#noise figure for second stage in dB

#calculations
F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio 
F_2ratio = exp((F_2/10)*log(10));#noise figure of second stage in ratio 
G_1ratio = exp((G_1/10)*log(10));#gain of first stage in ratio
F = F_1ratio + ((F_2ratio - 1)/(G_1ratio));#Overall noise figure
F_dB= 10*log10(F)##Overall noise figure in dB

#results

print "Overall noise figure (dB) = ", round(F_dB,2)

Overall noise figure (dB) =  10.37

Example 18 - pg 310

In [15]:
#calculate the overall noise figure and overall gain
import math
from math import exp, log10,log
#given
G_1 = 4.#gain in first stage in dB
G_2 = 10.#gain in second stage in dB
F_1 = 10.#noise figure for first stage in dB
F_2 = 10.#noise figure for second stage in dB

#calculations
F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio 
F_2ratio= exp((F_2/10)*log(10));#noise figure of second stage in ratio 
G_1ratio = exp((G_1/10)*log(10));#gain of first stage in ratio
G_2ratio = exp((G_2/10)*log(10));#gain of second stage in ratio
F = F_1ratio + ((F_2ratio - 1)/(G_1ratio));#Overall noise figure 
G = log10(G_1ratio *G_2ratio );
F_dB= 10*log10(F)##Overall noise figure in dB

#results
print "i.Overall noise figure (dB) = ",round(F_dB,2)
print "ii.Overall gain (dB) = ",G 
print "Note:There is mistake in calculation of overall gain in textbook"

i.Overall noise figure (dB) =  11.33
ii.Overall gain (dB) =  1.4
Note:There is mistake in calculation of overall gain in textbook

Example 19 - pg 310

In [16]:
#calculate the Overall noise figure
import math
from math import exp, log10,log
#given
G_1 = 15.#gain in first stage in dB
F_1 = 9.#noise figure for first stage in dB
F_2 = 20.#noise figure for second stage in dB

#calculations
F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio 
F_2ratio = exp((F_2/10)*log(10));#noise figure of second stage in ratio 
G_1ratio = exp((G_1/10)*log(10));#gain of first stage in ratio
F = F_1ratio + ((F_2ratio - 1)/(G_1ratio));#Overall noise figure 
F_dB= 10*log10(F)##Overall noise figure in dB

#results
print "Overall noise figure (dB) = ", round(F_dB,2)

Overall noise figure (dB) =  10.44

Example 20 - pg 311

In [17]:
#calculate the Noise temperature and overall noise temperature
import math
from math import exp, log10,log
#given
F_2 = 20.#noise figure of receiver in dB
G_1 = 40.#gain of low noise amplifier in dB
T_e1 = 80.#noise temperature of low noise amplifier in degree kelvin
T_0 = 300.#room temperature

#calculations
F_2ratio = exp((F_2/10)*log(10));#noise figure of receiver in ratio 
G_1ratio = exp((G_1/10)*log(10));#gain of  low noise amplifier
T_e2 = (F_2ratio-1)*T_0#noise temperature of the receiver in degree kelvin
T_e = T_e1 +(T_e2/G_1ratio)#overall noise temperature in degree kelvin

#results
print "i.Noise Temperature of the receiver (degkelvin) =  ",T_e2
print "ii.Overall noise temperature (degkelvin) = ",T_e

i.Noise Temperature of the receiver (degkelvin) =   29700.0
ii.Overall noise temperature (degkelvin) =  82.97

Example 21 - pg 311

In [18]:
#calculate the overall noise temperature and noise figure
import math
#given from the figure
G_1ratio = 1000.#gain of master amplifier 
G_2ratio = 100.#gain of TWT
G_3ratio = 10000.#gain of mixer and IF amplifier
F_2ratio = 4.#noise figure of TWT 
F_3ratio = 16.#noise figure of mixer and IF amplifier
T_0 =273 + 17.#ambident temperature in degree kelvin
T_e1 = 5.#temperature of master amplifier in degree kelvin

#calculaitons
F_1 = 1 + (T_e1/T_0);#noise figure of master amplifier
F = F_1 + ((F_2ratio - 1)/(G_1ratio)) + ((F_3ratio - 1)/(G_2ratio*G_1ratio));#Overall noise figure
F_dB = 10*math.log10(F);#overall noise figure in dB
T_e = (F - 1)*T_0;#overall noise temperature of the receiver 

#results
print "i.Overall noise temperature of the receiver (degreekelvin) = ",round(T_e,0)
print "ii.Overall noise figure (dB) = ", round(F_dB,5)

i.Overall noise temperature of the receiver (degreekelvin) =  6.0
ii.Overall noise figure (dB) =  0.08767