# Chapter 1:Introductory Topics¶

## Example 1.1 Page No 8¶

In [1]:
#Given
P1=0.001                                             #power
x=10**0

#calculation
import math
dB=10*math.log(0.001/0.001)
y=x*P1*600
V=math.sqrt(y)

#Result
print"V2 =",round(V,3),"V"
print"dBm(600)=20log(V2/0.775)"

V2 = 0.775 V
dBm(600)=20log(V2/0.775)


## Example 1.2 Page No 9¶

In [7]:
#Given
P=0.001                             #power
R=75                                #resistance of audio system
R1=50
x=(8/20.0)

#Calculation
import math
y=(10**x)
V2=(y*0.775)
V=math.sqrt(P*R)
V1=math.sqrt(P*R1)
dBm= 20*math.log(V2/0.775)

#Result
print"the dBm voltage reference for 50 ohm system is: ",round(V1,4),"V"
print"dBm(50)= 20log(V/0.2236)"

the dBm voltage reference for 50 ohm system is:  0.2236 V
dBm(50)= 20log(V/0.2236)


## Example 1.3 Page No 10¶

In [10]:
#Given
x=(10/10.0)                      #laser diode output

#Calculation
import math
y=(10**x)
P2=(y*0.001)
a=(math.log10(0.01/1.0))
z=(10*a)

#result
print"(a) P2 = ",P2,"W"              #convert +10dB to Watts
print"(b) dBW =",z,"dBW"

(a) P2 =  0.01 W
(b) dBW = -20.0 dBW


## Example 1.4 Page No 16¶

In [17]:
#Given
kT=(1.6*10**-20)
f=(1*10**6)                               #bandwidt, Hz
R=(1*10**6)                               #resistance, ohm

#calculation
import math
x=math.sqrt(kT*f*R)
#4kT at room temperature (17 degree C) is 1.6*10**-20 Joules

#Result
print"en = ",round(x,6),"Vrms"

en =  0.000126 Vrms


## Example 1.5 Page No 16¶

In [2]:
#Given

k=(1.38*10**-23)
T=(27+273)                             #temperature
f=(4*10**6)                            #bandwidth,Hz
R=100                                  #source resistance, ohm

#calculation
import math
x=math.sqrt(4*k*T*f*R)
# to convert degres to kelvin, add 273 in it

#result
print"en= ",round(x,8),"Vrms"

en=  2.57e-06 Vrms


## Example 1.6 Page No 18¶

In [26]:
#Given
x=10                           #input S/N power
y=5.0                          #utput S/N power
z=(x/y)

#Calculation
import math
a=(10*math.log10(z))
b=(10*math.log10(x))
c=(10*math.log10(y))
d=(b-c)

#Result
print"(a)NR = ",z
print"(b)NF = ",round(a,1),"dB"
print"(c) 10log(Si/Ni) =",b,"dB"
print" 10log(So/No) = ",round(c,0),"dB"
print"their difference = ",round(d,0),"dB"

(a)NR =  2.0
(b)NF =  3.0 dB
(c) 10log(Si/Ni) = 10.0 dB
10log(So/No) =  7.0 dB
their difference =  3.0 dB


## Example 1.7 Page No 21¶

In [5]:
#Given
BW=200*10**3                #bandwidth
k=(1.38*10**-23)
T=(273+22)                  #converting degrees C into kelvin
R=(10*10**3)
R1=300
NF1=3
NF2=8
NR1=2
NR2=6.31

#calculation
import math
df=((math.pi/2.0)*BW)
Pn=(k*T*df)
en=math.sqrt(4*Pn*R)
x=(14+20+20)                  #sum of the power gain of the three stages
y=(x/10.0)
Pg=(10**y)
Po=(Pn*Pg)
eno=math.sqrt(Po*R1)
pg1=(10**(1.4))
pg2=(10**(20))
NR=(NR1+((NR2-1)/pg1)+((NR2-1)/(pg1*pg2)))
NF=10*math.log10(NR)
No=(NR*Pn*Pg)
a=math.sqrt(No*R1)

#Result
print"(a) en(out)= ",round(eno,5),"V"
print"(b) NF = ",round(NF,2),"dB"
print"(c) No = ",round(a,6),"V"             #outputnoise voltage

(a) en(out)=  0.00031 V
(b) NF =  3.45 dB
(c) No =  0.000462 V


## Example 1.8 Page No 24¶

In [40]:
#Given
k=1.38*10**-23
T=(35+40+52)             #total temperature
df=(1*10**6)
Teq=52
To=290.0

#calculation
import math
Pn=(k*T*df)
x=(Teq/To)
NR=(x+1)
NF=(10*math.log10(NR))

#Result
print"NR = ",round(NR,2)      #noise ratio
print"NF =",round(NF,3),"dB"     #noise figure

NR =  1.18
NF = 0.716 dB


## Example 1.9 Page No 25¶

In [43]:
#Given
x=7*10**-3               # o/p power measured 400-Hz audio signal modulates a carrier
y=0.18*10**-3            # o/p power measured when a filter cancels 400-Hz portion of the o/p

#Calculation
import math
z=10*math.log10(x/y)

#Result

SINAD =  15.9 dB


## Example 1.10 Page No 26¶

In [44]:
#Given
i= 14*10**-3                 #dc current
R=50                         #resistance, ohm

#Calculation
import math
x=(20*i*R)
y=10*math.log10(x)

#Result
print"NF=",round(y,2),"dB"            #noise figure

NF= 11.46 dB


## Example 1.11 Page No 37¶

In [47]:
#Given
f=(12*10**3)
L=3*10**-3
C=(0.1*10**-6)
R=30             #resistance,ohm

#Calculation
import math
x=L*C
y=math.sqrt(x)
z=(2*math.pi*y)
a=(1/z)
Xl=(2*math.pi*f*L)
Xc=(1/(2*math.pi*f*C))
b=(Xl-Xc)**2
c=R**2
d=math.sqrt(c+b)

#Result
print"fr = ",round(a,2),"Hz"
#at 12kHz
print"Z = ",round(d,2),"ohm"

fr =  9188.81 Hz
Z =  98.26 ohm


## Example 1.12 Page No 38¶

In [6]:
#Given
R1=20                   #resistance, ohm
R2=1
L=1*10**-3              #inductor
C=0.4*10**-6            #capacitor
ein=50*10**-3
f=12*10**3             #frequency

#Calculation
import math
x=math.sqrt(L*C)
y=(1/(2*math.pi*x))
eo= ein*(R2/(R2+R1))
XL=(2*math.pi*f*L)
XC=(1/(2*math.pi*f*C))
a=(R1+R2)**2
b=(XL-XC)**2
z=math.sqrt(a+b)
zo=math.sqrt((R2**2)+b)
m=(ein*(zo/z))

#Result
print"resonant frequency is",round(y,2),"Hz"
print"o/p voltage at 12kHz =",round(m,3),"V"

resonant frequency is 7957.75 Hz
o/p voltage at 12kHz = 0.045 V


## Example 1.13 Page No 40¶

In [3]:
#Given
a=460*10**3
b=450*10**3
fr=455*10**3                         #frequency

#Calculation
import math
BW=a-b
Q=(fr/BW)
C=0.001*10**-6
x=(fr*2*math.pi)
y=(1/x)**2
z=y/C
R=(2*math.pi*z*BW)

#Result
print"(a)Bandwidth = ",BW,"Hz"
#filter's peak o/p occurs at 455kHz
print"(b)Quality factor = ",Q,"KHz"
print"(c)inductance =",round(z,5),"H"
print"(d)total circuit resistance= ",round(R,2),"ohm"

(a)Bandwidth =  10000 Hz
(b)Quality factor =  45 KHz
(c)inductance = 0.00012 H
(d)total circuit resistance=  7.69 ohm


## Example 1.14 Page No 42¶

In [7]:
#Given
R=2                      #resistance,ohm
L=3*10**-3               #inductance
C=0.47*10**-6            #capacitance

#Calculation
import math
x=(2*math.pi*math.sqrt(L*C))
y=1/x
XL=(2*math.pi*y*L)
Q=(XL/R)
Z=((Q**2)*R)
BW=(R/(2*math.pi*L))

#Result
print"(a) Resonant frequency= ",round(y,2),"Hz"
print"(b)Quality factor = ",round(Q,2)
print"(c)Maximam impedence= ",round(Z,1),"Ohm"
print"(d)Bandwidth = ",round(BW,1),"Hz"

(a) Resonant frequency=  4238.48 Hz
(b)Quality factor =  39.95
(c)Maximam impedence=  3191.5 Ohm
(d)Bandwidth =  106.1 Hz