Frequency Modulation PPT Physics Class 12

 Page 1


FREQUENCY MODULATION
The Chapter includes:
• Wave Forms
• Theory
• Modulation Index
• Bandwidth & Bessel 
functions
• Merits & Demerits
“The process of changing the frequency of a carrier   
wave in accordance with the AF signal.”
Page 2


FREQUENCY MODULATION
The Chapter includes:
• Wave Forms
• Theory
• Modulation Index
• Bandwidth & Bessel 
functions
• Merits & Demerits
“The process of changing the frequency of a carrier   
wave in accordance with the AF signal.”
Wave Forms
Uniform AF signal modulating 
the Carrier wave  frequency
Non-uniform AF signal 
modulating the Carrier 
wave  frequency
(Courtesy: Internet)
Page 3


FREQUENCY MODULATION
The Chapter includes:
• Wave Forms
• Theory
• Modulation Index
• Bandwidth & Bessel 
functions
• Merits & Demerits
“The process of changing the frequency of a carrier   
wave in accordance with the AF signal.”
Wave Forms
Uniform AF signal modulating 
the Carrier wave  frequency
Non-uniform AF signal 
modulating the Carrier 
wave  frequency
(Courtesy: Internet)
Theory:
The instantaneous frequency ‘ ?’of modulated wave is:
? = ?
c
+ kE
m
cos ?
m
t                                                          
(where k is proportionality constant which depends on the modulating system)
If cos ?
m
t = ± 1, then  ? = ?
c
± kE
m
or ? = ?
c
± ?
(where ? = kE
m  
is maximum or peak deviation in carrier frequency)          
Note that ? depends on the magnitude of E
m
and not upon ?
c
.
Instantaneous value of FM voltage is:   e = E
c
cos ?
? is given by the following steps:
d ? =  ? dt ? d ? =  2 ? ? dt ? d ? =  2 ? ( ?
c
+ kE
m
cos ?
m
t ) dt 
On integration,  we get
? = ?
c
t + ( ?/ ?
m
)  sin ?
m
t 
? e = E
c
cos [ ?
c
t + ( ?/ ?
m
)  sin ?
m
t] = E
c
cos ( ?
c
t + m
f
sin ?
m
t)
where  m
f
= ?/ ?
m
is modulation index for FM
e
m
= E
m
cos ?
m
t &  e
c 
= E
c
cos ( ?
c
t + ?)
Page 4


FREQUENCY MODULATION
The Chapter includes:
• Wave Forms
• Theory
• Modulation Index
• Bandwidth & Bessel 
functions
• Merits & Demerits
“The process of changing the frequency of a carrier   
wave in accordance with the AF signal.”
Wave Forms
Uniform AF signal modulating 
the Carrier wave  frequency
Non-uniform AF signal 
modulating the Carrier 
wave  frequency
(Courtesy: Internet)
Theory:
The instantaneous frequency ‘ ?’of modulated wave is:
? = ?
c
+ kE
m
cos ?
m
t                                                          
(where k is proportionality constant which depends on the modulating system)
If cos ?
m
t = ± 1, then  ? = ?
c
± kE
m
or ? = ?
c
± ?
(where ? = kE
m  
is maximum or peak deviation in carrier frequency)          
Note that ? depends on the magnitude of E
m
and not upon ?
c
.
Instantaneous value of FM voltage is:   e = E
c
cos ?
? is given by the following steps:
d ? =  ? dt ? d ? =  2 ? ? dt ? d ? =  2 ? ( ?
c
+ kE
m
cos ?
m
t ) dt 
On integration,  we get
? = ?
c
t + ( ?/ ?
m
)  sin ?
m
t 
? e = E
c
cos [ ?
c
t + ( ?/ ?
m
)  sin ?
m
t] = E
c
cos ( ?
c
t + m
f
sin ?
m
t)
where  m
f
= ?/ ?
m
is modulation index for FM
e
m
= E
m
cos ?
m
t &  e
c 
= E
c
cos ( ?
c
t + ?)
Deviation: The amount by which the frequency of the carrier 
wave is changed from its original unmodulated frequency.
The rate at which this change occurs is equal to modulating 
frequency.
Modulation Index: M I for F M is the ratio of maximum 
frequency deviation to the modulating frequency. m
f
= ?/ ?
m
Observations:
1. m
f
is measured in radians.  
2.  Eqn. for frquency modulated wave is sine of sine function 
which gives a complex solution whereby the modulated 
wave consists of a carrier frequency and infinite number of 
pairs of side bands (Bessel functions).
3.  In F M, the overall amplitude and hence the total 
transmitted power remains constant.
Page 5


FREQUENCY MODULATION
The Chapter includes:
• Wave Forms
• Theory
• Modulation Index
• Bandwidth & Bessel 
functions
• Merits & Demerits
“The process of changing the frequency of a carrier   
wave in accordance with the AF signal.”
Wave Forms
Uniform AF signal modulating 
the Carrier wave  frequency
Non-uniform AF signal 
modulating the Carrier 
wave  frequency
(Courtesy: Internet)
Theory:
The instantaneous frequency ‘ ?’of modulated wave is:
? = ?
c
+ kE
m
cos ?
m
t                                                          
(where k is proportionality constant which depends on the modulating system)
If cos ?
m
t = ± 1, then  ? = ?
c
± kE
m
or ? = ?
c
± ?
(where ? = kE
m  
is maximum or peak deviation in carrier frequency)          
Note that ? depends on the magnitude of E
m
and not upon ?
c
.
Instantaneous value of FM voltage is:   e = E
c
cos ?
? is given by the following steps:
d ? =  ? dt ? d ? =  2 ? ? dt ? d ? =  2 ? ( ?
c
+ kE
m
cos ?
m
t ) dt 
On integration,  we get
? = ?
c
t + ( ?/ ?
m
)  sin ?
m
t 
? e = E
c
cos [ ?
c
t + ( ?/ ?
m
)  sin ?
m
t] = E
c
cos ( ?
c
t + m
f
sin ?
m
t)
where  m
f
= ?/ ?
m
is modulation index for FM
e
m
= E
m
cos ?
m
t &  e
c 
= E
c
cos ( ?
c
t + ?)
Deviation: The amount by which the frequency of the carrier 
wave is changed from its original unmodulated frequency.
The rate at which this change occurs is equal to modulating 
frequency.
Modulation Index: M I for F M is the ratio of maximum 
frequency deviation to the modulating frequency. m
f
= ?/ ?
m
Observations:
1. m
f
is measured in radians.  
2.  Eqn. for frquency modulated wave is sine of sine function 
which gives a complex solution whereby the modulated 
wave consists of a carrier frequency and infinite number of 
pairs of side bands (Bessel functions).
3.  In F M, the overall amplitude and hence the total 
transmitted power remains constant.
Band Width & Bessel Functions
(Courtesy: Internet)