( 1 ) Modulation index ( m )
m = Amplitude change of
carrier wave / Normal carrier amplitude
= [ Vmax – Vmin
] / [ Vmax + Vmin ]
= Es / Ec
( 2 ) Carrier wave
Ec = [ ( Vmax
+ Vmin ) / 2 ]
( 3 ) Signal amplitude
Es = [ ( Vmax
– Vmin ) / 2 ]
( 4 ) Amplitude modulation wave
( a ) It has three sinusoidal waves
Amplitude Ec,
mEc / 2 and mEc / 2
( b ) It has three frequencies
Carrier frequency fc
Upper side band frequency
fc + fs
Lower side band frequency
fc – fs
Where fc =
Carrier frequency
fs = Signal frequency
|
Amplitude
|
Frequency
|
|
Ec |
fc |
|
m
Ec / 2 |
fc
+ fs |
|
m
Ec / 2 |
fc
– fs |
( 5 ) Carrier power
Pc = Ec2
/ 2R
( 6 ) Sideband power
Ps = m2Ec2
/ 4R
( 7 ) Total power in amplitude modulation
wave
PT = Pc
+ Ps
= Ec2
/ 2R [ ( 2 + m2 ) / 2 ]
( 8 ) Power carried by side
band
Ps / PT
= m2 / ( m2 + 2 )
|
Value of m |
Power carried by side
band |
|
Zero |
Zero |
|
0.5 |
11.5% power of AM wave |
|
1 |
33.3% power of AM wave |
( 9 ) Relation between side
band power and carrier power
Ps / Pc
= 0.5m2
Where
Ps = Side band power
Pc = Carrier power
m = Modulation index
( 10 ) Centre frequency of
frequency modulation
- The signal of frequency modulation has constant amplitude but varying frequencies above and below the carrier frequency.
- This carrier frequency is called as center frequency.
( 11 ) Maximum frequency
deviation
Δf = kEs
Where Es = Amplitude
of signal
k = frequency deviation constant
Modulating frequency =
maximum frequency deviation / Modulating frequency
( 12 ) Upper and lower sideband
frequencies in the FM Modulator
Upper sideband
frequencies = fc + fs
= fc + 2fs
= fc + 3fs
Lower sideband frequencies
= fc – fs
= fc – 2fs
= fc – 3fs
Where fc =
Carrier frequency and
fs = Modulating frequency
( 13 ) Bandwidth
BW = 2 [ fs + Δf
]
Where Δf = Frequency deviation and
fs = Modulating frequency
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