Important Communication Systems Formulas for JEE and NEET

 Page 1


PRINCIPLE OF COMMUNICATION
Transmission from tower of height h
 
 
? the distance to the horizon d
T
 = 
T
2Rh
? d
M 
= 
T R
2Rh 2Rh ?
Amplitude Modulation
? The modulated signal c
m
 (t) can be written as
c
m
(t) = A
c
 sin ?
c
t +
c
A
2
?
cos ( ?
C
 -  ?
m
) t –
c
A
2
?
cos ( ?
C
 + ?
m
)
? Modulation index 
m
a
c
kA Change in amplitude of carrier wave
m
Amplitude of original carrier wave A
? ?
where k = A factor which determines the maximum change in the
amplitude for a given amplitude E
m
 of  the modulating. If k = 1 then
m
a
 =   
max min m
c max min
A – A A
A A – A
?
? If a carrier wave is modulated by several sine waves the total modulated
index m
t
 is given by m
t
 = 
2 2 2
1 2 3
m m m ......... ? ? ?
? Side band frequencies
(f
c
 + f
m
)  = Upper side band (USB) frequency
            (f
c
 - f
m
)   = Lower side band (LBS) frequency
? Band width  = (f
c
 + f
m
) - (f
c
 - f
m
)  = 2f
m
? Power in AM waves :
2
rms
V
P
R
?
(i) carrier power 
2
c
2
c
c
A
A 2
P
R 2R
? ?
? ?
? ?
? ?
Page 2


PRINCIPLE OF COMMUNICATION
Transmission from tower of height h
 
 
? the distance to the horizon d
T
 = 
T
2Rh
? d
M 
= 
T R
2Rh 2Rh ?
Amplitude Modulation
? The modulated signal c
m
 (t) can be written as
c
m
(t) = A
c
 sin ?
c
t +
c
A
2
?
cos ( ?
C
 -  ?
m
) t –
c
A
2
?
cos ( ?
C
 + ?
m
)
? Modulation index 
m
a
c
kA Change in amplitude of carrier wave
m
Amplitude of original carrier wave A
? ?
where k = A factor which determines the maximum change in the
amplitude for a given amplitude E
m
 of  the modulating. If k = 1 then
m
a
 =   
max min m
c max min
A – A A
A A – A
?
? If a carrier wave is modulated by several sine waves the total modulated
index m
t
 is given by m
t
 = 
2 2 2
1 2 3
m m m ......... ? ? ?
? Side band frequencies
(f
c
 + f
m
)  = Upper side band (USB) frequency
            (f
c
 - f
m
)   = Lower side band (LBS) frequency
? Band width  = (f
c
 + f
m
) - (f
c
 - f
m
)  = 2f
m
? Power in AM waves :
2
rms
V
P
R
?
(i) carrier power 
2
c
2
c
c
A
A 2
P
R 2R
? ?
? ?
? ?
? ?
(ii)   Total power of side bands  P
sb
 = 
2
a c a c
2 2
a c
m A m A
m A
2 2 2 2
R 2R 4R
? ? ? ?
? ? ? ?
? ? ? ?
? ?
(iii)  Total power of AM wave P
T otal
 = P
c
 + P
ab
 =
2 2
c a
A m
1
2R 2
? ?
? ? ?
? ?
? ?
(iv)  
2
t a
c
P m
1
P 2
? ?
? ? ? ?
? ?
? ?
  and 
2
sb a
2
t
a
P m / 2
P
m
1
2
?
? ?
? ? ?
? ?
? ?
(v) Maximum power in the AM (without distortion) will occur when
m
a
 = 1 i.e., P
t
 = 1.5 P = 3P
ab
(vi) If I
c
 = Unmodulated current and I
t
 = total or modulated current
? ? ?
2
t t
2
c c
P
P
?
?
?
 ? ?
2
t a
c
m
1
2
? ?
?
? ? ? ?
? ?
?
? ?
Frequency Modulation
? Frequency deviation ? =   = (f
max
 - f
c
) = f
c
 - f
min
 = k
f
 . 
m
E
2 ?
? Carrier swing (CS) = CS = 2 × ?f
? Frequency modulation index (m
f
)
=. m
f
 = 
max c c min f m
m m m m
f – f f – f k E
f f f f
?
? ? ?
? Frequency spectrum = FM side band modulated signal consist of infi-
nite number of side bands whose frequencies are  (f
c
 ± f
m
), (f
c
 ± 2f
m
),
(f
c
 ± 3f
m
).........
? Deviation ratio = 
max
m max
( f)
(f )
?
? Percent modulation , m = 
actual
max
( f)
( f)
?
?