Important Formulas: Communication Systems

# 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)
?
?
```

## Physics for JEE Main & Advanced

289 videos|635 docs|179 tests

## Physics for JEE Main & Advanced

289 videos|635 docs|179 tests

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