Power efficiency of AM-DSB-TC
= total side band power / total power
m2
=
2 + m2
Total power of AM-DSB-TC = Carrier power + Upper side band power + Lower side band power
Power of a sine wave = k Amplitude2
Carrier power = k Ac2
Upper side band power = Lower side band power = k ⎛⎜ Ac m ⎞⎟
⎝
2
2
⎠
f = 1/T
ω = 2πf
−A
A
A
m
max
min
=
m=
+A
A
A
c
max
min
1
1
cos( A + B ) + cos( A − B )
2
2
1
1
sin ( A) sin (B ) = cos( A + B ) − cos( A − B )
2
2
1
1
cos( A)sin (B ) = sin ( A + B ) − sin ( A − B )
2
2
1
1
sin ( A) cos(B ) = sin ( A + B ) + sin ( A − B )
2
2
sin (at )
cos(at )
(
)
(
)
cos
sin
=
=
−
at
dt
at
dt
∫
∫
a
a
cos( A) cos(B ) =
cos(A+B) = cosAcosB – sinAsinB
cos(A-B) = cosAcosB + sinAsinB
sin(A+B) = sinAcosB + cosAsinB
sin(A-B) = sinAcosB – cosAsinB
sin2A = 2sinAcosA
cos2A = cos2A – sin2A
cos2A = 1 – 2sin2A
cos2A = 2cos2A – 1
sin(-A) = -sinA
cos(-A) = cosA
tan(-A) = -tanA
cos(90º - Θ) = sin Θ
sin(90º - Θ) = cos Θ
General form of an FM signal:
⎛
cos⎜⎜ 2πf c t
⎝
s(t ) = Ac
Instantaneous phase =
t
⎞
0
⎠
+ 2πf d ∫ m(τ )dτ ⎟⎟
θ (t ) = carrier phase + phase deviation
Instantaneous frequency = carrier frequency + frequency deviation
1 dθ (t )
2π dt
Δf = Am f d = Am k f
f (t ) =
Instantaneous frequency =
Peak frequency deviation in Hz =
Δf
fm
Modulation index of an FM signal =
β=
Bandwidth of an FM signal in Hz =
2nf m
Carson’s Rule: Bandwidth in Hz =
2Δf + 2 f m
Table of Symbols used in Electronic Communication Systems
Symbol
Ac
Am
term
Carrier amplitude
Units
volts
Message signal amplitude
volts
Amax
Maximum peak-to-peak voltgage
volts
of the AM signal envelope
Amin
Maximum peak-to-peak voltgage
volts
of the AM signal envelope
fc
Carrier frequency
Hz
fd
Frequency deviation sensitivity
Hz/volt
fm
Message signal frequency
Hz
∆f
Peak frequency deviation
Hz
k
Constant of proportionality
kf
Frequency deviation sensitivity
Hz/volt
n
Number of significant sidebands
No units
Table of Bessel Functions