Correct Answer - Option 4 : 100%
Concept:
The generalized AM expression is represented as:
s(t) = Ac [1 + μa mn (t)] cos ωc t
The total transmitted power for an AM system is given by:
\({P_t} = {P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)\)
Pc = Carrier Power
μ = Modulation Index
The above expression can be expanded to get:
\({P_t} = {P_c} + P_c\frac{{{μ^2}}}{2}\)
The total power is the sum of the carrier power and the sideband power, i.e.
\({P_s} = P_c\frac{{{μ^2}}}{2}\)
The power in a single sideband will be:
\({P_s} = \frac{1}{2}\times P_c\frac{{{μ^2}}}{2}\)
\(As \ P_c=\frac{A_c^2}{2}\),
the above can be written as:
\({P_s} = \frac{1}{2}\times \frac{A_c^2}{2}\frac{{{μ^2}}}{2}\)
\({P_s} = \frac{{{A_c^2μ^2}}}{8}\) ---(1)
The ratio of total sideband power to total input power gives the maximum transmission power efficiency.
Calculation:
Total sideband power is:
Multiplying equation (1) with 2, we will get total sideband power as:
\({P_{sb}} = \frac{{{A_c^2μ^2}}}{4}\)
When μ = 1,
\({P_{sb}} = \frac{{{A_c^2}}}{4}\)
Total efficiency (η) is given by:
\(η=\frac{P_{sb}}{P_T} \ \times \ 100\)
PT = Transmitted power
As Psb = PT in DSB-SC as the carrier is suppressed so:
η = 100%
Hence option (4) is the correct answer.
DSB -SC:
1) It is a form of Amplitude modulation where only the sidebands are transmitted and the carrier is suppressed.
2) The advantage is 66% power saving compared to conventional AM.
3) The Bandwidth requirement is of 2fm, with fm being the maximum frequency component of the message signal.
4) It is used for transmitting stereo information.
Comparison:
|
Parameter
|
SSB
|
DSB
|
VSB
|
|
Power
|
Less
|
High
|
Medium
|
|
Bandwidth
|
fm
|
2 fm
|
fm < BW < 2fm
|
|
Carrier Suppression
|
Complete
|
Complete
|
No
|
|
Sideband Suppression
|
One sideband completely
|
No
|
One sideband suppressed partially.
|
