GATE ECE (Electronics) Test: SSBSC (Single Sideband Suppressed Carrier)

The bandwidth of different modulation schemes are as shown:
AM → 2f_m
SSB-SC → f_m
For angle modulated schemes (FM and PM)
= 2(β + 1) f_m
f_m = message signal bandwidth
So, for SSB-SC, the bandwidth requirement is minimal.

Let, the channel is practical having finite attenuation of 'A' dB, and the single-sided noise power spectral density is given as 'N' W/Hz

Let the message signal spectrum is given as:

In the case of AM:-

B.W = 2f_m kHz (twice of message signal bandwidth)

In the case of SSB:-
B.W = f_m kHz (same as message signal bandwidth)

∴ SNR in the case of S.S.B is double that in the case of AM.

Statement-I is incorrect and Statement-II is correct.

1) General equation of SSB modulated wave:

2) Output of envelope detector to signal
Acos ω_ct → A
Application:
Equation of SSB modulated signal

the output of envelope detector = ½
The output of the envelope detector is a constant voltage signal
Hence option (d) which represents a constant voltage is correct.

The frequency spectrum of all the given modulation schemes is as shown:

Total power = Carrier power + Sideband power
In SSB, we have one sideband only hence the power is less than DSB and VSB.
In VSB, we have one sideband and some part of the other sideband and hence power is more than SSB and less than DSB.

Concept:
SSB (Single Side Band) modulation is a technique that allows only one sideband to pass saving bandwidth and power both.
Practically it is very difficult to pass only a single sideband.
Ex: If we consider a single-tone modulating signal as x(t) = cos ωmt, the SSB modulated wave with only the upper sideband will be represented as:
cos ((ω_c + ω_m)t) = cos ω_c.cos ω_mt – sin ω_c.sin ω_mt and with lower sideband only will be represented as: cos (ω_c - ω_m)t = cos ω_ct .cos ω_mt + sin ω_ct. sin ω_mt
where sin ω_mt is the Hilbert transform of the original message signal x(t) = cos ω_mt
Generalizing this for any signal m(t), we can say that the SSB modulated signal with only upper sideband will be:

Similarly, we can say that the SSB modulated signal with only lower sideband will be:

where m̂(t) is the Hilbert transform of m(t).
The generalized AM expression is represented as:
s(t) = A_c [1 + μ_a m_n (t)] cos ω_ct
The RF bandwidth of an SSB-AM signal is also 3 kHz. 

Concept:
Power of a transmitted AM wave is given as:

Power in the carrier = P_c
Power in both the sidebands is given by:

Since the power is distributed equally to the left and to the right side of the sideband, the power in one of the sidebands is given by:

Analysis:
In SSB-SC, the carrier and one of the sidebands are suppressed, and when the carrier and 1 of the sideband are suppressed, the amount of power saving will be:

The percentage of power saved will be calculated as:

Given μ = 0.80, the amount of power saving will be

The modulation technique that takes the lowest bandwidth is SSB-SC

Single Side Band (SSB SC):

• SSB SC is a form of amplitude modulation where only a single sideband is transmitted and 1 sideband and carrier are suppressed.
• The advantage of SSB is bandwidth and power-saving over both conventional AM and DSB SC, i.e. DSB SC has a more power consumption than SSB SC.
• The Bandwidth requirement is only fm, ∴ It needs half the bandwidth than the DSB-SC transmission.

Comparison:

Vestigial Sideband:
VSB (vestigial sideband) transmission transmits one sideband fully and the other sideband partially thus, reducing the bandwidth requirement.
Vestigial Sideband Modulation (VSB) is used for video modulation in TV transmission. 
The spectrum of a vestigial sideband is as shown:

Single Side Band (SSB SC)

• SSB SC is a form of amplitude modulation where only a single sideband is transmitted and 1 sideband and carrier are suppressed.
• In advantage of SSB is bandwidth saving and power saving over both conventional AM and DSB SC.

Double Side Band (DSB SC):

• DSB -SC is a form of Amplitude modulation where only the sidebands are transmitted and carrier is suppressed.
• The advantage is 66% power saving compared to conventional AM.

Phase Discrimination is used for the demodulation of Frequency Modulate signals.

Concept:
Total power in AM (P_T)= P_C( 1 + μ²/2 ) = P_C + P_Cμ²/2
where;
P_C → Carrier power 
μ → modulation index
Power of single sideband = ( P_Cμ²/2)/2 =  P_Cμ²/4

Calculation:
Given 
μ = 50% = 0.5
After suppressing carrier and a single sideband :

Percentage of power will be saved :