GATE ECE (Electronics) Test: Single Sideband (SSB) Modulation Free Online

Concept: 

The total transmitted power for an AM system is given by:

P_c = Carrier Power

m = Modulation Index

Analysis:

The above expression can be expanded to get:

The total power is the sum of the carrier power and the sideband power, i.e.

In conventional AM transmission, the power is equally distributed between the two sidebands, i.e.

∴ The power contained in a single sideband in amplitude modulation is 

Concept:

Total power in AM (P_T)= P_C ( 1 + μ²/2 ) = PC + PCμ2/2

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 :

P_T = (P_C + P_Cμ²/2) - (P_C + P_Cμ²/4) = P_Cμ²/4

Percentage of power will be saved :

= [(P_C + P_Cμ²/2 )- P_Cμ²/4 ]/P_C ( 1 + μ²/2 ) × 100

= (1 + μ²/4)/( 1 + μ²/2 ) × 100

= (1 + (0.5)²/4)/( 1 + (0.5)²/2 ) × 100

= 94.44 %

In single-sideband (SSB) modulation only the upper sideband or the lower sideband is transmitted (the carrier is suppressed).

• The major problem with the detection techniques in SSB is to have a coherent source at the receiver.
• If the frequency error becomes a function of time then it becomes difficult to recover the original signal.
• Since demodulation is hard in SSB signals, a low power carrier wave is transmitted with the SSB, which is called PILOT CARRIER.
•  This can be received and amplified at the receiving end to demodulate the SSB signal.

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.

Analysis:

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

Conclusion:

Generalizing this for any signal m(t), we can say that the SSB modulated signal with only upper sideband will be:

m(t) cos ω_ct – m̂(t) sin ω_ct,

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

m(t) cos ω_ct + m̂(t) sin ω_ct,

where m̂(t) is the Hilbert transform of m(t).

SSB/SC is generated using a balanced modulator circuit as shown:

Where π/2 phase shifter gives the Hilbert transform of the incoming signal. 

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.

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

Additional Information

• The following methods are used for the demodulation of Single Side Band (SSB) signals.
  • The Filter Method
  • The Phasing Shift Method
  • The Weaver Demodulator
  • Fourier based Demodulation.
• The following methods are used for the demodulation of Frequency Modulated (FM) signals.
  • ​Frequency discrimination method
  • Phase discrimination method.

​Hence, phase discriminator is used as demodulator of SSB

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.

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:
m(t) cos ω_ct – m̂(t) sin ω_ct,

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

m(t) cos ω_ct + m̂(t) sin ω_ct

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. 

We are given:

• Message signal: m(t)=cos(ω_m​t)
• Carrier: cos⁡(ω_ct)
• SSB modulation is used to generate s(t)
• Then s(t) is passed through an ideal envelope detector
• We are to find the output of the envelope detector

Step 1: SSB Modulation Basics

For a message m(t)=cos⁡(ω_mt), its Single Sideband (SSB) modulation with carrier frequency ω_c​ yields one of:

• Upper Sideband (USB):

• Lower Sideband (LSB):

So in either case, SSB yields a single cosine at shifted frequency, and there's no carrier component.

Step 2: Envelope Detector

An envelope detector works correctly only when there is a carrier present and the modulation is AM (amplitude modulation). However, SSB does not have a carrier, so the envelope detector will not recover the original signal properly.

Instead, the output of an envelope detector on a pure sinusoid like cos⁡((ω_c ± ω_m)t is simply:

Envelope = constant = 1

Because the envelope of a cosine wave with constant amplitude is just a flat line at 1.

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

Single Side Band (SSB SC):

1) SSB SC is a form of amplitude modulation where only a single sideband is transmitted and 1 sideband and carrier are suppressed.

2) 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.

3) The Bandwidth requirement is only f_m, ∴ It needs half the bandwidth than the DSB-SC transmission.

Comparison: