DSB & SSB MODULATION - velchuriblog.files.wordpress.com · 1. Balanced Modulator 2. Ring Modulator...

ANALOG COMMUNICATIONS VELCHURI

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UNIT-II

DSB & SSB MODULATION

Syllabus: DSBSC Time and Frequency domain description-Bandwidth of DSB-SC wave, Power calculation in DSB-SC Wave, Generation of DSBSC Waves-Balanced Modulator, Ring modulator, Coherent detection of DSB-SC Modulated Wave-Effect of Phase Error, Effect of Frequency Error and COSTAS Loop. SSBSC Time and Frequency domain description-Power Relations in SSB-Wave, Generation methods of AM SSB Waves -Frequency discrimination, Phase discrimination, Weavers method, Demodulation of SSB Waves-Coherent Detection, Envelop Detector, VSB modulation: Time and Frequency domain description, Generation of VSB Modulated wave, Comparison of AM Techniques, Applications of different AM Systems.

Disadvantages of Standard AM wave:

❖ Due to large time constant, some distortion occurs which is known as diagonal

clipping i.e., selection of time constant is somewhat difficult.

❖ Power wastage takes place in DSB-FC transmission.

❖ DSB-FC is bandwidth inefficient system.

What is DSB-SC and Why?

❖ The equation of single tone AM wave is expressed as

𝑆𝐴𝑀(𝑡)= Accosωct + µ𝐴𝑐

2[cos(𝜔𝑐 + 𝜔𝑚)] +

µ𝐴𝑐

2[cos(𝜔𝑐 − 𝜔𝑚)]

❖ In power calculation of AM signal, it has been observed that for single-tone sinusoidal

modulation, for 100% modulation about 67% of the total power is required for

transmitting the carrier which does not contain any information.

❖ Hence, if the carrier is supressed, only the sidebands remain and in this way a saving

of two-third power may be achieved at 100% modulation.

❖ The signal resulting from suppressing carrier from the modulated signal and remains

only TWO side bands is called DSB-SC Wave.

DSB-SC Time & Frequency domain analysis

❖ A DSB-SC signal can be obtained by simply multiplying modulating signal with carrier

signal. So we need to use a device called product modulator for the generation of

DSB-SC wave.

❖ The single-tone DSB-SC in time-domain is given by

𝑆𝐷𝑆𝐵(t) = 𝑚(𝑡)Accosωct = Amcosω𝑚t. Accosωct = AmAccosω𝑚t. cosωct

= Am𝐴𝑐


Am𝐴𝑐


❖ The single-tone DSB-SC in Frequency-domain is given by

𝑆𝐷𝑆𝐵(ω)= Am𝐴𝑐

2𝜋[𝛿(𝜔 − (𝜔𝑐 + 𝜔𝑚)) + 𝛿(𝜔 + (𝜔𝑐 + 𝜔𝑚))] +

Am𝐴𝑐

2𝜋[𝛿(𝜔 − (𝜔𝑐 − 𝜔𝑚)) + 𝛿(𝜔 + (𝜔𝑐 − 𝜔𝑚))]



Figure 2.1 Generation of DSB-SC Wave

Figure 2.2 Spectrum of DSB-SC Wave

Single-tone Modulation:

In single-tone modulation modulating signal consists of only one frequency component

where as in multi-tone modulation modulating signal consists of more than one frequency

components.

The single-tone DSB-SC in time-domain is given by

𝑆𝐷𝑆𝐵(t) = 𝑚(𝑡)Accosωct = Amcosω𝑚t. Accosωct = AmAccosω𝑚t. cosωct

= Am𝐴𝑐


Am𝐴𝑐


The single-tone DSB-SC in Frequency-domain is given by

𝑆𝐷𝑆𝐵(ω)= Am𝐴𝑐

2𝜋[𝛿(𝜔 − (𝜔𝑐 + 𝜔𝑚)) + 𝛿(𝜔 + (𝜔𝑐 + 𝜔𝑚))] +

Am𝐴𝑐

2𝜋[𝛿(𝜔 − (𝜔𝑐 − 𝜔𝑚)) + 𝛿(𝜔 + (𝜔𝑐 − 𝜔𝑚))]

Figure 2.3 Spectrum of DSB-SC Wave as samples



Power Calculation in DSB-SC Wave:

𝑃𝐷𝑆𝐵 = 𝑃𝐿𝑆𝐵 + 𝑃𝑈𝑆𝐵 =𝐴𝑚

2 . 𝐴𝑐2

8+

𝐴𝑚2 . 𝐴𝑐

2

8=

𝐴𝑚2 . 𝐴𝑐

2

4

Percentage of Power saving in DSB-SC Wave:

Note:

✓ The time domain displays of DSB-FC with 100% and DSB-SC signal looks exactly

same. The only difference is carrier undergoes 1800in DSB-SC .

✓ The bandwidth of DSB-SC is same that of DSB-FC wave, that is 2fm.

Generation of DSB-SC Wave:

To generate DSB-SC wave, two methods are available. They are

1. Balanced Modulator

2. Ring Modulator

❖ Balanced Modulator:

✓ DSB-SC is obtained by using two AM modulators arranged in a balanced

configuration to cancel out the carrier.

✓ The input applied to the top AM modulator is m(t), whereas that applied to the lower

AM modulator is – m(t).

✓ These two AM modulators should connect in balanced configuration.

✓ These two modulators have the same amplitude sensitivity.

✓ The time domain displays of DSB-FC with 100% and DSB-SC signal looks exactly

same. The only difference is carrier undergoes 1800in DSB-SC.



✓ The bandwidth of DSB-SC is same that of DSB-FC wave, that is 2fm.

Figure 2.4 Balanced Modulator

Hence, except for the scaling factor 2𝑘𝑎the balanced modulator output is equal to product

of the modulating signal and the carrier signal. The Fourier transform of s (t) is given by

S (f) =𝑘𝑎Ac[𝑀(𝑓 − 𝑓𝑐) + 𝑀(𝑓 + 𝑓𝑐)]. Assume that the message signal is band-limited to

the interval −𝜔 ≤ 𝑓 ≤ 𝜔.

Figure 2.5 DSB-SC signal (Balanced Modulator output)



Figure 2.6 Bandwidth of DSB-SC signal

Ring Modulator:

❖ It consists of four diodes, an AF transformer T1 and an RF transformer T2.

❖ The carrier signal is assumed to be a square wave with frequency fc and it is

connected between the centre taps of the two transformers.

❖ The DSB-SC output is obtained at the secondary of the RF transformer T2

❖ The four diodes are connected in series connection should form a ring structure, so it

named as ring modulator.

❖ The diodes are controlled by a square- wave carrier c (t) of frequency fc, which

applied longitudinally by means of two canter-tapped transformers.

❖ If the transformers are perfectly balanced and the diodes are identical, there is no

leakage of the modulation frequency into the modulator output.

Figure 2.7 Ring Modulator circuit

❖ The operation can be divided into different modes as with and without the

modulating signal.

➢ Mode 1: Carrier Suppression: To understand how carrier suppression takes place,

assume that the modulating signal is absent i.e. x(t) = 0



(i) Operation in the Positive half-cycle of Carrier:

As shown in the figure, the diodes D1 and D2 are forward biased and the diodes D3 and D4

are reverse biased. We can observe that the direction of the currents flowing through the

primary windings of output transformer T2 are equal and opposite to each other. Therefore,

the magnetic fields produced by these currents are equal and opposite and cancel each

other. Hence, the induced voltage in secondary winding is zero. Thus, the carrier is

supported in the positive half-cycle other.

Figure 2.8 Operation in the Positive half-cycle of Carrier

ii) Operation in the Negative half-cycle of Carrier:

In this mode also let us assume that the modulating signal is zero. In the negative half-cycle

of the carrier, the diodes D3 and D4 are forward biased and the diodes D1 and D2 are

reverse biased. The currents flowing in the upper and lower halves of the primary winding

of T2 are again equal and in opposite directions. This cancels the magnetic fields. Thus, the

output voltage in this mode also is zero. Thus, the carrier is suppressed in the negative half-

cycle as well.

Figure 2.9 Operation in the Negative half-cycle of Carrier



It is important to note that the perfect cancellation of the carrier will take place if and only if

he characteristics of the diodes are perfectly matched and the center-tap is placed exactly at

the center of the primary transformer T2.

➢ Mode 2 : Operation in Presence of Modulating Signal

i) Operation in the Positive half-cycle of Modulating Signal

Now, let us discuss the operation when RF carrier and modulating signal both are applied.

As we apply the low frequency modulating signal through the input audio transformer T1,

there are many cycles of the carrier signal, in the positive half cycle of the modulating signal.

In the positive half-cycle of the carrier, D1 and D2 are ON and secondary of T1 is applied as it

is across the primary of T2. Hence, during the positive half cycle of carrier, the output of T2

is positive as shown in figure.

Figure 2.10 Operation in the Positive half-cycle of Modulating signal

In the negative half-cycle of the carrier, the diodes D3 and D4 are turned ON and the

secondary of T1 is applied in a reversed manner across the primary of T2 as shown in

equivalent circuit of figure. Thus, the primary voltage of T2 is negative and output voltage

also becomes negative.

ii) Operation in the Negative half-cycle of Modulating Signal

When modulating signal reverses the

polarities, the operation of the circuit

is same as that in the positive half-

cycle discussed earlier. Now, the only

difference is that the diode pair D3

D4 will produce a positive output

voltage whereas D1 D2 will produce

a negative output voltage.

Figure 2.10 Operation in the Negative half-cycle of Modulating signal



Figure 2.11 Wave forms of DSB-SC signal

Coherent Detection of DSB-SC:

Figure 2.12 Coherent Detection of DSB-SC signal



The message signal m(t) may be recovered from a DSB-SC modulated wave s(t) with a

locally generated sinusoidal wave and then low-pass filtering the product as shown in

Figure. It is assumed that the local oscillator output is exactly synchronized, in both

frequency and phase with the carrier wave c(t) used in the product modulator to generate

s(t). This method of demodulation is called “Coherent Detection”.

Let us assume that the local oscillator frequency at the receiver is the same frequency as the

carrier, but arbitrary phase difference φ, measured with respect to the carrier wave c(t).



Synchroniztion techniques in DSB-SC:

Pilot Carrier:

✓ A small amount of carrier known as pilot carrier is transmitted along with the

modulated signal from transmitter. It is separated at receiver with appropriate filter.

✓ This system, where a weak carrier signal transmitted along with DSB-SC signal is

known as partially suppressed carrier system.

✓ DSB-SC signal with partially suppressed carrier system is equal to over modulated AM

signal.

Squaring Circuit: In this received modulated signal is squared by squaring circuit.

Figure 2.13 Squaring Circuit



Costa’s Receiver:

✓ This system is used for synchronous detection of DSB-SC signal.

✓ If ϕ=0, then output of I-channel is desired modulating signal, and Q-channel output is

zero due to quadrature null effect.

✓ If ϕ≠0 and very small, then I-channel output almost unchanged and Q-channel output

is not zero that proportional to sin ϕ.

✓ Phase discriminator provides a D.C control signal which may correct local oscillator

phase error.

Figure 2.14 COSTA’S Receiver system

Single Side Band (SSB):

✓ In DSB-SC it is observed that there is symmetry in the band structure. So, even if one

half is transmitted, the other half can be recovered at the received.

✓ By doing so, the bandwidth and power of transmission is reduced by half.

✓ Depending on which half of DSB-SC signal is transmitted, there are two types of SSB

modulation

1. Lower Side Band (LSB) Modulation

2. Upper Side Band (USB) Modulation



Generation of Single Side Band (SSB):

There are two generation techniques are available for SSB modulated wave. They are

1. Filter method (Frequency Discrimination)

2. Phase-shift method.

➢ Filter method (Frequency Discrimination): Band Pass Filter is used here to pass

required side band only.

For a filter to be physically realizable, the transmission band separating the pass-band from

the stop band must have a finite width. The band-pass filter demands that there be an

adequate separation between the lower sideband and the upper sideband of the DSB-SC

modulated wave produced at the output of the product modulator. Such a requirement can

only be satisfied if the message signal m(t) applied to the product modulator has an energy

gap in its spectrum



Time-domain description of SSB Wave:

Unlike DSB-SC modulation, the time-domain description of SSB modulation is not as

straightforward. To develop the time-domain description of SSB modulation, we need a

mathematical tool known as Hilbert Transform.

➢ Phase-Shift Method:

Unlike DSB-SC modulation, the time-domain description of SSB modulation is not as

straightforward. To develop the time-domain description of SSB modulation, we need a

mathematical tool known as Hilbert Transform.



Adding above two output equations

Performance comparison of Generation techniques:



Synchronous detection of SSB:



❖ Power saving in SSB System:

❖ Advantages of SSB:

❖ Disadvantages of SSB:

❖ Applications of SSB:



Vestigial Side Band (VSB):

❖ To overcome the following are the drawbacks of SSB signal, VSB modulation is used.

It can viewed as a compromise between SSB and DSB-SC.

1. Generation of an SSB signal is difficult.

2. Selective filtering is to be done to get the original signal back.

3. Phase shifter should be exactly tuned to 90𝑜 .

❖ In VSB

1. One sideband is not rejected fully.

2. One sideband is transmitted fully and a small part (vestige) of the other sideband is

transmitted.



Generation of VSB:



Demodulation of VSB(Synchronous Detection):



Transmission bandwidth of VSB is

VSB Modulation − Advantages:

✓ Highly efficient.

✓ Reduction in bandwidth.

✓ Filter design is easy as high accuracy is not needed.

✓ The transmission of low frequency components is possible.

✓ Possesses good phase characteristics.

VSB Modulation − Disadvantages:

✓ Bandwidth when compared to SSB is greater.

✓ Demodulation is complex.

VSB Modulation − Applications:

✓ Used for the transmission of television signals.

✓ This is the most convenient and efficient technique when bandwidth usage is

considered.

❖ Comparison of various AM systems:

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