Carrier Acquisition, Need for Carrier Acquisition & Techniques

What is Carrier Acquisition? The Need For Carrier Acquisition & Its Techniques

What is Carrier Acquisition?

In suppressed carrier communication, the demodulation process requires an identical local carrier at the demodulator. This local carrier needs to have same frequency and phase as the transmitted signal. which is acquired using carrier acquisition.

The process of acquiring or extracting carrier frequency from the received signal is called carrier acquisition.

Why We Need Carrier Acquisition?

Amplitude Modulated Suppressed Carrier signal needs a locally generated signal having the same phase and frequency as the received signal (carrier signal).

If the frequency or phase of the signal is different than the received signal, then the demodulated message signal we get will be distorted or may be completely destroyed. To avoid such problems and get a clear message signal, we need an identical carrier.

Suppose we receive a DSB-SC signal which is m(t)cos(ω_ct + ϴ_i) and the carrier generated by demodulator has a frequency (ω_c+Δω) and phase ϴ_o i.e. the local carrier is 2cos((ω_c+Δω)t+ϴ_o).

Thus the demodulated signal e(t) will be:

e(t) = m(t) cos(ω_ct + ϴ_i) 2cos((ω_c+Δω)t+ ϴ_o)

e(t) = 2m(t) cos(ω_ct + ϴ_i) cos((ω_c+Δω)t+ ϴ_o)

e(t) = m(t) [cos {(ω_c+ω_c+Δω) t +ϴ_i+ϴ_o} + cos(Δωt+ ϴ_i-ϴ_o)]

e(t) = m(t) cos {(ω_c+ω_c+Δω) t +ϴ_i+ϴ_o} + m(t)cos(Δωt+ ϴ_i-ϴ_o)

By passing through Low-pass filter

e(t) = m(t)cos(Δωt+ ϴ_i-ϴ_o)

If the frequency difference Δω = 0 and phase difference (ϴ_i-ϴ_o) = 0. Then

e(t) = m(t)

Which means the message signal is successfully received.

However, if the frequency difference Δω = 0 and phase difference (ϴ_i-ϴ_o) ≠0. Then

e(t) = m(t)cos(ϴ_i-ϴ_o)

This means that the message signal is attenuated by factor cos(ϴ_i-ϴ_o). if (ϴ_i-ϴ_o)= π/2 , then e(t) = 0 and the message signal is completely destroyed.

Another case is if the phase difference (ϴ_i-ϴ_o) =0 and frequency difference Δω ≠ 0. Then

e(t) = m(t)cos(Δωt)

This equation implies that the same message signal is multiplied with a sinusoid of frequency Δω. Δω is usually very small. which means that the message signal will go from maximum to zero at the rate of two times its frequency. This is called beating effect. This beating effect distorts the original signal even if the Δω is very small.

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Techniques Of Carrier Acquisition

There are few different techniques used for carrier acquisition. Some of them are given below.

Phase-Locked Loop (PLL)

Phase locked loop, commonly known as PLL is one of the most widely used circuit for carrier acquisition. It tracks the phase and frequency of the incoming/reference signal and generates a stable frequency signal.

A PLL is made up of 3 components

• VCO
• Phase detector
• Loop filter

VCO

VCO stands for the voltage controlled oscillator. It generates frequency signal, which is controlled by an external voltage signal. The frequency signal produced by VCO is

ω(t) = ω_c + ce_o(t)

ω_c is free running frequency when external voltage e_o(t) is zero. C is constant of VCO & e_o(t) is the external voltage signal. The frequency is increased or decreased according to this voltage signal e_o(t).

Phase Detector

A Multiplier is used as a phase detector. It has 2 input signals, a reference signal & the output of VCO.

It generates a signal proportional to the phase difference between the two signals.

Suppose the input signal is Asin(ω_ct + ϴ_i) & output is Bcos(ω_ct + ϴ_o),then its product is

e(t) = Asin(ω_ct + ϴ_i) Bcos(ω_ct + ϴ_o)

e(t) = AB/2 sin(2ω_ct + ϴ_i + ϴ_o) + AB/2 sin(ϴ_i – ϴ_o)

The high-frequency term is filtered the loop filter discussed below.

Loop Filter

This loop filter is actually a narrow band low pass filter. It blocks any high-frequency components from its input signal (output of multiplier) and generates a dc voltage. which is supplied as input to the VCO.

The signal after passing through loop filter becomes

e_o(t) = AB/2 sin(ϴ_i – ϴ_o)

If the phase difference (ϴ_i – ϴ_o) is not zero then the signal e_o(t) will generate DC voltage & supplies to the VCO. This voltage leads to increment in the VCO frequency.

The process is repeated until the frequency & phase matches the input signal. Such case is called in phase lock or phase coherent state.

Carrier Acquisition In DSB-SC

In DSB-SC scheme the level carrier can be regenerated using two methods discussed below.

Signal Squaring Method:

This method is used for carrier acquisition in DSB-SC communication.

The block diagram of signal-squarer is given below.

The received DSB-SC signal x(t) is first passed through a squarer, which takes the square of the signal.

The received signal x(t) is:

x(t) = m(t)cos ω_ct

The output y(t) of squarer is:

y(t) = x²(t)

y(t) = (m(t)cos ω_ct)²

y(t) = m²(t)cos² ω_ct

y(t) = ½ m²(t)(1+cos 2ω_ct)

y(t) = ½ m²(t)+ ½ m²(t)cos 2ω_ct

As we can see, m²(t) is a non-negative signal i.e. it is positive for every value of t. Therefore, it has positive average (DC) value.

Let suppose the average value of m²(t)/2 is k then

½ m²(t) = k + ϕ(t)

Now the signal y(t) can be expressed as:

y(t) = ½ m²(t)+ (k + ϕ(t))cos 2ω_ct

y(t) = ½ m²(t)+ k cos 2ω_ct + ϕ(t)cos 2ω_ct

After passing through the narrow-band band-pass filter, it will block m²(t) completely because of its ω=0. k cos 2ω_ct will flow through. However, some parts of ϕ(t)cos 2ω_ct will also flow out because it has almost no power at 2ω_c. Thus the signal y₀(t) becomes:

y₀(t) = k cos 2ω_ct + ϕ(t)cos 2ω_ct

The next stage is PLL. The PLL will block any residual frequencies & produce a stable frequency signal z(t), which is :

z(t) = k cos 2ω_ct

The last stage of signal squarer is the divider. The divider divides the frequency of the input signal by two. Thus the output signal becomes a pure sinusoidal wave of frequency ω_c.

The output r(t) of signal squarer is:

r(t) = k cos ω_ct

COSTAS Loop

John P.Costas was an Electrical engineer. In 1950, he invented the method to use a modified PLL to regenerate the carrier signal in suppressed carrier communication. This circuit is known as Costas loop.

Costas loop is used to acquire the carrier signal in DSB-SC communication.

Block Diagram

The block diagram of Costas loop is given below:

This diagram shows the received signal DSB-SC signal m(t)cos(ω_ct+ϴ_i) is multiplied with local carriers cos(ω_ct+ϴ_o) & sin(ω_ct+ϴ_o) separately to get x₁(t) and x₂(t) respectively.

The VCO generates the local carrier cos(ω_ct+ϴ_o), which is phase shifted by –π/2 to generate sin(ω_ct+ϴ_o).

The signal x₁(t) and x₂(t) is given by:

x₁(t) = m(t)cos(ω_ct+ϴ_i) cos(ω_ct+ϴ_o)

x₁(t) = ½ m(t){cos(ϴ_i– ϴ_o) +cos(2ω_ct+ ϴ_i +ϴ_o)}

x₁(t) = ½ m(t)cos(ϴ_i– ϴ_o) +½ m(t)cos(2ω_ct+ ϴ_i +ϴ_o)

x₂(t) = m(t)cos(ω_ct+ϴ_i) sin(ω_ct+ϴ_o)

x₂(t) = ½ m(t){sin(ϴ_i– ϴ_o) +sin(2ω_ct+ ϴ_i +ϴ_o)}

x₂(t) = ½ m(t)sin(ϴ_i– ϴ_o) +½ m(t)sin(2ω_ct+ ϴ_i +ϴ_o)

The signal x₁(t) & x₂(t) is then passed through low pass filter, it blocks high frequency components & allow low frequency components. Thus producing y₁(t) & y₂(t) for the signal x₁(t) & x₂(t) respectively.

y₁(t) = ½ m(t)cos(ϴ_i– ϴ_o)

y₂(t) = ½ m(t)sin(ϴ_i– ϴ_o)

These two signals y₁(t) & y₂(t) are then multiplied to produce z(t) as:

z(t) = ½ m(t)cos(ϴ_i– ϴ_o) ½ m(t)sin(ϴ_i– ϴ_o)

z(t) = ⅛ m²(t){sin(0) + sin2(ϴ_i– ϴ_o)}

z(t) = ⅛ m²(t) sin2(ϴ_i– ϴ_o)

Thus the signal z(t) will produce a DC voltage depending on the phase difference (ϴ_i– ϴ_o).

If there is any phase difference then this signal will produce DC voltage.

The narrowband low-pass filter will suppress any frequency components and produce a pure DC signal. This DC signal will either increase or decrease the frequency of the VCO.

When the frequency and phase of the input signal and matches the VCO output, then the phase difference (ϴ_i– ϴ_o) = 0 and the DC output of Narrowband LPF becomes 0. In such case, the VCO output remains unchanged.

The output of the VCO is the acquired carrier we need & the signal y₁(t) is the demodulated message signal.

y₁(t) = ½ m(t)cos(ϴ_i– ϴ_o)

y₁(t) = ½ m(t)cos(0)

y₁(t) = ½ m(t)

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Carrier Acquisition In SSB

In single sideband (SSB) communication, the methods of carrier acquisition do not work as it did in the DSB-SC. The signal-squaring method & Costas loop does not work. The reason is that after squaring SSB signal, the product terms does not contain a pure sinusoid of the carrier frequency as in DSB-SC. So extracting the carrier through such method does not work.

However, if we transmit a carrier signal of low power with SSB signal, it can be extracted using a narrowband band-pass filter. The said signal is then amplified, in such way the demodulator will know the frequency & phase of the carrier signal.

Vestigial Sideband (VSB) has the same situation as SSB and it also needs a separate carrier with the transmitted signal.