ANALOG COMMUNICATION Lecture 09

Carrier Acquisition in Suppressed Carrier Schemes

Lesson 09 EEE 352 Analog Communication Systems Mansoor Khan EE Dept. CIIT Islamabad Campus

Carrier Acquisition • In SC transmissions, we have to generate a carrier with the same frequency and phase that the carrier at the transmitter. • Consider the case of DSB-SC where a received signal is

 DSBSC (t )  m(t ) cos ct • and the local carrier is

2 cosc   t    • therefore we have errors in frequency and phase

Carrier Acquisition (cont) • The product of the received signal and the local carrier is

e(t )  m(t ) cos ct  2 cosc   t   

 m(t )cos t     cos2c   t    • After the LPF we have

eo (t )  m(t )cos t   

Carrier Acquisition (cont) • Let’s consider two cases. First   0 • In this case

eo (t )  m(t )cos 

• The output is proportional to m(t) because the factor is a constant • The output is maximum when δ=0 and minimum (zero) when δ=±π/2 Thus, this kind of phenomenon only attenuates the output without adding distortion

• Unfortunately delta is not constant. This may occur for example because of variations in the propagation path.

Carrier Acquisition (cont) • Now consider the second case • In this case

  0,   0

eo (t )  m(t ) cos t

• The output is distorted as well, the output is m(t) multiplied by a low frequency oscillation. • This beating is catastrophic even for a small frequency

Carrier Acquisition (cont) • To ensure identical carrier frequencies at the emitter and receiver we can use crystal oscillators • Other method is to send a carrier or pilot at a reduced level along with the sidebands. Then is filtered at the receiver with a very narrow filter

Phase Locked Loop (PLL) • The PLL can be used to track the phase and frequency of the carrier component of an incoming signal. • It is then useful for synchronous demodulation of AM signals with suppressed carrier or with a pilot • PLL has three basic components: – A VCO or Voltage Controlled Oscillator – A multiplier, serving as a phase detector or a phase comparator – a loop filter H(s)

Phase Locked Loop (cont)

Phase Locked Loop (cont) • PLL works just like feedback system, the signal fed back tends to follow the input signal to minimize the error. The quantity to compare is the phase in this case • The VCO oscillates linearly with the input voltage

 (t )  c  ceo (t ) • Where “c” is a constant and wc is the free running frequency of the VCO. This is the one when the input signal is zero

PLL Operation • Let the input to the PLL be

A sinc t   i 

• Let the output of VCO be

B cosc t   o 

• The multiplier output x(t) will be

x(t )  AB sin(c t   i ) cosc t   o  AB sin( i   o )  sin(2c t   i   o )  2

PLL Operation (cont) • The filter is a low pass narrow filter therefore the error signal is AB sin( i   o ) eo (t )  2 AB  sin( e ) 2

• Where θe is the phase error, which is linear for small error

PLL Operation (cont) • We have two cases: Input frequency changes or phase changes • If input frequency is increased, the input changes to

A sin c  k t   i 



 A sin ct  ˆi



• Where ˆi  kt   i • Thus the increase in frequency causes θi to increase thereby increasing θe which in turn increases input voltage to the VCO

PLL Operation (cont) • The VCO increases the frequency because the input voltage increased to match the increase in the input frequency • If the input frequency decreases the same reasoning applies

• The PLL tracks the input sinusoid. The two signals are said to be phase coherent or in phase lock

PLL Operation (cont) • A PLL tracks the incoming frequency only over a finite range of frequency shift. This range is called the hold-in or locks range • The frequency range over which the input will cause the loop to lock is called the Pull-in or Capture range

Carrier Acquisition in DSB-SC • Signal Squaring Method • Costas Loop

Signal Squaring Method • This method is explained in the following block diagram xt   mt  cos wct   2

1 2 1 m t   m 2 t  cos 2wct 2 2

• The squarer output will be

1 2 1 2 xt   mt  cos wct   m t   m t  cos 2wct 2 2 2

• Now m2(t) is a non negative signal and therefore has non zero average value in contrast to m(t)

Signal Squaring Method (cont) • Let the average value, which is the dc component of m2(t)/2, be k then 1 2 m t   k   (t ) 2 • Where  t is a zero mean baseband signal minus its dc component



1 2 1 2 xt   m t   m t  cos 2wct 2 2



1 2 m t   k cos 2wct   t  cos 2wct 2

Signal Squaring Method (cont)



• Where  t is a zero mean baseband signal minus its dc component

1 2  m t   k cos 2wct   t  cos 2wct 2

• First term of x(t) is suppressed by Narrow BPF centered at 2ωc • Third term has zero dc value at 2ωc thus only residue of third term passes through Narrow BPF having pass band