ANALOG COMMUNICATION Lecture 09

Carrier Acquisition in Suppressed

Carrier Schemes

Lesson 09

EEE 352 Analog Communication Systems Mansoor Khan

EE Dept.

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

• and the local carrier is

• therefore we have errors in frequency and phase

t

t

m

t

_c SC DSB





_

(

)



(

)

cos









_c







t







cos

2

Carrier Acquisition (cont)

• The product of the received signal and the local carrier is

• After the LPF we have















 











 m t t t t e( ) ( )cos _c 2cos _c

 





































m

(

t

)

cos

t

cos

2

_c

t

 



















m

t

t

t

e

_o

(

)

(

)

cos

Carrier Acquisition (cont)

• Let’s consider two cases. First • In this case

• 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.

0





 



cos





) ( ) (t m t e_o 

Carrier Acquisition (cont)

• Now consider the second case • In this case

• 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

0

,

0











 

t

t

m

t

e

_o

(

)



(

)

cos





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)

• 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

• Where “c” is a constant and w_c is the free running frequency of the VCO. This is the one when the input signal is zero

)

(

)

(

t





_c



ce

_o

t

PLL Operation

• Let the input to the PLL be • Let the output of VCO be

• The multiplier output x(t) will be



_c

t

_i



A

sin









_c

t

_o



B

cos









_{c o}



i c

t

t

AB

t

x

(

)



sin(







)

cos









sin( ) sin(2 )



2 i o ct i o AB

_

_

_

_

_

_

_

_

_



PLL Operation (cont)

• The filter is a low pass narrow filter therefore the

error signal is

• Where θ

_e

is the phase error, which is linear for small

error



sin( )



2 ) ( _{i o} o AB t e 







) sin( 2 e AB

_



PLL Operation (cont)

• We have two cases: Input frequency changes or phase changes

• If input frequency is increased, the input changes to

• Where

• Thus the increase in frequency causes θ_i to increase thereby increasing θ_e which in turn increases input voltage to the VCO







_c k t _i



Asin



 



 Asin





_ct 



ˆ_i



i i

kt





ˆ





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

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

Carrier Acquisition in DSB-SC

• Signal Squaring Method

• Costas Loop

Signal Squaring Method

• This method is explained in the following block diagram

• The squarer output will be

• Now m2_{(t) is a non negative signal and therefore has non zero}

average value in contrast to m(t)

 t m t wt m  t m  t wt x _c cos2 _c 2 1 2 1 cos 2  2  2 

 

t



m

 

t

w

t



m

 

t

m

 

t

w

t

x

_c

cos

2

_c

2

1

2

1

cos

2



2



2



Signal Squaring Method (cont)

• Let the average value, which is the dc component of m2_(t)/2,

be k then

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

 

( ) 2 1 ₂ t k t m  



 

t



 

t m

 

t m

 

t w t x cos2 _c 2 1 2 1 _{2  2} 

 

t k w t

 

t w t m cos2 _c cos 2 _c 2 1 ₂

_

  

Signal Squaring Method (cont)

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

• 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 << 4B.

• x(t) consists of pulses of k located at ωc which are passed along with the residue of third term which will be suppressed by the PLL which tracks kcos2 ωc t.

• PLL output after passing through frequency divider yields the desired carrier.

 

t



 

t k w t

 

t w t m cos2 _c cos 2 _c 2 1 ₂

_

  

Needs Multiplexing – Process of transmitting two or more signals simultaneously

Multiplexing : Applications



Four communication applications that would be prohibitively

expensive or impossible without multiplexing are:

_{Telephone systems} _Telemetry

_Satellites

The

current

techniques

that

can

accomplish this include



frequency division multiplexing (FDM)



_{time division multiplexing (TDM)}

Synchronous vs statistical TDM



_wavelength

_division

_multiplexing

(WDM)



_{code division multiplexing (CDM)}

Types of Multiplexing



The two most common types of multiplexing are



_{Frequency-division multiplexing (FDM)}

 Generally used for analog information.

 Individual signals to be transmitted are assigned a different frequency within a common bandwidth.



_{Time-division multiplexing (TDM)}

 Generally used for digital information.

 Multiple signals are transmitted in different time slots on a single channel.

These two basic methods are illustrated below. M₁ M₂ M₃ M₄ M₅ time freq B_L B_H B time freq M₁ M2 M3 M₄ M5 t B_L B_H M₁ M₂ M₃ M₄ M₅ B_L B_H B M₁ M₂ M₃ M₄ M₅ t t FDM TDM t B_L B_H

TDM: messages occupy all the channel bandwidth but for short time intervals of time

FDM: all signals are transmitted at the same time (all the time) but in different frequency bands

Frequency Division Multiplexing

FDM: all signals are transmitted at the same time (all the time) but in different frequency bands

FDM



FDM(Frequency-Division Multiplexing)

 is an analog technique that can be applied when the bandwidth of a link (useful bandwidth of the medium excess) is greater than the combined bandwidths of the signals to be transmitted

FDM signal generation



FDM process

 each telephone generates a signal of a similar frequency range

FDM signal generation

modulated onto different carrier frequencies

Requires its own carrier frequency

Composite signal

FDM signal generation

FDM signal generation



Demultiplexing

 separates the individual signals from their carries and passes them to the waiting receivers.

FDM signal generation

FDM signal generation

FDM: Composite signal spectrum

FDM: Composite signal spectrum

For telephony, the physical line is divided (notionally) into 4kHz bands or channels, i.e. the channel spacing is 4kHz. Thus we now have:

f

Bandlimited Speech Guard Bands

4kHz

Frequency Division Multiplex

• Advantages:

 _{no dynamic coordination needed}

• Disadvantages:

 _{waste of bandwidth}

if traffic distributed unevenly

 _{guard spaces} k₃ k₄ k₅ k₆ f t c Channels k_i

Frequency Division Multiplexing



Example : CableTelevision

 coaxial cable has a bandwidth of approximately 500Mhz

 individual television channel require about 6Mhz of bandwidth for transmission

 How many channels it will carry??

Frequency Division Multiplexing

Each broadcast stations carries an information signal (voice & music ) which occupies bandwidth between 0Hz ~5kHz

Impossible to differentiate or

separate one station’s transmission from another

Example 1

Assume that a voice channel occupies a bandwidth of 4

KHz. We need to combine three voice channels into a link

with a bandwidth of 12 KHz, from 20 to 32 KHz. Show

the configuration using the frequency domain without the

use of guard bands.

Solution

Shift (modulate) each of the three voice channels to a

different bandwidth

Example 2

Five channels, each with a 100-KHz bandwidth, are to be

multiplexed together. What is the minimum bandwidth of

the link if there is a need for a guard band of 10 KHz

between the channels to prevent interference?

Solution

For five channels, we need at least four guard bands.

This means that the required bandwidth is at least

Example: analogue carrier system for

telephony

Analog Carrier Systems

• Hierarchy of FDM schemes

• Group

— 12 voice channels (4kHz each) = 48kHz

— Range 60kHz to 108kHz

• Supergroup

— 60 channel

— FDM of 5 group signals on carriers between 420kHz and 612 kHz

• Mastergroup

Synchronous Time Division

Multiplexing

• The original time division multiplexing.

• The multiplexor accepts input from attached devices in a round-robin fashion and transmit the data in a never ending pattern.

• T-1 and ISDN telephone lines are common examples of synchronous time division multiplexing.

Synchronous Time Division

Multiplexing

• If one device generates data at a faster rate than other devices, then the multiplexor must either sample the incoming data stream from that device more often than it samples the other devices, or buffer the faster incoming stream.

• If a device has nothing to transmit, the multiplexor must still insert a piece of data from that device into the multiplexed stream.

Synchronous TDM

• Very popular

• Line will require as much bandwidth as all

the bandwidths of the sources

Statistical Time Division Multiplexing

• A statistical multiplexor transmits only the data from active workstations (or why work when you don’t have to).

• If a workstation is not active, no space is wasted on the multiplexed stream.

• A statistical multiplexor accepts the incoming data streams and creates a frame containing only the data to be transmitted.

Statistical TDM is useful for applications in which the low-bit-rate streams have speeds that vary in

Statistical Time Division Multiplexing

• A statistical multiplexor does not require a line over as high a speed line as synchronous time division multiplexing since STDM does not assume all sources will transmit all of the time!

• Good for low bandwidth lines (used for LANs)

TDM(cont’d)



Inverse Multiplexing

 takes the data stream from one high-speed line and breaks it into portion that can be sent across several lower speed lines simultaneously, with no loss in the collective data rate

TDM(cont’d)



Multiplexing

and inverse

multiplexing

high-speed _{breaks it into}

TDM(cont’d)



Why do we need inverse multiplexing ?

 wants to send data, voice, and video each of which requires a different data rate.

• [example]

 _{voice - 64 Kbps link}  _{data - 128 Kbps link}  _{video - 1,544 Mbps link}