data communication, lecture5 - sharif

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1 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

Data Communication, Lecture5

Some Analog Systems

Data Communication, Lecture 5


Analog Carrier Wave SystemsCarrier wave techniques form a bases for telecommunication systemsMultiplexing techniques

• Frequency Division Multiplexing (FDM)• Quadrature-carrier multiplexing

– Phase-locked loop (PLL)• FM-demodulator• frequency synthesis



Frequency-division multiplexing (FDM)



FDM receiver

First the FDM wave is demodulated. Then each subcarrieris detected by using separate bandpass filters anddetectors.

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Advanced FDM: xDSL with OFDMConventional FDM:– Each channel occupies accurately certain frequency band– Bandwidth efficiency increased by using SSB modulation– Usage of guard bands wastes resources– A lot of filtering functions (complex circuitry)

Modern FDM: OFDM (orthogonal frequency division multiplexing) and DMT (discrete multitone modulation) yield increased spectral adaptation. Applied in xDSL (digital subscriber line techniques).

DMT with cable attenuation only

DMT with cable attenuation, interferenceand cross-talk

rejected sub-band



Phase-locked loops (PLLs)

Phase-locked loop is a feedback arrangement capable to synchronize itself to a noisy external referenceThe output signals of the loop can be used to produce for instance multitude of locked frequenciesPLL application areas include...– modulators– demodulators– frequency synthesis– multiplexers– signal processors



The PLL principle

The PLL circuit consists of– phase comparator (in the figure below the multiplier)– lowpass filter– feedback amplifier– VCO (voltage controlled oscillator), whose output

frequency is linearly proportional to input amplitudePrinciple: phase difference of Xc(t) and v(t) adjusts VCO

Phase comparator output iscomparable to phase difference of input signals



PLL phase comparator realizationsCircuits: (a) analog and (b) digital phase comparator circuitNote that for (a) output is proportional to– input signal phase difference– input signal amplitudes (unintended AM thus harmful)

In (b) AM effects are compensated and response is more linear

XOR-circuit 1 1sin( cos( ) sin( ) sin( )2 2a β α β α β) = − + +

ideal

pulse ratio: 50/50

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FM detection by PLL

( ) 2 ( )tv vt K y t dtφ π ∫=

time domain

phase domain

frequency domain

( )( )

( ) ( )

v

t

v

d ttdt

t d

φω

φ ω α α−∞∫

⎧ =⎪⎨⎪ =⎩ 1 1( ) ( ) (0) ( )22

t

v d V f V fj f

λ λ δπ−∞

⇔ +∫

sin ( ) ( ) ( ) ( )ε ε φ φ≈ = − vt t t t



PLL FM-demodulator: the feedback analysis

1

1 2

( )( ) ( )1 ( ) ( )

H fY f X fH f H f

=+

( )( ) ( )1 ( ) /1 ( ) ( )

( )( )

a

a v

v

a v

K H fY f fK H f K jf

jfKH f fK jf KH f

K K K

= Φ+

= Φ+

=

Solve transfer function with feedback:

This is applied to the linearized PLL yielding relationship between the input phase and output voltage:

( )2 1( ) ( ) ( ) ( ) ( )Y f X f H f Y f H f= −

1 2 1( ) ( ) ( ) ( ) ( ) ( )Y f H f H f Y f X f H f+ =( )Y f



Applying the FM signal to the linearized PLL model

Remember the FM wave:

where the modulating signal is denoted by x(t). The input FM phase to the system is thus

This is in frequency domain:

assuming no DC component or V(0) = 0, or

( ) / 2 ( )d t dt f x tφ π ∆=

( ) 2 ( )t

t f x dφ π λ λ∆ ∫=

( ) 2 ( ) /( )f f X f j fπ π∆Φ = 2

0

1 1( ) ( ) (0) ( )22tv d V f V f

j fλ λ δ

π=

∫ ⇔ +1 44 2 4 43



Applying FM signal to the detector... (cont.)

Thus the input is and the output is

where the loop equivalent transfer function is

Assume that the first order LP function is used or

( ) ( ) /( )f f X f jf∆Φ =1 ( ) ( )( ) ( ) ( )

( ) L

v v

jfKH f f X fY f f H fK jf KH f K

∆= Φ =+

( )( )( ) ( / )L

H fH fH f j f K

=+

1( )1 ( / )LH f

j f K=

+( )( ) ( ), 1

1 ( / )v v

f fX f WY f X fK j f K K K

∆ ∆⇒ ≈ ≈ <<+

( ) ( )v

fy t x tK

∆⇒ ≈

Y(f)

a vK K K=

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PLL based frequency synthesizer

VCOVCO

Filt.Filt.PhasedetectorPhase

detector

Divide by10

Divide by10

10out inf f=

inf

By adjusting thedivider differentfrequencies can be producedwhose phase is locked into fin

Reference signal finis locked for instanceto the fundamental frequency of a crystal oscillator

data communication, lecture5 - sharif

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