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

Data Communication, Lecture5

Some Analog Systems

Data Communication, Lecture 5

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

Analog Carrier Wave Systems Carrier wave techniques form a bases for telecommunication

systems Multiplexing techniques

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

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

Data Communication, Lecture 5

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

Frequency-division multiplexing (FDM)

Data Communication, Lecture 5

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

FDM receiver

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

Data Communication, Lecture 5

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Advanced FDM: xDSL with OFDM Conventional 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

Data Communication, Lecture 5

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Phase-locked loops (PLLs)

Phase-locked loop is a feedback arrangement capable to synchronize itself to a noisy external reference

The output signals of the loop can be used to produce for instance multitude of locked frequencies

PLL application areas include...– modulators– demodulators– frequency synthesis– multiplexers– signal processors

Data Communication, Lecture 5

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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 amplitude Principle: phase difference of Xc(t) and v(t) adjusts VCO

Phase comparator output iscomparable to phase difference of input signals

Data Communication, Lecture 5

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

PLL phase comparator realizations Circuits: (a) analog and (b) digital phase comparator circuit Note 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

ideal

pulse ratio: 50/50

Data Communication, Lecture 5

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

FM detection by PLL

( ) 2 ( )tv v

t K y t dt

time domain

phase domain

frequency domain

( )( )

( ) ( )

v

t

v

d tt

dt

t d

1 1( ) ( ) (0) ( )22

t

v d V f V fj f

sin ( ) ( ) ( ) ( ) v

t t t t

Data Communication, Lecture 5

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

PLL FM-demodulator: the feedback analysis

1

1 2

( )( ) ( )

1 ( ) ( )H f

Y f X fH f H f

( )( ) ( )

1 ( ) /

1 ( )( )

( )

( )

a

a v

v

a v

K H fY f f

K H f K jf

jfKH ff

K jf KH f

K K K

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

Data Communication, Lecture 5

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

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 t

( ) 2 ( )t

t f x d

( ) 2 ( ) /( )f f X f j f

0

1 1( ) ( ) (0) ( )22t

v d V f V fj f

Data Communication, Lecture 5

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

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 1 ( ) ( )

( ) ( ) ( )( ) L

v v

jfKH f f X fY f f H f

K jf KH f K

( )( )

( ) ( / )L

H fH f

H f j f K

1( )

1 ( / )LH f

j f K

( )

( ) ( ), 11 ( / )

v v

f fX f WY f X f

K j f K K K

( ) ( )v

fy t x t

K

Y(f)

a vK K K

Data Communication, Lecture 5

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

PLL based frequency synthesizer

VCOVCO

Filt.Filt.Phasedetector

Phasedetector

Divide by10

Divide by10

10out in

f 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