October 2013Lectured by

Assoc Prof. Thuong Le-Tien

Slides with references from HUT Finland, Mc. Graw Hill Co., and A.B. Carlson’s Communication Systems book

ANALOG MODULATION SYSTEMS

Analog Carrier Wave Systems

Carrier wave techniques form a bases for telecommunication systems

Topics today in CW-applications:

– Single conversion radio receiver

• FM radio (analog) stereo multiplexing

– Measurement equipment

• Spectrum analyzer

– Multiplexing techniques

• Frequency Division Multiplexing (FDM)

• Quadrature-carrier multiplexing

– Phase-locked loop (PLL)

• FM-demodulator

• frequency synthesis

• Costas loop

Heterodyne Single-conversion receiver

Assume reception of a bandpass signal

Multiplication at the receiver with the local oscillator signal having frequency of fLO yields signals at two CW-bands

Therefore, IF can be selected asor LO can be selected as

( ) ( )cos ( )c c

x t A t t t

( ) ( ) ( )

( )cos( )cos ( )

( )cos ( ) / 2 ( )cos ( ) / 2

IF LO c

LO c

LO c LO c

x t x t x t

A t t t t

A t t t A t t t

IF LO cf f f

LO c IFf f f

Mirror frequency

Select for IF for instance

For the reason that cosine is even function there are two frequency bands that convert to intermediate frequency namely

This means that both bandpass signals at the received frequencies are converted to the intermediate frequency.

Example: Assume we set

therefore receiver picks signals at the bands of

However, this is usually not wanted, and the other band must be filtered away by the first bandpass filter at the receiver

( )cos ( ) / 2m LO c

A t t t

110MHz, 10MHzLO IFf f

'

' ,

IF LO c LO c c LO

c LO IF c LO IF

LO IF

110MHz 10MHz

= 120MHz 100MHz

c LO IFf f f

Filtering mirror frequencies (image rejection filtering)

(selected)

' 2 (see the figure)

IF LO C

C LO IF

C C IF

f f f

f f f

f f f

*Should pass the messagebut not the mirror image

*

2 IFf

2T RF IFB B f

Single conversion - basic characteristics

SC can be used with all CW methods

The RF stage provides image rejection

The IF stage provides gain and interference rejection

– note that the fractional BW= BT/fIF is selected by adjusting fIF Remember from the second lecture that system design is easier

if the fractional bandwidth is kept relatively small: For analog FM broadcasting:

when it was required

Tuning of the receiver to a desired band is easy by adjusting the local oscillator. (Often BRF is selected to be so wide and fLO so high that the first bandpass filter (amplifier) center frequency requires no tuning, as usually in FM radios)

0 01 0 10

. / . B f

/ 200kHz /10.6MHz 0.02IF IF

B f

Example of Frequency ConversionScanning spectrum analyzer

VCO, BRF and BIF filters form together a scanning bandpass filter (SBF)

Ramp generator takes care of sweeping SBF

After the IF filter the envelope detector yields signal whose power is comparable to the power that has passed the SBF

Sweep rate and BIF determine system resolution. High resolution->small BIF and sweep rate as discussed soon

When larger sensitivity is desired sweep rate must be decreased

Spectrum analyzer includes often integrator (or averaging function) to improve SNR via inclusion of multiple sweep data

BRFBIF

Frequency-division multiplexing (FDM)

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

AT & T FDM hierarchy in PSTN

voice channel

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

FM stereo multiplexing (MPX-system) The MPX encoder utilizes various linear modulation methods

L+R and L-R signals are transmitted on different channels

SCA (Subsidiary Communication Authorization) is used to transmit background music for selected subscribers

FM stereo decoder System is based on detecting both L+R and L-R signals from

which the R and L can be calculated

Compatibility to mono-phonic transmission is granted by using the unmodulated L+R and DSB modulated L-R signal at 23-53 kHz that is automatically filtered out in mono-phonic reception

Quadrature-carrier multiplexing

Two signals x1 and x2 are transmitted via same channel

Signals can be analog or digital CW or baseband signals (QPSK, DSB, SSB ...)

Task: show that the signals x1 and x2 can be detected independently at the receiver!

x t A x t t x t tC C C C( ) ( )cos( ) ( )sin( )

1 2

( )Cx t

Quadrature-carrier reception

In order to detect the x1 component multiply by the cos-wave:

In order to detect the x2 component multiply by sin-wave:

Note

– Second-order frequency must be filtered away

– The local oscillator must be precisely in-phase to the received signal, otherwise cross-talk will follows

cos( ) ( )cos( ) ( )sin( )

( ) cos( ) / ( )sin( ) /

C C C

C C

t x t t x t t

x t t x t t

1 2

1 21 2 2 2 2

sin( ) ( )cos( ) ( )sin( )

( ) cos( ) / ( )sin( ) /

C C C

C C

t x t t x t t

x t t x t t

1 2

2 11 2 2 2 2

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

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

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 2

a

ideal

pulse ratio: 50/50

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

PLL FM-demodulator: the feedback analysis

1

1 2

( )( ) ( )

1 ( ) ( )

H fY f X f

H 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

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

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 ( / )L

H fj f K

( )( ) ( ), 1

1 ( / )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

PLL based frequency synthesizer

VCOVCO

Filt.Filt.Phasedetector

Phasedetector

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

Detecting DSB using PLL-principle

An important application for PLLs is in synchronization of receiver local oscillator in synchronous detection

In the Costas PLL (below) two phase discriminators are used to:

– cancel out DSB modulation x(t) in the driving signal

– synchronize the output frequency to the center frequency of the DSB spectra (the suppressed carrier)

– to detect the DSB signal

Cos

tas

PL

L d

etec

tor

for

DS

B

PD: phase detector (=multiply+LPF)

Loop drives phase error to zero

LPF yields constant (zero) output when loop is locked to carrier

1sin cos sin 2 sin 02ss ss ss ss

Frequency synthesizer with fixed and adjustable outputs

Linearized PLL models (a) time domain (b) phase (c) frequency domain

Monochrome

TV transmitter

Monochrome TV receiver

The aspect ratio

Color subcarrier modulation system

The chrominance signal

The luminance signal

Color demodulation system

Color vector

Scene capabilities of conventional NTSC system and HDTV

Viewing angles as a function of distance (a) conventional NTSC (b) HDTV

HDTV transmitter

HDTV receiver