Transcript Exponential Carrier Wave Modulation

S-72.245 Transmission Methods in
Telecommunication Systems (4 cr)
Carrier Wave Modulation Systems
Analog Carrier Wave Systems


2
Carrier wave techniques form a bases for telecommunication
systems
Topics today in CW-applications:
• FM radio (analog) stereo multiplexing
– Measurement equipment
• Spectrum analyzer
– Multiplexing techniques
• Frequency Division Multiplexing (FDM)
– Phase-locked loop (PLL)
• FM-demodulator
• frequency synthesis
• Costas loop
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Single
-conversion

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
xc (t )  A(t )cos ct   (t )
xIF (t )  xLO (t ) xc (t )
 A(t )cos( LOt )cos  ct   (t ) 
 A(t )cos  LO   c  t   (t )  / 2  A(t )cos  LO   c  t   (t )  / 2

Therefore, IF can be selected as f IF  f LO  f c
or LO can be selected as f LO  f c  f IF
*also called as heterodyne-receiver
3
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Mirror frequency


Select for IF for instance Am (t ) cos  LO   c  t   (t )  / 2
For the reason that cos is even function there are two frequency
bands that convert to intermediate frequency namely
           ' 
  '     ,    
IF
LO
c

c
LO
LO
IF
c
c
c
LO
LO
IF
This means that both bandpass signals at the received
frequencies  LO   IF are converted to the intermediate
frequency.
Example: Assume we set
f LO  110MHz, f IF  10MHz
therefore receiver picks signals at the bands of
f c  f LO  f IF  110 MHz  10 MHz
= 120 MHz  100 MHz

4
However, this is usually not wanted, and the other band must be
filtered away by the first bandpass filter at the receiver
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Filtering mirror frequencies
(image rejection filtering)
2 f IF
BT  BRF  2 f IF
f IF  f LO  f C
f C  f LO  f IF (selected)
 f C '  f C  2 f IF (see the figure)
*
*Should pass the message
but not the mirror image
5
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
SC 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
BIF / f IF  200kHz /10.6MHz  0.02

6
when it was required 0.01  B / f0  0.1
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)
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Scanning spectrum analyzer
7
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
BRF






8
BIF
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
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Example: averaging improves SNR

Assume white Gaussian noise with variance s2 (random part) is
added into a sinusoidal signal (deterministic part) and thus the
signal SNR is
PS (V / 2) 2 V 2
SNR1  
 2
2
PN
sN
2s N
How much SNR can be expected to improve by n-fold
averaging?
Ans:
or in dB:
(nV / 2) 2 nV 2
SNRn 
 2  nSNR1
2
ns N
2s N
 SNR  10log10 ( SNRn )  10log10 ( SNR1 )
 10log10 ( SNRn / SNR1 )  10log10 ( n)
9
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Frequency-division multiplexing (FDM)
10
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
First the FDM wave is demodulated. Then each subcarrier
is detected by using separate bandpass filters and
detectors.
11
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
AT & T FDM hierarchy in PSTN
voice channel
combining realized by PCM
12
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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
rejected sub-band
DMT with cable
attenuation, interference
and cross-talk
13
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
FM stereo multiplexing (MPX-system)



14
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
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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
15
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

Two signals x1 and x2 are transmitted via same channel
xC (t )  AC x1 (t )cos( C t )  x2 (t )sin( C t )

Signals can be analog or digital CW or baseband signals
(QPSK, DSB, SSB ...)
xC (t )
Task: show that the signals x1 and x2 can be detected
independently at the receiver!
16
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

In order to detect the x1 component multiply by the cos-wave:
cos( C t ) x1 (t )cos( C t )  x2 (t )sin( C t )
 x1 (t ) 1  cos(2 C t ) / 2  x2 (t )sin(2 C t ) / 2

In order to detect the x2 component multiply by sin-wave:
sin( C t ) x1 (t )cos( C t )  x2 (t )sin( C t )
 x2 (t ) 1  cos(2 C t ) / 2  x1 (t )sin(2 C t ) / 2

17
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
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Phase-locked loops (PLLs)



18
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
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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 is
comparable to phase difference of input signals
19
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
pulse ratio: 50/50
ideal
XOR-circuit
sin(a  cos(  )  1 sin(   )  1 sin(   )
2
2
20
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
FM detection by PLL
time domain
sin  (t )   (t )   (t )  v (t )
 (t )  2 K  y(t )dt
v
v
dv (t )

 (t )  dt

t
v (t )    ( ) d


21
phase domain
t
frequency domain
t

v ( ) d  
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

1
V ( f )  1 V (0) ( f )
2
j 2 f
PLL FM-demodulator: the feedback analysis
Solve transfer function with feedback:
Y( f )
Y ( f )   X ( f )  H 2 ( f )Y ( f )  H1 ( f )
Y ( f )  H1 ( f ) H 2 ( f )Y ( f )  X ( f ) H1 ( f )
Y( f ) 
H1 ( f )
X(f )
1  H1 ( f ) H 2 ( f )
This is applied to the linearized PLL yielding relationship
between the input phase and output voltage:
Ka H ( f )
Y( f ) 
( f )
1  K a H ( f ) K v / jf
1 jfKH ( f )

( f )
K v jf  KH ( f )
(K  Ka Kv )
22
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Applying the FM signal to
the linearized PLL model

Remember the FM wave:
d (t ) / dt  2 f  x(t )
where the modulating signal is denoted by x(t). The input FM
phase to the system is thus
 (t )  2 f  x( )d 

t

This is in frequency domain: ( f )  2 f  X ( f ) /( j  f )
assuming no DC component or V(0) = 0, or
 v ( ) d  
t
1
V ( f )  1 V (0) ( f )
2
j 2 f
0
23
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Applying FM signal to the detector... (cont.)

Thus the input is ( f )  f  X ( f ) /( jf ) and the output is
1 jfKH ( f )
f X ( f )
Y( f ) 
( f ) 
HL ( f )
K v jf  KH ( f )
Kv
where the loop equivalent transfer function is
Y(f)
HL ( f ) 
H( f )
H ( f )  j( f / K )
K  Ka Kv

Assume that the first order LP function is used or
f
f
X(f )
W
1
Y( f )  
  X ( f ),  1
Kv 1  j( f / K ) Kv
K
1  j( f / K )
f
 y (t )   x(t )
Kv
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
HL ( f ) 
24
PLL based frequency synthesizer
Reference signal fin
is locked for instance
to the fundamental frequency
of a crystal oscillator
f in
Phase
detector
Divide by
10
divider different
frequencies can be produced
whose phase is locked into fin
25
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Filt.
VCO
f out  10 f in
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
Costas PLL detector
for DSB
PD: phase detector (=multiply+LPF)
Loop drives phase
error to zero
26
LPF yields constant (zero)
output when loop is locked
to carrier
sin  ss cos  ss  1 sin 2 ss  sin 0   ss
2
Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen