s-72.245 transmission methods in telecommunication systems (4 cr) carrier wave modulation systems
TRANSCRIPT
S-72.245 Transmission Methods in Telecommunication Systems (4 cr)
Carrier Wave Modulation Systems
2 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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
3 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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
*also called as heterodyne-receiver
( ) ( )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
4 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Mirror frequency Select for IF for instance For the reason that cos 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 IF
f f
'
' ,IF LO c LO c c LO
c LO IF c LO IF
LO IF
110MHz 10MHz
= 120MHz 100MHzc LO IF
f f f
5 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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 message but not the mirror image
*
2 IFf
2T RF IFB B f
6 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 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
7 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Scanning spectrum analyzer
8 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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
9 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Example: averaging improves SNR
Assume white Gaussian noise with variance 2 (random part) is added into a sinusoidal signal (deterministic part) and thus the signal SNR is
How much SNR can be expected to improve by n-fold averaging?
Ans:
or in dB:
2 2
1 2 2
( / 2)2
S
N N N
P V VSNR
P
2 2
12 2
( / 2)2
n
N N
nV nVSNR nSNR
n
10 10 1
10 1 10
10log ( ) 10log ( )
10log ( / ) 10log ( )SNR n
n
SNR SNR
SNR SNR n
10 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
Frequency-division multiplexing (FDM)
11 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.
12 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
AT & T FDM hierarchy in PSTN
voice channel
Note: nowadays respective combining realized by PCM
13 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
DMT with cable attenuation, interferenceand cross-talk
rejected sub-band
14 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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
15 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
16 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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
17 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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
18 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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
19 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 iscomparable to phase difference of input signals
20 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
21 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
22 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
23 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
24 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
( )( ) ( ), 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
25 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 fin
is locked for instanceto the fundamental frequency of a crystal oscillator
26 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen
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