Angle Modulation (FM/PM) by Erol Seke For the course “Communications” ESKİŞEHİR OSMANGAZİ UNIVERSITY
Angle Modulation (FM/PM)
by Erol Seke
For the course “Communications”
ESKİŞEHİR OSMANGAZİ UNIVERSITY
Changing the frequency and phase angle of the carrier signal with the message
signal are called “Frequency Modulation” (FM) and “Phase Modulation” (PM)
respectively. The class of such techniques is called “Angle Modulation”.
))()(cos()( tpttAtu c
phase deviation constant for PM
dt
tdtfi
)(
2
1)(
instantaneous frequency
))(cos()( ttAtu cc dt
tdt ci
)()(
so
Let )(tm be the message signal )()( tmkt p
dt
tdtmkt ci
)()()(
frequency deviation constant for FM
dt
tdti
)()(
))(cos()( tAtu c
center frequency deviation around center
dt
tdftf ci
)(
2
1)(
or
or
Phase is only meaningful with a particular given frequency, cannot be thought of independent entities
FMdmk
PMtmk
tt
f
p
,)(2
,)(
)(
FMtmk
PMtmdt
dk
tdt
d
f
p
,)(2
,)(
)(
or
FM modulator)(tm
PM modulator dt)(tm
PM modulator)(tm
FM modulatordt
d)(tm
)cos()( tAtx mExample : Tone signal is given. Find FM and PM waveforms.
)cos()()( tAktxkt mppPM
)sin()()( tAk
dxkt m
m
t
FM
(PM)
(FM)
therefore))cos(cos()( tAktAtu mpcc
))sin(cos()( tAk
tAtu m
m
cc
(PM)
(FM)
FMPM
Example :
Rectangular wave as message signal.
Note that neither FM nor PM changes the
amplitude of the carrier.
PM
FM
FM changes the frequency
PM changes the phase of the carrier
Remember that when there is only a finite
number of frequency values, it is FSK.
When there is only a finite number of
phase values, it is called PSK.
Spectral Characteristics of Angle Modulated Signals
Let ))2sin(2cos()( tftfAtu mcc
Modulation index
}Re{)()2sin(2 tfjtfj
mcc eeAtu
Since is periodic it can be represented by Fourier series)(tu
m
mm
f
tfjntfj
mn dteefC
/1
0
2)2sin(
2
0
))sin((
2
1dueC uuj
n
Let tfu m2
This integral is called the Bessel function
of the first kind of order n)(nJ
The Fourier series is
n
tnfj
n
tfj mm eJe 2)2sin(
)(
FM
f
tmk
PMtmk
m
f
p
2
|})(max{|
|})(max{|
Therefore
n
ctnfj
nc
tfjeeJAtu m
22
)(Re)(
n
mcnc tnffJAtu ))(2cos()()(
Actual bandwidth of FM/PM is infinite. So we usually define a finite “effective bandwidth”
Bessel function can be represented by a series expansion
0
2
2
)!(!
)()1()(
k
knk
nnkk
J
For small β!2
)(n
Jn
n
n
(approximation)
For 2n )(nJ is negligible.
Therefore only the first sideband corresponding to n=1 is of importance.
The effective bandwidth of an angle modulated signal is, in general, given by
mc fB )1(2 which contains the 98% of the signal power.
Modulation index Frequency of the sinusoidal message signal (or BW of m(t))
For the message signal )2cos()( tfatm m
FMff
ak
PMfak
fB
m
m
f
mp
mc
,)1(2
,)1(2
)1(2
increasing a increases the effective bandwidth
increasingmf increases the bw.
proportional increase in PM (large)
additive increase in FM (small)
Generation of Narrowband FM/PM (Phasor View)
re
im phase of the carrier
re
imsum
90° phase shifted carrier
with lower amplitude
re
sum
changing amplitude of this carrier deviates the phase angle of the sum
(do AM) (get PM)
Generation of Narrowband FM/PM
90phase delay
)(tx
)cos( tc)sin( tc
PM
90phase delay
)(tx
)sin( tc)cos( tc
FM dt
-
+
-
+
AM
AM'
AM demodulatorFM to AM convertorFM
AM
Message signal
Demodulation
This is usually an LTI system whose response curve is
approximately an increasing linear line in the related band.
Approximately linear region
Balanced Discriminator
VCO
DiscriminatorBPF LPFFM
Message signal
voltage Controlled Oscillator
AM
demod.
(for center freq stability)
General Commercial Receiver
RF Amplifier
RF
OSC
IF Demodulator Audio
AGC
MixerTune
Volume
FM band is selected to be 87.5 to 108.0 MHz (not in all countries)
with 200 kHz band for each station
f
M=L+R
Baseband Signal 15kHz 23kHz 53kHz
DSB-SC centered at 38kHz
S=L-R
19kHz pilot tone
(in phase with 38kHz carrier)
Mono FM receivers will only receive L+R
Stereo receivers will do: L=(M+S)/2 and R=(M-S)/2
Stereo FM
New baseband signal
ExampleBlock diagram of stereo AM/FM transmitter
right(t)
left(t)
M(t)
S(t)
-
38 kHz
19 kHz
freq. dup.
RF modulator Stereo AM/FM
RF carrier
ExampleBlock diagram of stereo AM/FM receiver
right(t)
left(t)
M(t)
S(t)
-
38 kHz
19 kHz
freq. dup.
RF
demodulatorStereo AM/FM
LPF
fc=15kHz
RF carrier
sharp-filter
19 kHz
M+S
LPF
fc=15kHz
M-S
Hmw : Add some blocks for Mono-transmitter reception