Fm and Pm

Frequency
and
Phase


Modulation


Sharlene
Katz


James
Flynn


Overview


•  History


•  Why
FM?

Noise
problems
with
linear


modulation
systems:
AM/SSB/DSB


•  Definitions:

Deviation,
WBFM,
NBFM


•  Very
popular
for
VHF
voice


10/14/08


2


Definition
of
an
FM
Signal


•  For
a
baseband
signal,
x(t):


[

x FM (t) = Ac cos 2πf c t + 2πk f

∫ x ( τ ) dτ ]

t

−∞

–  kf
is
the
frequency
deviation
constant
in
Hz/volt


–  A
constant
envelope
signal
with
varying


frequency/phase


–  The
instantaneous
frequency
is:


f i (t) = f c + k f x(t)

–  Maximum
frequency
deviation
=Δf=
kf|x(t)|max


10/14/08


3


FM
Signal
‐
Time
Domain


•  For
a
pulse
train
baseband
signal:


Baseband


signal,
x(t)


FM
signal


10/14/08


4


FM
Signal
‐
Time
Domain


•  For
a
sinusoidal
baseband
signal:


Baseband


signal,
x(t)


FM
signal


10/14/08


5


FM
Signal
–
Frequency
Domain


•  For
a
1
KHz
sinusoidal
baseband
signal
(tone


modulation)
and
10
KHz
carrier


Spacing
=
1
KHz


Wider


than
an


AM
or


DSB
signal


f
(Hz)


10/14/08


10
KHz


6


Deviation
and
Bandwidth


•  Instantaneous
Frequency:

fc
+
kfx(t)


•  Frequency
deviation:

Δf=kfx(t)


•  Maximum
frequency
deviation,
Δf
=
kf|x(t)|max


–  For
tone
modulation:

Δf
=
kfAm


•  Deviation
Ratio,
D
=
Δf/W


–  For tone modulation: Modulation index, b = Df/fm

–  b
<<
1:

narrowband
FM,
NBFM


–  b
>>
1:

wideband
FM,
WBFM


•  Bandwidth,
BW
=
2(D+1)W,
or
BW
=
2(b+1)fm


10/14/08


7


FM
MODULATION


•  Spectrum

vs.
modulation
index,
β


–  Spectra
have
a
typical
trapezoidal
shape
in
linear


frequency
and
amplitude
in
decibels.


2
x
deviation


≈
‐3
to
‐6dB
per
fm


≈
‐3
to
‐6dB
per
fm


carrier


FM
MODULATION


FM
MODULATION


FM
MODULATION


demos


FM
MODULATION


•  Comparison
to
AM/SSB/DSB


AM


2
fm


DSB


2
fm


SSB


fm


FM


2
(β+1)fm


SNR


LINEAR


LINEAR


LINEAR


EFFICIENCY


33%


50%


100%


NON‐

LINEAR


≤
100%*


COMPLEXITY


LOW


MODERATE


MODERATE


HIGH


BANDWIDTH


FM
MODULATION


•  Threshold
Effect


• ...