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Fm And Pm Essay

640 words - 3 pages

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

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3


FM
Signal
‐
Time
Domain

•  For
a
pulse
train
baseband
signal:

Baseband

signal,
x(t)


FM
signal


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4


FM
Signal
‐
Time
Domain

•  For
a
sinusoidal
baseband
signal:

Baseband

signal,
x(t)


FM
signal


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5


FM
Signal
–
Frequency
Domain

•  For
a
1
KHz
sinusoidal
baseband
signal
(tone
 ...view middle of the document...


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


•  Capture
effect:


Signals
more
than
6dB
down
will

not
interfere.


FM
MODULATION

•  SDR
Program
for
NBFM

TRANSMIT

transmit_path

GUI


INTERFACE

(ptt
_block)


USRP

RECEIVE

receive_path


FM
MODULATION

•  TRANSMIT
PATH
(always
running)

48kS/s


Audio

Gain


Audio

Source

Transmit
Enable

from
GUI


48kS/s


3/2


Resampler


32kS/s


FM

Modulator


320kS/s


Transmit

Gain


320kS/s

To

USRP


FM
MODULATION

•  RECEIVE
PATH
(always
running)

256kS/s

from

USRP


Low
Pass

Filter


64kS/s


FM

Demodulator


32kS/s

Squelch

Receive

Enable

from

GUI


Audio

Sink


48kS/s


2/3

Resampler


32kS/s


32kS/s


Audio

Gain


Definition
of
a
PM
Signal

•  For
a
baseband
signal,
x(t):

x PM (t) = Ac cos[2πf c t + k p x(t)]

–  kp
is
the
frequency
deviation
constant
in
rad/volt

–  A
constant
envelope
signal
with
varying

frequency/phase

–  The
instantaneous
phase
is:

θ i (t) = 2πf c t + k p x(t)

–  The
instantaneous
frequency
is:

k p dx(t)
f i (t) = f c +
2π dt

10/14/08


17


PM
Signal
‐
Time
Domain

•  For
a
pulse
train
baseband
signal:

Baseband

signal,
x(t)


PM
signal


10/14/08


18


PM
Signal
‐
Time
Domain

•  For
a
sinusoidal
baseband
signal:

Baseband

signal,
x(t)


PM
signal


10/14/08


19


PM
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


20


Bandwidth
Comparison
for
FM/PM

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

•  FM:



•  For tone modulation: Modulation index, b = Df/
fm
•  BW = 2(kfAm + fm)
•  PM:


•  For
tone
modulation:

Modulation
index,
b = kpAm
•  BW = 2(kpAm+1)fm
•  Increasing frequency has a more profound effect on the BW
of PM

10/14/08


21


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