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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

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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

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
256kS/s
from
USRP

Low Pass
Filter

64kS/s

FM
Demodulator

32kS/s
Squelch
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

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17

PM Signal ‐ Time Domain
•  For a pulse train baseband signal:
Baseband
signal, x(t)

PM signal

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18

PM Signal ‐ Time Domain
•  For a sinusoidal baseband signal:
Baseband
signal, x(t)

PM signal

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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
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21

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