Frequency and Phase Modulation

Frequency
and
Phase
 Modulation
 Sharlene
Katz
 James
Flynn
Overview
 •  History
 •  Why
FM?

Noise
problems
with
linear
 modulation
systems:
AMSSBDSB
 •  Definitions:

Deviation,
WBFM,
NBFM
 •  Very
popular
for
VHF
voice
 101408
 2
Definition
of
an
FM
Signal
 •  For
a
baseband
signal,
x(t):
 – k f
is
the
frequency
deviation
constant
in
Hzvolt
 – A
constant
envelope
signal
with
varying
 frequencyphase
 – The
instantaneous
frequency
is:
 – Maximum
frequency
deviation
=Δf=
kf|x(t)|max
 x FM (t) = Ac cos 2πf ct + 2πk f x(τ)dτ −∞ ∫ t fi(t) = fc + k f x(t) 101408
 3
FM
Signal
‐
Time
Domain
 •  For
a
pulse
train
baseband
signal:
 Baseband
 signal,
x(t)
 FM
signal
 101408
 4
FM
Signal
‐
Time
Domain
 •  For
a
sinusoidal
baseband
signal:
 Baseband
 signal,
x(t)
 FM
signal
 101408
 5
FM
Signal
–
Frequency
Domain
 •  For
a
1
KHz
sinusoidal
baseband
signal
(tone
 modulation)
and
10
KHz
carrier
 f
(Hz)
 10
KHz
 Spacing
=
1
KHz
 Wider
 than
an
 AM
or
 DSB
signal
 101408
 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
=
k fAm
 •  Deviation
Ratio,
D
=
ΔfW
 –  For tone modulation: Modulation index, b = Dffm –  b

1:

wideband
FM,
WBFM
 •  Bandwidth,
BW
=
2(D+1)W,
or
BW
=
2(b+1)fm
 101408
 7
FM
MODULATION
 •  Spectrum

vs.
modulation
index,
β
 – Spectra
have
a
typical
trapezoidal
shape
in
linear
 frequency
and
amplitude
in
decibels.
 carrier
 2
x
deviation
 ≈
‐3
to
‐6dB
per
fm
 ≈
‐3
to
‐6dB
per
fm
FM
MODULATION
FM
MODULATION
FM
MODULATION
 demos
FM
MODULATION
 •  Comparison
to
AMSSBDSB
 AM
 DSB
 SSB
 FM
 BANDWIDTH
 2
f m
 2
fm
 fm
 2
(β+1)fm
 SNR
 LINEAR
 LINEAR
 LINEAR
 NON‐ LINEAR
 EFFICIENCY
 33%
 50%
 100%
 ≤
100%
 COMPLEXITY
 LOW
 MODERATE
 MODERATE
 HIGH
FM
MODULATION
 •  Threshold
Effect
 •  Capture
effect:


Signals
more
than
6dB
down
will
 not
interfere.
FM
MODULATION
 •  SDR
Program
for
NBFM
 GUI

 INTERFACE
 (ptt
_block)
 TRANSMIT
 transmit_path
 RECEIVE
 receive_path
 USRP
FM
MODULATION
 •  TRANSMIT
PATH
(always
running)
 Audio
 Source
 Audio
 Gain
 32

 Resampler
 48kSs
 48kSs
 32kSs
 320kSs
 FM
 Modulator
 Transmit
 Gain
 Transmit
Enable
 from
GUI
 320kSs
 To
 USRP
FM
MODULATION
 •  RECEIVE
PATH
(always
running)
 256kSs
 from
 USRP
 Low
Pass
 Filter
 64kSs
 FM
 Demodulator
 32kSs
 Squelch
 32kSs
 Audio
 Gain
 Receive
 Enable
 from
 GUI
 23
 32kSs
 Resampler
 Audio
 48kSs
 Sink
Definition
of
a
PM
Signal
 •  For
a
baseband
signal,
x(t):
 – k p
is
the
frequency
deviation
constant
in
radvolt
 – A
constant
envelope
signal
with
varying
 frequencyphase
 – The
instantaneous
phase
is:
 – The
instantaneous
frequency
is:
 x PM (t) = Ac cos2πf ct + k p x(t) θ i(t) = 2πfct + kpx(t) fi(t) = fc + k p 2π dx(t) dt 101408
 17
PM
Signal
‐
Time
Domain
 •  For
a
pulse
train
baseband
signal:
 Baseband
 signal,
x(t)
 PM
signal
 101408
 18
PM
Signal
‐
Time
Domain
 •  For
a
sinusoidal
baseband
signal:
 Baseband
 signal,
x(t)
 PM
signal
 101408
 19
PM
Signal
–
Frequency
Domain
 •  For
a
1
KHz
sinusoidal
baseband
signal
(tone
 modulation)
and
10
KHz
carrier
 f
(Hz)
 10
KHz
 Spacing
=
1
KHz
 Wider
 than
an
 AM
or
 DSB
signal
 101408
 20
Bandwidth
Comparison
for
FMPM
 •  Bandwidth,
BW
=
2(D+1)W,
or
BW
=
2(b+1)fm
 •  FM:


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

Modulation
index,
b = k pAm •  BW = 2(kpAm+1)fm •  Increasing frequency has a more profound effect on the BW of PM
 101408
 21


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, = f/fm –  

1:

wideband
FM,
WBFM
 •  Bandwidth,
BW
=
2(D+1)W,
or
BW
=
2( +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
 •  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( +1)fm
 •  FM:


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

Modulation
index,
 = kpAm •  BW = 2(kpAm+1)fm •  Increasing frequency has a more profound effect on the BW of PM
 10/14/08
 21