Angle Modulation
ANGLE MODULATION
results whenever the phase angle θ of a
sinusoidal wave is varied with respect to time
Angle modulated wave expression:
m(t ) Vc cos[ct (t )]
m(t) = angle modulated wave
Vc = peak carrier amplitude (volts)
ωc = carrier radian frequency
θ(t) = instantaneous phase deviation (radians)
ANGLE MODULATION
θ(t) as a function of the modulating signal
if vm(t) - modulating signal, the angle modulation:
θ(t) = F[vm(t)]
Where vm(t) = Vmsin(ωmt)
ωmt = angular velocity of the modulating signal
(2πfm rad)
fm = modulating signal frequency(Hz)
Vm = peak amplitude of the modulating
signal(volts)
ANGLE MODULATION
the difference between freq. and phase
modulation – which property of the carrier (freq
or phase) is directly varied by the modulating
signal and which property is indirectly varied
Carrier freq is varied – its phase also varied
FM – the carrier frequency is varied directly
in accordance with modulating signal
PM – the carrier phase is varied directly in
accordance with modulating signal
ANGLE MODULATION
Direct frequency modulation (FM)
varying the frequency of a constant-amplitude carrier
directly proportional to the amplitude of the modulating
signal at a rate equal to the frequency of the modulating
signal
Direct phase modulation (PM)
varying the phase of a constant-amplitude carrier
directly proportional to the amplitude of the modulating
signal at a rate equal to the frequency of the modulating
signal
ANGLE MODULATION
Angle modulated signal
m[t] in frequency domain
fc is changed when acted on
by a modulating signal vm[t]
The magnitude and direction
of the freq. shift (Δf) –
proportional to the amplitude
and polarity of the modulating
signal (Vm)
ANGLE MODULATION
The rate at which freq.
changes are occurring is
equal to the freq. of the
modulating signal (fm)
Example
positive modulating signal
produces an increase in
frequency
negative modulating signal
produces a decrease in
frequency
ANGLE MODULATION
Phase θ of the carrier is
changing proportional to
the amplitude of the
modulating signal vm[t]
The relative angular
displacement (shift) of the
carrier phase in radian in
respect to the reference
phase – phase deviation
(Δθ)
ANGLE MODULATION
The relative displacement of the
carrier freq. in Hz in respect to
its un-modulated value –
frequency deviation (Δf)
The magnitude of the freq and
phase deviation is proportional
to the amplitude of the
modulating signal (Vm)
The rate at which the change
are occurring is equal to the
modulating signal frequency (fm)
ANGLE MODULATION
ANGLE MODULATION
FM – maximum frequency deviation (change in the
carrier freq.) occurs during the maximum positive
and negative peaks of the modulating signal (freq.
deviation is proportional to the amplitude of the
modulating signal)
PM – the maximum freq. deviation occurs during
the zero crossings of the modulating signal (the
freq. deviation is proportional to the slope or first
derivative of the modulating signal)
Phase Deviation and Modulation Index
General form of modulated wave:
m(t ) Vc cos[ct m cos(mt )]
mcos(ωmt) - instantaneous phase deviation, θ(t)
m represents the peak phase deviation in radians
peak phase deviation – modulation index
Modulation index definition determines either it is
FM or PM
Phase Deviation and Modulation Index
PM – the modulation index is proportional to the
amplitude of the modulating signal, independent of
its frequency
m KVm
m = modulation index and peak phase deviation (Δθ)
K = deviation sensitivity (radians per volt)
Vm = peak modulating-signal amplitude (volts)
radians
mK Vm (volts ) radians
volt
Phase Deviation and Modulation Index
Rewrite:
m(t ) Vc cos[ct KVm cos(mt )]
m(t ) Vc cos[ct cos(mt )]
m(t ) Vc cos[ct m cos(mt )]
Phase Deviation and Modulation Index
FM – the modulation index is directly proportional to
the amplitude of the modulating signal and
inversely proportional to the frequency of the
modulating signal
K1Vm
m (unitless )
m
m = modulation index (unitless)
K = deviation sensitivity (radians per sec per volt)
Vm = peak modulating-signal amplitude (volts)
ωm = radian frequency (radians per second)
Phase Deviation and Modulation Index
radians
K1 Vm (volts )
volts s
m (unitless)
m (radian / s)
m = modulation index (unitless)
K = deviation sensitivity (radians per sec per volt)
Vm = peak modulating-signal amplitude (volts)
ωm = radian frequency (radians per second)
Phase Deviation and Modulation Index
Deviation sensitivity to be expressed in hertz/V
K1Vm
m (unitless )
fm
m = modulation index (unitless)
K = deviation sensitivity (radians per sec per volt)
Vm = peak modulating-signal amplitude (volts)
fm = radian frequency (radians per second)
hertz
K1 Vm (volts)
m
volts
(unitless)
f m (hertz )
Frequency Deviation
Frequency deviation
the change in frequency that occurs in the carrier when it is
acted on by a modulating-signal frequency
given as a peak frequency shift in hertz (Δf)
2Δf – peak to peak – carrier swing
For FM
deviation sensitivity is given in hertz per volt
peak frequency deviation – product of the deviation
sensitivity and peak modulating signal voltage
f K1Vm ( Hz )
Frequency Deviation
Modulation index in FM rewritten as:
f ( Hz )
m (unitless )
f m ( Hz )
Rewrite m(t) m(t ) Vc cos[ct
K1Vm
sin(mt )]
fm
f
m(t ) Vc cos[c t sin(mt )]
fm
m(t ) Vc cos[ct m sin(mt )]
Frequency Deviation
With PM – both the modulating index and peak
phase deviation are directly proportional to the
amplitude of the modulating signal and unaffected
by its frequency
With FM – both modulation index and the frequency
deviation are directly proportional to the amplitude
of the modulating signal, and the modulation index
is inversely proportional to its frequency.
Frequency Deviation
Question
Determine the peak frequency deviation (Δf) and
modulation index, m for FM modulator with
deviation sensitivity K1 = 5 kHz/V
modulating signal vm(t) = 2 cos(2π2000t)
Determine the peak phase deviation, m for a PM modulator
with
deviation sensitivity K = 2.5 rad/V
modulating signal vm(t) = 2 cos(2π2000t)
Angle Modulation vs. Amplitude Modulation
Advantages
Noise immunity
Man-made noise results in unwanted amplitude variations (AM
noise)
FM and PM receiver include limiters that remove most of the
AM noise before final demodulation. This process cannot be
used with AM as removing AM noise also remove the information
Noise performance and SNR improvement
Limiters used in FM and PM reduces the noise level and
improve SNR during demodulation
With AM, noise within signal cannot be removed
Angle Modulation vs. Amplitude Modulation
Capture effect
Allows a receiver to differentiate between two signals received
with the same frequency, providing that one signal is at least as
twice as high in amplitude as the other.
AM – if 2 or more signals are received with the same frequency,
both will be demodulated and produce audio signals
Power utilization
With AM – most transmitted power is contained in the carrier
and the information is contained in the lower power sidebands
the carrier power remains constant with modulation and the
sideband power simply adds to the carrier power
With FM and PM – total power remains constant regardless is
modulation is present
Power is taken from the carrier with modulation and redistributed
in the side bands – angle modulation puts most of its power in
the information
Angle Modulation vs. Amplitude Modulation
Disadvantages
Bandwidth
Angle Modulation – produces many side frequencies – much
wider bandwidth than AM
Circuit complexity and cost
complex design of FM and PM modulators, demodulators,
transmitter and receivers than AM counterparts
large scale integration ICs reduces the cost of manufacturing
Observations from previous figure
FM and PM waveforms are identical except for
their time relationship
For FM, the maximum frequency deviation
occurs during the maximum positive and
negative peaks of the modulating signal
For PM, the maximum frequency deviation
occurs during the zero crossings of the
modulating signal (i.e. the frequency deviation
is proportional to the slope or first derivative of
the modulating signal)
