ANGLE MODULATION
ANGLE MODULATION – is a
modulation technique which varies the
phase angle of a high – frequency carrier
signal in proportion with the
instantaneous amplitude of a modulating
signal.
Forms of Angle Modulation
Frequency Modulation (FM)
Phase Modulation (PM)
Frequency Modulation (FM)
Is an angle modulation method in which
the frequency of a constant-amplitude carrier
signal is varied in proportion with the amplitude
of the modulating signal at a rate equal to the
frequency of the modulating signal.
Phase Modulation (PM)
Is an angle modulation method in which the
phase of a constant-amplitude carrier signal is
varied in proportion with the amplitude of the
modulating signal at a rate equal to the frequency
of the modulating signal.
Mathematical Principle of Angle Modulation
The general expression of a modulated carrier wave
is given by:
m(t) = Vc cos [ct +
Ө(t)]
where: m(t) = angle-modulated wave
Vc = peak carrier amplitude (volts)
c = carrier radian frequency
Ө(t) = instantaneous phase deviation
(rads)
The general expression of a phase-modulated
carrier wave is given by:
mPM(t) = Vc cos [ct + k1 Vm cos 2πfm(t)]
or
mPM(t) = Vc cos [2πfc(t) + k1 Vm cos
2πfm(t)]
where: mPM(t) = PM wave voltage
Vc = peak carrier voltage
fc = carrier frequency
k1 = deviation sensitivity
Vm = peak modulating signal amplitude (V)
fm = modulating signal frequency
The general expression of a frequency-modulated
]
carrier wave is given by:
mFM(t) = Vc cos [ct + ]
where: mFM(t) = FM wave voltage
Vc = peak carrier voltage
fc = carrier frequency
fm = modulating signal frequency
= the frequency deviation
General Waveform of FM and PM waves
Parameters of Angle-Modulated Wave
• Phase Deviation
• Frequency Deviation
• Percent Modulation
• Deviation Ratio
• PM and FM power
Phase Deviation
For PM waveform, the phase deviation or
modulation index is given by:
m= = k1 Vm
For FM waveform, the phase deviation or
modulation index is given by:
where:
m= m = modulation index or peak phase deviation
(rad)
k1 = deviation sensitivity for PM modulators
m= (rad/s.V)
fm k2 = deviation sensitivity for FM modulators
(rad/s.V)
Vm = peak modulating signal amplitude (V)
fm = modulating signal frequency
Frequency Deviation
For PM waveform, the frequency deviation is given
by:
=k1 Vm fm
For FM waveform, the frequency deviation is given
by:
=k1 Vm
where:
= the frequency deviation
k1 = deviation sensitivity for PM modulators (rad/s.V)
k2 = deviation sensitivity for FM modulators (rad/s.V)
Vm = peak modulating signal amplitude (V)
fm = modulating signal frequency
Frequency Deviation
For PM waveform, the frequency deviation is given
by:
=k1 Vm fm
For FM waveform, the frequency deviation is given
by:
=k1 Vm
where:
= the frequency deviation
k1 = deviation sensitivity for PM modulators (rad/s.V)
k2 = deviation sensitivity for FM modulators (rad/s.V)
Vm = peak modulating signal amplitude (V)
fm = modulating signal frequency
FM PM
Phase (k1 Vm)/fm k1 Vm
Deviation( m )
Frequency k1 Vm k1 Vm fm
Deviation,
Percent Modulation
For PM and FM, the percentage modulation is given
by:
x
%m = 100%
Where:
%m = percentage modulation
= actual frequency deviation of carrier
signal (Hz)
= maximum frequency deviation (Hz)
Deviation Ratio
Worst-case modulation index which produces
the widest output frequency spectrum.
DR =
FREQUENCY SPECTRUM
The number of significant sidebands is determined by the
modulation index. The greater the modulation index, more
sidebands will become significant and the wider the
bandwidth required. Bessel function table can determine
how many sidebands are significant as a function of the
modulation index.
• Frequency modulation produces an infinite
number of sidebands, even for single-tone
modulation
• Sidebands with amplitude less than about 1%
of the total signal voltage can usually be
ignored;
• for practical purposes an angle-modulated
signal can be considered to be band-limited. In
most cases, though, its bandwidth is much
larger than that of an AM signal.
• the table and graph of Bessel functions represent
normalized voltages for the various frequency
components of an FM signal
• J0 represents the component at the carrier frequency
• J1 represents each of the first pair of sidebands, at
frequencies of ƒc + ƒm and ƒc − ƒm
• J2 represents the amplitude of each of the second pair
of sidebands, which are separated from the carrier
frequency by twice the modulating frequency
• All of the Bessel terms should be multiplied by the
voltage of the unmodulated carrier to find the actual
sideband amplitudes
example
• For an FM modulator with a modulation index
m = 1, a modulating signal
Vm(t)=Vmsin(2π1000t), and an unmodulated
carrier Vc(t)=10sin(2π500kt), determine
a. Number of sets of significant side frequencies
b. Their amplitudes
c. Then, draw the frequency spectrum showing
their relative amplitudes.
The Bandwidth Requirements
For Narrowband FM (Low Modulation index, m ≤ 0.25)
BW = 2fm
For Wideband FM (High Modulation index, m ≥ 100 )
BW = 2
By using Bessel Function Table
BW = 2nfm
fm = modulating signal frequency
n = number of significant sidebands
By using Carson’s Rule (Approximate)
BW = 2 (fm +
)
example
• For an FM modulator with a peak frequency
deviation ∆f = 10 kHz, a modulating-signal
frequency fm=10 kHz, Vc = 10 V, and a 500-kHz
carrier, determine:
a. Actual minimum bandwidth from the
Bessel function table.
b. Approximate minimum bandwidth using
Carson’s rule
PM and FM power
Pt = Pc+ 2( P1+P2+P3+…+Pn )
Where:
Pc= P1 = …
Voltages in Vrms
An FM signal has a deviation of 3 kHz and a modulating frequency of
1 kHz. Its total power is 5 W, developed across a 50 resistive load.
The carrier frequency is 160 MHz.
(a) Calculate the RMS signal voltage.
(b) Calculate the RMS voltage at the carrier frequency and each of
the first three sets of sidebands.
(c) Calculate the frequency of each sideband for the first three
sideband pairs.
(d) Calculate the power at the carrier frequency, and in each
sideband, for the first three pairs.
(e) Determine what percentage of the total signal power is
unaccounted for by the components described above.
(f) Sketch the signal in the frequency domain, as it would appear
on a spectrum analyzer. The vertical scale should be power in
dBm, and the horizontal scale should be frequency.
Threshold Effect
This effect can be traced to the use of the limiter.
Capture Effect
Refers to the case of two co-channel or adjacent channel
FM signal being received at the same time by an FM receiver.
When this occurs, the FM receiver will treat the weaker signal
as interference and the weaker signal as inference and the
stronger signal as is said to have captured the receiver.
Pre-emphasis Network
Is a high pass filter which increases the S/N ratio at the
higher-frequency ends of the FM signal at the by allowing the
high-frequency modulating signals to modulate the carrier at
the higher level resulting to larger frequency deviations than
the original amplitudes would have produce.
SIGNAL LEVEL
NOISE
LEVEL
Before Pre-emphasis After Pre-emphasis
De-emphasis Network
Is a low pass filter that attenuates the higher
frequency signals at the receiver after the
demodulation has been performed and restores the
original amplitude-versus frequency characteristics to
the information signals.
FM and PM
FM to PM (indirect) – an FM modulator preceded by a
differentiator (high-pass filter) generates PM waveform.
P M to FM (indirect) – a PM modulator preceded by an
integrator (low-pass filter) produces an FM waveform.
APPLICATIONS
1. COMMERCIAL RADIO BROADCASTING
2. TELEVISION SOUND TRANSMISSION
3. TWO-WAY FM RADIO
4. MOBILE TELEPHONE SERVICE
5. CELLULAR RADIO SYSTEM
6. FM MICROWAVE RADIO COMMUNICATIONS
ADVANTAGES OF ANGLE OVER AMPLITUDE
MODULATION
• Noise Immunity
• Signal-to-Noise Ratio Improvement
• Capture Effect
• Efficiency of utilized power
DISADVANTAGES OF ANGLE OVER AMPLITUDE
MODULATION
• Wider Bandwidth for Transmission
• Circuit Complexity and Cost
END
