Angle modulation

1. DIT
Dar es Salaam institute of Technology (DIT)
ETU 07123
Introduction to Communication System
Ally, J
jumannea@gmail.com

2. DIT
Angle Modulation

3. DIT
Angle modulation overview
 In the last subtopic, we investigated the effect of slowly varying the
amplitude of a sinusoidal carrier wave in accordance with the
baseband signal.
 There is another way of modulating a sinusoidal carrier wave,
namely, Angle Modulation in which the angle of the carrier wave is
varied according to the baseband signal.
 In this method of modulation, the amplitude of the carrier wave is
maintained constant
 An important feature of angle modulation is that it can provide better
discrimination against noise and interference than amplitude
modulation.
 However, this improvement in performance is achieved at the
expense of increased transmission bandwidth; that is, angle
modulation provides us with a practical means of exchanging channel
bandwidth for improved noise performance. Such a tradeoff
is not possible with amplitude modulation, regardless of its form.

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Basic definitions
 Let denote the angle of a modulated sinusoidal carrier, assumed to
be a function of the message signal. We express the resulting angle-
modulated wave as
 There are an infinite number of ways in which the angle may be
varied in some manner with the message (baseband) signal. However,
we shall consider only two commonly used methods, phase modulation
and frequency modulation, defined as follows:
1) Phase modulation (PM) is that form of angle modulation in which the
angle is varied linearly with the message signal m(t), as shown as
The term represents the angle of the unmodulated carrier; and the
constant represents the phase sensitivity of the modulator, expressed
in radians per volt on the assumption that m(t) is a voltage waveform.

5. DIT
Basic definitions(2)
The phase-modulated signal s(t) in the time domain is given by
2) Frequency modulation (FM) is that form of angle modulation in which
the instantaneous frequency is varied linearly with the message
signal m(t), as shown by
The term fc represents the frequency of the unmodulated carrier, and
the constant kf represents the frequency sensitivity of the modulator,
Integrating above equation with respect to time and multiplying the
result by 2π, we get
where, for convenience, we have assumed that the angle of the
unmodulated carrier wave is zero at t = 0. The frequency-modulated
signal in the time domain is given by

6. DIT
Frequency Modulation
 The FM signal s(t) is a nonlinear function of the modulating signal
m(t), which makes frequency modulation a nonlinear modulation
process.
 Consider then a sinusoidal modulating signal defined by
 The instantaneous frequency of the resulting FM signal equals
where
 The quantity is called the frequency deviation, representing the
maximum departure of the instantaneous frequency of the FM signal
from the carrier frequency
 A fundamental characteristic of an FM signal is that the frequency
deviation is proportional to the amplitude of the modulating signal
and is independent of the modulation frequency.

7. DIT
Frequency Modulation(2)
 The angle of the FM signal is obtained as
 The ratio of the frequency deviation to the modulation frequency
is commonly called the modulation index of the FM signal. We
denote it by and so write
and
The FM signal itself is given by
 Depending on the value of the modulation index , we may distinguish
two cases of frequency modulation:
 Narrowband FM, for which is small compared to one radian.
 Wideband FM, for which is large compared to one radian.

8. DIT
FM Bandwidth and Carson’s Rule
 Frequency Deviation: ∆f=kf max|m(t)|
 Maximum deviation of fi from fc: fi=fc+kfm(t)
 an approximate rule for the transmission bandwidth of an FM signal
generated by a single-tone modulating signal of frequency fm, as
follows:
The ralation is know as Carson’s Rule:
 B depends on maximum deviation from fc AND how fast fi changes
 Narrowband FM: ∆f<<fm⇒B≈2fm
 Wideband FM: ∆f>>fm⇒B≈2∆f

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Example 1
 In North America, the maximum value of frequency deviation is
fixed at 75 kHz for commercial FM broadcasting by radio. If we take
the modulation frequency W = 15 kHz,which is typically the
"maximum" audio frequency of interest in FM transmission, we find
that the corresponding value of the deviation ratio is
using carlson rule by replacing β by D, and replacing fm by W, the
approximate value of the transmission bandwidth of the FM wave is

10. DIT
Example 2
Determine the percent modulation of an FM signal which is
being broadcast in the 88-108 MHz band having a carrier
swing of 125kHz.
Solution:

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Narrowband FM
 Expanding the relation FM signal resulting from the use of a sinusoidal
modulating signal, we get
 Assuming that the modulation index is small compared to one
radian, we may use the following approximations:
and
hence
 Above equation defines the approximate form of a narrowband FM
signal produced by a sinusoidal modulating signal

12. DIT
Narrowband FM(2)
 The equation for narrowband FM signal can be expanded as
 This expression is somewhat similar to the corresponding
one defining an AM signal, which is as follows:
where is the modulation factor of the AM signal.
 We see that in the case of sinusoidal modulation, the basic
difference between an AM signal and a narrowband FM
signal is that the algebraic sign of the lower side frequency in
the narrowband FM is reversed.
 Thus, a narrowband FM signal requires essentially the same
transmission bandwidth (i.e., 2fm) as the AM signal.

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Generation of narrowband FM signal
 This modulator involves splitting the carrier wave into two paths.
One path is direct; the other path contains a -90 degree phase-shifting network
and a product modulator, the combination of which generates a DSB-SC
modulated signal.
 The difference between these two signals produces a narrowband FM signal,
but with some distortion.

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Generation of wideband FM signal
 There are two basic methods of generating frequency-modulated
signals by using Direct method and Indirect method
 In the direct method the carrier frequency is directly varied in
accordance with the input baseband signal, which is readily
accomplished using a voltage-controlled oscillator (VCO).
 In the indirect method, the modulating signal is first used to produce a
narrowband FM signal, and frequency multiplication is next used to
increase the frequency deviation to the desired level.
 The indirect method is the preferred choice for frequency modulation
when the stability of carrier frequency is of major concern as in
commercial radio broadcasting.

15. DIT
Generation of wideband FM signal by
Indirect method
 After band-pass filtering of the nonlinear device's output v(t), we have a new FM
signal defined by
 whose instantaneous frequency is

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FM Detection
 In theory just need differentiator and envelope detection for FM.
Many techniques used in practice (mostly VCO).
 Differentiator and Envelope Detector
 Zero Crossing Detector
 Uses rate of zero crossings to estimate fi
 Phase Lock Loop (PLL)
 Uses Voltage Controlled Oscillator (VCO) and feedback to
extract m(t)
∫++=′
t
fcfcc dmktftmkfAts
0
])(22sin[)](22[)( ττππππ

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FM Demodulation by VCO
Phase
Detector
Loop Amplifier and
Low Pass Filter
VCO
sfm(t) m(t)

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Noise in Analogue Modulation
 To undertake such a study we follow the customary practice by
formulating two models:
 Channel model, which assumes a communication channel that is
distortionless but perturbed by additive white Gaussian noise
(AWGN).
 Receiver model, which assumes a receiver consisting of an ideal
band-pass filter followed by an ideal demodulator appropriate for the
application at hand; the band-pass filter is used to minimize the
effect of channel noise.
 Figure which shows the noisy receiver model that combines the
above two assumptions.

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AM Signal Noise Analysis
 The channel signal-to-noise ratio for AM
 The output SNR of an AM receiver using an envelope detector is
 The figure of merit for AM is
 Consider modulating wave
 The corresponding AM wave is
where μ=kaAm is the modulation factor. For a load resistor of 1Ω,
when μ=1 (i.e. 100% modulation), we get the figure of merit equal to 1/3.

20. DIT
FM Signal Noise Analysis
 Channel signal-to-noise ratio
 Output signal-to-noise ratio
 Figure of merit for FM
 The modulated FM signal is
 For a load resistor of 1Ω,
 The output signal-to-noise ratio is
 where β=Δf/W is the modulation index, the figure of merit for FM is
FM offers the possibility of improved noise
performance over AM when
that is,

21. DIT
Thanks!
Technology changes but communication lasts.