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TELECOMMUNICATIONS
ENGINEERING
Analog Transmission Systems
INSTRUCTOR
MD. MAMUNUR RASHID
TONMOY
Faculty of Engineering
Department of Electrical and Electronic
Engineering
Types of Analog Modulation
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Types of Analog Modulation:
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
Amplitude Modulation (AM)
Angle Modulation
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
Frequency Modulation (FM)
Phase Modulation (PM)
Amplitude Modulation (AM)
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
In AM, the information signal varies the amplitude of the carrier sine wave.
The instantaneous value of the carrier amplitude changes in accordance with the
amplitude and frequency variations of the modulating signal.

The carrier frequency remains constant during the modulation process, but its
amplitude varies in accordance with the modulating signal.

An increase in the amplitude of the modulating signal causes the amplitude of
the carrier to increase.
An increase or a decrease in the amplitude of the modulating signal causes a
corresponding increase or decrease in both the positive and the negative peaks
of the carrier amplitude.
An imaginary line connecting the positive peaks and negative peaks of the
carrier waveform (the dashed line in Fig:1) gives the exact shape of the
modulating information signal. This imaginary line on the carrier waveform is
known as the envelope.


Amplitude Modulation (AM)
The signals illustrated in Figs.1 and 2
show the variation of the carrier amplitude
with respect to time and are said to be in
the time domain.

Fig. 2: A simplified method of representing an
AM high-frequency sine wave.
Fig. 1: Amplitude modulation. (a) The modulating or
information signal. (b) The modulated carrier.
Amplitude Modulation (AM)
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In amplitude modulation, it is particularly important that the peak value of the
modulating signal be less than the peak value of the carrier. Mathematically,
Vm > Vc
Keep in mind that the peak value of the carrier is the reference point for the
modulating signal; the value of the modulating signal is added to or subtracted
from the peak value of the carrier.
The instantaneous value of either the top or the bottom voltage envelope can be
computed by using the equation:
v1 = Vc + vm = Vc + Vm sin 2πfmt
which expresses the fact that the instantaneous value of the modulating signal
algebraically adds to the peak value of the carrier.

Thus we can write the instantaneous value of the complete modulated wave v2 by
substituting v1 for the peak value of carrier voltage Vc as follows:
v2 = v1 sin 2πfct
v2 = (Vc + Vm sin 2πfmt) sin 2πfct = Vc sin 2πfct + (Vm sin 2πfmt) (sin 2πfct )
Amplitude Modulation (AM)
v2 = (Vc + Vm sin 2πfmt) sin 2πfct = Vc sin 2πfct + (Vm sin 2πfmt) (sin 2πfct )
Where v2 is the instantaneous value of the AM wave (or vAM), Vc sin 2πfct is the
carrier waveform, and (Vm sin 2πfmt) (sin 2πfct ) is the carrier waveform multiplied by
the modulating signal waveform. It is the second part of the expression that is
characteristic of AM.
Fig. 3: Amplitude modulator showing input and output signals.
Amplitude Modulation (AM)

Modulation Index:
As stated previously, for undistorted AM to occur, the modulating signal voltage, Vm
must be less than the carrier voltage, Vc.
m = Vm /Vc
Here, m is the modulation index.

Percentage of modulation:
Multiplying the modulation index by 100 gives the percentage of modulation. For
example, if the carrier voltage is 9V and the modulating signal voltage is 7.5V, the
modulation factor is 0.8333 and the percentage of modulation is 0.833*100 = 83.33.
Amplitude Modulation (AM)

Overmodulation and Distortion:
The modulation index should be a number between 0 and 1. If the amplitude of the
modulating voltage is higher than the carrier voltage, m will be greater than 1,
causing distortion of the modulated waveform.
Simple distortion is illustrated in Fig. 4, Here a sine wave information signal is
modulating a sine wave carrier, but the modulating voltage is much greater than the
carrier voltage, resulting in a condition called overmodulation.
Fig. 4: Distortion of the envelope
caused by overmodulation where
the modulating signal amplitude
Vm is greater than the carrier
signal Vc .
Amplitude Modulation (AM)
 Sidebands and the Frequency Domain:
Whenever a carrier is modulated by an information signal, new signals at different
frequencies are generated as part of the process. These new frequencies, which are
called side frequencies, or sidebands.
The sidebands occur at frequencies that are the sum and difference of the carrier
and modulating frequencies.
 Sideband Calculations:
When only a single-frequency sine wave modulating signal is used, the modulation
process generates two sidebands.
If the modulating signal is a complex wave, such as voice or video, a whole range
of frequencies modulate the carrier, and thus a whole range of sidebands are
generated.
Amplitude Modulation (AM)
The upper sideband fUSB and lower sideband fLSB are computed as:
and
fUSB = fc + fm
fLSB = fc - fm
where fc is the carrier frequency and fm is the modulating frequency.
The existence of sidebands can be demonstrated mathematically, starting with the
equation for an AM signal described previously:
v2 = Vc sin 2πfct + (Vm sin 2πfmt) (sin 2πfct )
By using the trigonometric identity that says that the product of two sine waves is:
sin A sin B = cos [(A -B)/2 ] - [cos (A+B)/2]
and substituting this identity into the expression a modulated wave, the instantaneous
amplitude of the signal becomes:
v2 = Vc sin 2πfct + [(Vm / 2) cos 2πt (fc - fm)] - [(Vm / 2) cos 2πt (fc + fm)]
Carrier
LSB
USB
Amplitude Modulation (AM)
 For
example, assume that a 400-Hz tone modulates a 300-kHz carrier. The upper
and lower sidebands are:
 fUSB
 fLSB

= 300,000 + 400 = 300,400 Hz or 300.4 kHz
= 300,000 - 400 = 299,600 Hz or 299.6 kHz
Frequency-Domain Representation of AM:
Another method of showing the sideband signals is to plot the carrier and sideband
amplitudes with respect to frequency, as in Fig. 5. Here the horizontal axis represents
frequency, and the vertical axis represents the amplitudes of the signals.
Fig. 5: A frequency-domain
an AM signal (voltage).
display
of
Amplitude Modulation (AM)
Figure 6 shows the relationship between the time- and frequency-domain displays
of an AM signal. The time and frequency axes are perpendicular to each other. The
amplitudes shown in the frequency-domain display are the peak values of the carrier
and sideband sine waves.
Fig. 6: The relationship between the time and frequency domains.
Amplitude Modulation (AM)
Whenever the modulating signal is more complex than a single sine wave tone,
multiple upper and lower sidebands are produced by the AM process.
For example, a voice signal consists of many sine wave components of different
frequencies mixed together. Recall that voice frequencies occur in the 300- to 3000Hz range. Therefore, voice signals produce a range of frequencies above and below
the carrier frequency, as shown in Fig. 7. These sidebands take up spectrum space.
The total bandwidth of an AM signal is calculated by computing the maximum and
minimum sideband frequencies. This is done by finding the sum and difference of
the carrier frequency and maximum modulating frequency (3000 Hz, or 3 kHz, in Fig.
7).
Fig: 7: The upper and lower
sidebands of a voice modulator
AM signal.
Amplitude Modulation (AM)
Example:
For example, if the carrier frequency is 2.8 MHz (2800 kHz), then the maximum and
minimum sideband frequencies are:
fUSB = 2800 – 3 = 2803 kHz and fLSB = 2800 – 3 = 2797 kHz

The total bandwidth is simply the difference between the upper and lower sideband
frequencies:
BW = fUSB - fLSB = 2803 – 2797 = 6 kHz
As it turns out, the bandwidth of an AM signal is twice the highest frequency in the
modulating signal: BW = 2fm, where fm is the maximum modulating frequency. In the
case of a voice signal whose maximum frequency is 3 kHz, the total bandwidth is :
BW = 2(3 kHz) = 6 kHz
Amplitude Modulation (AM)
Single-Sideband Communications:
Two-thirds of the transmitted power appears in the carrier which itself conveys no
information. The real information is contained within the sidebands.

One way to overcome this problem is simply to suppress the carrier. By
suppressing the carrier, the resulting signal is simply the upper and lower
sidebands. Such a signal is referred to as a Double-Sideband suppressed carrier
(DSB-SC). Double-Sideband suppressed carrier modulation is simply a special
case of AM with no carrier.
Double and Single Sidebands:
Amplitude Modulation generates two sets of sidebands, each containing the same
information. The information is redundant in an AM or DSB signal. Therefore, all the
information can be conveyed in just one sideband.

Eliminating one sideband produces a single sideband (SSB) signal.
Eliminating the carrier and one sideband produces a more efficient AM Signal.
Amplitude Modulation (AM)

DSB Signals:
Fig. 8: A frequency-domain display of DSB signal.
Amplitude Modulation (AM)
SSB Signals:
In DSB transmission, since the sidebands are the sum and difference of the carrier
and modulating signals, the information is contained in both sidebands. As it turns
out, there is no reason to transmit both sidebands in order to convey the
information. One side-band can be suppressed; the remaining sideband is called a
single-sideband suppressed carrier (SSSC or SSB) signal.

Fig. 9: SSB in frequency domain.
Amplitude Modulation (AM)
Vestigial sideband:
An unusual form of AM is that used in TV broadcasting. A TV signal consists of the
picture (video) signal and the audio signal, which have different carrier
frequencies. The audio carrier is frequency-modulated, but the video information
amplitude-modulates the picture carrier. The picture carrier is transmitted, but one
sideband is partially suppressed.
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Video information typically contains frequencies as high as 4.2 MHz.
A fully amplitude-modulated TV signal would then occupy 2(4.2 MHz)= 8.4 MHz.
This is an excessive amount of bandwidth that is wasteful of spectrum space
because not all of it is required to reliably transmit a TV signal.
To reduce the bandwidth to the 6-MHz maximum allowed by the FCC for TV signals,
a portion of the lower sideband of the TV signal is suppressed, leaving only a small
part, or vestige, of the lower sideband.
Amplitude Modulation (AM)
This arrangement, known as a vestigial sideband (VSB) signal, is illustrated in Fig.
10. Video signals above 0.75 MHz (750 kHz) are suppressed in the lower (vestigial)
sideband, and all video frequencies are transmitted in the upper sideband.
Fig. 10: Vestigial sideband transmission of a TV picture signal.
Frequency Modulation (FM)
Frequency Modulation:
In Frequency Modulation, the carrier’s instantaneous frequency deviation from its
unmodulated value varies in proportion to the instantaneous amplitude of the
modulating signal.

Fig. 11: Different types of
Modulation
Frequency Modulation (FM)

The FM signal s(t) define by Equation below is a nonlinear function of the
modulating signal m(t) which makes frequency modulation a nonlinear modulation
process.

Consider then a sinusoidal modulating signal define by:
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The instantaneous frequency of the resulting FM signal is:

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The quantity Δf is called the frequency deviation, representing the maximum
departure of the instantaneous frequency of the FM signal form the carrier frequency
fc.
A fundamental characteristic of an FM signal is that the frequency deviation Δf is
proportional to the amplitude of the modulating signal and is independent of the
modulating frequency.
Frequency Modulation (FM)
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The angle θi(t) of the FM signal is obtained as:

The ratio of the frequency deviation Δf to the modulation frequency fm is
commonly called the modulation index of the FM signal.

The modulation index is denoted by β:
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The parameter β represents the phase deviation of the FM signal, i.e. the
maximum departure of the angle θi(t) from the angle 2πfct of the unmodulated
carrier. β is measured in radians.

The FM signal itself is given by:
Frequency Modulation (FM)
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Depending on the value of the modulation index β, we may distinguish two
cases of frequency modulation:
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
Narrow-band FM, for which β is small compared to one radian.
Wide-band FM, for which β is large compared to one radian.
Narrow-band frequency modulation:
Expanding the last equation, we get : (Assuming β is small compared to one radian)

This expression is somewhat similar to the corresponding one defining an AM signal:
where μ is the modulation factor of the AM signal.
Frequency Modulation (FM)
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Wide-band Frequency Modulation:

Final Equation:
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We can develop further insight into the behavior of the Bessel function Jn(β) by
making use of the following properties:

For n even, we have Jn(β)=J-n(β); on the other hand, for n odd, we have Jn(β)= -J-n(β);
That is:

For small values of the modulation index β, we have:
Carson’s Rule
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Carson’s Rule:
An approximation for the bandwidth of an FM signal is given by:
BW = 2(Maximum frequency deviation + highest modulated frequency)
BW = 2 (∆fc + fm)

NBFM is defined by the condition:
∆f<<W
BFM=2W
This is just like AM. No advantage here.

WBFM is defined by the condition:
This is what we have for a true FM signal.
∆f>>W
BFM=2 ∆f
Frequency Modulation (FM)
Frequency Modulation (FM)
Frequency Modulation (FM)
END