Module 2

Amplitude Modulation Fundamentals, AM circuits, Frequency Division

Multiplexing

➢ Modulation is an electronic technique for transmitting information efficiently from one place
to another.
1. Baseband transmission:
In a communication system, baseband information signals like audio, video, digital
signals can be sent directly and unmodified over the medium. Such a transmission is
called baseband transmission.
e.g. In many telephones, intercom systems, wired LAN’s, computer networks using
ethernet cables
2. Broadband Transmission:
The message signal or baseband intelligence signal or baseband voice, video or digital
signal modify another high frequency signal, the carrier. The carrier wave is usually a
sine wave generated by an oscillator. The intelligence signal changes the carrier in a
unique way. The modulated carrier is amplified and sent to the antenna for transmission.
This process is called broadband transmission.
e.g. cellular networks, cable TV, Satellite communication, fiber optics, internet access
using coaxial cables.

Need for Modulation:

1. Reduces the height of antenna

2. Prevents Interference and allows multiplexing
3. Increases the range of communication
4. Improves the signal quality.
5. Enables wireless communication

1. Reduces the height of antenna

Height of an antenna is a function of wavelength (λ). The minimum height of an antenna

is given by λ/4.
𝜆 𝑐
𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑎𝑛 𝑎𝑛𝑡𝑒𝑛𝑛𝑎 = =
4 4𝑓

𝑤ℎ𝑒𝑟𝑒, 𝑐 = 3𝑋108 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡

𝑓 𝑖𝑠 𝑡ℎ𝑒 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑖𝑛𝑔 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

3𝑋108
𝑙𝑒𝑡 𝑓 = 15𝑘𝐻𝑧, 𝑎𝑛𝑡𝑒𝑛𝑛𝑎 ℎ𝑒𝑖𝑔ℎ𝑡 = = 5000 𝑚𝑒𝑡𝑒𝑟𝑠
4𝑋15000
3𝑋108
𝑙𝑒𝑡 𝑓 = 1𝑀𝐻𝑧, 𝑎𝑛𝑡𝑒𝑛𝑛𝑎 ℎ𝑒𝑖𝑔ℎ𝑡 = = 75 𝑚𝑒𝑡𝑒𝑟𝑠
4𝑋1000000
Direct transmission of low frequency signals requires impractically tall antennas.
Modulation shifts the signal to a higher frequency, reducing the required antenna height.
 2. Prevents Interference and allows multiplexing

All audio signals ranges from 20Hz to 20 KHz. Transmission of signal from various
sources causes mixing of signals. So, it is difficult to separate these signals at the
receivers. Using Modulation, signal from each source is modulated with different
carrier frequency. This process prevents interference, enabling efficient multiplexing
and ensuring clear signal transmission.

3. Increases the range of Communication

Low frequency signals have poor attenuation and they get highly attenuated, So they
cannot be transmitted for longer distances. Since Modulation increases the frequency
of the signa, so they can be transmitted over longer distances.

4. To improve the signal Quality

Low frequency signals are more affected by noise and distortion during transmission.
Since modulation shifts signals to high frequency, where noise interference is less.

5. To Enable wireless communication

Wireless communication relies on high frequency modulated signals for transmission.
Low frequency signals cannot be efficiently radiated as Electro Magnetic waves.

Amplitude Modulation Fundamentals:

Amplitude modulation is the process of varying the amplitude of the carrier signal in
accordance with the instantaneous amplitude of the modulating signal.

A sine wave modulating signal can be expressed as

𝑣𝑚 = 𝑉𝑚 sin(2𝜋𝑓𝑚 𝑡) − − − − − − − − − (1)

𝑣𝑚 𝑖𝑠 𝑡ℎ𝑒 𝑖𝑛𝑠𝑡𝑎𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑠𝑖𝑔𝑛𝑎𝑙.

𝑉𝑚 𝑖𝑠 𝑡ℎ𝑒 𝑝𝑒𝑎𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑠𝑖𝑔𝑛𝑎𝑙.

𝑓𝑚 𝑖𝑠 𝑡ℎ𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑛𝑔 𝑠𝑖𝑔𝑛𝑎𝑙.

The carrier wave can be expressed as

𝑣𝑐 = 𝑉𝑐 sin(2𝜋𝑓𝑐 𝑡) − − − − − − − − − (1)

𝑣𝑐 𝑖𝑠 𝑡ℎ𝑒 𝑖𝑛𝑠𝑡𝑎𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑠𝑖𝑔𝑛𝑎𝑙.

𝑉𝑐 𝑖𝑠 𝑡ℎ𝑒 𝑝𝑒𝑎𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑢𝑛𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑒𝑑 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑠𝑖𝑔𝑛𝑎𝑙.

𝑓𝑐 𝑖𝑠 𝑡ℎ𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑠𝑖𝑔𝑛𝑎𝑙.

In the Figure shown above, the modulating signal uses the peak value of the carrier rather than
zero as its reference point. The envelope of the modulating signal varies above and below the
peak carrier amplitude. That is the zero-reference line of the modulating signal coincides with
the peak value of the unmodulated carrier.
The instantaneous value of either the top or the bottom voltage envelope can be computed by
using the equation

𝑣1 = 𝑉𝑐 + 𝑣𝑚 − − − − − − − − − − − − − (3)

𝑣1 = 𝑉𝐶 + 𝑉𝑚 sin(2𝜋𝑓𝑐 𝑡) − − − − − − − − − − − − − − − (4)

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.

𝑣𝐴𝑀 = 𝑣1 sin(2𝜋𝑓𝑐 𝑡)

𝑣𝐴𝑀 = (𝑉𝐶 + 𝑉𝑚 sin(2𝜋𝑓𝑚 𝑡)) sin(2𝜋𝑓𝑐 𝑡)

𝑣𝐴𝑀 = 𝑉𝑐 sin(2𝜋𝑓𝑐 𝑡) + 𝑉𝑚 sin(2𝜋𝑓𝑚 𝑡) sin(2𝜋𝑓𝑐 𝑡) − − − − − − − − − − − − − −(5)

In equation (5) 𝑉𝑐 sin(2𝜋𝑓𝑐 𝑡) 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑤𝑎𝑣𝑒𝑓𝑜𝑟𝑚.

𝑉𝑚 sin(2𝜋𝑓𝑚 𝑡) sin(2𝜋𝑓𝑐 𝑡) 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑤𝑎𝑣𝑒𝑓𝑜𝑟𝑚 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑛𝑔 𝑠𝑖𝑔𝑛𝑎𝑙

Waveform.
A circuit that changes a lower-frequency baseband or intelligence signal to a higher-frequency
signal is usually called a modulator. A circuit used to recover the original intelligence signal
from an AM wave is known as a detector or demodulator.

Modulation Index and Percentage of Modulation

The ratio of the peak amplitude of the modulating signal and the peak amplitude of the carrier
signal is known as the modulation index (also called the modulating factor or coefficient, or
the degree of modulation).

𝑉𝑚
𝑚= − − − − − − − − − (6)
𝑉𝑐
Multiplying the modulation index by 100 gives the percentage of modulation. For example. if
the carrier voltage is 9 V and the modulating signal voltage is 7.5 V. the modulation factor is
0.8333 and the percentage of modulation is 0.833 X 100 = 83.33.
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, i.e. causing distortion of the modulated waveform. This condition is called
overmodulation.

If the distortion is great enough, the intelligence signal become unintelligible. Distortion of
voice transmissions produces garbled, harsh, or unnatural sounds in the speaker. Distortion of
video signals produces a scrambled und inaccurate picture on a TV screen.

The ideal condition for AM is when Vm=Vc or m=1 which gives 100 percent modulation. This
results in the greatest output power at the transmitter and the greatest output voltage at the
receiver, with no distortion.

Percentage of Modulation

𝑽𝒎𝒂𝒙 − 𝑽𝒎𝒊𝒏 = 𝟐𝑽𝒎

𝑽𝒎𝒂𝒙 − 𝑽𝒎𝒊𝒏
𝑽𝒎 = − − − − − − − − − − − (𝟏)
𝟐
𝑽𝒄 = 𝑽𝒎𝒂𝒙 − 𝑽𝒎
(𝑽𝒎𝒂𝒙 − 𝑽𝒎𝒊𝒏 )
𝑽𝒄 = 𝑽𝒎𝒂𝒙 −
𝟐
𝑽𝒎𝒂𝒙 + 𝑽𝒎𝒊𝒏
𝑽𝒄 = − − − − − − − − − − − −(𝟐)
𝟐
𝑽𝒎 𝑽𝒎𝒂𝒙 − 𝑽𝒎𝒊𝒏
𝒎𝒐𝒅𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒊𝒏𝒅𝒆𝒙, 𝒎 = = − − − − − −(𝟑)
𝑽𝒄 𝑽𝒎𝒂𝒙 + 𝑽𝒎𝒊𝒏
The amount or depth of AM is more commonly expressed as the percentage of modulation
rather than as a fractional value. The percentage of modulation is 100 X m. The maximum
amount of modulation without signal distortion is 100 percent. where Vm and Vc are equal. At
this time, Vmin=0 and Vmax=2Vm , where Vm is the peak value of the modulating signal.
Example :

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, occur in the frequency spectrum directly above and directly below the carrier
frequency. More specifically, 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.

The upper sideband fUSB and the lower sideband fLSB are computed as

𝑓𝑈𝑆𝐵 = 𝑓𝑐 + 𝑓𝑚 𝑓𝐿𝑆𝐵 = 𝑓𝑐 − 𝑓𝑚

𝑤ℎ𝑒𝑟𝑒 𝑓𝑐 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑎𝑛𝑑 𝑓𝑚 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑛𝑔 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

𝑣𝐴𝑀 = 𝑉𝑐 (1 + 𝑚𝑠𝑖𝑛2𝜋𝑓𝑚 𝑡)𝑠𝑖𝑛2𝜋𝑓𝑐 𝑡------------------(1)

𝑣𝐴𝑀 = 𝑉𝑐 sin(2𝜋𝑓𝑐 𝑡) + 𝑚𝑉𝑐 𝑠𝑖𝑛2𝜋𝑓𝑚 𝑡𝑠𝑖𝑛2𝜋𝑓𝑐 𝑡------------------(2)

By using the trigonometric identity

cos (𝐴 − 𝐵) cos (𝐴 + 𝐵)
𝑠𝑖𝑛𝐴 𝑠𝑖𝑛𝐵 = −
2 2
𝑚𝑉𝑐
𝑣𝐴𝑀 = 𝑉𝑐 𝑠𝑖𝑛2𝜋𝑓𝑐 𝑡 + [cos (2𝜋𝑡(𝑓𝑐 − 𝑓𝑚 ) − cos (2𝜋𝑡(𝑓𝑐 + 𝑓𝑚 )] --------------------(3)
2

Where the first term is the carrier, the second term containing the difference (𝑓𝑐 − 𝑓𝑚 ) is the
lower side band and the third term containing the sum (𝑓𝑐 + 𝑓𝑚 ) is the upper side band.
An AM signal is a composite signal formed from several components.

By taking fourier transform of equation (3) we get

𝑉𝑐 𝑚𝑉𝑐
𝑣𝐴𝑀 (𝑓) = [𝛿(𝑓 − 𝑓𝑐) − 𝛿(𝑓 + 𝑓𝑐)] + [𝛿(𝑓 − (𝑓𝑐 − 𝑓𝑚 )) + 𝛿(𝑓 + (𝑓𝑐 − 𝑓𝑚 ))]
𝑗2 4
𝑚𝑉𝑐
− [𝛿(𝑓 − (𝑓𝑐 + 𝑓𝑚 )) + 𝛿(𝑓 + (𝑓𝑐 + 𝑓𝑚 ))] − − − − − − − (4)
4
By taking the magnitude of the above equation

We have carrier component at 𝑓 = ±𝑓𝑐

Upper sideband component at 𝑓 = ±(𝑓𝑐 + 𝑓𝑚 )

Lower sideband component at 𝑓 = ±(𝑓𝑐 − 𝑓𝑚 )

frequency(f)

Bandwidth of AM signal:

𝐵𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ = 𝑓𝑈𝑆𝐵 − 𝑓𝐿𝑆𝐵

= 𝑓𝑐 + 𝑓𝑚 − (𝑓𝑐 − 𝑓𝑚 )

BW = 2𝑓𝑚

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 signal consists of many sine wave components of different frequencies mixed
together. The voice frequencies occur in the 300- to 3000-Hz range.

Therefore voice signal produce a range of frequencies above and below the carrier frequency
as shown in below Figure.
These sidebands take up spectrum space. The total bandwidth of an AM signal is calculated by
computing the maximum and minimum sideband frequencies

For example, if the carrier frequency is 2.8 M Hz (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 the difference between the upper and lower sideband frequencies:

BW =fUSB – fLSB= 2803 - 2797 = 6 kHz

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 simply
BW = 2fm= 2X 3000=6kHz.

Problem:

Example: AM broadcast station

An AM broadcast station has a total bandwidth of 10 kHz. In addition, AM broadcast stations
are spaced every 10 kHz across the spectrum from 540 to 1600kHz. The sidebands from the
first AM broadcast frequency extend down to 535 kHz and up to 545 kHz, forming a 10-kHz
channel for the signal. The highest channel frequency is 1600 kHz with sidebands extending
from 1595 up to 1605 kHz. There are a total of 107 10-kHz wide channels for AM radio
stations.
 Frequency spectrum of AM broadcast band

AM power:
In radio transmission, the AM signal is amplified by a power amplifier and fed to the antenna.

The AM signal is a composite of several signal voltages namely, the carrier and the two
sidebands and each of these signals produces power in the antenna. The total transmitted power
𝑃𝑇 is simply the sum of the carrier power 𝑃𝑐 and the power in the two sidebands 𝑃𝑈𝑆𝐵 𝑎𝑛𝑑 𝑃𝐿𝑆𝐵 .

𝑃𝑇 = 𝑃𝑐 + 𝑃𝑈𝑆𝐵 + 𝑃𝐿𝑆𝐵 − − − − − − − −(1)

𝑣𝐴𝑀 = 𝑉𝑐 (1 + 𝑚𝑠𝑖𝑛2𝜋𝑓𝑚 𝑡)𝑠𝑖𝑛2𝜋𝑓𝑐 𝑡------------------(2)

𝑣𝐴𝑀 = 𝑉𝑐 sin(2𝜋𝑓𝑐 𝑡) + 𝑚𝑉𝑐 𝑠𝑖𝑛2𝜋𝑓𝑚 𝑡𝑠𝑖𝑛2𝜋𝑓𝑐 𝑡 − − − −(3)

𝑚𝑉𝑐 𝑉𝑚
𝑣𝐴𝑀 = 𝑉𝑐 𝑠𝑖𝑛2𝜋𝑓𝑐 𝑡 + cos (2𝜋𝑡(𝑓𝑐 − 𝑓𝑚 )) − cos (2𝜋𝑡(𝑓𝑐 + 𝑓𝑚 ))
2 2
where the first term is the carrier, the second term is the lower sideband, and the third term is
the upper sideband.
𝑉𝑚
Modulation index, 𝑚 =
𝑉𝑐

𝑉𝑚 = 𝑚𝑉𝑐
The total power becomes

𝑃𝑇 = 𝑃𝑐 + 𝑃𝑈𝑆𝐵 + 𝑃𝐿𝑆𝐵

𝑉𝑐2 𝑚2 𝑉𝑐2 𝑚2 𝑉𝑐2

𝑃𝑇 = + +
2𝑅 8𝑅 8𝑅
𝑉𝑐2 𝑚𝑉𝑐2
𝑃𝑇 = +
2𝑅 4𝑅
𝑉𝑐2 𝑚2
𝑃𝑇 = (1 + )
2𝑅 2
𝑚2
𝑃𝑇 = 𝑃𝑐 (1 + )
2
𝑉2
𝑐 𝑚2 𝑉𝑐2 𝑚2
Carrier power, 𝑃𝑐 = 2𝑅 𝑠𝑖𝑑𝑒𝑏𝑎𝑛𝑑 𝑝𝑜𝑤𝑒𝑟, 𝑃𝑈𝑆𝐵 = 𝑃𝐿𝑆𝐵 = = 𝑃𝑐
8𝑅 4
The total sideband power 𝑃𝑆𝐵 = 𝑃𝑈𝑆𝐵 + 𝑃𝐿𝑆𝐵

𝑚2 𝑚2 𝑚2
𝑃𝑆𝐵 = 𝑃 + 𝑃 = 𝑃
4 𝑐 4 𝑐 2 𝑐

In the real world, it is difficult to determine AM power by measuring the output voltage and
𝑉2
calculating the power with the expression 𝑃 = . However, it is easy to measure the current
𝑅
in the load. For example, you can use an RF ammeter connected in series with an antenna to
observe antenna current. When the antenna impedance is known, the output power is easily
calculated by using the formula

𝑃𝑇 = 𝐼𝑇2 𝑅

𝑚2
𝑃𝑇 = 𝑃𝑐 (1 + )
2
𝑚2
𝐼𝑇2 𝑅 = 𝐼𝐶2 𝑅 (1 + )
2

𝑚2
𝐼𝑇2 = 𝐼𝐶2 (1 + )
2

𝑚2
𝐼𝑇 = 𝐼𝑐 √(1 + )
2

The carrier itself conveys no information. The carrier can be transmitted and received. but
unless modulation occurs, no information will be transmitted. When modulation occurs,
sidebands are produced. It is concluded that, all the transmitted information is contained
within the sidebands.

Assuming 100% modulation, where modulating factor m=1

𝑚2
𝑃𝑇 = 𝑃𝑐 (1 + )
2
3 2
𝑃𝑇 = 𝑃𝑐 ( ) 𝑃𝑐 = 𝑃𝑇
2 3

𝑃𝑇 = 𝑃𝑐 + 𝑃𝑈𝑆𝐵 + 𝑃𝐿𝑆𝐵

𝑃𝑇 = 𝑃𝑐 + 𝑃𝑆𝐵
 2 1
𝑃𝑆𝐵 = 𝑃𝑇 − 𝑃𝑐 = 𝑃𝑇 − 𝑃𝑇 = 𝑃𝑇
3 3
From the above equations it is concluded that, Only one-third of the total transmitted power is
allotted to the sidebands, and the remaining two-thirds is literally wasted on the carrier. The
carrier power represents two-thirds of the total transmitted power.

Efficiency of AM wave:
𝑈𝑠𝑒𝑓𝑢𝑙 𝑝𝑜𝑤𝑒𝑟
The Power efficiency of AM wave = 𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑤𝑒𝑟 𝑋 100%

𝑠𝑖𝑑𝑒𝑏𝑎𝑛𝑑 𝑝𝑜𝑤𝑒𝑟
% 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 𝑋 100%
𝑇𝑜𝑡𝑎𝑙 𝑝𝑜𝑤𝑒𝑟

𝑚2
%𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 2 𝑃𝑐 =
𝑚2
𝑋 100%
𝑚2 2 + 𝑚2
(1 + )
2 𝑃𝑐

𝑚2
%𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 𝑋100 %
2 + 𝑚2
1
For 100% modulation, m=1 %𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 3 𝑋100% = 33.33%

Advantages of AM or DSBFC (Double side band Full carrier):

1. It is widely used, because transmitters and receivers are less complex.

2. Cost effective

Disadvantages of AM:
1. Most of the transmitted power is wasted as carrier power, since carrier itself conveys
no information.
2. The bandwidth requirement of AM wave is 2fm, which is high. This is due to
transmission of both the sidebands. Only sideband is sufficient to transmit information.
Thus the bandwidth of DSB-FC is actually double than actually required.
3. AM wave gets easily affected due to noise. Since the information is contained in the
envelope, noise will change the envelope in a random manner. Hence the performance
of AM wave is poor in presence of noise.

Applications of AM wave

1. AM radio broadcasting
2. CB radio
3. TV broadcasting
4. Aircraft tower communication
5. AM is also widely used in combination with phase modulation to produce quadrature
amplitude modulation (QAM) which facilitates high-speed data transmissions in
modems. cable TV. and some wireless applications.
Problems:
1.
Single – Sideband Modulation
One way to improve the efficiency of amplitude modulation is to suppress the carrier signal
and eliminate one sideband. SSB is a form of AM that offers unique benefits in some types of
electronic communication.

DSB Signals:
The first step in generating an SSB signal is to suppress the carrier, leaving the upper and lower
sidebands. This type of signal is referred to as a double- sideband suppressed carrier (DSSC or
DSB) signal. The benefit is that no power is wasted on the carrier. Double-sideband suppressed
carrier modulation is simply a special case or AM with no carrier.
The DSB signal is obtained by multiplying carrier with modulating signal

𝑉𝐷𝑆𝐵 = 𝑉𝑚 sin(2𝜋𝑓𝑚 𝑡) 𝑋 𝑉𝑐 𝑠𝑖(2𝜋𝑓𝑐 𝑡)

𝑉𝑚 𝑉𝑐
= {cos(2𝜋(𝑓𝑐 − 𝑓𝑚 )𝑡 − cos(𝑓𝑐 + 𝑓𝑚 ) 𝑡} − − − −(1)
2

The DSB signal contains upper sideband component and lower sideband component. The
carrier component is suppressed.
A unique characteristic of the DSB signal is the phase transitions that occur at the lower-
amplitude portions of the wave. As shown in figure above, there are two adjacent positive-
going half-cycles at the null points in the wave indicates phase transitions.

As shown in the frequency domain display of a DSB signal, the spectrum space occupied by a
DSB signal is the same as that for a conventional AM signal.

Double-sideband suppressed carrier signals are generated by a circuit called a balanced

modulator. The purpose of the balanced modulator is to produce the sum and difference
frequencies but to cancel or balance out the carrier.

The elimination of the carrier in DSB AM saves considerable power.

DSB is not widely used because the signal is difficult to demodulate (recover) at the receiver.

One important application for DSB. however, is the transmission of the color information in a
TV signal.

SSB Signals:

a) Spectrum of SSB signal b) SSB signal

In DSB transmission, since the sidebands are the sum and difference of the carrier and
modulating signals, the information is contained in both sidebands. There is no reason to
transmit both sidebands in order to convey the information. One sideband can be suppressed,
the remaining sideband is called a single-sideband suppressed carrier (SSSC or SSB) signal.
SSB signals offer four major benefits.

1. The primary benefit of an SSB signal is that the spectrum space it occupies is only one-
half that of AM and DSB signals. This greatly conserves spectrum space and allows
more signals to be transmitted in the same frequency range.
2. All the power devoted to the carrier and the other sideband can be channeled into the
single sideband, producing a stronger signal that should carry farther and be more
reliably received at greater distances. Alternatively, SSB transmitters can be made
smaller and lighter than an equivalent AM or DSB transmitter because less circuitry
and power are used.
3. Because SSB signals occupy a narrower bandwidth, the amount of noise in the signal
is reduced.
 4. There is less selective fading of an SSB signal over long distances. An AM signal is
really multiple signals, at least a canier and two sidebands. These are on different
frequencies. So they are affected in slightly different ways by the ionosphere and upper
atmosphere. which have a great influence on radio signals of less than about 50 M Hz.
The carrier and sidebands may arrive at the receiver at slightly different times, causing
a phase shift that can in turn cause them to add in such a way as to cancel one another
rather than add up to the original AM signal. Such cancellation or selective fading is
not a problem with SSB since only one sideband is being transmitted.

Disadvantages of DSB and SSB

The main disadvantage of DSB and SSB signals is that they are harder to recover or demodulate
at the receiver. Demodulation depends upon the carrier being present. If the carrier is not
present, then it must be regenerated at the receiver and reinserted into the signal. To faithfully
recover the intelligence signal, the reinserted carrier must have the same phase and frequency
as those of original carrier. This is a difficult requirement.

To solve this problem, a low-level carrier signal is sometimes transmitted along with the two
sidebands in DSB or a single sideband in SSB. Because the carrier has a low power level, the
essential benefits of SSB are retained, but a weak carrier is received so that it can be amplified
and reinserted to recover the original information. Such a low-level carrier is referred to as a
pilot carrier. This technique is used in FM stereo transmissions as well as in the transmission
of the color information in a TV picture.

Signal Power Considerations:

An SSB transmitter sends no carrier, so the carrier power is zero.

In SSB, the transmitter output is expressed in terms of peak envelope power(PEP),the

maximum power produced on voice amplitude peaks. PEP is computed by the equation

P = V2 / R.
2
𝑉𝑟𝑚𝑠
𝑃𝐸𝑃 =
𝑅
The PEP input power is simply the dc input power of the transmitter's final amplifier stage at
the instant of the voice envelope peak. It is the final amplifier stage dc supply voltage multiplied
by the maximum amplifier current that occurs at the peak or

𝑃𝐸𝑃 = 𝑉𝑠 𝐼𝑚𝑎𝑥

where Vs = amplifier supply voltage

Imax = current peak

The voice amplitude peaks are produced only when very loud sounds are generated during
certain speech patterns or when some word or sound is emphasized. During normal speech
levels, the input and output power levels are much less than the PEP level. The average power
is typically only one-fourth to one-third of the PEP value with typical human speech:
𝑃𝐸𝑃 𝑃𝐸𝑃
𝑃𝑎𝑣𝑔 = 𝑂𝑅 𝑃𝑎𝑣𝑔 =
3 4
Problem:

Applications of DSB and SSB

Both DSB and SSB techniques are widely used in communication.

SSB signals are still used in some two-way radios.

Two-way SSB communication is used in marine applications, in the military and by hobbyists
known as radio amateurs (hams).

DSB signals are used in FM and TV broadcasting to transmit two-channel stereo signals and
to transmit the color information for a TV picture.
Vestigial Sideband Modulation

In vestigial Sideband Modulation, along with one sideband a small portion of the other
sideband is also transmitted.

VSB modulation balances bandwidth efficiency of SSB and simplicity of DSB-SC signal
transmission.

VSB AM is 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 Video information typically contains frequencies as high as 4.2 MHz. A fully
amplitude-modulated TV signal would then occupy 2(4.2) = 8.4 MHz. This is an excessive
amount of bandwidth that is wasteful or 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 portion or vestige,
of the lower sideband. This arrangement, known as a vestigial sideband (VSB) signal. Video
signals above 0.75 MHz (750kHz) are suppressed in the lower (vestigial) sideband, and all
video frequencies are transmitted in the upper sideband.

The newer high-definition or digital TV also uses VSB but with multilevel digital modulation
called VSB.

Figure (3)

Amplitude Modulators
Amplitude modulators are generally one of two types:
1) Low level Amplitude Modulator
2) High level Amplitude Modulator
Low Level Amplitude Modulator
Low-level modulators generate AM with small signals and thus must be amplified considerably
if they are to be transmitted.
In low-level modulator circuits, the signals are generated at very low voltage and power
amplitudes. The voltage is typically less than 1V, and the power is in milliwatts. In systems
Using low-level modulation, the AM signal is applied to one or more linear amplifiers. as
shown in Figure (2) to increase its power level without distorting the signal. These amplifier
circuits: class A, class AB or class B which raise the level of the signal to the desired power
level before the AM signal is fed to the antenna.

Figure (2)

1. Diode Modulator:

Figure 1: Amplitude Modulation with a diode

One of the simplest amplitude modulators is the diode modulator. The practical implementation
shown in Figure 1.
It consists of a resistive mixing network, a diode rectifier, and an LC tuned circuit. The carrier
is applied to one input resistor and the modulating signal to the other. The mixed signals appear
across R3. This network causes the two signals to be linearly mixed, i.e., algebraically added
as shown in figure (c).

The composite waveform is applied to a diode rectifier. The diode is connected so that it is
forward-biased by the positive-going half-cycles of the input wave. During the negative
portions of the wave, the diode is cut off and no signal passes. The current through the diode is
a series of positive-going pulses whose amplitude varies in proportion to the amplitude of the
modulating signal as shown in figure(d).

These positive-going pulses are applied to the parallel tuned circuit made up of L and C. which
are resonant at the carrier frequency. Each time the diode conducts, a pulse of current flows
through the tuned circuit. The coil and capacitor repeatedly exchange energy, causing an
oscillation at the resonant frequency. The oscillation of the tuned circuit creates one negative
half-cycle for every positive input pulse. High amplitude positive pulses cause the tuned circuit
to produce high-amplitude negative pulses. Low-amplitude positive pulses produce
corresponding low-amplitude negative pulses. The resulting waveform across the tuned circuit
is an AM signal, as shown in figure (e).
The Q of the tuned circuit should be high enough to eliminate the harmonics and produce a
clean sine wave and to filter out the modulating signal and low enough that its bandwidth
accommodates the sidebands generated.
Because the nonlinear portion of the diode's characteristic curve occurs only at low voltage
levels, signal levels must be low, less than a volt, to produce AM. At higher voltages, the diode
current response is nearly linear. The circuit works best with millivolt-level signals.
 2. Transistor Modulator

Figure 2: A simple transistor Modulator

To perform modulation, we use non-linear circuits. These circuits can be passive or active.
Besides providing modulation, active circuits also gives power gain. Transistor is an active
device, whereas diode is passive. In practice, Transistor modulator is preferred over diode
modulator.

Transistor modulation consists of a resistive mixing network, a transistor, and an LC tuned

circuit as shown in above figure. The emitter-base junction of the transistor serves as a diode
and nonlinear device. Modulation and amplification occur as base current controls a larger
collector current. The LC tuned circuit oscillates (rings) to generate the missing half cycle. The
output is an AM wave.

High level Amplitude Modulator

High-level modulators produce AM at high power levels, usually in the final amplifier stage of
a transmitter.

In high-level AM, the modulator varies the voltage and power in the final RF amplifier stage
of the transmitter. The result is high efficiency in the RF amplifier and overall high-quality
performance.
Collector Modulator

The output stage of the transmitter is a high-power class C amplifier. Class C amplifiers
conduct for only a portion of the positive half-cycle of their input signal. The collector current
pulses cause the tuned circuit to oscillate (ring) at the desired output frequency. The tuned
circuit, therefore reproduces the negative portion of the carrier signal.

The modulator is a linear power amplifier that takes the low-level modulating signal and
amplifies it to a high-power level. The modulating output signal is coupled through modulation
transformer T1 to the class C amplifier. The secondary winding of the modulation transformer
is connected in series with the collector supply voltage Vcc of the class C amplifier.

With a zero-modulation input signal, there is zero-modulation voltage across the secondary of
T1, the collector supply voltage is applied directly to the class C amplifier. and the output carrier
is a steady sine wave.

When the modulating signal occurs, the ac voltage of the modulating signal across the
secondary of the modulation transformer is added to and subtracted from the dc collector
supply voltage. This varying supply voltage is then applied to the class C amplifier. causing the
amplitude of the current pulses through transistor Q1 to vary. As a result, the amplitude of the
carrier sine wave varies in accordance with the modulated signal.

When the modulation signal goes positive, it adds to the collector supply voltage, thereby
increasing its value and causing higher current pulses and a higher-amplitude carrier. When the
modulating signal goes negative, it subtracts from the collector supply voltage, decreasing it.

For 100 percent modulation, the peak of the modulating signal across the secondary of T1 must
be equal to the supply voltage. When the positive peak occurs, the voltage applied to the
collector is twice the collector supply voltage. When the modulating signal goes negative, it
subtracts from the collector supply voltage. When the negative peak is equal to the supply
voltage, the effective voltage applied to the collector of Q1 is zero. producing zero carrier
output as shown in figure (1).

In practice, 100 percent modulation cannot be achieved with the high-level collector modulator
circuit shown, because of the transistor's nonlinear response to small signals. To overcome this
problem, the amplifier driving the final class C amplifier is collector-modulated
simultaneously.
Figure (1)

Collector modulator Waveforms

Problem:
Amplitude Demodulators:
Demodulators, or detectors, are circuits that accept modulated signals and recover the original
modulating information.

Diode Detectors or Envelope Detector:

The simplest and most widely amplitude demodulator is the diode detector
As shown the AM signal is usually transformer-coupled and applied to a basic half wave
rectifier circuit consisting of D1 and R1 .

During positive half cycle of AM signal, the diode is forward biased, capacitor charges quickly
to peak value of input. When the input signal falls below capacitor voltage, diode becomes
reverse biased and the capacitor discharges through resistor R1.

As a result, the voltage across R1 is a series of positive pulses whose amplitude varies with the
modulating signal. A capacitor C1 connected across resistor R1 effectively filtering out the
carrier and thus recovering the original modulating signal.

The discharging time constant or C1 and R1 is chosen to be long compared to the period of the
carrier. As a result, the capacitor discharges only slightly during the time that the diode is not
conducting.

If the discharging time constant is too long, the capacitor discharge will be too slow to follow
the faster changes in the modulating signal. This is referred to as diagonal distortion.

If the discharging time constant is too short, the capacitor will discharge too fast and the carrier
will not be sufficiently filtered out.
1 1
𝑖. 𝑒. , 𝑅1 𝐶1 ≫ 𝑓 and 𝑅1 𝐶1 ≪ 𝑓
𝑐 𝑚

1 1
≪ 𝑅1 𝐶1 ≪
𝑓𝑐 𝑓𝑚
1
The charging time constant 𝑅𝑠 𝐶1 must be short compared with the carrier period 𝑓 , Where Rs
𝑐
is the internal resistance of the diode
1
i.e., 𝑅𝑠 𝐶 ≪
𝑓𝑐
When the next pulses comes along, the capacitor again charges to its peak value. When the
diode cuts off, the capacitor again discharges a small amount into the resistor. The resulting
waveform across the capacitor is a close approximation to the original modulating signal.
Because the capacitor charges and discharges, the recovered signal has a small amount or ripple
on it, causing distortion of the modulating signal.

Because the diode detector recovers the envelope of the AM signal, which is the original
modulating signal, the circuit is sometimes referred to as an envelope detector.

Distortion of the original signal can occur if the time constant of the load resistor R 1 and the
shunt filter capacitor C1 is too long or too short.

The dc component in the output is removed with a series coupling or blocking capacitor, C1

Diode detector waveforms:

Balanced Modulators: Lattice Modulators
A balanced modulator is a circuit that generates a DSB signal, suppressing the carrier and
leaving only the sum and difference frequencies at the output.

Lattice Modulators

Figure 1: Lattice Type balanced Modulator

One of the most popular and widely used balanced modulators is the diode ring or lattice
modulator, consisting of an input transformer T1, an output transformer T2 and four diodes
connected in a bridge circuit. The carrier signal is applied to the center taps of the input and
output transformers and the modulating signal is applied to the input transformer T1. The output
appears across the secondary of the output transformer T2.

operation of the circuit:

case 1: Without modulating signal

i) During Positive half cycle of the carrier

Assume that the modulating input is zero. When the polarity of the carrier is positive,
diodes D 1 and D2 are forward-biased and D3 and D4 are reverse biased and act as
open circuits. As shown in the circuit above, current divides equally in the upper and
lower portions of the primary winding of T2. The current in the upper part of the winding
produces a magnetic field that is equal and opposite to the magnetic field produced by
 the current in the lower half of the secondary. The magnetic fields thus cancel each
other out. No output is induced in the secondary and the carrier is effectively
suppressed.

ii) During the Negative half cycle of the carrier

When the polarity of the carrier reverses. as shown in above figure diodes D1 and D2 are revered
and diodes D3 and D4 conduct. Again, the current flows in the secondary winding of T1 and the
primary winding of T2 . The equal and opposite magnetic field produced in T2 cancel each other
out. The carrier is effectively balanced out and its output is zero. The degree of carrier
suppression depends on the degree of precision with which the transformers are made and the
placement of the center tap.

Case 2: With Modulating Signal

Now assume that a low-frequency sine wave is applied to the primary of T1 as the modulating
signal. The modulating signal appears across the secondary of T1.

The diode switches connect the secondary of T1 to the primary of T1 at different times
depending upon the carrier polarity.
When the carrier polarity is as shown in Fig.2, diodes D1 and D2 conduct and act as closed
switches. At this time, D3 and D4 are reverse biased and are effectively not in the circuit. As a
result, the modulating signal at the secondary of T1 is applied to the primary of T2 through D1
and D2.

When the carrier polarity reverses, D1 and D2 cut off and D3 and D4 conduct. Again, a portion
of the modulating signal at the secondary of T1 is applied to the primary of T2, but this time
the leads have been effectively reversed because of the connections of D3 and D4. The result is
a 180° phase reversal. With this connection, if the modulating signal is positive. the output will
be negative, and vice versa.
Figure 4: Waveforms in the lattice-type balanced modulator. (a) Carrier. (b) Modulating signal.
(c) DSB signal- primary (d) DSB output.

The carrier is operating at a considerably higher frequency than the modulating signal.
Therefore, the diodes switch off and on at a high rate of speed causing portions of the
modulating signal to be passed through the diodes at different times. The DSB signal appearing
across the primary of T2 as shown in figure 4 (c). The steep rise and fall of the waveform are
caused by the rapid switching of the diodes. Because of the switching action the waveform
contains harmonics of the carrier. The secondary of T2 is a resonant circuit as shown, and
therefore the high-frequency harmonic content is filtered out, leaving a DSB signal like that
shown in Figure 4 (d).
Frequency Division Multiplexing: Transmitter-Multiplexer, Receiver-
Demultiplexer.
Multiplexing is the process of simultaneously transmitting two or more individual signals over
a single communication channel, cable or wireless.

In frequency-division multiplexing (FDM), multiple signals share the bandwidth of a common

communication channel.

Transmitter-Multiplexers:

Figure 1: The transmitting end of an FDM system.

Figure 1, shows a general block diagram or an FDM system. Each signal to be transmitted feed
a modulator circuit. The carrier for each modulator (fc) is on a different carrier frequency. Each
input signal is given a portion of the bandwidth. The resulting spectrum is illustrated in Figure
below
Any of the standard kinds of modulation can be used, including AM, SSB, FM, PM, or any of
the various digital modulation method. The FDM process divides up the bandwidth of the
single channel into smaller equally spaced channels, each capable of carrying information in
sidebands. The modulator output containing the sideband information are added algebraically
in a linear mixer. The resulting output signal is a composite of all the modulated subcarrier.
This signal can be used to modulate a radio transmitter or can itself be transmitted over the
single communication channel. Alternatively, the composite signal can become one input to
another multiplexed system.

Receiver-Demultiplexers

The receiving portion of an FDM system is shown above. A receiver pick up the signal and
demodulate it, recovering the composite signal. This is sent to a group of bandpass filters, each
centered on one of the carrier frequencies. Each filter passes only its channel and rejects all
Sothers. A channel demodulator then recovers each original input signal.

FDM Applications: Telemetry, FM stereo Broadcasting., Telephone systems, Cable TV. S