# What is Amplitude Modulation, Derivations, Types,and Applications

The earliest AM signal was broadcasted in the year 1901 by an engineer Reginald Fessenden. He is a Canadian and he took a nonstop sparkle transmission as well as located a carbon-based microphone within the lead of an antenna. The sound waves affect the microphone by changing its resistance, and transmission intensity. Even though very simple, signals were easy to hear over a few hundred meters of distance, though there was a harsh sound will occur with the sparkle. By the beginning of nonstop sine wave signals, broadcasting improved extensively, and amplitude modulation will become common for voice transmissions. Currently, the amplitude is used in broadcasting the audio on the short-wave, long medium bands, as well as for bi-directional radio communication on VHF used for aircraft.

## What is Amplitude Modulation?

The amplitude modulation definition is, an amplitude of the carrier signal is proportional to (in accordance with) the amplitude of the input modulating signal. In AM, there is a modulating signal. This is also called an input signal or baseband signal (Speech for example). This is a low-frequency signal as we have seen earlier. There is another high-frequency signal called carrier. The purpose of AM is to translate the low-frequency baseband signal to a higher freq signal using the carrier. As discussed earlier, high-frequency signals can be propagated over longer distances than lower frequency signals. The derivatives of amplitude modulation include the following.

The modulating Signal (Input Signal) Vm = Vm sin ωmt

Where Vm is the instantaneous value and Vm is the maximum value of the modulating (input) signal.

fm is the frequency of the modulating (input) signal and ωm = 2π fm

The Carrier Signal Vc = Vc sin ωct

Where Vc is the instantaneous value and Vc is the maximum value of the carrier signal, fc is the frequency of the carrier signal and ωc = 2π fc.

The amplitude modulation equation is,

VAM = Vc +Vm= Vc + Vm sin ωmt
vAM = VAM sin θ = VAM sin ωct
= (Vc + Vm sin ωmt) sin ωct
= Vc (1+m sin ωmt) sin ωct where m is given by m = Vm/Vc

#### Modulation Index

Modulation Index is defined as the ratio of the amplitude of the modulating signal and the amplitude of the carrier signal. It is denoted by ‘m’

Modulation Index m = Vm/Vc

Modulation Index is also known as Modulation factor, Modulation coefficient or degree of modulation

“m” shall have a value between 0 and 1.

“m” when expressed as a percentage is called % modulation.

Vm = Vmax-Vmin/2

Vc = Vmax-Vm

Vc = Vmax- (Vmax-Vmin/2) = Vmax + Vmin/2

Therefore, Vm/Vc = (Vmax-Vmin/ Vmax + Vmin)

#### Critical Modulation

It happens when modulation Index (m) =1. Note, during critical modulation Vmin =0

M = Vm/Vc = (Vmax-Vmin/ Vmax + Vmin) = (Vmax/Vmax) = 1

Substitute V m = 0 Therefore at critical modulation m = Vm/Vc

Substitute m = 1. Therefore at critical modulation Vm = Vc

### What is Over Modulation and Sidebands of AM?

This can occur when m>1

That is (Vm / Vc) > 1. Therefore Vm > Vc. In other words, the modulating signal is greater than the carrier signal.

The AM signal will generate new signals called sidebands, at frequencies other than fc or fm.

We know that VAM = (Vc + m Vm sin ωmt) sin ωct

We also know that m = Vm / Vc. Therefore Vm = m.Vc

Therefore,

Case1: Both input signal and carrier signal are sine waves.

VAM = (Vc + m Vc sin ωmt) sin ωct

= Vc sin ωct + m Vc sin ωmt . Sin ωct

Recall SinA SinB = 1/2 [ cos (A-B) – cos (A + B)]

Therefore VAM = Vc sin ωct + [ mVc/2 cos (ωc – wm)t] ─ [mVc/2 cos (ωc + wm)t]

Where Vc sin ωct is carrier

mVc/2 cos (ωc – wm)t is lower side band

mVc/2 cos (ωc + wm)t I supper sideband

Therefore AM signal has three frequency components, Carrier, Upper Sideband and Lower Side Band.

Case 2: Both input signal and carrier signal are cos waves.

VAM = (Vc + m Vc cos ωmt) cos ωct

= Vc cos ωct + mVc cos ωmt. cos ωct

Recall Cos A Cos B =1/2  [cos (A ─B) + cos (A + B)]

Therefore VAM = Vc cos ωct + [mVc/2 cos (ωc – wm)t] + [mVc/2 cos (ωc + wm)t]

Where Vc cos ωct

mVc/2 cos (ωc – wm)t is lower sideband

mVc/2 cos (ωc + wm)t supper sideband

Therefore AM signal has three frequency components, Carrier, Upper Sideband and lower side Band

#### Bandwidth of AM

The bandwidth of a complex signal like AM is the difference between its highest and lowest frequency components and is expressed in Hertz (Hz). Bandwidth deals with only frequencies.

As shown in the following figure

Bandwidth = (fc – fm) – (fc + fm) = 2 fm

The power levels in carrier and sidebands

There are three components in the AM wave. Unmodulated carrier, USB & LSB.

Total Power of AM is = Power in the

Unmodulated carrier + Power in USB +Power in LSB

If R is the load, then Power in AM = V2c/R + VLSB2/R + VUSB2/2

#### Carrier Power

Peak carrier Power = V2c/R

Peak Voltage = Vc, therefore RMS voltage = Vc/√2

RMS carrier power =1/R [Vc/√2]2= V2c/ 2R

#### RMS Power in Side bands

PLSB = PUSB = VSB2/R = 1/R [mVc/2/√2]2

= m2 (Vc)2 / 8R= m2/4 X V2c/2R

We know that V2c/2R =Pc

Therefore PLSB = m2/4 x Pc

Total power = v2c/2R + m2Vc2/8R + m2Vc2/8R

v2c/2R [ 1 + (m2/4) + (m2/4)] =  Pc [ 1 + (m2/4) + (m2/4)]

PTotal = Pc [ 1 + m2/2 ]

Modulation Index in terms of Total Power (PTotal) and Carrier Power (Pc)

PTotal = Pc [1+m2/2]

PTotal/ Pc = [1+m2/2]

m2/2 = PTotal/Pc – 1

m = √2 (PTotal/Pc – 1)

#### Transmission Efficiency

In AM there are three power components Pc, PLSB and PUSB

Out of these Pc is an unmodulated carrier. It is wasteful as it carries no information at all.

The two sidebands carry, all the useful information and therefore useful power is spent only in Sidebands

#### Efficiency (η)

A ratio of transmitted power which contains the useful information (PLSB + PUSB) to the total transmitted power.

Transmission efficiency = (PLSB + PUSB) / (PTotal)

η = Pc [m2/4 + m2/4] / Pc [1 = m2/2] = m2/2+m2

η % = (m2/2+m2) X 100

#### Amplitude Demodulation

The inverse of the modulator and it recovers (decodes) the original signal (what was the modulating signal at the transmitter end) from the received AM signal.

#### Envelop Detector

AM is a simple wave, and the detector is a demodulator. It recovers the original signal (what was the modulating signal at the transmitter end) from the received AM signal. The detector consists of a simple half-wave rectifier which rectifies the received AM signal. This is followed by a low pass filter which removes (bypasses) the high-frequency carrier waveform the received signal. The resultant output of the low pass filter will be the original input (modulating) signal.

The incoming AM signal is transformer coupled HW rectifier conducts during positive cycles of AM and cuts off negative cycles of AM. Filter capacitor C filters (bypasses) the high-frequency carrier (fc) and allows only the lower frequency (fm). Thus, the filter output is the original input (modulating) signal.

### Types of Amplitude Modulation

The different types of amplitude modulations include the following.

#### 1) Double sideband-suppressed carrier (DSB-SC) modulation

• The transmitted wave consists of only the upper and lower sidebands
• But the channel bandwidth requirement is the same as before.

#### 2) Single sideband (SSB) modulation

• The modulation wave consists only of the upper sideband or the lower sideband.
• To translate the spectrum of the modulating signal to a new location in the frequency domain.

#### 3) Vestigial sideband (VSB) modulation

• One sideband is passed almost completely and just a trace of the other sideband is retained.
• The required channel bandwidth is slightly in excess of the message bandwidth by an amount equal to the width of the vestigial sideband.

The advantages of amplitude modulation include the following.

• Amplitude modulation is economical as well as easily obtainable
• It is so simple to implement, and by using a circuit with fewer components it can be demodulated.
• The receivers of AM are inexpensive because it doesn’t require any specialized components.

The disadvantages of amplitude modulation include the following.

• The efficiency of this modulation is very low because it uses a lot of power
• This modulation uses amplitude frequency several times to modulate the signal by a carrier signal.
• This declines the original signal quality on the receiving end & causes troubles in the signal quality.
• AM systems are susceptible toward the generation of noise generation.
• The applications of amplitude modulation limits to VHF, radios, & applicable one to one communication only

Thus, this is all about an overview of amplitude modulation. The main advantage is that since a coherent reference is not required for demodulation as long as 0 < u < 1, the demodulator becomes simple and inexpensive. The main disadvantage of this modulation is the wastage of carrier power. It is used in many commercial broadcast applications, it is sufficient to justify its use. Here is a question for you, what is pulse amplitude modulation?