Amplitude Modulation

Let carrier wave be represented by the equation
v~^c=V~^ccos(ω~^ct) ----- (1)
Let Modulating Signal be represented by the equation
v~^m=V~^mcos(ω~^mt) ----- (2)

After Amplitude Modulation Amplitude of the carrier varies according to the instantaneous value of modulating signal. The total Amplitude of the Modulated carrier is given as

V~^A~^M = V~^c+V~^mcos(ω~^mt)

The Expression for AM Wave is

v~^A~^M = V~^A~^Mcos(ω~^ct)
=(V~^c+V~^mcos(ω~^mt))cos(ω~^ct)
=V~^ccos(ω~^ct)+V~^mcos(ω~^mt)cos(ω~^ct)
=V~^c(cos(ω~^ct)+m~^acos(ω~^mt)cos(ω~^ct)) , ( Since V~^m/V~^c = m~^a)



Now use the formula CosA.CosB = $ 1 #_ 2 $ [Cos(A+B)+Cos(A-B)]

v~^A~^M = V~^c(cos(ω~^ct)+ $ m~^a #_ 2 $ [cos(ω~^mt+ω~^ct)+cos(ω~^mt-ω~^ct)]

=V~^ccos(ω~^ct)+ $ m~^aV~^c #_ 2 $ cos2π(f~^m+f~^c)t+ $ m~^aV~^c #_ 2 $ cos2π(f~^m-f~^c)t

Types of Corrosion

Different types of corrosion are:

1. Differential metal corrosion or Galvanic Corrosion
2. Differential Aeration corrosion
3. Stress Corrosion

1. Differential metal corrosion:

When two metals of different electrode potential or two dissimilar metals are in contact, the metal with lower electrode potential or more reactive metal act as anode and undergoes corrosion. Potential difference between the metals causes the corrosion.

The factors determining the rate of corrosion

2. Differential aeration corrosion:

Difference in the concentration of oxygen on the surface of oxygen causes the differential aeration corrosion. The part of metal over which oxygen concentration is less becomes anode and gets corroded. The metal surface over which oxygen concentration is high becomes cathode, because cathodic reaction involves consumption of oxygen.

3. Stress Corrosion:

The corrosion taking place at stress points of metals formed due to welding, hammering, bending, etc. the atoms under stressed part get high energy and get higher oxidation potential than that of stress free part. hence stressed part becomes anode and stress free part becomes cathode and corrosion takes place.

Corrosion Science - Definition and Theory

Definition:

Corrosion is defined as destruction and consequent loss of metals through chemical or electrochemical attack by the environment.

Main Types of Corrosion:
1. Dry Corrosion
2. Wet Corrosion

Theory of Corrosion:

Corrosion takes place in a metal due to the formation of anodic and cathodic regions in the same metal surface, or when two metals are kept in contact with each other.

Oxidation and Reduction reactions takes place at Anode and Cathode Respectively. Since Oxidation involves liberation of electrons, metal undergoes corrosion at anodic region. The liberated electrons move towards cathodic region constituting corrosion current. The corrosion product is formed due to the diffusion of metal ions liberated at anodic and cathodic regions.

Corrosion Reactions:

At anode oxidation takes place liberating electrons. Metal atoms are converted into metal ions.

M --> M^n^++ne^-

Cathodic Reactions are of several types. The most common types are explained here. They are:
1. Hydrogen Evolution ( Hydrogen type Corrosion )
2. Oxygen Absorption ( Oxygen type Corrosion )

1. Hydrogen Evolution Type:

It takes place in the Absence of oxygen

(i) Acidic Medium:

2H^++2e^--->H~^2

(ii) Basic or Neutral Medium:
2H~^2O+2e^--->H~^2+2OH^-

2. Oxygen absorption type

This type of reaction takes place in the presence of oxygen.

(i) Acidic Medium:
O~^2+4e^-+4H^+-->2H~^2O

(ii) Basic or Neutral Medium:
H~^2O+O~^2+e^---> 4OH^-