Half Wave Dipole- Complete derivation

Types of Antennas or antenna elements:

There are 5 basic elements., such as 

1. Alternating current element(dl): is a linear antenna whose current distribution is assumed to be constant.

2. Short Dipole: is a linear antenna whose current distribution is assumed to be triangular

3. Short Monopole: is a linear antenna whose current distribution is assumed to be triangular.

4. Half Wave Dipole: is a linear antenna whose current distribution is assumed to be Sinusoidal.

5. Quarter Wave Monopole: is a linear antenna whose current distribution is assumed to be Sinusoidal.

Before defining the radiation from the element or antenna of interest, one should understand the concept of radiation. The basic equation for radiation is given by  

The following points need to check, to state or to prove the existence of the radiation;

• If the charge is not moving, no Current & no radiation
• If the charge is moving with uniform velocity,

              a) there is no radiation if a wire is straight,

              b) there is radiation if a wire is of nonregular (like bent, curved, truncated, terminated)

• If the charge is oscillating in a time-motion, it radiates even if the wire is straight

Radiation from a Half-wave dipole: 

v Steps:

• Write the expression for the assumed current distribution
• Write an expression for Retarded Vector Magnetic Potential [A]
• Write the Expressions for the components of [A] in the Cartesian Coordinate system
• Write the Expressions for the components of [A] in the Spherical Coordinate system
• Obtain the components of H from or
• Obtain the components of E from or
• Identify the radiation and near field components
• Obtain power & Total avg. Power using Poynting Vector (Pr)
• Identify Radiation Resistance(Rr)
• Calculate all basic parameters