Light Emitting Diode (LED)

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  Light Emitting Diode (LED) Introduction A Light Emitting Diode (LED) is a semiconductor device that converts electrical energy directly into light energy. It is a special type of PN junction diode that emits light when it is operated in the forward-bias condition . LEDs are widely used in electronic and electrical systems because they are small in size, consume less electrical power, have a long operating life, and can produce light in different colours. Common applications of LEDs include: Indicator lamps Digital displays Traffic signals Remote-control systems Automotive lighting Decorative lighting Street lighting Electronic instruments Television and computer displays Optical communication systems The basic principle behind LED operation is electroluminescence .   What is an LED? A Light Emitting Diode is a PN junction semiconductor device that emits visible or invisible light when current flows through it in the forward direction. T...
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Radiation from Linear Antenna: Theory, Derivation, Radiation Pattern, Power Density, and Applications (Complete Guide)

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Radiation from Linear Antenna

Introduction

A linear antenna is used in electromagnetic wave communication. It consists of a straight conducting wire through which alternating current flows. The oscillating charges in the antenna produce changing electric and magnetic fields that propagate away from the antenna as electromagnetic (EM) waves.

The study of radiation from a linear antenna forms the foundation of antenna engineering. It helps us understand how radio transmitters, television broadcasting, satellite communication, radar, and wireless systems work.

A short linear antenna is also called a Hertzian dipole or elementary dipole because its length is much smaller than the wavelength.

 


What is Radiation from a Linear Antenna?

Definition

Radiation from a linear antenna is the process by which electrical energy supplied to the antenna is converted into electromagnetic waves and transmitted through free space.

The alternating current in the antenna creates time-varying electric and magnetic fields. These fields detach from the antenna and travel outward at the speed of light.

Construction of a Linear Antenna

A linear antenna consists of

  • Thin conducting wire
  • AC source
  • Feed point at the center
  • Length generally equal to λ/2 or much smaller than λ

The antenna may be

  • Short dipole
  • Half-wave dipole
  • Long dipole

The Hertzian dipole is the simplest theoretical model.

Working Principle

When an alternating voltage is applied,

  1. Electrons move back and forth.
  2. Current changes continuously.
  3. Electric field changes with time.
  4. Magnetic field changes simultaneously.
  5. According to Maxwell's equations, changing electric and magnetic fields generate each other.
  6. These fields propagate away from the antenna as electromagnetic waves.

Thus,

Electrical Energy → Electromagnetic Radiation

Radiation Mechanism

The radiation process occurs because accelerated charges emit electromagnetic waves.

During one AC cycle

Positive Half Cycle

  • Current flows upward.
  • Positive charges accumulate at one end.
  • Electric field expands.

Negative Half Cycle

  • Current reverses.
  • Charges reverse.
  • Electric field reverses.

The continuous reversal produces propagating EM waves.

Linear Antenna as a Hertzian Dipole

For theoretical analysis,

Length

l << λ

where

l = antenna length

λ = wavelength

Current is assumed constant throughout the antenna.

This approximation simplifies the derivation.

Electromagnetic Fields Produced

A linear antenna produces

Electric Field (E)

Acts in the θ-direction.

Magnetic Field (H)

Acts in the φ-direction.

Both fields are perpendicular.

Direction of propagation

E × H

This is the direction of the electromagnetic wave.

Assumptions for Derivation

The derivation assumes

  • Thin conductor
  • Uniform current
  • Free space
  • Sinusoidal current
  • Short antenna
  • Far-field observation

Current Distribution

Current varies with time as


I =I0​cos(ωt)

where

I₀ = maximum current

ω = angular frequency

t = time

Magnetic Vector Potential

The magnetic vector potential is

A=μI0​l​/4πr cos(ωt−βr)

where

μ = permeability

β = phase constant

r = distance

Far Field Approximation

For

r>>λ

only radiation terms remain.

Near-field terms become negligible.

Electric Field Equation

The electric field of a short dipole is

Eθ​=jηβI0​l​/4πr sinθe−jβr

where

η = intrinsic impedance of free space

β = wave number

Magnetic Field Equation

The magnetic field is

Hϕ​=j βI0​l​/4πr sinθe−jβr

Relationship Between E and H

E=ηH

Where

η =120π Ω

This is the intrinsic impedance of free space.

Important Observations

The radiation field

  • decreases as 1/r
  • increases with current
  • depends upon antenna length
  • depends upon angle θ

Angular Dependence

Since

E∝sinθ

Maximum radiation

θ=90∘

Minimum radiation

θ=0∘

and

180∘

Thus no radiation exists along the antenna axis

Radiation Pattern

The radiation intensity follows

U∝sin2θ

Characteristics

  • Doughnut shape
  • Maximum broadside
  • Zero along axis
  • Symmetrical

Three-Dimensional Radiation Pattern

The 3D pattern resembles a toroid (doughnut).

The antenna is located at the center.

Maximum radiation occurs perpendicular to the antenna.

Two-Dimensional Radiation Pattern

In polar coordinates

           maximum

 

              ●

         ●         ●

 

     ●               ●

 

     ●               ●

 

         ●         ●

              ●

 

           Minimum

Power Density

Power flow is represented by the Poynting vector

S=E×H

Average power density

Pavg​=1​/2EH

Units

W/m²

Total Radiated Power

Integrating power density over the entire sphere,

Pr​=ηβ2I02​l2​/12π

Radiation Resistance

Radiation resistance converts electrical energy into radiated power.

Definition


P=1/2 I2Rr

For a short dipole

Rr​=80 π2 (l/λ​)2

Radiation resistance is usually very small.

Directivity

The directivity of a Hertzian dipole is

D=1.5
This means radiation is 1.5 times stronger than an isotropic radiator in the direction of maximum radiation.

Gain

Gain is

G=ηa​D

where

ηₐ = antenna efficiency

Polarization

A linear antenna produces

Linear polarization

depending upon its orientation.

Examples

Vertical antenna → Vertical polarization

Horizontal antenna → Horizontal polarization

Near Field and Far Field

Near Field

  • Close to antenna
  • Energy stored
  • Reactive fields dominate

Far Field

  • Radiation dominates
  • E and H perpendicular
  • Wave behaves like plane wave

Energy Flow

Energy travels away from the antenna.

Direction

Electric Field

↓

Magnetic Field

↓

Poynting Vector

↓

Propagation

Factors Affecting Radiation

Radiation depends upon

  • Antenna length
  • Frequency
  • Current
  • Operating wavelength
  • Input power
  • Surrounding medium

Advantages

  • Simple design
  • Low cost
  • Easy construction
  • Omnidirectional in azimuth
  • Suitable for communication
  • Good theoretical model
  • Disadvantages
  • Low efficiency (short dipole)
  • Small radiation resistance
  • Narrow bandwidth
  • Limited gain
  • Requires matching circuits

Applications

Radiation from linear antennas is widely used in

  • Radio broadcasting
  • Television transmission
  • Mobile communication
  • Wi-Fi systems
  • Satellite communication
  • Radar systems
  • Amateur radio
  • Aircraft communication
  • Military communication
  • Educational laboratories

Comparison: Short Dipole vs Half-Wave Dipole

Feature

Short Dipole

Half-Wave Dipole

Length

Much less than λ

λ/2

Current

Uniform

Sinusoidal

Radiation

Lower

Higher

Efficiency

Low

High

Gain

Small

Moderate

Important Formula Summary

Quantity

Formula

Current

 

I=I0​cosωt

Electric Field

 

Eθ​=jηβI0​l​/4πr sinθe−jβr

Magnetic Field

 

Hϕ​=j βI0​l​/4πr sinθe−jβr

Wave Impedance

 

E=ηH

Poynting Vector

 

S=E×H

Average Power

 

P=1​/2EH

Radiation Resistance

 

Rr​=80π2(l/λ)2

Directivity

1.5

 

Conclusion

Radiation from a linear antenna is a fundamental concept in electromagnetic theory and communication engineering. An alternating current flowing through a straight conductor produces changing electric and magnetic fields, which detach from the antenna and propagate through space as electromagnetic waves. The radiation is strongest in the direction perpendicular to the antenna axis and zero along the axis, producing a characteristic doughnut-shaped radiation pattern. Understanding the electric field, magnetic field, radiation resistance, power density, directivity, and applications of linear antennas provides the basis for studying advanced antenna systems used in modern wireless communication, radar, satellite links, and broadcasting.

 

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