Dipole Antennas: Theory, Radiation Patterns & Interactive Simulator

This interactive tutorial explores the theoretical principles of dipole antennas. Examine current distributions, electric and magnetic field components, and use the real-time HTML5 simulator to study how changes in dipole length modify radiation patterns and beamwidth.

Theory of Dipole Antennas

Dipole antennas are economical, straightforward to manufacture, and widely deployed (e.g., standard television antennas). Consider a dipole antenna of total length \(2L\) centered at the origin of a spherical coordinate system.

Assuming the current distribution along the z-axis follows:

\[ I(z) = I_m \sin(\beta(L - |z|)) \]

where \(I_m\) is maximum current amplitude, \(\beta = 2\pi/\lambda\) is the wave number, \(\lambda\) is wavelength, and \(L\) is half-length (\(-L \le z \le L\)). Far-field electric and magnetic components are approximated by:

\[ E_\theta = \frac{60 I_m}{r} \left[ \frac{\cos(\beta L \cos\theta) - \cos(\beta L)}{\sin\theta} \right] \] \[ H_\phi = \frac{I_m}{2\pi r} \left[ \frac{\cos(\beta L \cos\theta) - \cos(\beta L)}{\sin\theta} \right] \]

The average radiated power density (Poynting vector magnitude) is:

\[ P_{av} = \frac{15 I_m^2}{\pi r^2} \left[ \frac{\cos(\beta L \cos\theta) - \cos(\beta L)}{\sin\theta} \right]^2 \]

Interactive Simulation

Examine power density distribution versus polar angle \(\theta\) as half-length \(L\) changes. The half-power beamwidth marks antenna directivity.

Radiation Pattern (Polar Plot)

Dipole Half-Length L (in λ) 0.25 λ

Peak Current Iₘ (A) 1.0 A

Radiation Pattern

Half-Power Points (-3dB)

Pattern Characteristics:

Total Dipole Length: 0.5 λ

Half-Power Beamwidth: 78°

Directivity: 2.15 dBi

Maximum Power Density: 4.77 W/m² at r = 1m

Field Components Visualization

Observation Angle θ (degrees) 90°

Distance r (meters) 10 m

Field Values at Observation Point:

Electric Field E₀: 0.60 V/m

Magnetic Field Hᵩ: 1.59 mA/m

Power Density Pₐᵥ: 0.48 W/m²

Wave Impedance: 377 Ω

Current Distribution Along Dipole

Current Distribution I(z)

The sinusoidal current distribution equation:

\[ I(z) = I_m \sin(\beta(L - |z|)), \quad -L \leq z \leq L \]

Maximum Current (at center): 1.0 A

Current at ends: 0.0 A

Wavelength: 3.0 m (at 100 MHz)

Power Density vs. Angle

Normalized power density function relative to \(\theta\):

Key Observations:

Symmetric behavior about \(\theta = 90^\circ\)
Nulls occur where pattern intensity hits zero
Side lobes emerge when dipole length exceeds \(\lambda/2\)

Dipole Antennas