Aperture Antennas

This interactive tutorial explores the theoretical foundations and field characteristics of circular aperture antennas. Use the simulation panels below to evaluate how altering the radius relative to wavelength influences radiation patterns, beam width, and directivity.

Theory — Circular Apertures

z y x O a P(r,θ,φ) θ φ r = distance θ = polar angle φ = azimuthal angle E_θ E_φ Circular Aperture in Spherical Coordinates
Figure: Circular aperture (broken blue) of radius a in the xy-plane, with observation point P defined by spherical coordinates (r, θ, φ).
The electric field components E_θ and E_φ are shown at point P.

A circular aperture antenna radiates electromagnetic waves. At a far-field observation point, the electric field components in spherical coordinates are:

\[ E_r = 0 \] \[ E_\theta = j \frac{k a^2 E_0 e^{-j k r}}{r} \left\{ \sin \phi \left[ \frac{J_1 (k a \sin \theta)}{k a \sin \theta} \right] \right\} \] \[ E_\phi = j \frac{k a^2 E_0 e^{-j k r}}{r} \left\{ \cos \theta \cos \phi \left[ \frac{J_1 (k a \sin \theta)}{k a \sin \theta} \right] \right\} \]

Where: - \(a\) is the radius of the circular aperture, - \(r\) is the distance to the observation point, - \(k = 2 \pi / \lambda\) is the wave number, - \(E_0\) is the constant field over the aperture, - \(J_1\) is the first-order Bessel function of the first kind, - \(\theta\) is the polar angle from the z-axis (normal to aperture), - \(\phi\) is the azimuthal angle in the xy-plane.

The polar pattern depends strongly on the radius \(a\) relative to the wavelength \(\lambda\): increasing the radius narrows the main lobe and increases directivity.

Radiation Pattern (Polar)

Value: 1 λ
Main lobe always visible. Larger radius → narrower beam.

Radiation Pattern (Rectangular)

Shows E-field amplitude along x (blue, φ=0) and y (red, φ=π/2). Both main lobe and sidelobes are visible for any radius.