Babinet's principle - in Radiofrequency Structures

Description

In physics, Babinet’s principle states that the diffraction pattern from an opaque body is identical to that from a hole of the same size and shape except for the overall forward beam intensity. It was formulated in the 1800s by French physicist Jacques Babinet.

Babinet’s principle can be used in antenna engineering to find complementary impedances. A consequence of the principle is shown in the formula shown.

In addition, Zslot is not only the impedance of the slot, but can be viewed as the complementary structure impedance (a dipole or loop in many cases). In addition, Zmetal is often referred to as Zscreen were the screen comes from the optical definition. It is noteworthy that the thin sheet or screen does not have to be metal, but rather any material that supports a current density vector leading to a magnetic potential vector. One issue with this equation, is that the screen must be relatively thin to the given wavelength (or range thereof). If it is not, modes can begin to form or fringing fields may no longer be negligible.

Related formulas

Variables

Zminput impedances of the metal radiating pieces (ohm)
Zslotinput impedances of the slot radiating pieces (ohm)
ηintrinsic impedance of the media in which the structure is immersed (ohm)