fraunhoferdist

R2026b

Fraunhofer distance

Since R2026b

Syntax

distance = fraunhoferdist(aper,lambda)

Description

distance = fraunhoferdist(aper,lambda) returns the distance to the Fraunhofer radiative zone of a radiator at wavelength lambda. This distance marks the transition from the Fresnel radiative zone to the Fraunhofer radiative zone. The input argument aper is the maximum width of the radiator aperture along any diameter.

Examples

Fraunhofer Distance of Radiator

Compute the Fraunhofer distance for a rectangular-shaped radiator having a one-by-two meter aperture. The radiated signal frequency is 30 kHz.

f = 30.0e3;
aper = [1 2];
lambda = physconst("LightSpeed")/f;
fd = fraunhoferdist(sqrt(aper*aper'),lambda)

fd = 
0.0010

Input Arguments

aper — Radiator aperture size

positive scalar

Radiator aperture size, specified as a positive scalar. The aperture size is the maximum width of the radiator aperture along any diameter. Units are in meters.

Example: 2.0

Data Types: double

lambda — Wavelength

positive scalar

Wavelength, specified as a positive scalar. Units are in meters.

Example: 1e4

Data Types: double

Output Arguments

distance — Fraunhofer distance of radiator

positive scalar

Fraunhofer distance (d_frau) of the radiator, returned as a positive scalar. Units are in meters. This distance marks the transition from the from hee near-field radiative Fresnel zone to the This distance marks the transition from the near-field radiative Fresnel zone to the Fraunhofer zone.

Data Types: double

Algorithms

The Fraunhofer distance d_frau is defined as

$$d_{\text{frau}}=\frac{2D^2}{\lambda },$$

where D is the maximum width of the radiator aperture along any diameter. λ is the wavelength. Units are in meters.

References

[1] IEEE Standards Antennas and Propagation Society, IEEE Recommended Practice for Antenna Measurements, 2001.

[2] Selvan, Krishnasamy T., and Ramakrishna Janaswamy, "Fraunhofer and Fresnel Distances: Unified Derivation for Aperture Antennas." IEEE Antennas and Propagation Magazine 59, no. 4 (June 2017): 12–15.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2026b