Beam Width Half-maximum (BWH) Calculator
Use this calculator to determine the Half-Power Beamwidth (HPBW) of a uniformly illuminated circular aperture, such as an antenna or a telescope, given the wavelength of the electromagnetic wave and the aperture's diameter.
Understanding Beam Width Half-maximum (BWH)
The Beam Width Half-maximum (BWH), often referred to as Half-Power Beamwidth (HPBW), is a critical parameter in fields like antenna design, optics, and acoustics. It quantifies the angular width of a main lobe of a radiation pattern or beam at which the power density has fallen to half of its maximum value (i.e., -3 dB from the peak).
In simpler terms, imagine a flashlight beam. The HPBW would be the angle between the two points on either side of the brightest center where the light intensity is exactly half of the brightest point. A narrower HPBW indicates a more directional beam, concentrating energy in a smaller angular region, while a wider HPBW suggests a broader, less focused beam.
Why is HPBW Important?
- Antenna Design: For communication systems, a narrow HPBW means the antenna can transmit or receive signals from a very specific direction, improving signal-to-noise ratio and reducing interference. Satellite dishes, for example, have very narrow beamwidths.
- Telescopes and Optics: In optical systems, HPBW relates to the angular resolution – the ability to distinguish between two closely spaced objects. A smaller HPBW allows for finer detail.
- Radar Systems: The HPBW determines the angular precision with which a radar can locate targets.
How is HPBW Calculated?
For a uniformly illuminated circular aperture (like a parabolic dish antenna or a circular lens), the Half-Power Beamwidth (HPBW) can be approximated by the following formula:
HPBW (radians) ≈ 0.886 * (λ / D)
Where:
- λ (Lambda) is the wavelength of the electromagnetic wave.
- D is the diameter of the circular aperture.
To convert this to degrees, we multiply by 180 / π:
HPBW (degrees) ≈ 0.886 * (λ / D) * (180 / π)
It's crucial that the wavelength (λ) and the aperture diameter (D) are expressed in the same units for the calculation to be accurate.
Examples of BWH Calculation
Let's look at some practical examples:
Example 1: Wi-Fi Antenna
Consider a Wi-Fi signal operating at 2.4 GHz. The wavelength (λ) for 2.4 GHz is approximately 0.125 meters (12.5 cm). If we have a small dish antenna with an aperture diameter (D) of 0.3 meters (30 cm):
- Wavelength (λ): 0.125 m
- Aperture Diameter (D): 0.3 m
- HPBW (radians) = 0.886 * (0.125 / 0.3) ≈ 0.369 radians
- HPBW (degrees) = 0.369 * (180 / π) ≈ 21.1 degrees
This relatively wide beamwidth is typical for consumer Wi-Fi antennas, allowing for broad coverage.
Example 2: Optical Telescope
Imagine a small amateur telescope observing visible green light with a wavelength (λ) of 550 nanometers (550 x 10-9 meters). If the telescope's objective lens has an aperture diameter (D) of 0.1 meters (10 cm):
- Wavelength (λ): 550 x 10-9 m
- Aperture Diameter (D): 0.1 m
- HPBW (radians) = 0.886 * (550 x 10-9 / 0.1) ≈ 4.873 x 10-6 radians
- HPBW (degrees) = 4.873 x 10-6 * (180 / π) ≈ 0.000279 degrees
This extremely narrow beamwidth highlights the high angular resolution of optical telescopes, allowing them to resolve very fine details in distant objects.