¹/₂-power (3 dB) beam widths for parabolic reflector systems

Accuracies of the angles above are limited to about 2-3 digits due to the accuracy (or lack, thereof) of the input values.

That is: 12.34567, and 0.001234567 should be considered as 12.3 and 0.00123 respectively!

Decibel ratios are presentable with one decimal, same order of accuracy applies also on the numbers of bits.

The computation method:

Source for this page

• Wavelength: Lambda_[mm] = 299.792 / f [GHz]

• From the diffraction approximation:
  Half-power (3dB) beam-width_[radians] = Lambda * ff / D

• Gain comes from diffraction approximation via:
  voltage gain = Pi * D / ( Lambda * ff ),

  then:
  

  power gain	= voltage-gain2 * eta
  	= eta * ( Pi * D / ( Lambda * ff ))2,

  and finally in [dBi]:
  power gain_[dBi] = 10 * log₁₀( ( eta * Pi * D / ( Lambda * ff ))²)

• "Bits" for half-power beam-width per 2*Pi:
      = log₂( 2 * Pi * D / ( Lambda * ff ))

• Pointing needs to be circa factor 10 better than the 3dB beam-width.

• Tracking needs to be another factor 10 better than pointing!
  The more there are bits, the merrier.

• Each factor 10 means 3.322 "bits" for encoder resolution. ( 1/log₁₀(2) )

• Figure-of-Merit: G/T is computed as:
  

  G/T[dB/K]   =	Power gain[dBi]
  	- 10 * log10( Temp[K] )

The 3dB beam-width depends a lot also about the aperture illumination pattern, which also defines side-lobe patterns, etc.

The magic "1.3" above is for illumination pattern which is maximum at the center, and falls down linearly to the edge, where it reaches zero.

Above the Figure of Merit (G/T) is determined computationally from given inputs. Referred SETI-League article describes how to do it from measurement data:

SETI-League: Determination of G/T

Matti Aarnio <matti.aarnio@zmailer.org>; OH2MQK