sdr.parabolic_antenna(freq: ArrayLike, diameter: ArrayLike, efficiency: ArrayLike = 0.55) → tuple[NDArray[float64], NDArray[float64]]

Calculates the gain \(G\) and beamwidth \(\theta\) of a parabolic reflector.

Parameters:
freq: ArrayLike

The frequency \(f\) in Hz of the signal.

diameter: ArrayLike

The diameter \(d\) in meters of the parabolic reflector.

efficiency: ArrayLike = 0.55

The efficiency \(0 \le \eta \le 1\) of the parabolic reflector.

Returns:

  • The gain \(G\) in dBi.

  • The half-power beamwidth \(\theta\) in degrees.

Notes

\[G = \left( \frac{\pi d f}{c} \right)^2 \eta\]

\[\theta = \arcsin \left( \frac{3.83 c}{\pi d f} \right)\]

Examples

A 1 meter dish at 1 GHz with 55% efficiency has a gain of 17.8 dBi and a 3-dB beamwidth of 21.4 degrees.

In [1]: sdr.parabolic_antenna(1e9, 1)
Out[1]: (17.810210290266568, 21.437435887991374)

A 2 meter dish at 1 GHz with 55% efficiency has a gain of 23.8 dBi and a 3-dB beamwidth of 10.5 degrees. Since the antenna gain is proportional to the square of the reflector diameter, doubling the diameter results in a 6 dB increase in the gain, which we observe.

In [2]: sdr.parabolic_antenna(1e9, 2)
Out[2]: (23.830810203546193, 10.529544741425365)