Antenna Parameters

Antenna Calculations

References:

• [1] Timothy Pratt, Jeremy E. Allnutt, “Satellite Communications”, 3rd Ed.

• [2] Couch, Leon W.. Digital & Analog Communication Systems.

• [3] Recommendation ITU-R S.465-6.

class linkbudget.antenna.Antenna(freq, gain=None, diameter=None, efficiency=None, label='Dish')

Parabolic antenna

Parameters:

• freq (float) – Operating frequency in Hz.

• gain (float) – Antenna gain in dB.

• diameter (float) – Diameter in m.

• efficiency (float) – Aperture efficiency.

• label (str) – Label used for logs.

Note

According to [1], the aperture efficiency is typically in the range 0.5–0.75 for parabolodial reflector antennas, lower for small antennas and higher for large Cassegrain and Gregorian antennas. For instance, Table 8-4 in [2] assumes an aperture efficiency of 0.56.

effective_aperture

Effective aperture area.

gain_db

Antenna gain in dBi.

_calc_eff_aperture(diameter, aperture_efficiency)

Compute the antenna’s effective aperture area

The effective aperture area is given by:

\[A_e = \eta A,\]

where \(A\) represents the antenna’s physical aperture area and \(\eta\) is the aperture efficiency.

If the aperture is circular with a diameter \(D\) in meters (or radius \(r\)), the physical aperture area is given by:

\[A = 𝜋 r^2 = \frac{𝜋 D^2}{4}.\]

Hence, the effective aperture area becomes:

\[A_e = \frac{\eta 𝜋 D^2}{4}.\]

Parameters:

• diameter (float) – Diameter in m.

• aperture_efficiency (float) – Aperture efficiency.

Returns:

Effective aperture area in square meters (m^2).

_calc_gain(freq, effective_aperture)

Calculate the parabolic dish gain

The gain in linear units is given by:

\[G = \frac{4𝜋A_e}{𝜆^2},\]

where \(A_e\) is the effective aperture and 𝜆 is the wavelength.

Parameters:

• freq (float) – Operating frequency in Hz.

• effective_aperture (float) – Effective aperture in square meters.

Returns:

Gain in dB.

_infer_diameter(effective_aperture, aperture_efficiency)

Infer the diameter of an equivalent parabolic reflector

The physical aperture area \(A\) can be expressed in terms of the effective aperture \(A_e\) and the aperture efficiency \(\eta\), as follows:

\[A = \frac{A_e}{\eta}.\]

If the aperture is circular with a diameter D in meters, the physical aperture area is given by:

\[A = \frac{𝜋 D^2}{4}.\]

Hence, it follows that:

\[D = \sqrt{\frac{4 A_e}{\eta \pi}}.\]

Note

This inference is useful when working with a non-parabolic antenna, such as a flat-panel antenna. In this case, you may know the antenna gain and aperture efficiency specifications, but not the physical diameter and aperture of the antenna. Meanwhile, the diameter may still be required for computations such as the tropospheric scintillation model from Recommendation ITU-R 618 (see, e.g., ITU-Rpy).

Parameters:

• effective_aperture (float) – Effective aperture in square meters.

• aperture_efficiency (float) – Aperture efficiency.

Returns:

Diameter in meters (m) of an equivalent parabolic reflector with the same aperture efficiency.

Return type:

float

_infer_eff_aperture(freq, gain_db)

Infer the effective aperture area from the antenna gain

The effective aperture area can be inferred from the gain and wavelength, as follows:

\[A_e = \frac{G 𝜆^2}{4𝜋}.\]

Parameters:

• freq (float) – Operating frequency in Hz.

• gain_db (float) – Antenna gain in dB.

Returns:

Effective aperture area in square meters (m^2).

Return type:

float

off_axis_gain(angle)

Compute the off-axis co-polar antenna gain

Based on the reference earth station radiation pattern from ITU-R S.465-6 (01/2010 version) and the APEREC026V01 standard from the ITU-R antenna pattern list in https://www.itu.int/en/ITU-R/software/Pages/ant-pattern.aspx.

Parameters:

angle (float) – Off-axis angle in degrees relative to the boresight. Must be within the [0, 180°) range.

Returns:

(float) Off-axis antenna gain in dBi.