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Antenna

GainPattern

__init__(res_deg, pattern_type='ideal', gain_dBi=10, beamw_deg=60)

Gain Pattern simulation. Used to create a irradiation diagram used for futher signal propagation. The diagram simulation is devided in \(N\) components that represents the angular resolution of the simulation based on a angle \(\theta\), the expression for \(N\):

\[ \begin{equation} N = \frac{360}{\theta} \end{equation} \]
Where
  • \(N\) is the number of components (ArcComponents) on the wavefront simulation.
  • \(\theta\) is the angular precision of the wavefront simulation in degrees.

Parameters:

Name Type Description Default
res_deg float

Angular precision degree (\(\theta\)) used for irradiation diagram precision.

 required
pattern_type string

Pattern for the irradiation diagram, used for select the pattern equation.

 'ideal'
gain_dBi float

Max gain in dBi of the antenna.

10
beamw_deg deg

Beamwidth of the antenna (Beam from max dBi to -3dB).

 60

isotropic_gain()

Function to create a isotropic antenna, which in 2D corresponds to the same gain in all possible directions. Based on that, the equation to isotropic can be expressed as:

\[ \begin{equation} G(\theta, \phi) = G_i \end{equation} \]
Where
  • \(G\) is the gain of the antenna on a angle \(\theta\) and \(\phi\)
  • \(G_i\) is a constant of gain for the antenna.

Returns:

Name Type Description
gain_dBi_matrix float

Matrix of gain for \(\theta\) and \(\phi\).
Reference:

Merill I. Skolnik - Introduction To Radar Systems Third Edition (Pg - 18)

ideal_gain(atten_db=-40)

Function to create a ideal irradiation pattern for setorial transmission, which corresponds to the \(\cos\) decay on beamwidth range and a very low gain outside the beamwidth range. The expression to calculate this pattern is given by:

\[ \begin{equation} G(\theta) = \begin{cases} \cos^n(\theta), & |\theta| \leq \dfrac{\theta_{3\text{dB}}}{2} \\ \epsilon, & |\theta| > \dfrac{\theta_{3\text{dB}}}{2} \end{cases} \end{equation} \]
Where
  • \(G\) is the gain of the antenna on a angle \(\theta\).
  • \(n\) is a variable for the angle directivity.
  • \(\epsilon\) is a attenuation value for outside the beamwidth (\(-40dB\) by default).

Parameters:

Name Type Description Default
atten_db float

\(\epsilon\) is a attenuation value for outside the beamwidth (\(-40dB\) by default).

 -40

Returns:

Name Type Description
H_plane float

Gain vector of irradiation pattern on Horizontal Axis.
V_plane float

Gain vector of irradiation pattern on Vertical Axis.
Reference:

Merill I. Skolnik - Introduction To Radar Systems Third Edition (Pg - 18)

sinc_gain(atten_db=10)

Function to create an irradiation pattern based on a squared sinc function, commonly used to approximate the radiation pattern of a uniformly illuminated linear aperture. The normalized gain pattern is given by:

\[ \begin{equation} G(\theta) = \left[ \frac{\sin(\frac{2\pi}{\theta_{3\text{dB}}} \sin(\theta))}{\frac{2\pi}{\theta_{3\text{dB}}} \sin(\theta)} \right]^2 \cdot e^{-\alpha |\theta|} \end{equation} \]
Where
  • \(G(\theta)\) is the normalized antenna gain
  • \(\alpha\) is the sidelobe attenuation factor
  • \(e^{-\alpha |\theta|}\) is an exponential attenuation used to suppress sidelobes

Parameters:

Name Type Description Default
atten_db float

Exponential attenuation factor used to suppress sidelobes.

 10

Returns:

Name Type Description
gain_db_vec ndarray

Gain vector in dB.
References:

C. A. Balanis - Antenna Theory: Analysis and Design, 4th Ed., Chapter 10
R. C. Hansen - Phased Array Antennas

cosine_gain(atten_db=9)

Function to create a sectoral irradiation pattern, similar to a omnidirectional vertical 2D plane, based on a cosine power model. The radiation pattern is defined as:

\[ \begin{equation} G(\theta) = \cos^{n \cdot \alpha}(\theta) \end{equation} \]
Where
  • \(G(\theta)\) is the normalized antenna gain
  • \(n\) is a variable for the angle directivity.
  • \(\alpha\) is the sidelobe attenuation factor

Parameters:

Name Type Description Default
atten_db float

Exponential attenuation factor used to suppress sidelobes.

 9

Returns:

Name Type Description
gain_db_vec ndarray

Gain vector in dB.
References:

C. A. Balanis - Antenna Theory: Analysis and Design, 4th Ed.
T. S. Rappaport - Wireless Communications: Principles and Practice