Antenna Array Calculator

This calculator computes the main beam direction and an approximate half‑power beamwidth (HPBW) for a uniform linear array.
For a linear array with \(N\) elements, element spacing \(d\) (in wavelengths), and a progressive phase shift \(\beta\) (in degrees), the main beam is steered according to \[ k\,d\cos\theta_0+\beta_{\rm rad}=0 \quad\Longrightarrow\quad \cos\theta_0=-\frac{\beta_{\rm rad}}{2\pi\,d}. \] The HPBW is approximated as \( \mbox{HPBW} \approx \frac{50.8}{N\,d}\) (in degrees).

* Enter the number of elements, the spacing (in wavelengths), and the phase shift (in degrees).

Step 1: Enter Array Parameters

Example: 8

Example: 0.5 wavelengths

Example: 0° (for broadside)

Derived from: \( k\,d\cos\theta_0+\beta=0 \) with \( k=2\pi \) and \( \mbox{HPBW}\approx\frac{50.8}{N\,d} \).


Practical Example:
For \(N=8\), \(d=0.5\) wavelengths, and \(\beta=0^\circ\), the array is broadside and the HPBW is approximately \( \frac{50.8}{8\times0.5} \approx 12.7^\circ\).

Antenna Array Calculator (In-Depth Explanation)

Antenna Array Calculator (In-Depth Explanation)

The Antenna Array Calculator is a powerful tool used to determine two key parameters for a uniform linear antenna array: the main beam direction and the approximate half-power beamwidth (HPBW). These parameters are critical for designing phased arrays and beamforming systems, allowing engineers to steer the main beam and control the directional characteristics of the antenna system.

Table of Contents

  1. Overview of Antenna Arrays
  2. Key Concepts and Parameters
  3. Main Beam Direction and HPBW Formulas
  4. Step-by-Step Calculation Process
  5. Practical Examples
  6. Common Applications
  7. Conclusion

1. Overview of Antenna Arrays

A uniform linear antenna array consists of multiple antenna elements arranged in a straight line, with a constant spacing between them. By introducing a progressive phase shift between adjacent elements, the main beam of the array can be steered in a desired direction. This configuration is widely used in radar, wireless communications, and other applications where directional control of the radiated energy is required.

2. Key Concepts and Parameters

To accurately compute the main beam direction and the half‑power beamwidth (HPBW) for an antenna array, the following parameters are essential:

  • Number of Elements (\(N\)): Total number of antenna elements in the array.
  • Element Spacing (\(d\)): The distance between adjacent elements, expressed in wavelengths.
  • Progressive Phase Shift (\(\beta\)): The phase difference between the signals of successive elements (in degrees).

3. Main Beam Direction and HPBW Formulas

For a uniform linear array, the main beam is steered by applying a progressive phase shift. The direction of the main beam is given by:

\( \theta_{\text{main}} = \arcsin\left(\frac{\beta}{360 \, d}\right) \)

Here, \(\theta_{\text{main}}\) is the angle (in radians) at which the main beam is directed, based on the element spacing and phase shift.

The approximate half‑power beamwidth (HPBW) of the array is estimated using the formula:

\( \text{HPBW} \approx \frac{50.8}{N \, d} \) (in degrees)

This approximation provides an indication of the angular spread of the main lobe, which is critical for understanding the array’s directivity.

4. Step-by-Step Calculation Process

  1. Input the Array Parameters:
    • Enter the number of elements (\(N\)).
    • Enter the element spacing (\(d\)) in wavelengths.
    • Enter the progressive phase shift (\(\beta\)) in degrees.
  2. Calculate the Main Beam Direction:
    • Use the formula:
      \( \theta_{\text{main}} = \arcsin\left(\frac{\beta}{360 \, d}\right) \)
    • Convert \(\theta_{\text{main}}\) from radians to degrees if desired.
  3. Calculate the Half‑Power Beamwidth (HPBW):
    • Apply the formula:
      \( \text{HPBW} \approx \frac{50.8}{N \, d} \)
  4. Interpret the Results:

    The main beam direction indicates where the antenna array is pointed, and the HPBW reveals the angular width of the main lobe at half of its maximum power.

5. Practical Examples

Example 1: Steering the Main Beam

Given: An antenna array with \(N = 10\) elements, an element spacing of \(d = 0.5\) wavelengths, and a progressive phase shift of \(\beta = 45^\circ\).

Main Beam Calculation:

\( \theta_{\text{main}} = \arcsin\left(\frac{45}{360 \times 0.5}\right) = \arcsin\left(\frac{45}{180}\right) = \arcsin(0.25) \)

Evaluating:

\( \theta_{\text{main}} \approx 0.2527 \text{ radians} \approx 14.47^\circ \)

HPBW Calculation:

\( \text{HPBW} \approx \frac{50.8}{10 \times 0.5} = \frac{50.8}{5} \approx 10.16^\circ \)

Thus, the main beam is steered to approximately \(14.47^\circ\) with an HPBW of about \(10.16^\circ\).

Example 2: Narrower Beamwidth

Given: A larger array with \(N = 20\) elements, element spacing \(d = 0.5\) wavelengths, and a progressive phase shift of \(\beta = 30^\circ\).

Main Beam Calculation:

\( \theta_{\text{main}} = \arcsin\left(\frac{30}{360 \times 0.5}\right) = \arcsin\left(\frac{30}{180}\right) = \arcsin(0.1667) \)

Evaluating:

\( \theta_{\text{main}} \approx 0.1675 \text{ radians} \approx 9.6^\circ \)

HPBW Calculation:

\( \text{HPBW} \approx \frac{50.8}{20 \times 0.5} = \frac{50.8}{10} \approx 5.08^\circ \)

The main beam is directed at approximately \(9.6^\circ\) and the half‑power beamwidth is about \(5.08^\circ\).

6. Common Applications

  • Radar Systems: Steering beams for target detection and tracking.
  • Wireless Communications: Directing signals in phased array antennas for improved coverage.
  • Satellite Communications: Enhancing directional gain and interference rejection.
  • Beamforming: Optimizing signal strength in multi-antenna systems.

7. Conclusion

The Antenna Array Calculator for uniform linear arrays provides an efficient method to determine the main beam direction and approximate half‑power beamwidth. By using the formulas:

\( \theta_{\text{main}} = \arcsin\left(\frac{\beta}{360 \, d}\right) \)
\( \text{HPBW} \approx \frac{50.8}{N \, d} \)

where \(N\) is the number of elements, \(d\) is the element spacing (in wavelengths), and \(\beta\) is the progressive phase shift (in degrees), engineers can precisely steer the beam and control the directional properties of the array. This calculator is essential for designing high-performance antenna systems in radar, wireless communications, and satellite applications.