Linear Array Calculator
Calculate directivity, broadside HPBW, array length, and grating lobe safety bounds for a uniform linear array (ULA).
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Inputs
Live
Math
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Related
Enter parameters and click Calculate to view results
Formula & Theory
L = (N−1)d | HPBW ≈ 50.8 / (N · d/λ) | D₀ = N² / [1 + 2 Σ (N−k) sinc(2k·π·d/λ)]This formula is used to calculate antenna parameters for linear array calculator.
Overview
The Linear Array Calculator helps RF engineers, antenna designers, radar engineers, wireless communication specialists, researchers, and students analyse the performance of a Uniform Linear Array (ULA). By entering the number of antenna elements, element spacing, and single-element gain, the calculator determines array length, array factor gain, estimated total realized gain, half-power beamwidth (HPBW), first-null beamwidth (FNBW), and grating lobe status. It is widely used for phased array antennas, radar systems, 5G base stations, satellite communication, beamforming applications, microwave communication, radio astronomy, and advanced antenna array design.
Input Guide
Enter Number of Elements (N), Element Spacing (d/λ), Single Element Gain exactly in the units shown by this linear array. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.
- Number of Elements (N).
- Element Spacing (d/λ) — use λ.
- Single Element Gain — use dBi.
Output Guide
The results describe the calculated linear array values for the inputs you entered. Check each value against the available space, selected components, feed system, and operating conditions before making a final design decision.
How This Calculator Works
The Linear Array uses L = (N−1)d | HPBW ≈ 50.8 / (N · d/λ) | D₀ = N² / [1 + 2 Σ (N−k) sinc(2k·π·d/λ)]. Supply Number of Elements (N), Element Spacing (d/λ) (λ), Single Element Gain (dBi) in the displayed units, then use the calculated values as the first engineering target for this antenna arrays design or analysis.
Design Notes
A linear antenna array combines multiple radiating elements to produce higher directivity, narrower beamwidth, and greater antenna gain than a single element. The spacing between adjacent elements has a major influence on radiation characteristics, beamwidth, sidelobe levels, and grating lobe formation. For broadside arrays, element spacing is typically maintained near 0.5 wavelengths to maximise gain while preventing grating lobes. Increasing the number of elements generally improves directivity and reduces beamwidth but also increases physical size and feed network complexity. Practical array performance depends on mutual coupling, amplitude tapering, phase errors, feed-line losses, manufacturing tolerances, scan angle, element radiation pattern, and environmental conditions.
Build and Tuning Notes
Use the calculated array dimensions and beam characteristics as the initial design targets before electromagnetic simulation or prototype fabrication. Maintain accurate element spacing and equal phase distribution for broadside arrays unless beam steering is intentionally required. Verify impedance matching, array factor, radiation pattern, gain, sidelobe levels, and beamwidth using a vector network analyser (VNA), anechoic chamber measurements, or antenna measurement range. Electromagnetic simulation using CST Studio Suite, Ansys HFSS, FEKO, NEC, or Altair Feko is recommended to evaluate mutual coupling, feed network performance, and beamforming accuracy before manufacturing.
Frequently Asked Questions
What is a linear antenna array?
A linear antenna array consists of multiple antenna elements arranged in a straight line with controlled spacing and excitation. The array combines the radiation from individual elements to increase gain, improve directivity, and shape the radiation pattern.
What is a Uniform Linear Array (ULA)?
A Uniform Linear Array is a linear antenna array in which all antenna elements are equally spaced and excited with equal amplitude. ULAs are widely used in radar, beamforming, wireless communication, and phased array systems.
Why is element spacing important?
Element spacing directly affects beamwidth, array gain, sidelobe levels, and the formation of grating lobes. A spacing of approximately 0.5 wavelengths is commonly used to achieve high performance while avoiding unwanted radiation lobes.
What are grating lobes?
Grating lobes are unwanted secondary radiation beams that appear when antenna elements are spaced too far apart, typically around one wavelength or greater. They reduce antenna performance and may cause interference in wireless systems.
Where are linear antenna arrays commonly used?
Linear antenna arrays are widely used in phased array radar, 5G and 6G base stations, satellite communication, radio astronomy, microwave links, smart antennas, adaptive beamforming, sonar, and direction-finding systems.
Why can measured array performance differ from calculated values?
Actual array performance depends on mutual coupling, feed network losses, phase imbalance, amplitude errors, element tolerances, manufacturing accuracy, environmental conditions, scan angle, and measurement uncertainty. Electromagnetic simulation and practical testing should be used to validate the final antenna array.
Alex Warren
B.Sc. in Electrical & Electronic Engineering (EEE)
Alex specialises in antenna design and wave propagation. His expertise helps ensure these calculators present practical RF concepts, useful design estimates, and clear engineering guidance for students, HAM operators, and wireless professionals.