Circular Array Calculator
Calculate element spacing and ideal gain for a uniformly excited circular array.
3
Inputs
Live
Math
3
Related
Enter parameters and click Calculate to view results
Formula & Theory
Arc spacing = 2πr/N, Array gain ≈ 10 log10(N)This formula is used to calculate antenna parameters for circular array calculator.
Overview
The Circular Array Calculator determines adjacent arc spacing, array gain, and total estimated directivity (dBi) for Uniform Circular Arrays (UCA). Widely utilized in 360-degree direction finding (DF), radar, satellite communication, and wireless base stations, circular arrays provide full azimuthal beam scanning without pattern degradation.
Input Guide
Enter Elements, Array Radius, Element Gain exactly in the units shown by this circular array. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.
- Elements.
- Array Radius — use λ.
- Element Gain — use dBi.
Output Guide
The results describe the calculated circular 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 Circular Array uses Arc spacing = 2πr/N, Array gain ≈ 10 log10(N). Supply Elements, Array Radius (λ), 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
Uniform Circular Arrays position $N$ elements symmetrically around a ring of radius $r$. Unlike linear arrays, UCAs can electronically steer a main beam throughout $360^{circ}$ in azimuth while maintaining a nearly invariant directional beam shape. Inter-element arc length is calculated as $d = (2pi r)/N$. To eliminate grating lobes and maintain smooth beam steering, adjacent element spacing should ideally be kept between $0.5lambda$ and $0.75lambda$.
Build and Tuning Notes
When designing circular arrays for DOA (Direction of Arrival) estimation or beamforming, feed each element with precise phase and amplitude weights derived from Bessel function expansions. Account for mutual coupling between elements, which can distort active element patterns and alter input impedances. Validate beam synthesis and radiation patterns using 3D electromagnetic simulation software (such as HFSS or CST Studio) or anechoic chamber turntable measurements.
Frequently Asked Questions
What is a Uniform Circular Array (UCA) and why is it used?
A Uniform Circular Array arranges antenna elements symmetrically in a circle. Its principal advantage is $360^{circ}$ symmetric azimuthal coverage and uniform beam-steering capability, making it ideal for direction finding (DF) and wireless base station spatial multiplexing.
How is element spacing calculated in a circular array?
Inter-element arc spacing is calculated by dividing the circumference of the array circle ($2pi r$) by the total number of elements ($N$): $\text{Spacing} = (2pi r) / N$.
What happens if element spacing in a circular array exceeds 0.5λ?
Spacing elements beyond $0.5lambda ext{--}0.75lambda$ introduces grating lobes (secondary main beams) into visible space during electronic beam steering, reducing directive gain and creating spatial ambiguity.
How does Array Gain scale in a circular array?
Ideal array gain scales logarithmically with the number of isotropic elements ($N$): $\text{Array Gain (dB)} = 10 log_{10}(N)$. Total directivity is found by adding individual element gain ($G_e$) to array gain.
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.