Array Factor Calculator
Calculate the normalized array factor, array factor in dB, phase difference, main beam direction, and estimated array gain for a uniform linear antenna array.
4
Inputs
Live
Math
3
Related
Enter parameters and click Calculate to view results
Formula & Theory
AF = |sin(Nψ/2)/(N·sin(ψ/2))|, ψ = 2πd cosθ + βThis formula is used to calculate antenna parameters for array factor calculator.
Overview
The Array Factor Calculator evaluates the spatial radiation pattern, beam steering angle, phase shift ($psi$), and array directivity gain for a Uniform Linear Array (ULA). It allows RF engineers and phased array antenna designers to analyze main lobe positioning, side lobe levels, and grating lobe conditions.
Input Guide
Enter Number of Elements, Element Spacing, Observation Angle, Progressive Phase exactly in the units shown by this array factor. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.
- Number of Elements.
- Element Spacing — use λ.
- Observation Angle — use °.
- Progressive Phase — use °.
Output Guide
The results describe the calculated array factor 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 Array Factor uses AF = |sin(Nψ/2)/(N·sin(ψ/2))|, ψ = 2πd cosθ + β. Supply Number of Elements, Element Spacing (λ), Observation Angle (°), Progressive Phase (°) in the displayed units, then use the calculated values as the first engineering target for this antenna arrays design or analysis.
Design Notes
The Array Factor ($AF$) describes the far-field interference pattern created by combining isotropic radiators in a linear line. Total radiated pattern equals the Array Factor multiplied by the single element radiation pattern (Pattern Multiplication Principle). Main beam steering is achieved by applying a progressive phase shift ($eta$) between adjacent elements: $eta = -k cdot d cdot cos( heta_0)$. To prevent unwanted grating lobes (secondary main beams), element spacing ($d$) should typically be maintained at $lambda/2$ or smaller.
Build and Tuning Notes
When implementing phased arrays in hardware (such as Massive MIMO or radar beamformers), phase shifter resolution and amplitude tapering affect null depth and side lobe levels. Validate Array Factor calculations using EM simulation tools or multi-channel vector network analyzers (VNA). Ensure accurate mutual coupling compensation across individual RF channels to prevent steering angle deviations.
Frequently Asked Questions
What is Array Factor in antenna array design?
Array Factor ($AF$) is a mathematical representation of the far-field pattern produced by an array of identical isotropic radiators. It depends strictly on element geometry, count ($N$), spacing ($d/lambda$), observation angle ($ heta$), and progressive phase shift ($eta$).
How do you steer the main beam in a Phased Array?
The main beam direction ($ heta_0$) is steered electronically by adjusting the progressive phase difference ($eta$) between adjacent elements according to the equation: $eta = -2pi (d/lambda) cos( heta_0)$.
What causes Grating Lobes in an antenna array?
Grating lobes occur when inter-element spacing ($d$) exceeds half a wavelength ($lambda/2$). They create full-amplitude secondary main beams in unintended directions, wasting power and causing spatial interference.
How does the number of elements (N) affect array performance?
Increasing the number of elements ($N$) narrows the main beamwidth (improving spatial resolution), increases directivity gain ($10 log_{10}(N)$ dB), and increases the total number of pattern nulls and side lobes.
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.