Array Spacing Calculator
Calculate the maximum allowable antenna element spacing to prevent grating lobes for a specified scan angle in a uniform linear phased array.
2
Inputs
Live
Math
3
Related
Enter parameters and click Calculate to view results
Formula & Theory
dmax/λ = 1 / (1 + sin(θmax)), λ = c / fThis formula is used to calculate antenna parameters for array spacing calculator.
Overview
The Array Spacing Calculator determines the maximum safe inter-element spacing ($d/\lambda$) required to prevent grating lobes in uniform linear phased arrays. Essential for radar, 5G Massive MIMO, and electronic beam-steering architectures, this tool computes physical spacing limits based on frequency and maximum beam scan angle.
Input Guide
Enter Frequency, Maximum Scan Angle exactly in the units shown by this array spacing. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.
- Frequency — use MHz.
- Maximum Scan Angle — use °.
Output Guide
The results describe the calculated array spacing 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 Spacing uses dmax/λ = 1 / (1 + sin(θmax)), λ = c / f. Supply Frequency (MHz), Maximum Scan Angle (°) in the displayed units, then use the calculated values as the first engineering target for this antenna arrays design or analysis.
Design Notes
In phased array antenna design, grating lobes are secondary main beams that appear when inter-element spacing becomes too large relative to operating wavelength. To ensure the visible space contains only a single main beam up to a maximum electronic scan angle ($\theta_{\text{max}}$), element spacing must satisfy the classic grating lobe condition: $d/\lambda \le 1 / (1 + \sin(\theta_{\text{max}}))$. For broadside arrays ($\theta_{\text{max}} = 0^{\circ}$), this limit is $0.5\lambda$, while wide-angle scanning requires significantly tighter spacing.
Build and Tuning Notes
When laying out printed circuit board (PCB) patch arrays or dipole sub-arrays, maintain strict mechanical tolerances to avoid element-to-element grating lobe degradation. Note that tighter spacing increases mutual coupling between adjacent antenna elements, which can distort active element patterns and impact active input impedance matching. Compensate for mutual coupling via active impedance calibration or decoupling networks.
Frequently Asked Questions
What are Grating Lobes and why must they be avoided?
Grating lobes are identical copies of the main antenna beam that radiate power in unintended spatial directions. They occur when array element spacing exceeds critical thresholds, causing wasted radiated energy, decreased antenna gain, and severe angular ambiguities in radar and tracking systems.
How does Maximum Scan Angle affect required element spacing?
As the electronic scan angle increases toward end-fire (closer to $90^{\circ}$), the required spacing threshold drops dramatically. For example, a broadside array ($0^{\circ}$) allows up to $0.5\lambda$ spacing, whereas scanning to $90^{\circ}$ requires spacing to approach $0.5\lambda$ or less to completely suppress grating lobes from entering visible space.
Why is 0.5λ (half-wavelength) commonly chosen as a standard design spacing?
Half-wavelength spacing ($0.5\lambda$) represents a universal compromise: it prevents grating lobes for any scan angle up to $90^{\circ}$ while keeping physical spacing large enough to minimize severe mutual coupling between adjacent antenna elements.
How does mutual coupling impact close array spacing?
Placing antenna elements too close together increases electromagnetic mutual coupling (crosstown current induction). This alters individual active element radiation patterns, introduces input mismatch, and requires specialized decoupling structures or DSP calibration algorithms.
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.