Side Lobe Level Calculator
Calculate broadside first sidelobe level, HPBW, broadside first null angle, directivity, and grating lobe conditions for linear antenna arrays.
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Math
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Enter parameters and click Calculate to view results
Formula & Theory
AF(theta) = sin(Nψ/2) / [N·sin(ψ/2)] where ψ = 2pi(d/lambda)sin(theta) | HPBW ≈ 50.8° / ((N-1)·d/lambda) | D_0 ≈ NThis formula is used to calculate antenna parameters for side lobe level calculator.
Overview
This side lobe level calculator (also called a sidelobe calculator or antenna array calculator) evaluates the broadside performance of a uniformly-spaced linear antenna array: first sidelobe level (SLL), half-power beamwidth (HPBW), first null angle, directivity, and grating lobe risk. Enter the number of elements, element spacing in wavelengths, and an amplitude taper to see how your array design performs — the standard first-pass calculation for phased array antenna design, from HAM Yagi and collinear stacks to radar arrays and 5G massive-MIMO panels.
Input Guide
Enter Number of Elements (N) exactly as shown on the calculator. Confirm every unit, selected option, and decimal position before calculating so the side lobe level result matches the intended antenna arrays design case.
Output Guide
The output section reports First Sidelobe Level (SLL), Half-Power Beamwidth (HPBW), Broadside First Null Angle, Broadside Directivity (D₀), Broadside Grating Lobe Status, Aperture Physical Length (L), Applied Taper Profile for the values you entered. Use these values as design targets, then compare them with available space, component limits, feed system behavior, installation environment, and measured performance before finalizing the design.
How This Calculator Works
The Side Lobe Level applies AF(theta) = sin(Nψ/2) / [N·sin(ψ/2)] where ψ = 2pi(d/lambda)sin(theta) | HPBW ≈ 50.8° / ((N-1)·d/lambda) | D_0 ≈ N to the entered values. Calculate broadside first sidelobe level, HPBW, broadside first null angle, directivity, and grating lobe conditions for linear antenna arrays. Use the result as a first-pass antenna arrays target, then validate it against losses, tolerances, mounting, nearby conductors, feed-line effects, and measurement conditions.
Design Notes
Every linear antenna array design is a three-way trade-off between narrow beamwidth (angular resolution), low sidelobe level (interference rejection, reduced clutter and jamming susceptibility), and high directivity (gain). Uniform excitation maximizes directivity but is capped at a -13.26 dB first sidelobe that adding more elements cannot improve — only amplitude tapering (feeding edge elements less power than center elements) pushes sidelobes lower. This side lobe level calculator's taper options trace the classic trade-off curve: a cosine taper reaches roughly -23 dB SLL at modest directivity cost, cosine-squared reaches about -32 dB with a larger penalty, and binomial taper eliminates sidelobes entirely in the ideal case at the expense of the widest beamwidth and lowest directivity of the group. There's no free lunch in array design — every dB of sidelobe suppression is paid for in beamwidth, directivity, or both, because suppressing sidelobes necessarily under-utilizes the array's edge elements (aperture efficiency loss).
Build and Tuning Notes
Grating lobes are the failure mode every array designer needs to check for: once element spacing reaches or exceeds one wavelength, a second full-strength main beam (a grating lobe) appears in the array factor, indistinguishable in amplitude from the intended beam, which destroys pattern predictability and causes ambiguous direction-finding. This calculator flags grating lobe risk for the broadside (theta = 0°) case, but the safe spacing threshold tightens as soon as the array scans off-broadside — a common rule of thumb is d ≤ lambda/(1 + |sin theta_scan|), meaning a wide-scan-angle array needs noticeably tighter element spacing than one built for broadside-only operation. Most practical broadside array designs settle on spacing between 0.5 lambda and 0.9 lambda to balance beamwidth against grating-lobe risk. Also note that the HPBW and directivity approximations used here are standard array-factor formulas valid for reasonably large N (roughly N ≥ 8–10); for very small arrays (2–4 elements), these closed-form estimates lose accuracy and a full array-factor sweep across all theta gives more trustworthy results.
Inputs used by this calculator
- Number of Elements (N).
- Element Spacing (d/lambda) — use lambda.
- Amplitude Distribution / Taper Profile.
Frequently Asked Questions
What does a side lobe level calculator show for an antenna array?
It calculates the first sidelobe level (SLL), half-power beamwidth (HPBW), broadside first null angle, directivity, and whether grating lobes will appear, based on the number of array elements, their spacing in wavelengths, and the amplitude taper applied.
Why can't I get below -13.26 dB sidelobes with uniform element excitation?
A uniformly-fed linear array's sidelobe level is a fixed mathematical property of its sinc-like array factor pattern, staying at roughly -13.26 dB regardless of how many elements you add or how far apart they're spaced. Lowering sidelobes further requires tapering the amplitude fed to each element, not adding more uniformly-excited elements.
What is a grating lobe and why does it matter in array design?
A grating lobe is an unwanted secondary main beam that appears at full strength when element spacing is too large relative to wavelength — typically at or beyond one wavelength for a broadside array. Because it radiates as strongly as the intended main beam, it causes ambiguous direction-finding in radar, wastes transmit power, and increases susceptibility to interference.
What's the trade-off between sidelobe suppression and beamwidth in a phased array?
Tapering an array's amplitude distribution to lower sidelobes always broadens the main beam and reduces directivity relative to uniform excitation, since suppressing sidelobes under-utilizes the array's outer elements. Binomial taper is the extreme case: it eliminates sidelobes in theory but produces the widest beamwidth and lowest directivity of any common taper profile.
How does element spacing affect beamwidth, directivity, and grating lobes?
Increasing element spacing — up to just under one wavelength — narrows the beamwidth and raises directivity for a fixed number of elements, since the total aperture length grows with spacing. Push spacing past one wavelength at broadside, though, and a grating lobe appears, which is why most practical designs stay between roughly 0.5 lambda and 0.9 lambda.
When should I use a cosine, cosine-squared, or binomial taper?
Cosine taper is a good middle ground for moderate sidelobe suppression (~-23 dB) without a large directivity penalty. Cosine-squared trades more directivity for lower sidelobes (~-32 dB), useful when sidelobe-driven interference or clutter is a bigger concern than gain. Binomial taper is reserved for applications where sidelobes must be eliminated entirely and beamwidth/directivity loss is acceptable.
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.