What element spacing is optimal for a broadside array?

Half-wavelength spacing (d = λ/2) is the standard choice for broadside arrays. This spacing provides the narrowest beamwidth without introducing grating lobes. Spacing less than λ/2 widens the main beam and increases mutual coupling between elements, degrading efficiency. Spacing greater than λ/2 narrows the beam further but introduces grating lobes that appear at angles where the path length difference between adjacent elements equals a full wavelength. For a uniform broadside array with d = λ/2, the first grating lobe appears at ±90° (endfire), which is at the physical horizon and typically acceptable.

How does broadside array gain scale with element count?

For a uniform linear broadside array with N elements at half-wavelength spacing, the directivity is approximately N times the directivity of a single element. In decibels, adding elements increases directivity by 10·log₁₀(N): doubling the element count adds 3 dB. A 16-element broadside array of isotropic elements achieves 12 dBi directivity; with patch elements (6 dBi each), the array reaches approximately 18 dBi. The half-power beamwidth narrows proportionally: HPBW ≈ 0.886λ/(N·d) radians for a uniform amplitude taper.

What is the difference between broadside and endfire arrays?

A broadside array feeds all elements in phase so the main beam points perpendicular to the array axis. An endfire array applies a progressive phase shift equal to the element spacing in wavelengths (β·d) so the main beam points along the array axis. Broadside arrays produce a fan beam that is narrow in the array plane and wide in the orthogonal plane, suitable for azimuth scanning. Endfire arrays produce a cigar-shaped beam along the array axis, useful for applications like Yagi antennas and traveling-wave arrays where radiation along the structure is desired.

What is a Broadside Array? | Antenna Array Radiation Pattern

Definition & Principle

A broadside array is a linear or planar antenna array in which all elements are excited with equal phase (zero progressive phase shift), causing constructive interference in the direction perpendicular to the array axis and destructive interference in all other directions. The result is a main beam that points "broadside" to the array structure, with a beamwidth that narrows as the number of elements or the total array aperture increases.

The broadside condition is the simplest array excitation and serves as the reference configuration for understanding phased array beam steering. When a progressive phase shift δ is applied between elements, the beam scans away from broadside by an angle θ₀ = arcsin(δ/(βd)), where β = 2π/λ and d is the element spacing. With δ = 0, the beam remains at θ₀ = 0 (broadside). Broadside arrays are fundamental to base station antennas, radar panels, and satellite antenna panels where the primary coverage direction is perpendicular to the mounting surface.

Key Formulas

Array Factor (N-element uniform broadside):

AF(θ) = sin(Nπd sinθ/λ) / (N sin(πd sinθ/λ))

Half-Power Beamwidth:

HPBW ≈ 0.886λ / (N × d) [radians]

N = 8, d = λ/2: HPBW ≈ 0.886/(8×0.5) = 0.221 rad = 12.7°

Directivity (uniform, half-wave spacing):

D ≈ N × D_element

16 isotropic elements: D = 16 = 12 dBi

Array Configuration Comparison

Parameter	Broadside	Endfire	Scanned (Phased)	Planar Broadside
Phase Excitation	δ = 0	δ = βd	Variable δ	δ = 0 (both axes)
Beam Direction	Perpendicular	Along axis	Steerable	Normal to plane
Beam Shape	Fan beam	Cigar beam	Fan (scanned)	Pencil beam
HPBW (N=8, λ/2)	12.7°	~36°	12.7°/cosθ	12.7° × 12.7°
Directivity (N=8)	9 dBi	12 dBi	9 dBi (broadside)	18 dBi (8×8)
Grating Lobe Free	d ≤ λ	d ≤ λ/2	d ≤ λ/(1+sinθ)	d ≤ λ/2
Example	Base station panel	Yagi antenna	AESA radar	SATCOM flat panel

Practical Application

A 5G macro base station antenna panel uses a vertical broadside array of 8 cross-polarized patch elements at 3.5 GHz with λ/2 = 42.9 mm spacing. With all elements fed in phase, the vertical beamwidth narrows to approximately 12.7°, directing energy toward the ground-level coverage area rather than wasting it skyward. The horizontal pattern remains broad (~65° sector) determined by the individual patch element pattern. An electrical downtilt of 6° is applied by adding a linear phase progression of 27° between elements, shifting the beam below the horizon to optimize cell coverage without mechanical tilt adjustment. The array achieves 18 dBi gain per polarization (8 × patch directivity) with a front-to-back ratio exceeding 25 dB.

Frequently Asked Questions

What spacing is optimal for broadside?

Half-wavelength (d = λ/2) provides the narrowest beam without grating lobes. Less than λ/2 widens the beam and increases mutual coupling. Greater than λ/2 creates grating lobes at angles where path difference equals a full wavelength.

How does gain scale with element count?

Directivity is approximately N × D_element. Doubling elements adds 3 dB. A 16-element array of 6 dBi patches achieves ~18 dBi. HPBW narrows as 0.886λ/(N·d).

Broadside vs endfire?

Broadside: all elements in phase, beam perpendicular, fan beam pattern. Endfire: progressive phase shift, beam along axis, cigar beam. Broadside suits panel antennas; endfire suits Yagi and traveling-wave designs.

Broadside Array