What is the element spacing requirement for a phased array to avoid grating lobes?
Grating Lobe Prevention
Grating lobes are an artifact of the periodic element arrangement. The array factor has maxima whenever the inter-element phase difference ψ = kd sinθ + β equals a multiple of 2π. The main beam occurs at ψ = 0 (the intended beam direction). Grating lobes occur at ψ = ±2π, ±4π, etc. The grating lobe direction is: sinθgl = sinθ₀ ± nλ/d, where n is an integer. For the first grating lobe to be outside the visible region (|sinθ| > 1): d must satisfy d < λ/(1 + |sinθ₀|).
At mmWave frequencies, the half-wavelength spacing requirement results in very small element separations: d = 5.4 mm at 28 GHz, d = 3.8 mm at 39 GHz, d = 2.5 mm at 60 GHz. This dense spacing constrains the element design and the packaging of T/R modules behind each element. At 60 GHz: 256 elements fit in a 40mm × 40mm area.
Some systems deliberately accept grating lobes to use larger element spacing (which simplifies the mechanical design and reduces mutual coupling). This is acceptable when the scan range is limited or when the element pattern has a null in the grating lobe direction (element pattern suppression).
Frequently Asked Questions
What happens if I exceed λ/2 spacing?
Grating lobes appear at scan angles where sinθgl = sinθ₀ + λ/d falls within the visible region (|sinθ| < 1). The grating lobe has the same amplitude as the main beam (for uniform excitation), effectively splitting the radiated power and degrading the array's directivity. This is usually unacceptable.
Can I use non-uniform element spacing?
Yes. Aperiodic (non-uniform) element spacing breaks the periodicity that creates grating lobes. Random or optimized sparse arrays can use average spacing > λ/2 without grating lobes, but with elevated average sidelobe levels. This is used in radio astronomy (very large baseline arrays) and some radar applications.
Does triangular lattice help?
Yes. A triangular (hexagonal) lattice packing allows element spacing up to d = λ/√3 ≈ 0.577λ for full-hemisphere scanning, compared to d = λ/2 for a rectangular lattice. This 15% increase in spacing reduces the number of elements by 25% for the same aperture, which is a significant cost savings for large arrays.