Array Parameters
Number of elements N8
Element spacing d/λ0.50
Grating lobe free: d/λ < 1/(1+|sinθ₀|)
Scan angle θ₀0 °
Window Function
Grating Lobe Warning: Element spacing is too large. Grating lobes are present in visible space.
— °
HPBW (3dB beamwidth)
— dB
First sidelobe level
— dBi
Directivity
None
Grating lobe
Polar Radiation Pattern (normalized, linear)
AF(θ) — dB vs Angle
Theory Notes
Array Factor (linear array):
$$AF(\theta) = \sum_{n=0}^{N-1} w_n \cdot e^{j n k d \sin\theta}$$
where $k = 2\pi/\lambda$, steering phase: $\psi = kd(\sin\theta - \sin\theta_0)$
Uniform aperture (closed form):
$$|AF(\psi)| = \left|\frac{\sin(N\psi/2)}{N\sin(\psi/2)}\right|$$
Grating lobe condition: $d > \frac{\lambda}{1+|\sin\theta_0|}$
Engineering note: 5G mmWave (28 GHz) base stations use 64–256 element UPAs for beam steering.
Half-wavelength spacing (d = 0.5λ) is the standard design allowing full hemisphere scan without grating lobes.
The Dolph-Chebyshev taper achieves minimum beamwidth for a prescribed equiripple sidelobe level.