Antenna Array Beamforming Calculator

The core math describing the radiation pattern of a linear array is the Array Factor (AF). It sums the contributions from each antenna element, each with a specific weight and phase shift.

Here, $N$ is the number of elements, $w_n$ is the amplitude weighting (or "window") for the n-th element, $k = 2\pi/\lambda$ is the wavenumber, $d$ is the spacing between elements, and $\theta$ is the observation angle. The exponential term $e^{j n k d \sin\theta}$ represents the phase difference of the signal arriving at the n-th element.

When we want to steer the beam to a specific angle $\theta_0$, we introduce a progressive phase shift across the array. The pattern is often analyzed in terms of a generalized phase variable $\psi$.

For a uniform array (where all $w_n = 1$), the array factor simplifies to a closed-form expression. Its magnitude shows the classic sinc-like pattern, defining the main lobe and sidelobes.

The variable $\theta_0$ is your scan angle . Changing it shifts the entire pattern. The positions of the nulls (where the signal is zero) and the width of the main beam are determined by $N$ and $d$.

5G and mmWave Cellular Networks: This is the most direct application. At high frequencies like 28 GHz, signals attenuate quickly. Phased arrays in base stations and user devices form narrow, steerable beams to maintain a strong link. The simulator's parameters directly model the arrays used in these systems, where controlling sidelobe levels is crucial to avoid interfering with neighboring cells.

Radar and Military Systems: Phased array radars can electronically scan their beam across the sky at incredible speeds, without moving a heavy dish. This allows them to track multiple targets simultaneously. The "Sidelobe Level" control in the simulator relates to stealth technology—low sidelobes make a radar harder to detect from the side.

Satellite Communications: Modern satellites use phased arrays on their downlink beams to dynamically shape coverage areas on Earth. For instance, a satellite can focus more signal power over a densely populated city and less over an ocean, optimizing bandwidth. The beam steering you practice here is fundamental to that process.

Medical Imaging and Therapy: Ultrasound and certain cancer treatment systems use acoustic phased arrays. The same beamforming principles apply: by controlling the timing (phase) of signals from many transducers, they can focus ultrasonic energy precisely on a tumor deep inside the body without damaging surrounding tissue.

First, do you think "the more elements, the absolutely better"? While directivity indeed becomes sharper, in reality, cost, computational load, and physical installation space skyrocket. For example, doubling the number of elements from 16 to 32 only improves the beamwidth by about 1/√2 (approximately a 30% narrowing), requiring a cost-effectiveness judgment. Furthermore, you need complex circuitry and a control system to drive all elements, which also increases the risk of failure.

Next, the misconception that "the Hann window is the best." The Hann window certainly suppresses sidelobes, but it widens the main beam width, resulting in a directivity gain loss of about 1.5 dB. For instance, if your goal is precise communication with a distant point, a Uniform (equal amplitude) window, which has a sharper main beam even with somewhat higher sidelobes, might be more advantageous. Understand the trade-off of "what you sacrifice versus what you gain" according to your application.

A common pitfall in parameter setting is ignoring the combination of "scan angle" and "element spacing". Try it with the tool. You'll see that setting d=0.7λ and increasing the scan angle to 60 degrees causes a significant drop in main beam strength (the beam "degrades"). This is because the effective aperture appears smaller. In practical design, it's a golden rule to determine the element spacing after first verifying the scannable range via simulation.