PhysSandbox
Classical MechanicsWaves & SoundElectricity & MagnetismOptics & LightGravity & OrbitsLabs
🌙Astronomy & The Sky🌡️Thermodynamics🌍Biophysics, Fluids & Geoscience📐Math Visualization🔧Engineering🧪Chemistry

More from Electricity & Magnetism

Other simulators in this category — or see all 56.

View category →
NewUniversity / research

Yagi–Uda Antenna

Reflector, driven element, and directors: teaching pattern plus gain vs number of directors (schematic model).

Launch Simulator
NewUniversity / research

Smith Chart & Matching

Click to set normalized Z; series L/C along constant-r arcs and shunt L/C via Y = 1/Z; Γ, SWR, matching trail.

Launch Simulator
NewUniversity / research

VSWR & Standing Wave (Transmission Line)

Complex Z_L → Γ and VSWR; voltage magnitude envelope and animated Re{V} along a lossless line.

Launch Simulator
NewUniversity / research

Rectangular Waveguide TE₁₀

Dominant mode fields (E_y, H_x, H_z), cutoff f_c = c/(2a√ε_r), β and guide wavelength λ_g.

Launch Simulator
NewUniversity / research

Compton Scattering

Photon wavelength shift vs angle; λ_C ≈ 2.426 pm.

Launch Simulator
FeaturedSchool

Electric Field Visualizer

Place charges and watch field lines update in real time.

Launch Simulator
PhysSandbox

Interactive physics, chemistry, and engineering simulators for students, teachers, and curious minds.

Physics

  • Classical Mechanics
  • Waves & Sound
  • Electricity & Magnetism

Science

  • Optics & Light
  • Gravity & Orbits
  • Astronomy & The Sky

More

  • Thermodynamics
  • Biophysics, Fluids & Geoscience
  • Math Visualization
  • Engineering
  • Chemistry

© 2026 PhysSandbox. Free interactive science simulators.

PrivacyTermsContact
Home/Electricity & Magnetism/Phased Array

Phased Array

A phased array antenna uses multiple radiating elements to shape and steer a beam of electromagnetic radiation without physically moving the antenna. This simulator visualizes the fundamental principle behind this technology: the array factor for a uniform linear array. The radiation pattern in the far-field is determined by the constructive and destructive interference of waves from each element. The key mathematical description is the array factor, AF(θ) = Σ (from n=0 to N-1) e^{j n ψ}, where the total phase shift for the nth element is ψ = k d cosθ + β. Here, k is the wave number (2π/λ), d is the spacing between adjacent elements, θ is the observation angle from the array axis, and β is the applied progressive phase shift between elements, known as the steering phase. The simulator plots the normalized array factor, |AF(θ)|, against angle. By adjusting β, you electronically steer the main lobe (the direction of maximum radiation). Changing d alters the grating lobe structure, which are unwanted secondary maxima that appear when element spacing is too large. This model simplifies a real antenna by assuming isotropic point-source elements (no individual element pattern), an ideal far-field (Fraunhofer) region, and a lossless, perfectly coherent system. Interacting with it teaches core concepts of wave interference, spatial filtering, and how discrete sampling in space (the array) leads to periodic patterns in the angular domain. Students learn the critical design trade-off between steering range, beamwidth, and the avoidance of grating lobes.

Who it's for: Undergraduate engineering and physics students studying electromagnetics, antenna theory, or wave optics, as well as educators demonstrating wave interference and Fourier transform relationships in spatial domains.

Key terms

  • Array Factor
  • Beam Steering
  • Grating Lobes
  • Progressive Phase Shift (β)
  • Element Spacing (d)
  • Uniform Linear Array (ULA)
  • Wave Interference
  • Main Lobe

Array

8
0.5
0°

Steering the main lobe: phase ramps approximate true time delay for narrowband signals. Pattern ignores element pattern and mutual coupling.

Measured values

Array length3.50 λ

How it works

The same interference idea as Young’s slits, but in the radiation zone: electronic phase control steers energy without moving hardware.

Frequently asked questions

Why do unwanted 'grating lobes' suddenly appear when I increase the element spacing?
Grating lobes are a direct result of spatial aliasing. When the element spacing d exceeds λ/2, the phase difference between adjacent elements can exceed 180 degrees for some observation angles, creating additional directions where all waves add constructively. This is analogous to aliasing in time-domain signal sampling, where a high-frequency signal is misrepresented as a lower frequency if the sampling rate is too low. In antenna design, keeping d ≤ λ/2 typically ensures only one main lobe exists for all steering angles.
What physically controls the 'steering phase' (β) in a real phased array?
In a real system, β is controlled by phase shifters behind each antenna element. These are electronic components (e.g., diode or ferrite-based) that delay the signal to each element by a specific amount. By digitally commanding a progressive phase shift across the array, the wavefront emitted (or received) is tilted, steering the beam almost instantaneously. This is the key advantage over mechanically steered dishes, enabling rapid tracking and multi-target engagement in radar and modern communications.
Does this simulator show the complete radiation pattern of a real antenna?
No, this is a critical simplification. The plot shows only the 'array factor,' which assumes each element is an isotropic radiator (radiates equally in all directions). A real antenna element has its own directional pattern (the 'element factor'). The total radiation pattern is the product of the element factor and the array factor. The simulator isolates the effect of the array's geometry and phasing, which is the most important concept for understanding beamforming and steering.
How is 'beamwidth' related to the number of elements in the array?
Beamwidth, which measures the angular width of the main lobe, is inversely proportional to the total electrical size of the array. A larger number of elements (N) for a fixed spacing d makes the array physically longer, resulting in a narrower, more directive beam. This provides higher gain and better angular resolution. The simulator uses a fixed N, but the principle is evident: the main lobe sharpens as you add more sources of coherent interference.