Interactive Virtual Laboratory for Undergraduate Antenna Engineering
Understand the fundamental principle of beam steering in phased-array antennas using progressive phase shifting.
Investigate the relationship between inter-element phase difference and beam steering angle.
Analyze how the number of antenna elements affects beamwidth and directivity.
Observe the array factor pattern and its variation with steering angle.
Explore grating lobes formation when element spacing exceeds λ/2.
Apply theoretical knowledge to predict and verify beam steering performance.
A phased-array antenna consists of multiple radiating elements arranged in a specific geometry (linear, planar, or conformal). By controlling the phase and amplitude of the signal fed to each element, the radiation pattern can be electronically steered without physically moving the antenna structure. This capability is fundamental to modern radar, 5G communications, and satellite systems.
To steer the main beam to an angle θ₀ from broadside, a progressive phase shift β must be applied between adjacent elements:
β = -kd sin(θ₀)
where k = 2π/λ (wavenumber), d = element spacing, θ₀ = steering angle
The negative sign indicates that elements must be delayed progressively to steer the beam in the positive θ direction.
For a uniform linear array of N isotropic elements with uniform amplitude and progressive phase shift β, the normalized array factor is:
AF(θ) = (1/N) × |sin(Nψ/2) / sin(ψ/2)|
where ψ = kd(sin θ - sin θ₀)
Approximate formula for large N:
HPBW ≈ 0.886 × λ/(Nd cos θ₀)
Occur when: |sin θ₀ + mλ/d| ≤ 1
Avoid by keeping d ≤ λ/2 for scanning to ±90°
Increases with N. For uniform linear array:
D ≈ 2N(d/λ) (at broadside)
Set the number of elements N = 8, element spacing d = 0.5λ, and steering angle θ₀ = 0° (broadside). Observe the symmetric radiation pattern with maximum at 0°.
Gradually increase the steering angle from 0° to 30° in steps of 10°. Record the progressive phase shift β calculated for each angle. Observe how the main beam shifts while maintaining its shape.
Fix θ₀ = 30° and vary N from 4 to 16. Measure the approximate half-power beamwidth (HPBW) for each case. Verify that HPBW is inversely proportional to N.
Set N = 8 and θ₀ = 45°. Gradually increase d/λ from 0.5 to 1.0. Observe the appearance of grating lobes when d > 0.5λ. Record the angles where additional maxima appear.
Set θ₀ = 90° (endfire). Calculate the required phase shift and verify it matches the theoretical value β = -kd. Observe the radiation pattern directed along the array axis.
Vary the operating frequency while keeping physical spacing constant. Observe how electrical spacing (d/λ) changes affect the radiation pattern and grating lobe formation.
| Trial | N | d/λ | θ₀ (deg) | β (deg) | HPBW (deg) | Grating Lobes? |
|---|---|---|---|---|---|---|
| 1 | 8 | 0.5 | 0 | 0 | - | No |
| 2 | - | - | - | - | - | - |