Demo — Phased Array Simulator

Demo — Phased Array Simulator#

This is the interactive phased-array simulator we use in class, embedded here for self-study. It builds the array factor for a linear or planar array, steers the beam with element phasing, and visualizes the result five ways: a pattern plot, a 2D heatmap, the element phase fronts, a polar cut, and a 3D hemisphere. Use it to see the ideas from the reading — beam steering, beamwidth, side lobes, and grating lobes.

The idea#

Each element radiates the same signal with a programmed phase. Sloping the phase across the array tilts the wavefront and points the main lobe at the steering angle \(\theta_0\):

\[ \Delta\phi = \frac{2\pi}{\lambda}\,d\,\sin\theta_0. \]

Keep the spacing \(d \le \lambda/2\) to avoid grating lobes at broadside.

Interactive demo#

Open in full screen

Walkthrough#

Work the Pattern tab first, then Polar Cut, then Planar, then 3D Hemisphere.

  1. Baseline. Linear, \(M = 8\), \(d_x/\lambda = 0.50\), \(\theta_0 = 0\). Note the main lobe at boresight and the first side lobes near \(-13\) dB (uniform illumination).

  2. Steer it. Push \(\theta_0\) to \(30^\circ\), then \(60^\circ\). The main lobe moves to the steering angle and broadens by about \(1/\cos\theta_0\).

  3. Read the numbers. Switch to Polar Cut and read HPBW and SLL directly. At \(N = 8\), \(d = \lambda/2\), boresight, HPBW is about \(12.7^\circ\) — the in-class MATLAB anchor.

  4. Break it. Raise \(d_x/\lambda\) from \(0.50\) to \(0.80\). Grating lobes appear. EW implication: a poorly spaced array leaks full-strength energy in unintended directions.

  5. Go planar. Switch to Planar (\(M = 8\), \(N = 8\), \(d_x = d_y = \lambda/2\)) and steer \(\theta_0\) and \(\phi_0\). The 2D Heatmap shows the beam wandering across the hemisphere.

  6. See the cone. Open the 3D Hemisphere tab. Drag to rotate and confirm the focused cone with its surrounding side-lobe rings.

  7. Add the element factor. Toggle Element factor (cos θ). The distant side lobes pull back toward boresight — real elements have their own pattern that multiplies the array factor.

Key observations#

  • Uniform illumination → ≈ −13 dB side lobes. Tapering would lower them at the cost of a wider main beam.

  • HPBW broadens as \(1/\cos\theta_0\). Steering to \(60^\circ\) roughly doubles the beamwidth and costs about 3 dB of gain.

  • Grating lobes appear for \(d > \lambda/2\) at broadside — the angular-domain Nyquist limit.

  • A planar array’s beam is a 3D cone, steerable in both azimuth and elevation.

Source#

MATLAB · code/L6_ArrayFactorAndSteering.m↓

The in-class script builds the array factor for an \(N\)-element linear array, plots it in polar dB, steers the beam to \(0^\circ\), \(30^\circ\), and \(60^\circ\) to watch the HPBW broaden, and marks the first side-lobe level to confirm the \(-13.2\) dB rule.

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