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 every scan angle; the general steered limit is \(d \le \lambda/(1+|\sin\theta_0|)\), which the demo’s status panel tracks live.

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. The Status panel reports HPBW and peak SLL live, measured off the θ-cut on screen. At \(M = 8\), \(d = \lambda/2\), boresight it reads \(12.8^\circ\) and \(-12.8\) dB — the in-class MATLAB anchor. Drag \(M\) up to \(16\), then \(64\): the beam narrows to \(6.4^\circ\) and \(1.6^\circ\) while the SLL settles toward the \(-13.2\) dB uniform-illumination constant. Switch to Polar Cut to see the same beam drawn round.

  4. Break it. Raise \(d_x/\lambda\) from \(0.50\) to \(0.80\), then steer \(\theta_0\) to \(30^\circ\). The status panel flips to “⚠ grating lobes” (the steered limit is \(1/(1+\sin 30^\circ)\approx 0.67\)) and a grating lobe — a full-strength copy of the main lobe — rises near \(-49^\circ\). Watch the SLL readout jump to \(-0.0\) dB: a grating lobe is not a side lobe, it is a second main lobe. EW implication: a poorly spaced array leaks full-strength energy in unintended directions.

  5. Prove it is the steering, not the spacing. Set \(d_x/\lambda = 0.90\) and park \(\theta_0\) at \(0\) — clean, one lobe, SLL \(-12.5\) dB, because the broadside bound is \(d \le \lambda\). Now walk \(\theta_0\) up. The limit readout falls as you scan, and the warning trips partway. Same array, same spacing; only the scan angle changed. (This is the reading’s type-along, run backwards.)

  6. 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.

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

  8. 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. The rule is asymptotic in element count: at \(M = 8\) the panel reads \(28.8^\circ\) against a predicted \(25.6^\circ\), but by \(M = 64\) the measurement and the rule agree to within a percent.

  • Grating lobes appear when \(d\) exceeds \(\lambda/(1+|\sin\theta_0|)\) — keeping \(d \le \lambda/2\) is the angular-domain Nyquist choice that stays safe at every scan angle. Note what the bound does not say: at broadside it allows a full \(d \le \lambda\).

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

Source#

MATLAB bundle · L6_ArrayFactorAndSteering.m↓

The companion 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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