Steer a 16-element array and read its radiation pattern in the sandbox, and predict — before you read it off the screen — where the main beam points, how wide it is, and the spacing at which a grating lobe first appears.
An array does not swing on a motor: a linear phase ramp across N fixed elements — β_n = -n k d sin θ_0 — steers the summed array factor to any angle θ_0 you choose. Reading the main-beam direction, the half-power beamwidth (which narrows as 0.886 λ/(N d)), and the spacing at which a second, unwanted grating lobe appears is how you know what an array buys and what it costs.
Open the sandbox. It opens on a uniform broadside array at d = 0.5 λ, so a Reset gets you close. For this lab set the element count to N = 16, the taper to uniform and the element to isotropic. Each step names the one knob to change; leave everything else alone.
Elements N -> 16 Spacing d -> 0.5 lambda Taper -> uniform
Element -> isotropic Steering angle th0 -> 0 deg (change only in Step 1)
Watch the main-beam readout, the beamwidth readout and the phase-per-element readout beside the pattern plot — every number you predict is printed there.
Set the steering angle to θ_0 = 30°, keeping N = 16, d = 0.5 λ. Steering is a phase ramp, not a rotation. Predict the angle the main beam of the computed pattern points at, then read the main-beam readout.
The main beam of the measured pattern points at exactly 30° — put there by a phase ramp of β = -90° per element (-k d sin 30° at d = 0.5 λ), with nothing rotated.
Set the steering angle back to broadside, θ_0 = 0°, still N = 16, d = 0.5 λ, uniform taper. The half-power beamwidth of a uniform array is about 0.886 λ/(N d). Predict the beamwidth in degrees, then read the beamwidth readout (the width between the -3 dB points).
The beamwidth readout is about 6.36° — the width between the two -3 dB points located on the computed pattern, matching 0.886 λ/(N d) for N = 16. Double N and this beam halves.
Still at broadside, θ_0 = 0°, slowly increase the element spacing d. A second, full-height grating lobe appears once d/λ > 1/(1 + |sin θ_0|). Predict the spacing at which the first grating lobe appears at broadside, then sweep d and watch for it.
At broadside sin θ_0 = 0, so the limit is d/λ = 1/(1 + 0) = 1: a grating lobe first appears only once the spacing reaches a full wavelength, d = 1 λ — not λ/2. λ/2 is the usual default because it is the only spacing safe at every steering angle: the limit tightens to λ/2 only at endfire.
Everything above is waiting in the sandbox. Sweep the steering angle and watch the beam swing by phase alone, add elements and watch the beam narrow, widen the spacing to grow a grating lobe, and switch the taper to trade a lower side lobe for a wider beam.
- Steered the main beam to 30° with a phase ramp of β = -90° per element — no rotation
- Read the half-power beamwidth, about 6.36°, tracking 0.886 λ/(N d)
- Found the broadside grating-lobe limit at a full wavelength, d/λ = 1/(1 + |sin θ_0|) = 1 — not λ/2
- Every value you predicted is the demo's own array-factor arithmetic, not a picture