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Phased Array / 5G

Phased Array Antenna Beam Steering Simulator

Steer an N-element phased array electronically — without any mechanical motion — by tweaking the per-element phase. Adjust element count, spacing, frequency, steering angle and taper and watch the phase shift, beamwidth, gain, side-lobe level and grating-lobe onset update in real time.

Parameters
Element count N
Elements in a linear array (planar uses N×N or N×N/2)
Element spacing d
λ
Typically λ/2; larger values produce grating lobes
Carrier frequency f
GHz
Steering angle θ₀
°
Off-broadside steering angle
Amplitude taper
Window function that suppresses side-lobes
Array topology
Sets the number of phase shifters / T/R modules
Display angle range
°
Total angular span shown on the beam-pattern chart
Results
—
Per-element phase shift (deg)
—
HPBW (deg)
—
Array directivity (dB)
—
Total gain (dBi)
—
Side-lobe level (dB)
—
Grating lobe
—
Linear array + beam visualisation

Left: N-element linear array with per-element phase coded in colour. Right: polar beam pattern (main lobe blue, side-lobes pale). When a grating lobe enters the visible region it turns red as a warning.

Beam pattern — gain vs azimuth
Side-lobe level by taper
Theory & Key Formulas

$$\Delta\phi = \frac{2\pi d}{\lambda}\sin\theta_0,\qquad \text{HPBW} \approx \frac{51°}{N \cdot d/\lambda}\cdot\frac{1}{\cos\theta_0}$$

Δφ: progressive phase between adjacent elements. N: element count, d: spacing, λ: wavelength, θ₀: steering angle. Broadside HPBW is 51°/(N·d/λ); steering broadens it by 1/cos θ₀.

$$D_{\text{array}} \approx 10\log_{10}(N) - 1\ \text{[dB]},\qquad G_{\text{tot}} = D_{\text{array}} + G_{\text{elem}}$$

Simplified directivity of an N-element linear array (assuming d=λ/2). Element gain G_elem ≈ 5 dBi for a typical microstrip patch.

$$\frac{d}{\lambda} < \frac{1}{1+|\sin\theta_{\max}|}\quad\Rightarrow\quad\text{no grating lobe}$$

Grating-lobe avoidance. To steer out to θ_max=60° you need d<λ/1.866≈0.535λ.

Phased Array Antenna Beam Forming — Phase Control, Gain & Side-Lobes

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"Phased array" — that's the thing you hear about with 5G and self-driving radars, right? How is it different from a regular parabolic dish?
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Nice question. A parabolic dish chases its target by physically pointing the dish. That needs a mechanical gimbal and there's a hard limit on how fast you can slew. A phased array lays tiny elements (patch antennas) in a grid and just shifts the phase of the wave on each element electronically to steer the beam. You can hop the beam to a new direction in microseconds, which is exactly why an AEGIS destroyer can track hundreds of targets at once — that's the headline difference.
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How is "shifting the phase electronically" actually computed? When I set the steering angle θ₀ to 30° on the left, Δφ jumps to 90°…
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That's exactly the relation Δφ = (2πd/λ)·sin θ₀. With d=λ/2 and θ₀=30°, Δφ = 2π·0.5·sin30° = 2π·0.5·0.5 = π/2 rad = 90°. If you feed phases 0°, 90°, 180°, 270°, 360°… into successive elements, all of their waves line up exactly in phase along θ₀=30°. Move the θ₀ slider and you can watch the polar pattern on the right tilt accordingly.
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When I push d beyond 1λ the "Grating lobe" card turns red. What's that about?
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Grating lobes — the scariest thing in phased-array design. A "fake beam" with the same intensity as the main lobe shows up in the visible region (−90° to +90°). For radar that means ghost targets; for 5G it means interference. The avoidance rule is d/λ < 1/(1+|sin θ_max|), so keeping spacing near λ/2 is the golden rule. At 28 GHz 5G mmWave, λ≈10.7 mm, so d≈5.4 mm — that's the integration density Qualcomm's QTM052 RF modules pull off.
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Switching the taper from Uniform to Chebyshev drops the side-lobe level from −13 dB to −30 dB. Sounds like a free win — is there a catch?
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There absolutely is a trade-off. A taper attenuates the edge elements relative to the centre — basically a window function. Side-lobes drop, but the main-lobe half-power beamwidth (HPBW) widens, which means lower angular resolution. Gain drops slightly too. So AEGIS SPY-1, which prioritises clutter rejection, uses Taylor/Chebyshev. A 5G mmWave system that wants raw throughput stays closer to uniform. Side note: Starlink's flat panel is a PESA (passive — phase only on each element) while Patriot or F-35 AESAs put a full T/R module behind every element. Cost, performance and cooling are completely different worlds.
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There's also a "time delay" value. How is that different from a phase shift?
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Good catch, this is the deep end. A phase shifter applies Δφ at one carrier frequency. When the signal is wide-band (OFDM >100 MHz, SAR chirps spanning several GHz) every frequency in the band has its own λ, so the actual beam direction varies slightly with frequency. That's called beam squint, and it bites in wideband 5G and SAR. The fix is True Time Delay (TTD) — fibre-optic delay lines or CMOS LC delay lines that impose a physical Δt = d·sin θ₀/c on each element. The tool reports Δt in picoseconds, so you can confirm d=λ/2, θ₀=30°, f=28 GHz gives about 8.93 ps.

Frequently asked questions

The progressive phase between adjacent elements is Δφ = (2πd/λ)·sin(θ_0), where d is element spacing, λ is wavelength and θ_0 is the desired beam-pointing angle (steering angle). For d=λ/2 and θ_0=30°, Δφ=π/2 rad (90°). Feeding 0, Δφ, 2Δφ, … into the elements makes the waves from all elements add in phase along θ_0, so the beam steers electronically without any mechanical motion. This tool reports Δφ in degrees, and you can verify that N=32, d=λ/2, θ_0=30° gives exactly 90°.
A grating lobe (a spurious beam with the same gain as the main lobe) enters the visible region when the element spacing is too large for the chosen steering angle. The avoidance condition is d/λ < 1/(1+|sin θ_max|). At broadside (θ=0) d<λ is enough, but for ±60° steering you need d<λ/(1+sin60°)≈0.535λ. Keeping d at λ/2 is safe out to ±90° (d/λ·(1+1)=1.0 just at the boundary). The tool automatically flags grating lobes and shows an NG verdict when one is present.
Uniform excitation (all elements equal amplitude) has a sharp amplitude cut at the array edge, so diffraction fixes the worst side-lobe at −13.3 dB. Applying a taper (a window that reduces the amplitude of the edge elements relative to the centre) smooths the distribution and lowers the side-lobes: Taylor −25 dB, Chebyshev (equi-ripple) −30 dB and Hamming −42 dB are typical values. The trade-off is a wider half-power beamwidth (broader main beam for the same N). Radar applications that need clutter rejection use Taylor or Chebyshev, while 5G mmWave throughput-first systems stay closer to uniform.
Phase shifters impose Δφ at one carrier frequency, so a wideband signal experiences different steering angles at different frequencies — an effect called beam squint. It becomes a problem in wideband SAR or in 5G OFDM signals wider than ~100 MHz. True Time Delay (TTD) replaces phase shifters with physical delay elements (fibre, CMOS LC delay lines) that impose a real time delay Δt = d·sin(θ_0)/c per element. The tool reports this equivalent delay in picoseconds, e.g. d=λ/2, θ_0=30°, f=28 GHz gives Δt≈8.93 ps.

Real-world applications

Military and shipboard radar (AESA): the US Navy AEGIS SPY-1 (four fixed planar arrays, ~4096 elements each), Patriot PAC-3 guidance, and the nose-mounted AESA radars on the F-22/F-35 (APG-77 / APG-81, ~1500 elements) all demand multi-target tracking and µs-class beam switching that mechanical antennas simply cannot deliver. They are active arrays with a transmit/receive (T/R) module behind every element, dissipate kilowatts and require active cooling.

5G mmWave base stations and handsets: phased arrays now ship in volume at 28 GHz (n257/n258/n261) and 39 GHz (n260) — Qualcomm QTM052/QTM535, Samsung Galaxy S mmWave variants, AT&T and Verizon 5G base stations. 8×8 or 16×16 patch arrays with λ/2≈5 mm spacing run hybrid beamforming (HBF) to enable massive-MIMO spatial multiplexing.

Satellite communication and automotive radar: SpaceX Starlink user terminals (flat-panel PESA electronic scan), Continental ARS540 and similar 4D imaging radars (76–81 GHz, ~1000 elements), and 28 GHz development modules such as Anokiwave AWMF-0157. They lock onto LEO satellites without mechanical pointing, or resolve a pedestrian from a car 50 m away with 0.1° angular accuracy in an automotive sensor.

Weather radar, MRI and ultrasound: NEXRAD MPAR phased-array weather radars, phased-array MRI receive coils and phased-array ultrasound probes all exploit the same principle — interfering waves from many elements steered electronically. Verasonics research scanners and GE/Philips phased-array cardiac probes are typical examples; the formulas in this tool apply directly, only λ and frequency must be reinterpreted.

Common pitfalls

The biggest trap is "believing element spacing must always be exactly λ/2". λ/2 is just the upper limit that keeps the array grating-lobe-free out to ±90° — it is not a fixed value. If you only need to steer ±30° you can space elements as wide as d/λ < 1/(1+sin30°) = 2/3 ≈ 0.667, which cuts ~25% of the element count for the same aperture. Push d beyond λ/2 when you do need wide steering, however, and a grating lobe enters the visible region — ghost targets on radar, cross-cell interference for 5G. Decide on the required steering range and the acceptable SLL first, then pick d.

Next is "more elements always means more gain". In theory D ≈ 10log₁₀(N) gives 30 dB at N=1024, but in practice (i) the feed network gets lossier as N grows, (ii) T/R module calibration errors (±0.5 dB amplitude, ±5° phase) cost 1–3 dB of effective gain, (iii) mutual coupling distorts the edge-element pattern, and (iv) very large arrays become thermally limited so usable drive power drops. Treat the simplified formula as the "ideal upper bound" and budget 2–3 dB less for the actual hardware.

Finally, "as long as phase shifters are precise, wide-band signals will be fine". Phase shifters are designed for one frequency; a wide-band waveform sees different λ at each end of the band, so the beam squints. With a 64-element array steered to 60° at 28 GHz centre, 400 MHz bandwidth (1.4%) drifts the beam by ~0.4° across the band — about 30% of the HPBW (≈1.4°). Wide-band designs therefore mix in True Time Delay (fibre or CMOS LC delay lines), or use a hybrid sub-array architecture where TTD steers sub-arrays and phase shifters steer the elements within. The picosecond delay this tool reports is the first sizing number for that decision.

How to Use

  1. Enter the number of antenna elements (typically 8–64 for ULA configurations) and element spacing in wavelengths (0.4–0.5λ minimizes grating lobes).
  2. Set carrier frequency in GHz (e.g., 10 GHz for X-band radar, 28 GHz for 5G mmWave) and desired steering angle in degrees (−90° to +90°).
  3. The simulator calculates per-element phase shifts using the formula φₙ = (2π/λ)·d·sin(θ)·n, then computes HPBW, directivity, total gain, and side-lobe level; check for grating lobe presence when d·sin(θ) ≥ λ.

Worked Example

16-element ULA at 12 GHz (λ ≈ 25 mm) with 0.5λ spacing (12.5 mm) steering to 30°. Phase increment = 360° × 0.5 × sin(30°) = 90° per element. HPBBW ≈ 3.5°, directivity ≈ 18 dBi, side-lobe level ≈ −13 dB. No grating lobe since 0.5 × 0.5 = 0.25 < 1.0λ. Mechanical beam scan eliminated; electronic steer achieved in microseconds.

Practical Notes

  1. Grating lobes appear when element spacing exceeds 0.5λ at broadside; tighten spacing or reduce frequency if aliasing distorts far-field pattern in radar/communication systems.
  2. Phase quantization (e.g., 4-bit shifter = 22.5° steps) degrades gain by 0.5–1 dB; simulate with realistic bit-depth for phased array hardware design.
  3. Scan blindness occurs near end-fire (±90°); array impedance rises sharply—limit steering range to ±60° for practical S-band and X-band implementations.