Phased-Array Calculator

Quick-look sizing for a rectangular electronically scanned aperture — directivity, gain, 3 dB beamwidths, and EIRP from six numbers.

Array parameters

×
GHz
%
deg
deg
W
—dBi Directivity (at scan angle)
—dBi Gain (η × directivity)
—deg 3 dB beamwidth — scan plane Θ
—deg 3 dB beamwidth — cross plane Ψ
—dBW EIRP
Beyond θ ≈ 60° the ideal cos θ projected-aperture model turns optimistic — real element patterns and mismatch roll off faster. Treat these numbers as an upper bound.
Wavelength — Aperture in wavelengths — Aperture area — Elements on a λ/2 grid — RF power per element — Scan loss — EIRP — EIRP, linear —

Model & assumptions

  • Ideal rectangular aperture: peak directivity D₀ = 4πA/λ², reduced by cos θ (projected aperture) when the beam is steered off boresight.
  • Gain G = η D. Fold illumination taper and any feed/combiner loss you want counted into the efficiency entry — not into transmit power as well.
  • Broadside 3 dB beamwidth per axis is 0.886 λ/L (uniform illumination); tapered apertures run wider. Off boresight, the scan-plane and cross-plane widths follow the standard planar-array (Balanis) formulas — the scan-plane beam broadens as 1/cos θ. With θ = 0 and φ = 0, Θ and Ψ are simply the width-axis and height-axis beamwidths.
  • EIRP = Ptx(dBW) + G(dBi), with Ptx the total RF power delivered to the aperture. Power per element divides Ptx uniformly across the λ/2-grid element estimate.
  • Single beam, single polarization. No grating-lobe, phase-quantization, or scan-blindness effects — those depend on element pitch and lattice, which this quick-look doesn’t model.

The calculator is the easy part.

Element pitch and lattice, grating lobes, taper trades, T/R chain losses, thermals, calibration, and production test are where an ESA program is actually won or lost. That's the part we do — Emtera designed and built a 540-radiator Ka-band ESA tile down to its custom PA, LNA, and phase-shifter ICs.

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