A space solar power satellite converts sunlight to DC power, then feeds a phased-array or dish transmitter that radiates it Earthward as a coherent microwave beam. Because the transmit aperture is finite, diffraction spreads the beam — it never lands as a single point, so the receiving rectenna only captures the fraction of power that falls within its own aperture.
The standard engineering figure of merit for two circular apertures of area At (transmitter) and Ar (receiver), wavelength λ, separated by distance D, is the Goubau coupling parameter:
τ = (A_t · A_r) / (λD)²
A_t = π(D_t/2)², A_r = π(D_r/2)²
For τ ≪ 1 the beam is diffraction-spread far wider than the rectenna and most power is lost to the surrounding "spillover" ring; for τ ≳ 1 the apertures are optically well-matched and capture approaches unity. A widely used closed-form approximation for a tapered-illumination beam (after W. C. Brown's power-transmission analyses) is:
η ≈ 1 − exp(−τ)
The diffraction-limited spot diameter that the beam illuminates on the ground follows the Airy pattern of a uniformly illuminated circular aperture:
w ≈ 2.44 · λD / D_t
- Dt / Dr sliders — bigger apertures on either end raise τ and shrink the spillover ring; this is why real SPS studies (e.g. NASA/DOE 1979 reference design, JAXA's ongoing work) pair a ~1 km transmitter with a multi-km ground rectenna.
- Frequency — shorter wavelength (higher GHz) tightens the beam for the same apertures, but 2.45/5.8 GHz ISM bands are favoured in practice for atmospheric transparency and licensing.
- Distance — geostationary orbit (35,786 km) keeps the satellite fixed over one ground site all day; the slider lets you see how efficiency would change at other beaming ranges.
- Power delivered — assumes a fixed 2 GW transmitted RF beam; only the free-space coupling efficiency above is modeled, not the DC→RF and RF→DC conversion losses at each end.