Spacecraft and antenna sizing
حاسبة كسب الهوائي والفتحة الفعالة
Relate dish size, aperture efficiency, gain and pointing tolerance.
المحتوى التفصيلي متاح بالإنجليزية، بينما الحسابات والوحدات والنتائج تعمل بنفس المحرك الهندسي.
أدخل قيم التصميم ثم شغّل الحساب لمراجعة النتائج.
Swipe the diagram sideways to see the full view. With a keyboard, focus the diagram and use the arrow keys.
Understand the system
Physical versus effective aperture
A circular dish has projected area πD²/4. Effective aperture is efficiency times physical area; it represents the power captured from incident flux. At 10 GHz, 2 m and 70% efficiency, area is 3.1416 m² and effective area 2.1991 m².
D, λ: m; A, A_e: m²; η: fractional efficiency; G: linear power gain.
A physical aperture is an area, not a dimensionless gain.
Source: finalExam.pdf · PDF page 4
Common mistakes
- Use power gain 10 log, not voltage gain 20 log.
- Efficiency is 0.70, not 70.
- Area in dB needs the explicit reference 1 m².
Formula reference and symbol definitions
Physical aperture
A: m²; D: m
Circular projected aperture.
Example: For D = 2 m, A = π × 2²/4 = π ≈ 3.142 m².
Open related tool →Effective aperture
A_e,A: m²; η: fraction
Aperture efficiency defined consistently.
Example: For A = 3.142 m² and η = 0.70, Aₑ ≈ 2.199 m².
Open related tool →Aperture gain
G: linear; λ: m
Matched polarization and reciprocal antenna.
Example: For Aₑ = 1 m² and λ = 0.1 m, G = 4π/0.01 ≈ 1256.64 (linear).
Open related tool →Parabolic gain
D,λ: m; η: fraction
Far-field dish approximation.
Example: For D = 2 m, λ = 0.03 m and η = 0.70, G = 0.70(π × 2/0.03)² ≈ 30705.4.
Open related tool →Gain in dBi
G: linear power ratio
Isotropic reference.
Example: A linear power gain of 100 gives G = 10 log₁₀(100) = 20 dBi.
Open related tool →Course beamwidth
θ: degrees; lengths: same units
Approximate course illumination convention.
Example: For D = 2 m and λ = 0.03 m, course HPBW ≈ 75 × 0.03/2 = 1.125°.
Open related tool →