Antenna Aperture Sizing

Parabolic Antenna Aperture Sizing (space-systems/subsystems/antenna-aperture-sizing)

Use when the task is sizing the parabolic reflector antenna aperture of a spacecraft communications link in the reverse direction: the antenna gain is an INPUT handed over from the forward link design, and this leaf converts the required gain into the reflector diameter through the aperture efficiency, then reports the achieved gain of the sized aperture, the half-power beamwidth, the pointing accuracy requirement with its pointing loss, and the receive gain-over-temperature G/T. It implements the standard eta * (pi * D / lambda)^2 aperture model in pure Python, stdlib only, deterministic and offline. It pairs with space-systems/subsystems/ communication-link-budget, which supplies the required-gain input; the reverse-sizing pattern follows the precedent of the solar-array and battery leaves.

Domain quick reference

• Wavelength: lambda = c / f, with c = 299792458 m/s. S-band 2.2 GHz gives lambda about 0.13627 m.
• Aperture gain: G = eta * (pi * D / lambda)^2 linear, gain in dB is 10 * log10(G). The aperture efficiency eta defaults to 0.6, the typical parabolic reflector value, and must lie in (0, 1].
• Aperture from the required gain: D = (lambda / pi) * sqrt(G_lin / eta), with G_lin = 10**(gain_db / 10). This is the reverse of the gain law and the sizing step of this leaf.
• Required-gain assembly (terms taken from the forward link design): G_req = margin + path loss + other losses + 10 * log10(k * T * R)
  • transmit power, all terms in dB, k = 1.380649e-23 J/K, R the data rate, T the system noise temperature.
• Half-power beamwidth: theta_3dB = 70 * lambda / D degrees, the standard lambda/D approximation for a uniformly illuminated circular aperture.
• Pointing budget: allowed pointing error = pointing_fraction * theta_3dB, with pointing_fraction default 0.1; pointing loss = 12 * (pointing_fraction)^2 dB in the small-error approximation, so the default budget allows 0.360 deg error for 0.12 dB loss on a 3.60 deg beam.
• Gain over temperature: G/T = receive_gain_db - 10 * log10(T), dB/K, with T the receive system noise temperature.
• Units are SI: m, Hz, K, bps, dBW for transmit power, dB for gains and losses. ECSS frames the space communications context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the requirement: take the required antenna gain from the forward link design, or assemble it with required_gain_db(margin_db, path_loss_db, other_losses_db, data_rate_bps, noise_temp_k, transmit_power_dbw) when the link terms are available.
2. Convert the operating frequency to wavelength with wavelength(freq_hz).
3. Size the aperture: aperture_from_gain(gain_db, wavelength_m, eta) returns the reflector diameter in meters.
4. Confirm the size closes the gain: gain_from_aperture(diameter_m, wavelength_m, eta) returns (gain_lin, gain_db); the achieved gain must match the required gain to within 1e-6 dB.
5. Compute the beam: half_power_beamwidth(diameter_m, wavelength_m) returns theta_3dB in degrees; the beam narrows as the diameter grows.
6. Budget the pointing: pointing_budget(theta_3db_deg, pointing_fraction) returns the allowed error in degrees and the pointing loss in dB.
7. Rate the receive chain: gain_over_temperature(receive_gain_db, noise_temp_k) returns G/T in dB/K.
8. For the whole report in one call, antenna_sizing(required_gain_db, freq_hz, eta, noise_temp_k, pointing_fraction) returns the wavelength, diameter, achieved gain, beamwidth, pointing allowance and loss, G/T (None when the noise temperature is not given) and the gain error.
9. Confirm the deterministic checks with the contract test scripts/test_antenna_aperture_sizing.py.

Worked example

S-band downlink at f = 2.2 GHz, required gain 33.5 dBi, eta = 0.6, system noise temperature 150 K. Real module outputs:

• Wavelength: lambda = c / f = 0.136269 m (bound about 0.13627 m).
• Reflector diameter: aperture_from_gain(33.5, 0.136269, 0.6) = 2.6496 m, inside the 2.5-2.8 m magnitude bound (about 2.650 m).
• Achieved gain: gain_from_aperture(2.6496, 0.136269, 0.6) = 33.500000 dB; the gain error achieved minus required is 0.0 dB, within 1e-6.
• Beamwidth: half_power_beamwidth = 70 * 0.136269 / 2.6496 = 3.60017 deg, inside the 3.3-3.9 deg bound (about 3.60 deg).
• Pointing budget: allowed error 0.36002 deg (0.1 * 3.60017) with pointing loss 12 * 0.1^2 = 0.12000 dB, about 0.360 deg and 0.12 dB.
• Gain over temperature: G/T = 33.5 - 10 * log10(150) = 11.7391 dB/K, inside the 11-13 dB/K bound (about 11.74 dB/K).

Pitfalls

• Sizing from the wrong gain sense: the required gain is an INPUT handed over from the forward link budget, and this leaf works the reverse direction (gain to diameter); feeding a received-power or EIRP figure instead of the antenna gain sizes the wrong dish.
• Forgetting the wavelength changes the diameter: aperture scales as lambda / pi * sqrt(G/eta), so a frequency slip (S-band 2.2 GHz is lambda = 0.136269 m) directly rescales the reflector at fixed gain.
• Dropping the aperture efficiency: eta defaults to 0.6 and must lie in (0, 1]; an ideal eta = 1 sizing undersizes the real reflector, and the achieved gain must be checked with the round trip (gain error below 1e-6 dB in the worked example).
• Treating the pointing loss as negligible: the budget is 12 * (pointing_fraction)^2 dB against an allowed error of pointing_fraction * theta_3dB, so a sloppy pointing requirement eats the link margin the antenna was sized to close.
• Confusing gain and G/T: G/T = receive_gain_db - 10 log10(T) needs the receive noise temperature and comes back in dB/K; omitting the temperature returns None from the sizing dict rather than a number.
• Ignoring the beam narrowness of a big dish: beamwidth is 70 * lambda / D, so a large aperture needs a proportionally tighter pointing budget and a better star tracker or RF sensing than the 0.360 deg default allowance.

Verification

• Confirm antenna_sizing(33.5, 2.2e9, 0.6, 150.0) returns a diameter in 2.5-2.8 m, achieved gain 33.5 dB within 0.01 dB, beamwidth in 3.3-3.9 deg, G/T in 11-13 dB/K and an absolute gain error below 1e-6.
• Round trip: aperture_from_gain(gain_from_aperture(D)) recovers D to 1e-9.
• Beamwidth is monotonic decreasing in diameter; pointing fraction 0 gives zero pointing loss; doubling the noise temperature lowers G/T by 3.01 dB; the required gain rises 10 dB per decade of data rate and of noise temperature.
• ValueError rejection: frequency, diameter, wavelength, gain, data rate and noise temperature at or below zero, efficiency outside (0, 1], negative pointing fraction.
• Deterministic: no RNG, identical floats run to run; the convenience dict carries exactly the documented keys.
• Run the contract test offline: python3 scripts/test_antenna_aperture_sizing.py (35 tests, deterministic).

Related leaves

• space-systems/subsystems/communication-link-budget: the forward link budget that supplies the required-gain input this leaf sizes from.
• space-systems/subsystems/solar-array-sizing: the reverse-sizing pattern precedent in the same pack.
• space-systems/subsystems/spacecraft-battery-sizing: the companion power subsystem sizing leaf.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_antenna_aperture_sizing.py

The test covers the S-band sizing contract (diameter 2.5-2.8 m, beamwidth 3.3-3.9 deg, G/T 11-13 dB/K against the real module outputs), wavelength and aperture gain, aperture from a required gain with the 1e-9 round trip, the required-gain assembly scaling (10 dB per decade of data rate and noise temperature), half-power beamwidth monotonicity, the pointing budget at the default and zero fractions, gain over temperature with the 3.01 dB noise doubling identity, the end-to-end sizing convenience dict and its exact key set, ValueError rejection of every non-physical input, and run-to-run determinism.

Compliance

• Standards referenced, not reproduced: ECSS E-ST-70 (space data links and RF comms) is a free ESA download (ecss.nl/standards); the aperture relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.