Feed spillover reduces antenna efficiency when part of the feed’s radiation misses the reflector instead of contributing to its focused main beam. If 10% of the feed power spills past the reflector, spillover efficiency is 90%, costing about 0.46 dB of gain when all other factors stay constant. On receive, spillover directed toward warm ground can also raise antenna noise temperature and reduce sensitivity.
Table of Contents
How Spillover Lowers Gain
Spillover efficiency, ηsp, is the fraction of total radiated feed power intercepted by the intended reflector. If the missed fraction is s, then ηsp = 1 − s. This is a pattern-matching loss, not necessarily power absorbed as heat: energy can radiate into unwanted directions even when the feed has low resistive loss and good impedance matching.
For a circular aperture, gain is G = ηap(πD/λ)2, where D is diameter, λ is wavelength, and ηap is aperture efficiency at the stated reference plane. Spillover is only one contributor. Illumination taper, phase errors, blockage, polarization and dissipative losses also matter. Mismatch must be included separately when reporting realized gain. A 1983 JPL study explicitly included spillover, illumination, phase and cross-polarization in its aperture-efficiency definition. [1]
| Spillover | Spillover efficiency | Gain loss |
|---|---|---|
| 1% | 99% | 0.04 dB |
| 2% | 98% | 0.09 dB |
| 5% | 95% | 0.22 dB |
| 10% | 90% | 0.46 dB |
| 15% | 85% | 0.71 dB |
Each value uses Lsp = −10 log10(1 − s), with s expressed as a fraction. This isolates spillover; it does not predict the net gain change after a feed replacement, which can also change illumination and phase.
A Gain-Budget Example
Consider a calculated 3.7 m circular aperture at 6 GHz. Using λ = 0.04997 m gives 47.33 dBi at 100% aperture efficiency. If the combined efficiency of all terms other than spillover is assumed to be 65%, adding 10% spillover gives total efficiency 0.65 × 0.90 = 58.5% and gain 45.01 dBi, down from 45.46 dBi. These are illustrative calculations, not measured product specifications. If a quoted 65% already includes spillover, do not multiply by 0.90 again.
Why Edge Taper Is a Tradeoff
A wide feed pattern illuminates the reflector edge strongly but can send substantial power past it. A narrower pattern captures more of the feed’s power while illuminating the outer aperture less strongly. The useful target is the best combined spillover and illumination efficiency, rather than the lowest spillover alone.
For a centered prime-focus paraboloid, the rim half-angle seen from the focus is θ0 = 2 arctan[1/(4f/D)], where f is focal length. At f/D = 0.40, the angle is 64.01°. This geometry does not directly describe an offset aperture or the feed-to-subreflector angle in a Cassegrain system.
A Reproducible Feed-Matching Calculation
Assume an axisymmetric feed power pattern P(θ) = cosn(θ) from 0° to 90°, zero radiation behind the feed, and the feed at the focus. Here θ is measured from the feed axis toward the reflector. Choosing n = 2.79076 gives a −10 dB power level at the 64.01° rim. Integrating with the solid-angle weighting sin(θ) gives s = cosn+1(θ0).
| f/D | Rim half-angle | Feed power at rim relative to axis | Spillover | Spillover loss |
|---|---|---|---|---|
| 0.30 | 79.6° | −20.8 dB | 0.15% | 0.007 dB |
| 0.35 | 71.1° | −13.6 dB | 1.40% | 0.06 dB |
| 0.40 | 64.0° | −10.0 dB | 4.38% | 0.19 dB |
| 0.45 | 58.1° | −7.7 dB | 8.90% | 0.40 dB |
| 0.50 | 53.1° | −6.2 dB | 14.42% | 0.68 dB |
| 0.60 | 45.2° | −4.3 dB | 26.46% | 1.33 dB |
The practical lesson is visible at f/D = 0.50: the same feed now spills 14.42%, rather than 4.38%. The rim subtends a smaller angle. Conversely, the deep f/D = 0.30 dish captures almost all the modeled radiation but has much weaker edge illumination. This table calculates spillover, not total aperture efficiency.
A −10 dB edge level is a design choice, not a universal matching rule. Two real feeds can have the same edge level and different sidelobes or backlobes, producing different spillover. Request frequency-specific patterns for the proposed microwave feedhorn; a gain or VSWR value alone cannot establish the match.
Why Spillover Can Increase Receive Noise
On receive, the antenna responds to brightness temperature across its radiation pattern. Spillover that views warm ground can add much more noise than spillover that views cold sky. Ground pickup depends on elevation, surroundings and pattern shape; not all spilled power sees the ground. NASA’s 1986 brief on a dual-shaped subreflector describes tapering that reduces transmit spillover and receive noise pickup. [2]
In a simplified model, a ground-coupled pattern fraction sg contributes approximately sgTground to antenna temperature. If 5% couples to ground with brightness temperature 250 K, that contribution is 12.5 K. Relative to the same fraction viewing sky at Tsky, the increase is 0.05(250 − Tsky) K, not automatically 12.5 K.
For a separate gain-to-system-noise-temperature example, assume an additional 12.5 K raises Tsys from 100 K to 112.5 K at the same reference plane. With gain unchanged, G/T falls by 10 log10(112.5/100) = 0.51 dB. If gain also falls by 0.22 dB, the combined G/T penalty is about 0.73 dB. Include both effects without counting an existing noise contribution twice.
What Published Hardware Shows
JPL’s January 1962 report, A Simple Beamshaping Device for Cassegrainian Antennas, describes modified and unmodified systems and a subreflector modification that halved spillover to 1.3%. Its full-scale 85 ft modified antenna had a measured zenith antenna temperature of 9.5 K and measured aperture efficiency of 50%. The 9.5 K value describes the antenna temperature, not the sky alone. These are results from that historical configuration, not expected values for a modern commercial dish. [3]
The 1983 JPL design used a 157.1-wavelength main reflector, a shaped subreflector and an unblocked offset geometry. Its reported measured aperture efficiency was 84.9%, against 86.5% predicted. Both reflector shaping and spillover control were involved; the result cannot be attributed to spillover reduction alone. [1]
How to Diagnose a Feed Match
Record the Geometry and Operating Band
For a replacement-feed assessment, record diameter, focal length, reflector type, mounting reference, phase-center information, polarization, and exact transmit and receive frequencies. Check patterns across the band rather than only at its center. For a dual-reflector antenna, obtain the subreflector geometry and evaluate the complete antenna feed system.
Integrate the Full Pattern
Calculate ηsp as the integral of feed radiation intensity over the solid angle intercepted by the reflector, divided by its integral over the full sphere. Include sidelobes and back radiation. E- and H-plane cuts help reveal asymmetry, but two cuts alone do not determine a general three-dimensional integral. An axisymmetric approximation requires evidence that the pattern is sufficiently symmetric.
Compare Gain and Noise Under Controlled Conditions
Use a suitable antenna range and a standard gain horn with calibration data for the test frequency when performing a gain comparison. Record polarization alignment, cable losses, reference plane and measurement uncertainty. A low measured gain can also reflect defocus, surface error, blockage, mismatch or feed-network loss; matching one edge-taper value does not rule out spillover.
For a receive comparison, keep receiver settings and calibration stable and record elevation, weather and nearby obstructions. An elevation scan can reveal changes in noise pickup, but atmospheric emission and ground geometry also change with angle. A small noise rise does not, by itself, prove low spillover.
Change one variable at a time and compare both gain and system noise. A feed that reduces spillover may still lose gain through stronger taper or a shifted phase center. Increasing dish diameter at the same f/D and retaining the same normalized feed pattern increases collecting area but leaves this model’s spillover fraction unchanged.
The useful decision is whether the complete feed-reflector combination improves gain or G/T across the required band. Start with the measured pattern and geometry, then check the installed result against a loss budget that keeps spillover, illumination and receive noise separate.
