The “loss surface area” from a prime-focus feed

The “loss surface area” from a prime-focus feed is just the blocked (shadowed) aperture from the feed assembly (feed + support struts). You can estimate it with:

• Dish area: Adish=π(D/2)2A_\text{dish}=\pi (D/2)^2
• Feed blockage (assuming a circular feed of diameter dfd_f): Afeed=π(df/2)2A_\text{feed}=\pi (d_f/2)^2
• Strut blockage (very rough but handy): if you have NN struts of width ww running about a radius, projected area ≈N w (D/2)\approx N \, w \, (D/2)

So:

Ablocked≈Afeed+N w D2,Fraction blocked=AblockedAdishA_\text{blocked} \approx A_\text{feed} + N\,w\,\frac{D}{2}, \quad \text{Fraction blocked} = \frac{A_\text{blocked}}{A_\text{dish}}

Below is a concrete example using a fairly typical L-band prime-focus scalar/corrugated feed df=0.25 md_f = 0.25\,\text{m} with 3 struts each w=0.02 mw=0.02\,\text{m}:

Dish Ø (m)	Dish area (m²)	Blocked area (m²)	% of aperture blocked	Rough gain hit*
1	0.785	0.079	10.07%	~0.92 dB
3	7.069	0.139	1.97%	~0.17 dB
5	19.635	0.199	1.01%	~0.09 dB
10	78.540	0.349	0.44%	~0.04 dB

*Very rough: ηblock≈(1−fraction)2\eta_\text{block} \approx (1 – \text{fraction})^2, loss =10log⁡10ηblock=10\log_{10}\eta_\text{block}. Real losses depend on illumination taper and diffraction, so treat as ballpark.

Want different assumptions? Plug in your actual feed diameter and strut width/count with the same formulas. For reference, if your feed is smaller/larger:

• df=0.10 md_f=0.10\,\text{m}: a 1 m dish blocks ~4.8% (~0.43 dB), a 3 m dish ~1.4% (~0.12 dB).
• df=0.30 md_f=0.30\,\text{m}: a 1 m dish ~12.8% (~1.19 dB), a 3 m dish ~2.3% (~0.20 dB).