Ask Dr. SETI ®

Dear Dr. SETI:
Could you explain how the Efficiency Factor (k) used in calculating gain over isotropic radiation is derived? The formula I have states:

G = 10 * Log( k * ( (Pi * D/W) * (Pi * D/W) ) )

where:

• G = Gain over an isotropic radiator
• D = Diameter of the dish
• W = Wavelength
• k = 0.55 (usually)

RJ (via email)

The Doctor Responds:
The efficiency factor estimates how uniformly the surface of the dish is being illuminated by the feed. The .55 comes from measured performance of prime-focus dishes with a pyrimidal waveguide feedhorn, with no aperture blockage. Other feedhorn designs do a bit better (for example, the Ku-band DSS dishes get about 80% efficiency), while others do a bit worse (our SETI League feedhorn, under-illuminated for 15 dB edge taper, is only about 45% efficient). The best way to find your actual efficiency is to do a sun noise measurement, with a known noise temperature receiver. Then calculate the resulting antenna gain. Finally, comparing that to theoretical gain will tell you your efficiency.

Incidentally, as it happens I'm answering this email from NRAO Green Bank, where one of the radio astronomers reading over my shoulder just said the 55% efficiency standard was derived by the rectal extraction method.