sophiecentaur said:
What do you mean by that? If the aluminium of the rest of the horn is radiating the full black body radiation then how does a standard paraboloid antenna mange to look at weak signals? What is different about the aluminium face of the 'reflector?
My conceptual model of the Holmdel, which you have convinced me is wrong, is that there is a parabolic reflector which focuses the target radiation onto the end-point antenna (epa). Almost all of the target radiation which enters the horn through the aperture, gets focused onto this epa. The radiation from the horn only send a small part of its radiation onto the epa. I am not sure how to properly calculate this "small part" of the radiation, but I will give it a try. (See (9) below.) The final signal (filtered 2.73 K radiation) to noise (filtered 290 K radiation) calculation is
SNR = 16.5
Suppose we assume that the epa has a functional area which "sees" the radiation from the walls of the horn. Given an assumed parabolic reflector of about 1 m diameter (I now have come to understand that 1 m is a wrong calculation), assume the epa is a straight rod of length about 5 cm, and about a 1 mm radius. The area of the rod is then
(1) A
rod = π × 0.001 × 0.05 ~= 0.00015 m
2.
There are other factors:
(2) The power ratio corresponding to the temperatures:
Rpower = (290/2.73)4 ~= 1.3 × 108
(3) The 290 K radiating area
A290 ~= (1/2) * (4*6 m) * 16 m =~= 200 m2
(4) The 2.73 K radiating area
A2.73 = (1/4) × π × 36 m2 ~= 12 m2
Assume all of the (4) area is focused onto the epa.
(5) The fraction of the 290 K wall area radiation that hits the epa
Assume an average effective distance from a random wall point to the epa is 2 m.
Each point on the wall radiates on the average onto a hemisphere of
2 π 4 m2.
The fraction of the radiation that hits the epa is
R290 ~= 0.00015 m2 / 2 π 4 m2 ~= 0.000006
(5) The ratio of 290 K power hitting the epa to the 2.73 K power hitting the epa is
Rpower = 1.3 × 108 × 0.000006 × 200 m2 / 12 m2 ~= 13,000
(6) A useful black body radiation integral
f(x) = x3/(ex-1)
F(x) = ∫0x f(x) dx
F(∞) = π4 / 15 ~= 6.494
(7) The fraction of 2.73 K radiation between 90% and 110% of the peak 2.73 K frequency.
F2.73 = (F(β - F(α))/F(∞) ~= 0.24
α = 2.257
β = 3.386
(8) The fraction of 290 K radiation between 90% and 110% of the peak 2.73 K frequency.
F290 = (F(β* - F(α*))/F(∞) ~= 1.12 × 10-6.
α* = (2.73/290) × α = 0.0210
β* = (2.73/290) × β = 0.0315
(9) The final calculation! The signal to noise ratio (SNR) = ratio of the 2.73 K to 290 K power received by the epa and after filtering with a flat frequency range between 90% and 110% of the peak 2.73 K frequency.
SNR = F
2.73 / (F
290 × R
power)
~= 0.24 / (13,000 × 1.12 × 10-6)~= 16.5
BTW Sophie, I like the bit you have at the end of your posts.
Q. Can you play the piano?
A. Dunno, I have never tried.
I am not sure what you think it means, but I think it means that the answerer is naive in thinking that if he had previously tried, he would know. I have also decided that the answerer is probably a male.
Regards,
Buzz