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476 PHOTOVOLTAIC CONCENTRATORS<br />

If one designs a concentrator that accepts as a maximum input angle the half angle<br />

of the sun as seen from the Earth, about 1/4 ◦ , then it could have a maximum concentration<br />

of about 200 in the two-dimensional case and 40 000 in the three-dimensional case. Such<br />

a concentrator would accept light only directly from the surface of the sun. Regions of the<br />

sky outside this area would be rejected by the concentrator; that is, it would not reach the<br />

receiver. Interestingly, the concentration of 40 000 restores the radiative power density at<br />

the receiver to that at the surface of the sun. This leads to a simple proof of the above<br />

equations. Suppose we have a hot spherical radiator, which could be the sun but need not<br />

be, that is radiating black-body radiation. A portion of the radiation is intercepted by a<br />

concentrator as shown in Figure 11.20.<br />

r 1<br />

Source radiator, T R<br />

r 2<br />

q max, in<br />

Concentrator<br />

Radiator receiver, T rad<br />

Figure 11.20<br />

Geometry of a spherical radiator and concentrator

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