By Samuel J. Raff (Auth.)
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Additional info for Microwave System Engineering Principles
The gain of an antenna is a characteristic which defines its transmitting characteristics. The gain in any direction 1s defined with reference to an omnidirectional antenna. It is the ratio of the power radiated per unit solid angle in that direction to the power which would be radiated by a matched omnidirectional antenna with the same power coupled into i t ; usually expressed in dB. As with cross sectional a r e a , when we speak of the gain of an antenna without any directional reference we mean the gain in the principal direction or the direction in which the antenna is designed to transmit.
In this case we can designate the flux of energy per steradlan per unit bandwidth 1n any direction as φ(Τ]). 1) ο effective area of the antenna 1n the θ , Φ direction. This must be true for any antenna. Therefore, the Integral of the cross sectional area of an antenna over all directions has some fixed value which may depend upon frequency since Φ(T-j ) may depend upon frequency, but 1t 1s Independent of the antenna so long as 1t 1s matched. This 1s a rather surprising result. We are saying that a very large antenna and a very email antenna each placed in an ieotropic radiation field will collect exactly the same amount of energy.
4 Noise Temperature of Antennas. The noise temperature of an antenna 1s that temperature which corresponds to the thermal noise output which the antenna supplies to a matched receiver connected to 1t. To the approximation that the antenna is lossless, this m 47 power does not originate in the antenna Itself but is collected by 1t from the radiation field in which 1t 1s placed. The radiation temperature of the antenna can be calculated by taking its available thermal noise output power per unit of bandwidth and dividing it by Boltzman's constant2 k.