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## Functional frequency dependence

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Eq. 3 compares ultimate system performance for communication systems operating at different frequencies but with constant values of antenna area for both transmit and receive, constant transmitted power, and constant transmission losses. This equation, plotted in Fig. 1, indicates that with the above physical parameters fixed, performance increases linearly with frequency where quantum noise is dominant and with the square of frequency where thermal noise is dominant. As indicated in this figure, an ultimate system improvement of six orders of magnitude is possible by shifting communications from the microwave band to the visible light spectrum. While the actual achievement of this million-fold improvement is inhibited by the practical restrictions to be discussed, the frequency-dependent parameter, *M*, does represent an ultimate performance limit with respect to aperture dimensions—a limit which could be approached by investment of suitable effort. It sets a goal whose attainment will require development of new concepts and techniques.

**Transmitting antenna area**

The effective area of a spacecraft transmitting antenna is limited by one of three practical considerations:

- Weight and size limitations imposed by the vehicle,
- Antenna fabrication tolerances, and
- Transmitting beamwidth demanded by the limitation of pointing accuracy.

Although there is some interrelation among these factors (for example, an extensible antenna may be used for increased diameter at the expense of dimensional tolerances), one generally will dominate within a certain frequency range.

In Fig. 2 transmitting antenna area is plotted against frequency for different values of the three restrictive conditions. Horizontal lines indicating restrictions on effective diameter could result from such constraints as vehicle dimensions or weight. Fabrication tolerances limit achievable gain and effective aperture area. These tolerances generally are normalized as the ratio of rms dimensional deviation in effective path length to the diameter, σ/*D*. Since a given ratio implies a particular gain limit, effective antenna area is inversely proportional to the square of the frequency for a given σ/*D*.

Similarly, a given pointing accuracy requires a certain beamwidth and hence represents a gain limit. Thus, the same family curves can represent the restriction on the transmitting antenna area caused by either fabrication tolerance or pointing accuracy limitations. The curves, evaluated for an approximate 3-dB loss, result in lines of constant negative slope on the log-log plot of Fig. 2 and are labeled in terms of σ/*D*, beamwidth, and effective gain (3-dB loss from an ideal included).

From Fig. 2 the systems engineer can determine the frequency dependence of transmitting antenna area appropriate from assumptions of vehicle constraints, practical fabrication tolerances, and achievable pointing accuracy.