2. Power Transfer

Power Transfer

Transmitter Antenna

Antenna Diameter and Frequency of Transmission

The frequency of the link between the satellite and the earth was selected to be 24 GHz. The rationale behind this extends from the fact that we wanted to select a frequency in the ISM band. Out of the available frequencies in the ISM Band (2.4 GHz, 5.8 GHz, 24 GHz, 61 GHz, 122 GHz 245 GHz), we've chosen the highest possible (smallest antenna) that will yield a good surface roughness (see next section). Using a frequency too high might not be technologically feasible with current power electronics devices.

Surface Roughness ε [m RMS] and Surface Efficiency

This is the most critical parameter contributing to the overall antenna efficiency. It’s only dependent on the ε/λ ratio. An accuracy of 0.5 mm has been achieved on 100 m diameter dish in the past (Hachenberg et al., 1973; Godwin et al., 1986), so we predict that this accuracy can easily be improved with modern materials and the lack of forces deflecting the surface in space.

After assembly, the surface accuracy can be measured using Radio Holography, with a mm-wave transmitter on Earth, which will conveniently be in the far-field of the dish. This will require steering capabilities on the dish or a mobile source on the ground.

Fig. 1: Surface Eff. vs ε/λ

and Illumination Efficiency

How the dish is illuminated by the feed will determines it’s gain pattern, half-power beam width, illumination efficiency [1] and spill-over efficiency. The illumination function is typically of the form

where the illumination taper represents the fraction of the amplitude of the electric field at the edge of the antenna (r=1) relative to the center (r=0). Optimum combined illumination efficiency and spill-over efficiency occurs when the edge field strength level is about -10dB [2]. The feed shall be designed such as to obtain this value.

Gain Pattern

The “power pattern” is the square of the amplitude pattern and can be written in closed form when using an illumination of the form

[1]:

Fig2: Power gain vs angle

The maximum directivity for uniform illumination occurs for θ=0:

Half Power Beam Width

We calculate the beam width such as to compute the area on the ground where most of the power will be delivered. The HPBW contains about 95% of the total radiated power. It can be computed as a function of

and the ratio D/λ [1]:

b(

) is a polynomial fit to the HPBW, which can only be computed numerically.

Spill-Over Efficiency

The feed (if using a horn) is an aperture antenna, so we can assume the gain pattern is just like that of a dish. It's been found numerically by integrating the power pattern over the illumination and dividing by this same integral over the whole sphere:

Antenna Gain

It can be found by applying all the efficiencies to the directivity:

Inefficiencies due to blockage, de-focus and astigmatism have not been taken into consideration as it's believed that their contribution is negligible.

Receiving Array

Array v/s Single Dish Criteria

The use of an array for reception addresses 2 essential issues: (1) The difficulty to achieve a good surface accuracy on a structure which is several kilometers wide. (2) The mechanical difficulty that is to suspend the receiving horns at the focal point of a dish that is several kilometers wide.

Receiver Antenna

Each receiver antenna is characterized by the parameters bellow. These are electrically identical to the space antenna, with the exception that these have a square instead of circular aperture, such as to cover the area that would exist between circular antennas. To conservatively approximate the effect of this additional area, the spill over efficiency has been set to 100%, but the directivity has not been modified to account for the extra area.

Inefficiencies due to blockage, de-focus and astigmatism have not been taken into consideration as it's believed that their contribution is negligible.

Array configuration and Contribution of each antenna

The array will consist of 2180 antennas side by side covering the circular area of diameter

=5.4 [km] encompassed by the HPBW of the transmitter antenna. The relative contribution Z of each receiving antenna to the total received power is a function of its position (u,v) relative to the center of the array and the power pattern of the transmitter antenna. The figure below shown one quadrant of the array, where each dot represents an antenna and the z-axis is their relative received power in dB.

Fig 3: Dish quadrant spacial vs. relative received power

Array Gain and Receive Gain

The total power received is proportional to the sum of the individual contributions Z(u,v). We introduce the parameter “Array Gain”

, defined as the sum of all relative contributions. This allows us to calculate the receiver gain as

.

Overall Wireless Link

The total link gain is given by

where H = 35 286 [km] is the altitude of the satellite.

References

[1] Jacob W.M. Baars, The Paraboloidal Reflector Antenna in Radio Astronomy and Communication, Springer, 2007.

[2] Constantine A. Balanis, Antenna Theory, Third Edition, Wiley, 2005.