Transmitting Antenna Design
There are a couple of ways in which the size and cost of this part of the architecture can be analyzed and reduced. Equations 1 and 2 below are used to characterize the relationship between the size of the transmitter, the size of the receiver, and the frequency at which power is transmitted.
Equation 1.
Equation 2.
The parameter τ in (2) varies along the transmission efficiency shown in Figure 1. Usually the diameter of the transmitter is around 106 x λ. For a 1km diameter transmitter in GEO which is 36000km between the receiver and transmitter, beaming power at a frequency of 5.8 GHz, a receiver on the Earth would have a diameter of approximately 5.3km. This calculation is based on an assumption that the system is in a good situation with the transmission efficiency of 95%, then τ can be read as 2.4 in Figure 1.
Figure 1. Transmission Efficiency as a Function of Tau for Optimum Power Density Distribution
Figure 2 shows the impact that increasing power beam frequency has on the receiver diameter. In this case, the diameter of the space transmitting dish is 1km and the diameter of the rectenna array is 5.3km at 5.8GHz.
Figure 2. Frequency vs. Antenna Diameter
A graphical summary of the impact of increasing the diameter of the transmitter on the diameter of the receiver is shown in Figure 3.
Figure 3. Dimension Relationship Between Rectenna and Transmitting Antenna
A variety of innovative designs have matured to yield the current state-of-the-art in space-borne antenna systems. Since the mass and volume will be the dominating figures of merit, the mechanical configuration of the transmitting antenna is must be properly designed. Figure 1 shows a comparison of concepts for space antennas on the basis of operating frequency and diameter.
Figure 4. Mechanical Tradeoffs in Antenna Design
While frequency and diameter have a large influence on the chosen antenna implementation technology, other important design variables include deployed stiffness, thermal characteristics, joint tolerance and dimensional repeatability, and deployed surface-alignment/precision. It is evident from the figure above that the type of reflecting surface will be determined by the operating frequency, while the deployment capabilities will be determined by the aperture size. Also, the implementation options become fewer as the aperture size increases, regardless of operating frequency.
Since the diameter of the transmitting antenna is 1km, in-space assembly of modular structures for the antenna is the best option. With this method, the materials can be packed efficiently and transported into orbit much more cheaply. Once the materials are unpacked, autonomous robots can be used for space-assembly operations. The illustration in Figure 2 shows how this process could work.
Figure 5. Space Assembly of Large Diameter Antenna
Power Efficiency
Figure 6. Schematic Diagram of SSP System Key Components and Transmission Efficiency
For the magnetron we chose, the efficiency of solar power to microwave conversion can reach 87.5% with lifetime 50years. The efficiency is determined by principal elements of a beamed microwave transmission system shown in Figure 6. The transmission efficiency in the free space can be calculated using the Eq (3) or (4). The details of parameters used can be found in Table 1.
Equation 3. Logarithmic Transmission Efficiency
Equation 4. Linear Transmission Efficiency
Parameters are denoted as follows:
- Pr is the power density at the center of the receiving location
- Pt is the total radiated power from the transmitter
- At is the total area of the transmitting antenna
- λ is the wavelength
- r is the distance between the transmitter and the rectenna
Table 1. Parameters for Transmitter Antenna and Rectenna
References
http://descanso.jpl.nasa.gov/Monograph/series8/Descanso8_08.pdf
Brown, W.C.; Eves, E.E.; , “Beamed microwave power transmission and its application to space ,” Microwave Theory and Techniques, IEEE Transactions on , vol.40, no.6, pp.1239-1250, Jun 1992 doi: 10.1109/22.141357
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=141357&isnumber=3793
Arthur D. Little Inc., Brown and Root Inc., and Rice University, Solar Power Satellite Offshore; nna Study, NASA contract NAS 8-33023.
