Microwave Transmission through Atmospheric Densities Maturaarbeit/Extended Essay Author: Michael Krebs Supervisor: Heinz Anklin Co-Reader:[DATUM] Lukas Kaufmann [FIRMENNAME] [Firmenadresse] Wettingen, 11th November 2019 Table of Contents Introduction ............................................................................................................................................ 2 Theory ..................................................................................................................................................... 3 Concept of Microwave Transmission .................................................................................................. 3 Propagation in the Atmosphere .......................................................................................................... 5 Barometric Formula ............................................................................................................................ 7 Risk Assessment ...................................................................................................................................... 7 Experimental Method ............................................................................................................................. 8 Sender ................................................................................................................................................. 9 Problems with the Sender ............................................................................................................. 12 Receiver ............................................................................................................................................. 13 Requirements for the Measurements ............................................................................................... 14 Method of the Measurements .......................................................................................................... 14 Data Presentation ................................................................................................................................. 15 Radiation Field ................................................................................................................................... 15 Pressure Dependent Measurements ................................................................................................ 16 Discussion.............................................................................................................................................. 18 Data Interpretation ........................................................................................................................... 18 Data Uncertainties ............................................................................................................................. 20 Data Limitations ................................................................................................................................ 21 Conclusion ............................................................................................................................................. 22 Evaluation ............................................................................................................................................. 23 Bibliography .......................................................................................................................................... 24 Appendix ............................................................................................................................................... 27 Risk Assessment ................................................................................................................................ 27 Material List ....................................................................................................................................... 28 Raw Data ........................................................................................................................................... 28 1 Introduction This essay is based on revising the concept of an orbital solar power station (OSPS) and therefore in- vestigating into the research question; “To what extent does the atmospheric density on earth influence the energy loss of microwave transmission? “. The concept of such a station can be traced back to the year 1968.1 An OSPS would harvest the energy, produced by the sunlight, and convert it into electrical power. Due to atmospheric propagation the efficiency of collecting the sunlight outside earth’s atmos- phere is higher than on its surface. Out of the 1367 W/m2 which reaches earth’s atmosphere, only 1000 W/m2 actually make it through.2 Therefore it is interesting in the first place, to investigate for an alternative to exploit a greater amount of the sun’s energy, before it penetrates the atmosphere. In this work, the focus lies on the advantages and disadvantages of energy transmission from the sta- tion to the earth’s surface using microwaves by conducting a simplified experiment with a sender and receiver at three locations differentiated by their altitude. 1 „Space Based Solar Power“, Wikipedia, https://en.wikipedia.org/wiki/Space-based_solar_power#target- Text=In%201941%2C%20science%20fiction%20writer,first%20described%20in%20November%201968, Last accessed 5 November 2019. 2 „The sun as a source of energy“, Itacanet, https://www.itacanet.org/the-sun-as-a-source-of-energy/part-2- solar-energy-reaching-the-earths-surface/, Last accessed 5 November 2019. 2 Theory Concept of Microwave Transmission The concept of microwave transmission has been around since World War II, when the need for data transmission and radar became more prominent. Many countries have invested time and money into researching the characteristics of microwave-based data links, which is one of the main applications nowadays. By cutting the complexity of the system down to a minimum, the ultimate idea revolves around a mi- crowave transmitter and a microwave receiver. The transmitter consists of a power source, connected to a magnetron, where electrons begin to oscillate due to a magnetic field produced around them. This oscillation results in the creation of an electromagnetic wave, which is the combined wave front, as shown in Figure 1, of several waves traveling away from the magnetron. Figure 1; Illustration of an electromagnetic wave front The emitted energy needs to be converted from wave into electricity, for the concept of an OSPS. This process can be achieved by capturing the electromagnetic waves using a rectenna. A rectenna consists of two elements, being a dipole antenna and a radio frequency (RF) diode.3 The distance between the endings of the dipole antenna depends on the frequency being used. 3 „Rectenna“, Wikipedia, https://en.wikipedia.org/wiki/Rectenna, Last accessed 5 November 2019. 3 The RF get emitted radially and therefore decrease in power density by the formula shown below. In order to increase this density, the RF can be guided. This guidance can be evoked by the different types of transmitters in the form of an antenna, or in the case of this paper, a physical guidance using the effect of reflection by specific materials. 푃푡 푃 = 4휋푟2 The radial power intensity decline of waves can be described by the formula above, which divides the 4 initial power (푃푡) by the quadratic distance (푟) times 4휋. In the broad picture, microwave transmission serves as a dense and efficient energy transfer method between earth orbit and the ground, therefore cancelling the cosine-effect.5 This effect increases the amount of atmosphere the radiation has to penetrate through, depending on where on the planet the ground base is positioned. The origin of this effect is illustrated in Figure 2, which indicates the differ- ence between the area of plane B and plane C. Therefore, with increasing volume to be penetrated, the amount of propagation also increases. This leads to a greater loss of energy if a ground station is located anywhere remote from the equator. Figure 2; Illustration of the cosine-effect 4 Manning, Trevor, Microwave Radio Transmission Design Guide, Norwood: Artech House, 2009, p. 10. 5 M. Ewert & O. Fuentes, Modelling and simulation of a solar tower power plant, Achen: Achen University, p. 4. 4 Propagation in the Atmosphere The atmospheric propagation of electromagnetic waves plays a large role in microwave transmission. There are specifically three effects, which will be discussed due to their significance. Since any matter absorbs energy, the first effect in focus will be the absorption. As already mentioned, every atom absorbs waves. According to the Lambert-Beer law, every matter has its own absorption coefficient (α) which influences the initial energy intensity (퐼0) of a wave expo- nentially by the distance (푑) penetrated. This can be seen in the formula below, describing the Lam- bert-Beer law. −α푑 퐼(푑) = 퐼0푒 Furthermore, the formula of the absorption coefficient itself can be described by the product of the molar attenuation coefficient (n′′) of a material, times the angular frequency (푤) divided by the speed of light (푐).6 푤 α = 2n′′ 푐 This law therefore describes the exponential decline of the energy intensity of electromagnetic waves the further it gets penetrated. Looking at this law on the molecular basis, moisture in the atmosphere has a big effect. Though moisture only affects waves with a frequency higher than 11 GHz, it is nevertheless worth mentioning that this can have a great