## 3 Passive Phased Arrays with Integrated Metallic and Dielectric Waveguide Phase Shifters  
Phased arrays are most common, where the first phased array transmission was originally shown in 1905 by Nobel laureate [PERSON], who demonstrated enhanced transmission of radio waves in one direction. Figure 13 sketches an electronic steerable antenna array, receiving an arbitrary incident plane wave from a satellite, which leads to a time delay of \(\tau=\Delta/c_{0}=(d/c_{0})\cdot\cos(\Theta)\) from one radiating element to the next one, where \(d\) is the distance between adjacent radiating elements and \(c_{0}\) is the speed of light. This results in a differential phase shift along the equally spaced array with respect to the first radiating element of \(\xi_{n}=\sum_{n=1}^{N}(n-1)\cdot k\cdot d\cdot\cos(\Theta)\), where \(N=4\) is the total number of elements in our example. Figure 13: Sketch of an Electronically Steerable Antenna (ESA) array, receiving an incoming plane wave from a satellite (**left**) and its signal inputs and outputs (**right**). Therefore, the hardware implementation of Electronically Steerable Antennas (ESAs) in the analog domain requires by default tunable phase shifters with a differential phase shift of up to 360\({}^{\circ}\) beneath each radiating element of an array with a limited size of about \(\lambda_{0}/2\times\lambda_{0}/2\) (\(\lambda_{0}\) is the wavelength in free space), and in addition, variable gain amplifiers when beam-forming is desired. By adjusting the right phase shift \(\alpha_{n}=\sum_{n=1}^{N}(N-n)\cdot k\cdot d\cdot\cos(\Theta)\) of each radiating element (large to low from right to left), all their small signals are summed up properly in the feeding network to a provide maximum signal. \[S_{received}=\sum_{n=1}^{N}S_{n}e^{i[\alpha_{n}+(n-1)\cdot k\cdot d\cdot\cos \left(\Theta\right)]}=\sum_{n=1}^{N}S_{n}e^{i(N-1)\cdot k\cdot d\cdot\cos\left( \Theta\right)} \tag{7}\]  
This signal is being further proceed in the receiver (1) by frequency-down and analog-digital conversion, and (2) in the digital baseband. As a result of reciprocity, the same array can be used in the transmit mode, too. Then, the signal from the transmitter is first distributed equally by the feeding network to the phase shifter. By the proper electronic change of the relative phase of the small signal that each antenna element transmits, their overall contribution in the far field creates a larger focused beam in a particular direction. This beam can be directed instantaneously in any direction by fully electronic control, and hence, track the movement, e.g., of any satellite, no matter how or where you move, without the need for any mechanical moving parts. The gain and HPBW of an ESA are proportional and inversely proportional to the number of radiating elements. A \(16\times 16\) horn antenna array is exemplary shown in Figure 14 for a relay satellite in geostationary orbit, which will be discussed in Section 3.2. It consists of circular horns and a three-dimensional feeding network in rectangular waveguide topology because of its intrinsically low loss. Beam-steering capability is achieved with a plug-in solution of a partially LC-filled waveguide phase shifter (see Section 3.1) between horns and the feeding network. The key element of such phased arrays are the phase shifters, which can be realized in different line and waveguide topologies, and where tunability can be achieved by components in different technologies, as mentioned before. The focus here is on passive phase shifting by using the MLC technology only. As a measure for the performance of phase shifters, a figure-of-merit is defined by  
\[FoM=\frac{\Delta\varphi_{\max}}{IL_{\max}} \tag{8}\]  
Figure 14: Example of a \(16\times 16\) horn antenna array for a GEostationary Orbit (GEO) relay satellite. Beam-steering can be achieved by a plug-in solution of a partially LC-filled waveguide phase shifter (**middle**) between horns (**left**) and the feeding network (**right**).