## 2 Microwave Liquid Crystal Technology
### Performance Metric of Microwave Liquid Crystals
Similar resonator measurements for the precise small-band characterization of LCs were also carried out in [202; 203; 204; 205; 206; 207; 208], whereas wideband measurements were presented in [46; 209; 210; 211; 212] by using specifically temperature-controlled coaxial-transmission line setups, and in [77; 213; 214; 215; 216] by using some other line or capacitance characterization setups. Beyond these measurements in the micro- and mm-wave range, low-loss LCs were also characterized and analyzed at THz frequencies from 0.1 to 0.35 THz with a free-space CW THz system in [217] and with a THz time-domain spectroscopy setup from 0.15 to 1 THz in [218], from 0.2 to 2.5 THz in [219], and 0.3 to 1.5 THz in [220], and soon later, from 0.3 to 8 THz in [75]. The MLC technology at TU Darmstadt was established by the first author in 2002 in close collaboration with the Performance Materials Division of Merck KGaA, Darmstadt. Since then, Merck synthesized and provided novel nematic LC mixtures with the highest material's figure-of-merit, which were characterized over a wide frequency range from few GHz up to 8 THz. Beyond the lab-scale characterization setups above, a stable temperature-controlled LC-characterization system sketched in Figure 7 was built up, to measure the complex permittivity of new LCs at 19 and 30 GHz directly in Merck's laboratory with very high accuracy and perfect reproducibility [56; 58; 59]. This industrial-scale setup is presented in particular detail in [2; 74; 75; 208]. The design is based on the cavity perturbation method in [200; 201] with several improvements to extract the complex permittivity tensor by formulating the Maxwell equations as an eigen-susceptibility problem of the considered sample [221; 222] and by applying the variational approach to a triple-mode perturbation method [204]. This offers a direct solution of the desired material parameters by utilizing adequate and well-proven numerical techniques such as the Finite Element Method (FEM). The unloaded Q of the cylindrical  
Figure 6: Director \(\overset{\rightarrow}{n}\) parallel to the molecular long axis for a LC unit volume element and permittivity tensor. aluminum cavity, containing a small amount of LC in a quartz tube, is better than 4200, enabling detecting very low dielectric loss of LCs in a test. The LC orientation is controlled by means of a static magnetic field of 0.35 T, which is generated by permanent magnets. Very recently, measurements are extended to 60 GHz [223]. Table 1 resume the elastic and electromagnetic properties of a few selected nematic LC mixtures at 19 GHz and at room temperature, except for MDA-03-2838 and MDA-03-2844, which are characterized at 9 GHz. In addition, three well-known LCs from optics are included: K15 (5 CB) as a benchmark as well as E7 and BL006, since they have been widely used in many studies also for microwave applications. From literature to literature, the values of the parameters in Table 1 might slightly vary, generally due to measurement errors, but also because of different characterization techniques and equipment being used as well as different environmental factors such as humidity and temperature. The results of many more LC mixtures at different frequencies are summarized in [182]. In general, all microwave LCs offer low dielectric constants in both principal directions, typically in the range of 2.4 to 2.6 for perpendicular orientation and 2.9 and 3.5 for parallel orientation of the director \(\vec{n}\), thus satisfying low permittivity requirements. Loss tangents are typically tan\(\delta\)\(\leq\) 0.015. The following