IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 12, DECEMBER 2010 3079 Measurement of Dielectric Constants of Nematic Liquid Crystals at mm-Wave Frequencies Using Patch Resonator Mani Yazdanpanahi, Student Member, IEEE, Senad Bulja, Member, IEEE, Dariush Mirshekar-Syahkal, Senior Member, IEEE, Richard James, Sally E. Day, Member, IEEE, and F. Aníbal Fernández, Member, IEEE Abstract—A new technique for the measurement of dielectric constants of nematic liquid-crystal (LC) materials at millimeter- wave frequencies is presented. The proposed method utilizes an electric field to align the LC molecules, therefore offering safety and enormous size reduction over the method using the magnetic field to achieve LC directors’ orientation. The measurement device is planar and consists of a rectangular patch resonator with the LC cell directly beneath it. Two preconditioned surface preparations, corresponding to transverse and longitudinal rubbing of the patch surface and ground plane in contact with LC, are investigated. Using the same measurement device with the two preconditioned surfaces, the measurements of dielectric constants and dielectric constant anisotropy of a nematic LC commonly known as E7 are conducted, and the results are found to agree to within 1% while confirming earlier published data. Index Terms—Anisotropic media, dielectric measurements, liquid crystals (LCs), millimeter-wave resonators, permittivity measurement. I. I NTRODUCTION I NTEREST in reconfigurable RF devices has been the mo- tivation for the current gradual development of various voltage tuneable materials. Liquid crystals (LCs) are promis- ing tuneable materials as their dielectric properties can be controlled under an external bias field with negligible power consumption [1], [2]. Several nematic LC-based microwave devices have been reported in the literature, such as tuneable microstrip antennas [3], variable delay lines [4], phase shifters [5], and steerable reflect arrays [6]. Nematic LCs, which are largely used in display technol- ogy, are liquid anisotropic materials that exhibit a variation of relative dielectric permittivity when subjected to an external electric or magnetic field. These materials are relatively cheap Manuscript received July 31, 2009; revised December 23, 2009; accepted December 26, 2009. Date of current version November 10, 2010. The work is supported by the Engineering and Physical Sciences Research Council, U.K. The Associate Editor coordinating the review process for this paper was Dr. Sergey Kharkovsky. M. Yazdanpanahi, S. Bulja, and D. Mirshekar-Syahkal are with the School of Computer Science and Electronic Engineering, University of Essex, CO4 3SQ Colchester, U.K. (e-mail: myazda@essex.ac.uk). R. James, S. E. Day, and F. A. Fernández are with the Department of Electronic and Electrical Engineering, University College London, WC1E 7JE London, U.K. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2010.2062910 and respond to low voltages, which is an advantage, compared with ferroelectrics requiring high operating voltages. Their local macroscopic ordering is described by an order tensor, which represents the local orientation of the LC molecules (represented by a vector called director n) and the degree of ordering. The relative permittivity of the LC can be described in terms of this order tensor, which is normally a uniaxial tensor with nonzero principal components ε ⊥ and ε ‖ corresponding to the relative permittivities in the normal and parallel directions of the director with respect to the applied bias field. A number of factors influence the choice of an LC for an RF application. Improved and specialized LCs offering tem- perature stability, with large dielectric anisotropy (Δε r ), are being developed for some RF devices. However, it is believed that the main applications of nematic LCs in RF will be in and beyond millimeter-wave (mm-wave) frequencies where a small change in the director orientation significantly affects the wavelength and wave impedance. Therefore, characterization of the dielectric properties of the LC in mm-wave frequencies is essential and can be achieved by either resonant or broadband methods. The resonant technique is highly sensitive and offers precise characterization of the permittivity of a dielectric material. In [7], a cavity perturbation method is used to characterize nematic LCs at 9 and 35 GHz. The measurements were performed using rectangular waveguide resonators with two insertion holes for LC filling tubes. Alignment of the LC molecules was achieved in two orthogonal directions with a strong magnetic field. However, the use of a strong magnetic field for aligning LC molecules entails practical problems due to the large size, power consumption, and safety of the device producing the magnetic field. Consequently, it is more sensible to use the electric field for biasing the LC, as mentioned in [8] and [9]. In [8], a Fabry–Perot-like technique is used to obtain the dielectric constants of the LC. For this purpose, a metallic slit is formed as the sample holder, and the measurements are based on the transmission of radiation through the LC sample held in the absorber aperture. The horn antennas used for directing and collecting the plane wave are required to be at certain distances from the sample, and the sample holder has to be at a specific angle with respect to antennas to prevent strong interference between the device and the antennas. Therefore, the method requires a complex experimental setup to yield accurate results. 0018-9456/$26.00 © 2010 IEEE