This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 1 Dielectric Anisotropy Sensor Using Coupled Resonators Hector-Noel Morales-Lovera , Jose-Luis Olvera-Cervantes , Alonso Corona-Chavez , Senior Member, IEEE, and Tejinder Kaur Kataria, Member, IEEE Abstract—In this article, a new approach is proposed for the measurement of the uniaxial anisotropic dielectric constant of different planar samples by means of a single sensor. The sensor is based on a couple of straight-line coupled resonators in microstrip technology that can be excited in odd and even prop- agation modes. This sensor is designed on an isotropic substrate at the design frequency. Due to the electric field configuration specific for each mode, it is possible to relate these modes to the dielectric constant in two different directions (parallel and perpendicular) of a dielectric material placed on top of the sensor. This technique is used for the successful characterization of the dielectric constant anisotropic of anisotropic dielectrics (FR4, Rogers 4350B, and Arlon Diclad 880), and the isotropic material PTFE. Index Terms— Anisotropic, anisotropy, dielectric constant, FR4, printed circuit board (PCB), sample under test (SUT), uniaxial. I. I NTRODUCTION T HE dielectric constant (ε r ) is a measure of the dielectric material response when an external electric field is applied to it. In addition, the dielectric constant is related to the speed of the electromagnetic (EM) wave in a material; therefore, in transmission lines, such as microstrip lines, it is a parameter related to the wavelength in the substrate, time delay, characteristic impedance, among others [1]. For this reason, the precise dielectric characterization of the materials is of paramount importance to make reliable designs in the RF and microwave range. The dielectric anisotropy (different ε r for different direc- tions) is a physical phenomenon caused by the macroscopic characteristics in the structure of the material [2], [3], caus- ing an EM wave in an anisotropic medium to feel differ- ent propagation velocities in each direction. Consequently, the dielectric anisotropy causes the propagation and scattering characteristic to change according to the transmission line on a specific substrate. Some of the modern dielectric materi- als, such as FR4 and Rogers 4350B, are made of woven fiberglass, embedded in epoxy. As a consequence of the Manuscript received June 15, 2019; revised October 18, 2019; accepted November 23, 2019. (Corresponding author: Jose-Luis Olvera-Cervantes.) H.-N. Morales-Lovera, J.-L. Olvera-Cervantes, and A. Corona-Chavez are with the Department of Electronics, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), San Andrés Cholula 72840, Mexico (e-mail: jolvera@inaoep.mx). T. K. Kataria is with the Universidad de Guanajuato, Salamanca 36885, Mexico. Color versions of one or more of the figures in this article are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMTT.2019.2958265 nonhomogeneity in their structure, these kinds of materials are potentially anisotropic. They usually have a ε r for the direction parallel to the surface (ε k ) and a second in the perpendicular direction (ε ⊥ ). This phenomenon is known as uniaxial anisotropy. Normally, substrates for printed circuit board (PCB) are characterized by means of resonant pla- nar circuits techniques, using striplines [4]. Nevertheless, the method does not offer any information about substrate dielectric anisotropy. In the literature, some works can be found focusing on dielectric anisotropic characterization. Nonresonant methods determine the dielectric constant by means of the impedance and the propagation constant of a transmission line as in [5] and [6]. In [5], the anisotropy is determined from the measurement of the phase constant and a rigorous analysis of the spectral domain of the scatter characteristics of microstrip lines. On the other hand, in [6], it is shown how different configurations of the fiberglass fabric in the FR4 substrate influence the scatter characteristics of microstrip lines. The advantage of the nonresonant method is that ε r can be determined over a wide range of frequencies, but its accuracy and sensitivity are usually low, and tests are often destructive. On the other hand, resonant methods offer greater accuracy and sensitivity, but ε r can be known only at a single frequency (resonance frequency) or multiples of it. Resonant methods include the cavity perturbation method and the planar circuit method [7]. In the cavity perturbation method [8], [9], the sample under test (SUT) is introduced into the cavity, and placed in a region of maximum con- centration of electric field, and ε r is determined from the change in the cavity resonances properties when the sample is introduced. In [8], the TE 112 mode is used to measure the uniaxial dielectric constant; this mode has electric field lines perpendicular to each other, which allows to determine the ε k and ε ⊥ separately, selecting the corresponding mode by means of fine metallic needles. In [9], a two-resonator method is used with different propagation modes in each of them, measuring ε k with a resonator where the TE 011 mode propagates, and ε ⊥ with another resonator where the TM 010 mode is excited. In the planar circuit method, resonators are designed on a substrate to determine the dielectric characteristics of the mate- rial, relating the physical length of the resonator to the resonant frequency, and thus, deduct the ε r . Coupled resonators in microstrip and stripline technology (called RA resonators) are used in [10] and [11] to determine ε r in the horizontal and vertical direction of the substrate where the resonator was 0018-9480 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.