In this paper, a sensor using modified Split Ring Resonators (SRRs) is designed, simulated, fabricated, and used for advanced investigation and precise measurements of the real part and imaginary part solid dielectrics’ permittivity. Adding vertical strips tightly coupled to the outer ring of the SRR leads to the appearance of two resonant frequencies at 1.24 GHz and 2.08 GHz. This modified geometry also assures an improved sensitivity. Using the full wave electromagnetic solver, both the unloaded and loaded sensors are investigated. The numerical simulations are used to develop a mathematical model based on a curve fitting tool for both resonant frequencies, allowing to obtain analytical relations for real and imaginary parts of permittivity as a function of the sample’s thickness and quality factor. The sensor is designed and fabricated on 1.6 mm thick FR-4 substrate. The measurements of different samples, such as transparent glass, acrylic glass, plexiglass, and Teflon, confirm that the modified SRR sensor is easy to implement and gives accurate results for all cases, with measurement errors smaller than 4.5%. In addition, the measurements highlight the importance of the second resonant frequency in the cases in which numerical limitations do not allow the usage of the first resonant frequency (1 mm thick sample).

Modified Split Ring Resonators Sensor for Accurate Complex Permittivity Measurements of Solid Dielectrics

In this paper, a simple method of extracting dielectric material is proposed and copper surface roughness is taken into consideration. The measured results from W-band to D-band are shown to verify the proposed method of extracting complex permittivity of dielectrics. Besides, to validate the proposed transmission line technique, the full sets of complex S-parameters with an appropriate “through-reflect-line” (TRL) calibration pattern are measured as well. It also allows accurate determination of the dielectric constant and loss of thin sheet substrate materials. A great consistency between transmission line technique without calibration and TRL calibration method represents that systematic errors are small. In addition, different samples within the same set of packaging are measured and used to extract dielectric constant and loss tangent, which agree well with each other.

Extraction of Complex Permittivity of Dielectrics on Package from W-band to D-band

The frequency-dependent complex permittivity is determined for a printed circuit board laminate. For this purpose, measurements performed to an array of striplines are systematically processed. The methodology presents the advantage of employing lines embedded within the same laminate without requiring multiple prototypes. From the extracted data, a Debye model is implemented to yield a wideband representation of both, the relative permittivity and the loss tangent. Moreover, the line’s characteristic impedance is reconstructed and causal time-domain simulation results are achieved.

A Stripline Width-Array Method for Determining a Causal Model for the Complex Permittivity

Wideband permittivity and loss tangent curves for the dielectric laminate of a printed circuit board are obtained. For this purpose, the single-frequency data provided by the laminate manufacturer together with propagation constant experimentally obtained from stripline measurements are used. This allows for enabling the wideband simulation of interconnects while the dielectric material properties are defined respecting causality. Furthermore, using the extracted data, the dielectric and conductor effects on the signal attenuation and delay can be separated to analyze the corresponding impact on the propagation features of interconnects. This is demonstrated here through the implementation of an RLGC model up to 30 GHz.

Relative Permittivity and Loss Tangent Determination Combining Broadband S-parameter and Single-Frequency Resonator Measurements

Stripline can support pure TEM mode propagation but its signal trace is embedded inside substrate. GSG probe pad, microstrip line and via transitions are designed to allow GSG probing on substrate surface to measure S-parameters of stripline. The mismatch of transitions are removed by thru-line method to yield complex propagation constant of stripline. As propagation constant is measured, the e r and tanδ of the substrate can be calculated by closed-form equations. Measurement results of a low e r and low loss LTCC substrate show that longer LINE circuits can give more stable results in e r and tanδ.

LTCC Dielectric Constant and Loss Tangent Extraction by Thru-Line Method in Stripline

Traditional via wall substrate integrated waveguide (SIW) can be realized in PCB process. As it does not have continuous side walls, its equivalent width is required to extract substrate $\varepsilon_{\text{r}}$ from measured $\beta$ . This paper presents a metalized slot SIW (MS-SIW) that can be realized by PCB process and has continuous side walls. Continuous side walls allow the use of close form equation to extract substrate $\varepsilon_{\text{r}}$ from measured $\beta$ . Fabrication flow and circuit design for transmission line method to extract e r using MS-SIW is presented for $30\text{GHz}\sim 65\text{GHz}$ . Comparison with microstrip strip line method shows less than 2% difference in extracted dielectric constant.

Dielectric Constant Measurement Using Metallized Slot Substrate Integrated Waveguide at PCB Process

For wireless power transfer using linear-polarized transmitter (TX) and receiver antennas, the rotation and movement of receiving antenna cause received power variation. The received power pattern is proposed to describe the received power variation from a specific TX antenna under receiver rotation. By placing the peak of the received power pattern of additional TX antennas in null directions of the previous TX antenna, received power variation due to rotation can be compensated. With symmetrically placed TX antennas, the power variation due to location variation can be compensated. This article proposes a time-switching symmetric transmitting array combining both techniques to increase the sweet region for far-field wireless power transfer under rotation and location variation. A sweet region is an area in the 2-D case or volume in the 3-D case, which is defined as an area or a volume inside the TX array that can get guaranteed minimum received power under rotation. The received power calculation using the Friis equation with short dipole antenna pattern shows that a symmetric TX array can achieve a larger sweet region than an asymmetric TX array under the same total transmitted power. The efficiency for the receiver at the origin is 1/2 at the 2-D case and 1/3 at the 3-D case. In the experiment, a linear-polarized TX array at 915 MHz with monopole receiver antenna and power detector is used as the receiver to measure received power under rotation and location variation. Measurement results at 2-D and 3-D cases confirm the received power level predicted by calculation using the Friis equation. The power budget calculation for wirelessly powering a sensor module attached on a bee inside a beehive using the proposed 3-D TX array shows that it is feasible to deliver sufficient power to the sensor module regardless of the orientation and location of the bee inside the beehive.

Time-Switching Symmetric Transmitter Array to Increase Sweet Region for Far-Field Wireless Power Transmission Under Receiver Rotation and Location Variation

Yu-Heng Cai

Papers

LTCC Dielectric Constant and Loss Tangent Extraction by Thru-Line Method in Stripline

Dielectric Constant Measurement Using Metallized Slot Substrate Integrated Waveguide at PCB Process

Time-Switching Symmetric Transmitter Array to Increase Sweet Region for Far-Field Wireless Power Transmission Under Receiver Rotation and Location Variation