International Journal of Microwave Science and Technology

Volume 2015 (2015), Article ID 453710, 9 pages

http://dx.doi.org/10.1155/2015/453710

## Turn Ratio, Substrates’ Permittivity Characterization, and Analysis of Split Ring Resonator Based Antenna

^{1}Department of Electrical & Electronic Engineering, Olabisi Onabanjo University, PMB 5026, Ifo, Ogun State, Nigeria^{2}School of Electrical & Electronic Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia

Received 30 June 2015; Accepted 8 October 2015

Academic Editor: Walter De Raedt

Copyright © 2015 Seyi S. Olokede et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The turn ratio, coupling space between sections, and substrate permittivity effects on spilt ring resonator (SRR) are investigated. The analysis of the presented SRR with respect to the effects of substrate and number of gaps per ring to further characterize its peculiarities is experimented with miniaturized capability as our intent. Six different SRRs were designed with different turn ratios, and the sixth is rectangular microstrip patch centre-inserted. Different numbers and gap sizes are cut on the SRRs while the gap spacing between the conductors of the SRR was varied to determine their effects taking cognizance of the effects of different substrates. The designs were investigated numerically using 3D finite integration technique commercial EM solver, and the resulting designs were prototyped and subsequently measured. Findings indicate that the reflection coefficient of the MSRR with centre-inserted patch antenna is better compared to MSRR without the patch antenna irrespective of the laminate substrate board, and so is its gain.

#### 1. Introduction

The explosive growth in the demand for wireless communication and information transfer using mobile phone, satellites, and personal communications devices has created the need for advanced antenna design technology. Microstrip planar antennas are smart solutions for compact and cost effective wireless communication systems, in particular due to its significant attractive features of low profile, light weight, easy fabrication, low volume, low profile, ease of integration with printed circuit boards, low power handling capability of printed circuits, and conformability to mounting hosts [1]. Thus, these types of antennas are flexible due to their conformability. As such, smaller antennas are feasible based on the electrodynamics of the patch antenna, though they are limited by their electrical length, in particular the conventional patch antenna.

SRR and its derivatives have been one of the burning issues on antenna miniaturization at microwave and millimeter wave systems in recent times. One very notable attribute that makes SRRs stands out is the increasing need for the optimum usage of space in modern microwave circuits. High Q, low cost, and low radiation loss are extra additives that makes them common technology for filter designs [2–6], antenna design [7–11], and recently applicable in metamaterials [12, 13].

Theoretically, SRR structure exhibits the most common negative permeability characteristics. When the alternating magnetic field is applied perpendicular to the SRR plane, the electromagnetic feature of the SRR can be excited by a time-varying magnetic field with a nonnegligible component applied parallel to the ring axis. This will form a resonant circular current in the ring or rings and hence dictate the resonant frequency. It therefore behaves like a magnetic field driven by inductor and capacitor () resonant tanks that are externally driven by the magnetic field [14].

Hence in a rectangular multiple SRR (MSRR), the conductor trace with opposite sides of the SRR may be treated as coupled line sections. The total inductance is the sum of self-inductance of the sections and the mutual inductance between the turns on assumption that the magnitude and phase of the current across the sections are constant. On the other hand, SRR has maximum electric field density near the slit and, interestingly, the nature and the intensity of the fringing fields between the gaps, and also the number of rings determines the nature and the strength of the coupling. Ironically, the SRR has the maximum electric charge densities at the gap edges with opposite signs, whereas the current flow is optimum along the ring ribs opposite to the rib.

Therefore the effect of the magnetic field excitation at the perpendicular plane of the SRR with respect to its electromagnetic feature vis-à-vis, its resonance frequency, and the spacing between the parallel coupled sections and the effect of electric field intensity near the slits are examined in this work. Much more, the nature and the extent of the fringing field with respect to different dielectric substrate are investigated.

#### 2. Materials and Methods

The proposed SRR structure consists of number of concentric split ring resonators to obtain magnetic resonances at distinct frequencies. The value of each frequency can be adjusted by changing the design parameters such as the metal width () and gap size () for each ring as well as ring to interrings spacing (). As a result, increasing the number of rings () will increase the resonance frequency. Self-inductance also increases when the side length of the metal ring increases with a corresponding decrease in the resonance frequency of the resonator, as corroborated by Turkmen et al. [15].

The frequency response of the SRR is obtained using (1), where represent the total equivalent inductance while represent the equivalent capacitance. The value is obtained by using (2a), whereas is obtained using (2b) [16]:where , , and, . is the series capacitance between two adjacent rings, is the capacitance per unit length of the ring, constant (= 2.853) for wire loop of square geometry, and is the slit gap, whereas is the gap between the rings. The equation to calculate is stated in (3) while (4) defines the gap capacitance () between the slits, whereas is the relative dielectric permittivity of the substrate, is the characteristic impedance (set at 50 Ω), and is the speed of lightThe dimensions of the SRR were determined using the above equations with , , and . Figure 1 depicts the geometry of the SRR, Figure 2 is the proposed designs simulated using 3M EM microwave solver, and Figure 3 is the fabricated designs of the propose design. The optimized prototypes of the proposed were photoetched on Roger duroid laminate microwave substrate of permittivity () of 3.38, height of 0.813 mm, and metallization of 35 *μ*m; duroid permittivity () of 6.45, height of 2.5 mm, and metallization of 35 *μ*m; FR4 epoxy substrate of permittivity () of 2.4, height of 1.6 mm, and metallization of 35 *μ*m; and, finally, FR4 of permittivity () of 4.4, height of 5 mm, and metallization of 35 *μ*m. The resulting designs were tested using the HP 8720D (50 MHz–20 GHz) network analyzer in order to measure the reflection coefficients, the antenna impedance, and the voltage standing wave ratio (VSWR). For this measurement process, HP 8720D (50 MHz–20 GHz) network analyzer was used to measure the reflection coefficient, resonant frequency, bandwidth, and input impedance. For bandwidth measurement, −10 dB point was used to determine the range of frequency. Prior to measurement, a kit is required to calibrate the network analyzer at the frequency required for one port only. The recorded data from the network analyzer measurement was plotted and compared with simulated results. The connection configuration of the network analyzer is shown in Figure 4(a).