A Compact Triple Band EBG Using Interdigital Coplanar Waveguide Structure for Antenna Gain Enhancement

A new triple band EBG unit cell with compact size has been designed, fabricated, and tested. The proposed EBG unit cell is based on a square mushroom-like EBG (M-EBG) structure with an interdigital coplanar waveguide (ICPW). With this technique, the size of the proposed ICPW-EBG structure has been reduced from λ/2 to λ/4 compared with the conventional M-EBG unit cell dimension, which is 18 × 18 mm2. The proposed unit cell was designed in order to respond for three frequency bands at 1.8 GHz, 2.45 GHz, and 3.7 GHz. An array of 10 × 10 unit cell was also designed as a reflector with an overall dimension of 181.8 × 181.8 mm2. The dipole antennas were implemented over the designed reflector with a short distance of λ/8 to radiate electromagnetic wave. The simulation results showed that the ICPW-EBG reflector can improve directivity of the dipole antenna to be 9.12 dB at 1.8 GHz, 9.02 dB at 2.45 GHz, and 8.40 dB at 3.7 GHz. The measurement directivities agreed well with simulation results including 8.72 dB at 1.8 GHz, 8.56 dB at 2.4 GHz, and 8.1 dB at 3.7 GHz. This is the first design of triple band EBG unit cell with 50% size reduction compared with the conventional structure at the same frequency. The designed ICPW-EBG reflector with dipole antenna results in the triple band operation, low-profile and high gain suitable for modern wireless communication systems.


Introduction
Development and design of telecommunication equipment in this modern era must respond to the need of users. Most mobile equipment must be designed for use of multifrequency bands including LTE, WLAN, WiMax, and Bluetooth. Likewise, an antenna, one of the major communication equipment, needs not only to operate for multiple frequencies but also to have low profile, compact size, and high gain. However, design of an antenna having all these features is very complex. ere are many techniques to design an antenna to operate with multifrequency band, low profile, small size, and high gain. One of the popular techniques is to design the antenna with artificial material, which is not found in nature, called metamaterial having negative refractive index property, or left-hand material (LHM), theoretically discussed by V.G. Veselago in 1968 [1]. LHM has negative refractive index corresponding to negative relative dielectric permittivity and negative relative magnetic permeability values. e permittivity and permeability characteristics are the macroscopic responses of homogeneous medium when applying electromagnetic fields [2]. LHMs can be applied with electromagnetic devices in microwave and terahertz frequency bands such as antenna, balun, transmission line, and coupler component [3]. Especially, with the negative refractive index of LHMs, the antenna can improve their characteristics of antenna gain, wideband, and multiband [4]. e LHMs are divided into electromagnetic bandgap (EBG), single-negative (SNG), double-negative (DNG) materials, etc. [5]. From three types of LHMs, EBG can be designed on a variety of structures when applying to an antenna, resulting in low profile, improved directivity, and wideband operation [6][7][8]. EBG can be classified into three groups conforming to its geometric configuration: (1) one-dimension transmission lines, (2) two-dimension planar surface, and (3) three-dimension volumetric structures. Using the second geometry, the mushroom-like EBG (M-EBG) is commonly used due to uncomplicated structure and ease of analysis and design for several applications [9]. e M-EBG structure is composed of a patch, via hold, substrate, and ground plane. It has two superior characteristics of surface wave suppression and inphase plane-wave reflection [10].
In the published research study of EBG applied to improve antenna characteristics [11], the comparative analysis of 3 different types of planar EBG was presented. e first one is EBG fractal structure using a simple square patch of 10 mm, resulting in a band gap from 8 GHz to 15 GHz. e second is fork type of square patch 10 mm with a band gap from 7.7 GHz to 15 GHz. e third is spiral-shaped EBG with square patch of 10 mm dimension, which does not respond to −10 dB band gap. e number of unit cells in an array was also studied. It was found that increasing the number of unit cells could increase the band gap range to the lower frequency region. It was also concluded that the fork type structure gives better performances with a wider band gap. However, all structures of unit cells have large sizes of about λ/2 and it could not independently control the harmonic frequency bands. e second published research study in [12] proposed the uniplanar compact EBG (UC-EBG) and UC-EBG incorporated with interdigital structure called ID-UC-EBG, both having square patch EBG dimensions equal to 7.3 mm. Even though the fringe capacitances on the proposed EBG structures could compress the unit cell sizes to less than λ/2, they are still large. Also, the harmonic frequency bands could not be controlled and the structures with two layers are very complicated. In [13], the novel design of two triple band EBGs was presented. e first type is the double slotted type EBG (DSTEBG), in which the microstrip unit cell size is larger compared to the conventional one. It is found that the stop band shifts to the lower frequency side due to increase of capacitance. e gap between the EBG unit cells results in the stop band shifted to the higher frequency. e proposed DSTEBG can operate in three bands with the first band of 2.42-2.95 GHz, the second band of 5.82-6.30 GHz, and the third band of 8.72-9.28 GHz. e second type is triple side slotted EBG (TSSEBG), in which the slot width is increased, resulting in the second and third bands shifting towards the side of lower frequency due to increase of inductance. e proposed TSSEBG can operate with the first band of 4.29-4.65 GHz, the second band of 5.56-6.28 GHz, and the third band of 7.60-7.94 GHz. Even though the proposed EBG can control three frequency bands when increasing the gap between EBG unit cells, the size is still large.
Normally, the EBG unit cells are designed on the microstrip structure and analyzed by using a circuit model of the transmission line to obtain cell size at the desired resonant frequency [14]. However, the research in [15][16][17] used coplanar waveguide (CPW) structure to design EBG unit cells because of advantages like low dispersion, small size, and simple realization due to etching on one side and broadband performance [18]. For further size reduction, several techniques have been proposed such as uniplanar compact electromagnetic band gap (UC-EBG), slot-strip EBG structure, interdigital structure, and Hilbert curve structure [19][20][21]. To design the EBG structure, the interdigital technique is very pliable and effective for size reduction. e interdigital structure can increase capacitance value and decrease quality factor causing the compact sizes [22][23][24][25][26]. From the drawbacks of all research studies mentioned above, this research proposes a design of the new compact EBG unit cell, capable of controlling three frequency bands, modified from the M-EBG unit cell. e coplanar waveguide structure and interdigital technique have been employed to create the EBG for size reduction due to slow wave structure [27,28] and low profile with high gain antenna [29,30].
is new EBG is called the interdigital coplanar waveguide electromagnetic bandgap (ICPW-EBG). After that, the ICPW-EBG array is also designed to be a reflector used with dipole antennas for improved directivity at triple band frequency applied for LTE, WLAN, and WiMax [31].

Design of ICPW-EBG and Applications
e triple band ICPW-EBG reflector consists of two parts including EBG unit cell and array of unit cells. To design the triple band EBG unit cell, the interdigital coplanar waveguide structure is applied on the patch of M-EBG for minimizing size and controlling the resonance frequency as desired. e second part of the design is the ICPW-EBG array being used as an antenna reflector. e ICPW-EBG structure is qualified for disposal of surface wave on the surface of reflector, having only plane wave propagation reinforced with the propagation pattern of the source antenna. With the in-phase plane-wave reflection, the EBG reflector results in a low profile antenna. In this section, the triple band ICPW-EBG unit cell will be designed for LTE (1.8 GHz), WLAN (2.45 GHz), and WiMax (3.7 GHz) [31]. It is designed on FR-4 PCB with ε r of 4.4, loss tangent of 0.03, and substrate height of 1.6 mm with CST studio program. en the ICPW-EBG array as a reflector will be implemented and applied for dipole antennas.

Triple Band ICPW-EBG Unit Cell.
is section proposes the design of the compact triple band EBG unit cell. From the advantages of CPW structure, it was applied on a square patch of M-EBG, due to connectivity of the capacitor at the end of the proposed structure causing slow wave effect [27]. e CPW structure used in this design has a ground plane at bottom and semi grounds on top and operates in odd mode. In Figure 1, C i is the capacitance between transmission line and semi ground, C i ′ is the capacitance when the electrical field exists only in a dielectric layer and may be found from the corresponding couple strip line geometry, C g is the parallel plate capacitance between semi ground and transmission line to ground plane, and C f is the fringe capacitance. Normally, the values of C i ′ and C f have very small impact on the design to achieve the fundamental frequency resonance. e total capacitance of CPW (C CPW ) is very important and its value can be written in (1), where C is the speed of light, A is the width of transmission line, B is the width of transmission line to semi ground, and C Zt is the capacitance of the transmission line: when From the basic structure of CPW with ground plane, it is found that the capacitance between transmission line and semi ground (C i ) has more effect on the resonance frequencies. In order to control the second and third harmonic frequencies, the value of C i must be varied instead of C g because it is easier. en, the interdigital technique has been applied together with CPW to increase C i as the proposed structure shown in Figure 2. It can be seen that there is a finger between the transmission line and the semi ground. e gap and the impedance of the finger between both sides will cause a significant increase in C i . Considering the equivalence circuit in Figure 2, the transmission line is divided into three parts composed of Z a , Z b , and Z c , corresponding to the propagation constants β a , β b , and β c . From interdigital techniques, the inductance (jX L ) is less than the capacitance (−jX C ), so the C t � C i + C g has a significant effect on the transmission line. R 1 and R 2 are the losses in transmission line. In the case of Z a � Z b � Z c , the total impedance (Z t ) can be found in (3), where R is the ratio of unequal impedance in transmission line. e admittance Y a can be written as in (4).  International Journal of Antennas and Propagation From the interdigital connection with CPW transmission line, whether the impedance is equal to the step impedance, the C t is connected to the end of transmission line. It has a significant impact on the electrical lengths of transmission line, as shown in (5) and (6), when L t is the total length of the interdigital part, L f is the length of the finger, and n is the number of fingers. e C t has a very significant effect on the electrical length of the fundamental frequency (f 0 ) and the third resonance (f 2 ), while the second resonance (f 1 ) will have a little effect on electrical length.
It can be explained that C t value can control the fundamental and third resonance frequencies, while the combination of C t and step-impedance transmission line section can control the second resonance frequency. Furthermore, increasing capacitive value at the end of transmission line with interdigital technique leads to slow wave at transmission line, resulting in unit cell size reduction from λ/2 to λ/4. Based on the ICPW design, the next step is to design a pin on the ICPW structure. Location and size of the pin were optimized. When arranging two unit cells as shown in Figure 3(a), the capacitive (C a ) is found and the inductance (L p ) arises due to the pins and ground plane. e equivalence circuit of the ICPW-EBG unit cell is shown in Figure 3(b). e values of L p and C a are used to calculate the bandwidth according to (7) and (8). When a is the unit cell range with gap g being the gap width, W is the unit cell width, h is the thickness of substrate, and η 0 is the free space impedance. erefore, the design equation is changed from (5) to (9) that adds C a into this equation. It is concluded that C a has been taken into account resulting in the change of electrical lengths as shown in (9) and that C t and C a have more effect on the resonance frequencies of the ICPW-EBG unit cell as mentioned.  International Journal of Antennas and Propagation e capacitance causes a narrow bandwidth at the resonance frequency. To cover the required bandwidth of the resonance frequency with phase angle of 0 to 90 degrees, one technique commonly used is to increase the substrate thickness. In our design, the FR-4 substrate was employed. e design will determine the transmission line of the ICPW-EBG unit cell with 50 ohm impedance and phase of 0-90 degrees at the fundamental frequency of 1.8 GHz.
e phases at the second and third resonance frequencies of 2.45 GHz and 3.7 GHz can be controlled by varying the capacitance with interdigital technique. e structure and dimension of the proposed unit cell are shown in Figure 4 and Table 1. To get the required bandwidth, the resonance frequencies must be shifted to 1.94 GHz, 3.2 GHz, and 4.4 GHz, respectively. Figure 5 shows the simulation results of phase diagram. e S curve covers the bandwidth with phase of 0-90 degrees for all frequency bands including 1.66 GHz-1.92 GHz for 1.8 GHz band, 2.16 GHz-2.97 GHz for 2.45 GHz band, and 3.43 GHz-3.98 GHz for 3.7 GHz. e simulation of dispersion diagram is also shown in Figure 6. It can be seen that the bandgap had the lower band frequency at frequency of 1.71 GHz, the upper band frequency at 3.75 GHz, and the center band frequency at 2.73 GHz, covering the designed operating frequency. In addition, the size of ICPW unit cell is reduced from λ/2 to λ/4 by the slow wave effect within the structure. Figure 7 shows the comparison of dimension of ICPW-EBG unit cell and ordinary M-EBG unit cell at the same frequency of 1.8 GHz.
e simulations of E-field and H-field on the ICPW-EBG structure were performed. e results will be used for alignment of the antenna plane corresponding with the ICPW-EBG array plane for maximum efficiency. e simulation results are shown in Figures 8(a) and 8(b), where the E-field has significant impact on the interdigital section of structure at all resonance frequencies, while the H-field has very small impact. erefore, the antenna must be placed on Y-axis or parallel with the interdigital period. Based on the simulation result in Figure 9, there is no current density on the patch of ICPW-EBG unit cell.
is means that the ICPW-EBG structure has only plane wave propagation and eliminates surface wave.
Ground plane C g jX L < -jX C e 10 × 10 ICPW-EBG unit cells were arranged as an array with the gap between the unit cells of 1.8 mm. e total area of the array is 181.80 × 181.80 mm 2 as shown in Figure 10. is proposed array will be used as an antenna reflector, so the size of array must cover the antenna size. From simulation, it is found that the E field is parallel along the Y axis of the interdigital structure. e current density passes through the band gap at 1.8 GHz, 2.45 GHz, and 3.7 GHz, as shown in Figure 11. It does not affect the ICPW structure, so it can be used as a reflector for the antenna with wave propagation at three desired frequencies. With small unit cell size, the array of 10 × 10 unit cells as a reflector is also very small. In addition, with surface wave suppression and in-phase plane-wave reflection, it can enhance the directivity of dipole antenna when applying with compact ICPW-EBG reflector, working as a high-gain directional antenna. en the dipole antenna is designed as the electromagnetic radiating source to be used with the ICPW-EBG reflector. It is designed from a copper pipe with 3.46 mm (W 1 ) diameter and 0.46 mm (T) thickness. Figure 12 shows the dipole diagram and parameters designed at three frequencies of 1.8 GHz, 2.45 GHz, and 3.7 GHz. e antenna lengths of all dipoles at the three frequencies are 0.47λo, with their sizes optimized, resulting in all dimensions in Table 2.
From the previous ICPW-EBG array and dipole antenna design, this section will present the simulation results of the dipole antenna with ICPW-EBG reflector in order to observe the performances of ICPW-EBG on the dipole antenna. e dipole antenna was placed above ICPW-EBG reflector acting Figure 4: e geometry of ICPW-EBG unit cell.                Figures 14(a)-14(c). It was found that the current density flows in the gap between ICPW-EBG unit cell, but does not have current flow on the structure of ICPW-EBG unit cell. At the resonant frequency, it has a strong current density, which can be explained that when applying ICPW-EBG unit cell with an antenna, ICPW-EBG rejects the surface wave and has only the propagation wave that is complement to the propagation wave of the antenna.
is causes the antenna to have a higher directivity. Figures 15(a)-15(c) show simulation results of the observed surface current responses. It is found that at all frequencies there is no surface current. It is clearly seen that ICPW-EBG can eliminate the surface wave to be just an extra propagation wave to the antenna.
From the simulation results of ICPW-EBG reflector driven with dipole antennas, the ICPW-EBG structure can increase directivity of the dipole antennas and perform with directional pattern. e antenna directivities are improved to be 9.12 dB at 1.8 GHz, 9.02 dB at 2.45 GHz, and 8.40 dB at 3.7 GHz. e distance between antenna and reflector is reduced from λ/4 to λ/8. e ICPW-EBG can control the responses for three frequency bands. With small ICPW-EBG unit cell dimension of λ/4, arranging the ICPW-EBG with 10×10 cells makes the overall size of the ICPW-EBG reflector very compact. In conclusion, ICPW-EBG is simple and compact in structure and easy to design. In Table 3, the performance of the proposed ICPW-EBG antenna is compared with unit cell design and antenna design with the previous reference. e results of the measurement will be presented in the next section.

Measurement Results
In this part, the measurement of return losses and radiation patterns will be performed at three resonance frequencies. e structure of the proposed antenna was implemented as shown in Figure 16. For only dipole antenna, the measured bandwidths (higher 10 dB return loss) of 550  Figure 17. In addition, the measurement of radiation patterns was done as the results are shown in Figure 18. It is found that the antenna has directional radiation, where the antenna gains at the 1.8 GHz, 2.45 GHz, and 3.7 GHz frequencies are 8.72 dB, 8.56 dB, and 8.1 dB, respectively. It can be seen that the gains of the proposed antenna are higher compared with the dipole with PEC reflector. Also, the measured results agree very well with simulation results.

Conclusion
e new EBG unit cell with ICPW structure was proposed. e slow wave effect on the proposed structure could reduce the size of unit cell from λ/2 to λ/4 and can control the second and third resonance responses. e array of ICPW-EBG unit cells was formed with the dimension 181.8 × 181.8 mm. Moreover, the distance between the dipole antenna and the ICPW-EBG reflector was reduced from the normal distance of λ/4 to λ/8, resulting in a low profile system. In addition, the ICPW-EBG reflector could increase the antenna gain at the frequencies 1.8 GHz, 2.45 GHz, and 3.7 GHz to be 8.72 dB, 8.56 dB, and 8.1 dB, respectively. e radiation patterns at three frequencies are directional. Also, the measured bandwidths of the proposed antenna were 760 MHz, 750 MHz, and 710 MHz at 1.8 GHz, 2.45 GHz, and 3.7 GHz frequency bands, respectively.

Data Availability
e data used to support the findings of this study are included within the article.