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Design and modeling of TL MTM structure for antenna applications.


In recent trends, there has been growing interest in utilizing Electromagnetic Band Gap (EBG) structures in electromagnetic and antenna community. EBG structure is one of the meta-materials with the property to suppress electromagnetic wave propagation (stop band) in a certain frequency band. The structures are periodic geometries constructed by repetition of unit cell in one, two or three dimensions [1]. Its band gap features are revealed in the suppression of surface wave propagation that helps to improve antenna's performance such as increasing the antenna gain and reducing back radiation [2]. The 2-D geometries can be broadly classified into two categories: Textured (Mushroom) type and Planar (or Patterned) type structures. The planar EBG structures are via-less structures, which ease the manufacturing process. In addition, it is less sensitive to the incident angle and polarization.

Characterization of EBG structures is performed in full wave numerical simulation for the entire structure based on Finite Element Method [3] and equivalent circuit modeling based on lumped elements and transmission lines [4]. All high impedance structures can be studied on the basis of an effective model which consists of a resonant LC circuit. The fast and accurate modeling by transmission line model shows the computationally efficient results with respect to full wave electromagnetic analysis. Thus, circuit based transmission line models were developed as an alternative to time consuming 3-D full wave based model.

In [5], a simple lumped element model for the mushroom like EBG structures was proposed. Later, a model based on both transmission line theory and circuit elements were presented in [6]. In [7], transmission line segments were added to lumped element, that make more accurate prediction of the edges of the band gap as well as the center frequency. In [8] and [9], basic lumped element models were developed for meta-materials. In [10], model for an important class of planar EBG structure is developed over a wide range of frequency.

In this paper, a TL MTM structure is analyzed for its band gap using lumped element transmission line modeling in ADS and verified by reflection phase characterization using HFSS software. It is observed from both analyses that the proposed EBG has band gap at 5.2GHz.

Tl Mtm Structure:

The top view of the TL MTM structure unit cell is shown in Fig. 1. The Planar type EBG structure consists of two conductive layers. Between these two layers, a uniform substrate material FR4 (Fire Retardant) with dielectric constant 4.4 and thickness of 1.6 mm is used. Table. 1 summarizes the geometrical parameter values of unit cell with meander line section.

This EBG structure can be realized as a metal patches connected by meander lines. The details of meander line section are shown separately in Fig. 2. This meander section increases the effective inductance of the unit cell. The circuit parameters for meander line section are founded by closed form formulas [11]. To calculate the equivalent inductance of meander line, its section is decomposed into straight conductive segments.

The inductance of meander line can be calculated from the following expressions

t = 0.002 l [ln(2l/w+t) + 0-50049 + (w+t/3l)] (1)

[] = 2[L.sub.a] + [L.sub.b] + 2[L.sub.C] + [L.sub.d] + [L.sub.e] (2)

Where, L is the inductance in [mu]H; l is the length; w is the width; t is the thickness of the conducting segments in centimeter; [] is the total inductance of all the segments.

At resonance frequency, high impedance could be obtained and hence the EBG do not support any surface wave near the resonance frequency, resulting in a frequency band gap. The resonant frequency [[omega].sub.0] of a planar EBG can be approximated by equivalent inductance L and capacitance C and is given by expression

[[omega].sub.0] = 1/[square root of LC] (3)

The relative bandwidth of band gap is

BW = 1/[eta][square root of (L/C)] (4)

Where, [eta] is the free space wave impedance.

From this expression, the relative bandwidth is directly proportional to the inductance L and inversely proportional to the capacitance C. This means that, if inductance increases the bandwidth increases but alternatively the resonant frequency decreases. In this work, the meander line increases the inductance of the unit cell which in turn reduces the lower edge of the band gap.

Modeling Using Lumped Transmission Line Circuits:

In this section, the proposed EBG structure is modeled using transmission line circuits. For this structure, a lumped element equivalent circuit composed of L and C components is developed to represent the meander section. When these meander section interconnects conductor patches a capacitive element comes in parallel with the effective inductance.

The circuit parameters for meander line section are calculated by using the equation (1) and (2) and the value is L = 1.836 nH. The capacitance of meander line is calculated by using the gap capacitance between two adjacent patches and the value isC = 0.536 pF. Fig. 3 shows the equivalent circuit of the planar EBG structure. This circuit model of planar EBG structure is stimulated in ADS software. Fig. 4 shows the transmission coefficient for the proposed structure. From the stimulated result, the stop band frequency is obtained from 4.65GHz to 6.1 GHz.

The Fig. 5 shows the simulation setup of the EBG structure for reflection phase characterization in HFSS software. The boundary conditions like PEC and PMC are assigned for the unit cell. Fig. 6 shows the reflection phase plot of the planar EBG structure. It is verified that the reflection phase plot from HFSS also has the bandgap from 4.7GHz- 5.5 GHz with a center frequency at 5.25GHz. The band gap obtained from both circuit model and full wave Eigen mode solver are listed in Table II


A meandered planar Electromagnetic Band Gap structure is analyzed using lumped element transmission line model. The center frequency obtained from the structure is about 5.2GHz. The reflection phase is characterized using HFSS simulator and its transmission coefficient is analyzed using ADS software.


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[8.] Caloz,C.and T. Itoh, 2004. "Transmission line approach of left-handed (LH) materials and microstrip implementation of an artificial LH transmission line," IEEE Trans. Antennas Propag., 52(5): 1159-1166.

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(1) D. HelenaMargaret, (2) B. Manimegalai, (3) P. Kalaimathi

(1,3) Alagappa Chettiar College of Engineering and Technology, Karaikudi, Tamilnadu, India.

(2) Thiagarajar College of Engineering, Madurai, Tamilnadu, India.

Caption: Fig. 1: Top view of EBG unit cell

Caption: Fig. 2: Meander line section

Caption: Fig. 3: The equivalent transmission line model for the unit cell

Caption: Fig. 4: Transmission coefficient from ADS schematic

Caption: Fig. 5: Simulation setup of the EBG structure

Caption: Fig. 6: Reflection phase plot from HFSS software
Table I: Parameters Of Unit Cell

Parameter    L,W   [L.sub.p]   [L.sub.m]   [W.sub.m]   a

Value (mm)   7     4           1.5         1           0.45
Parameter    b     c           d           e           f
Value (mm)   0.5   0.3         0.9         0.3         0.1

Table II: Lower and Upper cut off frequencies

Results                         Lower frequency   Upper frequency
                                (GHz)             (GHz)

Circuit model                   4.65              6.1
Full wave Eigen mode solver     4.7               5.5
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Author:Margaret, D. Helena; Manimegalai, B.; Kalaimathi, P.
Publication:Advances in Natural and Applied Sciences
Date:May 1, 2017
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