## 1 Introduction

Nowadays, microstrip patch antennas are important device in wireless communication systems. These antennas have been successfully utilized in many communication systems [1,2,3] such as satellite communication/links (vehicular GPS), cellular communication system (GSM/CDMA), wireless personal area (Bluetooth links), wireless local area network (Wi-Fi) and synthetic aperture radar (SAR). There are different techniques by which these antennas can be designed for various wireless applications such as proximity coupling [4], aperture coupling [5,6], loading of notches [7], slots [8,9,10], parasitic elements [11], L-strip fed [12,13], microstrip line feeding [14,15,16,17,18,19]. One of the important techniques is inset feeding by which patch antenna can be excited to achieve dual-band and multi-band frequencies for wireless communications.

The various contributions of researchers and scientists on microstrip line feeding are reported such as, analysis and design of annular patch antenna with electromagnetically coupled microstrip feed line [14], crescent-shaped multiband planar monopole antenna for mobile wireless applications [15], microstrip antenna array formed by microstrip line fed tooth-like-slot patches [16], printed wide-slot antenna with a modified L-shaped microstrip line for wideband applications [17], microstrip line-fed printed wide-slot antenna with a parasitic center patch [18], broadband T-shaped microstrip-fed U-slot coupled patch antenna [19]. All the above reported papers are of microstrip line fed patch antennas which lack theoretical analysis, equivalent circuit diagram and has complicated antenna geometry.

In this view, the main objective of this paper is to present theoretical analysis, equivalent circuit diagram, total input impedance and radiating structures of microstrip line fed rectangular patch antenna with split-ring resonator (SRR)for wireless communications. Theoretical analysis of microstrip line fed rectangular patch antenna loaded with parasitic element and split-ring resonator has been presented using circuit theory concept based on modal expansion cavity model. The proposed antenna structures have been realized with the proto-type radiating structures to obtain dualband characteristics. Variation of dimensions of the proposed antenna for the gap between parasitic element, split-ring resonator, length and width of microstrip line are discussed in next section.

## 2 Antenna designs

A rectangular patch with SRR and parasitic patch antenna along with similar proto-type microstrip line fed patch antennas are shown in Fig. 1. The Fig. 1(a) shows the side view of antennas. Antenna 1 is shown in Fig. 1(b), conventional microsrtip line fed patch antenna of dimensions *L*×*W* is excited by the *50 Ω* microstrip line. Antenna 2 is shown in Fig. 1(c), it is similar to the Antenna1 except it has parasitic element of dimension *L*×*W* and gap between the fed patch and parasitic patch is *G*. Figure 1(d)-(e) is the proposed radiating structure with top and bottom view. The proposed radiating structure is Antenna 3 which has SRR on ground plane and parasitic patch is placed parallel to the fed patch on same plane at a distance *G*. A rectangular patch of dimension *L*×*W* is fed through microstrip line fed. The feeding is given at end of microstrip line via coaxial connector of diameter 0.72 mm. Design specification of the antennas are given in Table 1.

Design specifications of microstrip line feed patch antennasare given as

Thickness of dielectric substrate (H) | 1.5 mm |
---|---|

Permittivity of Substrate (ε)_{r} | 2.65 |

Loss tangent of substrate (tanδ) | 0.0015 |

Width of patch and parasitic patch (W) | 23 mm |

Length of patch and parasitic patch (L) | 58 mm |

Width of microstrip line (W)_{s} | 4.0 mm |

Gap between the feed patch and parasitic patch (G) | 4.0 mm |

Length of SRR’s (S)_{L} | 25.6 mm |

Width of SRR’s (S)_{w} | 25.6 mm |

Width of both SRR’s arm (S)_{a} | 12.65 mm |

Length of SRR’s arm (S)_{t} | 0.5 mm |

Gap between two SRR’s arms (g_{1}) | 0.5 mm |

Length of Microstrip line (L)_{s} | 22.5 mm |

Figure 2 shows the current distribution on radiating structure of the Antenna 3 at lower (0.9 GHz) and upper (1.8 GHz) resonance frequencies. From the figure, it has been observed that proposed radiating structure has two directions of currents flowing on the radiating patch. The first is normal to the patch and other current flows due to the coupling between the fed patch with parasitic patch and the radiating patch with SRR. These combine mechanism provide dual band operation.

## 3 Theortical analysis and its equivalent circuits

A simple rectangular patch is considered as a parallel combination of resistance *R*_{1}, inductance *L*_{1}, and capacitance *C*_{1} circuit and its input impedance is represented as *Z _{p}*. The equivalent circuit of the rectangular patch is shown in Fig. 3(a), where

*R*

_{1},

*C*

_{1}and

*L*

_{1}can be defined as [20,21],

Quality factor,

*Where*

*L*- Length of rectangular patch,

*W*- Width of rectangular patch,

*H*- Thickness of the substrate material,

*X*_{0}-x coordinates of feed point, i.e.,*X*_{0} = *L _{s}*,

*ε _{e}* - effective permittivity of the medium.

The equivalent circuit of the parasitic patch is shown in Fig. 3(b), its input impedance is represented as *Z _{pp}*, where

*R*

_{2},

*C*

_{2}and

*L*

_{2}can be calculated as

*R*

_{1},

*C*

_{1}and

*L*

_{1}with same equations, here

*X*

_{0}is considered as 0. The equivalent circuit diagram of the gap between the fed patch and the parasitic patch

*Z*is shown in Fig. 3(c), which is represented as the combination of capacitances

_{cc}*C*and

_{g}*C*

_{p1}. The expression of gap capacitance

*C*and plate capacitance

_{g}*C*

_{p1}of the microstrip line can be calculated as [22,23,24]

Where,

*C _{L}* is the terminal capacitance of the open circuited conductor is given as,

where *C _{ll}* is the conductor extension length,

*ε*is effective dielectric constant.

_{eff}*Z*_{0}is characteristic impedance of the patch, *c* is the velocity of light.

The microstrip line of the rectangular patch is considered as combination of *L* and *C*. The equivalent circuit of the microstrip line rectangular patch is shown in Fig. 3(d), where *L _{L}* and

*C*are inductance and capacitance of strip [22, 23].

_{L}Resonance frequency of the microstrip line antenna is given as,

where

*L _{es}* =

*L*+

_{S}*ΔL*,

_{S}*ε _{re}*- Effective dielectric constant,

L_{es} -Effective increase in length of strip,

*ε _{r}* -Dielectric constant,

The characteristic impedance of microstrip line [20,21,22],

Therefore, the total input impedance (*Z _{in}*) of antenna can be calculated by equivalent circuit diagram Fig. 4 as

where *L _{c}* and

*C*is the inductance and capacitance of SRR’s can calculated as [24].

_{c}Now using equation (10) the total input impedance of the proposed antenna is calculated. Their various antenna parameters such as reflection coefficient, VSWR and return loss are calculated as:

Reflection Coefficient

where

*Z* is the input impedance of the microstrip fed (50 Ω).

and RL=20 log |r|

## 4 Discussion of results

The antennas 1, 2, and 3 have been simulated using software IE3D based on Method of Moments. Figure 5 presents the variations of reflection coefficients for different radiating structures. Antenna1 is resonating at 4.1 GHz below −10 dB offer a bandwidth of 139 MHz (3.94-4.12 GHz) which can be utilized for satellite communication. Antenna 2 is resonating at three distinct frequency modes 3.144 GHz, 3.252 GHz and 3.804 GHz. In theses frequency bands only 3.804 GHz frequency has efficient bandwidth of 441 MHz (3.696-3.864 GHz) that can be utilized for down link in satellite communication. Antenna 3 resonates at two distinct frequencies modes 0.9 GHz and 1.8 GHz below −10 dB and meets the requirement of mobile communication. It is observed that on incorporating parasitic elements and SRR resonating frequencies shift toward lower side. This is due to the increase radiation resistance of the proposed antenna. There is a dip at 1.5 GHz in proposed antenna, this is observed because gap between the parasitic patch and fed as well as gap between SRR arms.

Figure 6 shows the variation of reflection coefficient with frequency for the proposed antenna. The simulated, theoretical and reported experimental results of the microstrip line fed rectangular patch antenna with parasitic element and SRR are in close agreement. From figure it is observed that the antenna shows dual frequency behavior with frequency ratio 2.0 (Simulated) and 2.12 (theoretical). Theoretical results are based on circuit theory concept based on cavity model whereas simulated results are obtained using IE3D software that is based on Method of Moments. Further, analysis of the antenna 3 is shown in figures 7 to 10 which are based on circuit theory concept are described below.

From Figure 7, it is observed that on decreasing the substrate thickness (*H*=1.5 mm to 0.5 mm) frequency ratio decreases from 2.0 to 1.27 whereas on increasing the substrate thickness (*H*=1.5 mm to 2.5 mm) frequency ratio increases to 2.96. This happens because on increasing and decreasing the height of the substrate equations (1), (4) and (6) are effected which is responsible for variation in resonance frequency of the radiating patch.

Figure 8 shows the variation of reflection coefficient with frequency on decreasing (*W _{s}*=4 mm to 2 mm) and increasing (

*W*=4 mm to 6 mm) the width of microstrip line, there is no change in the frequency ratio of upper to lower resonance frequency whereas slight shifting is observed on both upper and lower resonance frequencies. This is due to the capacitance

_{s}*C*which is directly proportion to width of microstrip line

_{L}*W*, from equation (7).

_{s}From Figure 9, it is observed that on increasing the length of the microstrip line (*L _{s}* =21.6 mm to 29.6 mm), lower and higher resonance frequencies shift towards lower resonance side whereas there is no change in the frequency ratio of upper to lower resonance frequency. This affects the equation (8) as resonance frequency of the microstrip line

*f*is inversely proportional to the length microstrip line

*L*.

_{s}Figure 10 shows that on decreasing gap between the fed patch and parasitic patch (*G*=4 mm to 3 mm), the upper and lower resonance frequencies shift towards the lower side. Further, on increasing *G*=4 mm to 7 mm, upper and lower resonance frequencies shift towards higher side. This happens because the gap capacitance *C _{g}* is affected on increasing and decreasing the gap between fed patch and parasitic patch

*G*i.e., from equation (4),

*C*changes exponentially on variation of

_{g}*G*. Thus, there is no huge variation on varying

*G*.

From Figure 11, shows the radiation pattern at lower (0.9 GHz) and higher (1.8 GHz) resonance frequency and antenna shows circular polarization. The 3 dB beam width at lower resonance frequency for *E _{theta}*, phi=0° is 130.33° and

*E*, phi=90° is 88.92° whereas at higher resonance frequency for

_{theta}*E*, phi=0 is 165.83° and

_{theta}*E*, phi=0 is 83.7°.

_{theta}## 5 Conclusion

From the above analysis it is inferred that theoretical results are in close agreement with simulated and reported experimental results for inset fed rectangular patch antenna loaded with parasitic element and split ring resonator. The frequency ratio of the proposed antenna depends on microstrip length and width, thickness of dielectric substrate and gap between parasitic patch. The proposed antenna has frequency ratio 2.0 and maximum gain 1.8 dBi. The proposed antennas can be utilized for wireless communications such as mobiles and down linking for satellite communications.

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