Rectangular Notch Loaded Dual Band Annular Ring Patch Antenna

In this article, a dual band annular ring patch antenna is theoretically investigated using the equivalent circuit concept.Two symmetrical rectangular notches are etched in radiating ring patch with respect to feed point. It is observed that the resonant frequency is directly proportional to the notch width and notch length. The bandwidth of the antenna at lower and higher ends are 134 MHz(1.815-1.681GHz) and 212MHz (2.8492.637GHz) respectively for given antenna specifications. The calculated results are compared with the IE3D simulation software and previously reported results based on Artificial Neural Network (ANN). The theoretical results obtained from the proposed analysis are in good agreement with the simulated and ANN based results.


I. Introduction
Annular Ring Microstrip Antennas (ARMA) have received much attention because of their low profile, light weight and reduced size suitable for many portable wireless devices [1][2].The size of the annular ring patch is smaller than circular or rectangular patch when it resonates in its fundamental TM 11 mode.Annular ring antennas also exhibit broadband nature when operated near TM 12 mode.The radiation efficiency of ring antenna is better than the circular patch antenna because in ring antenna, the edges at the inner and outer radii causes more fringing while in circular patch antenna, fringing occurs at the outer edge [3].In annular ring antennas, the multiband characteristics can be easily obtained by adjusting the higher modes.A multiple-frequency antenna can reduce the installation space and provides advantage in cost and size.In the last two decades, many techniques for the design of patch antennas with multiple frequency operation have been reported such as single layer shorted pin microstrip antennas [4], gap couple annular ring antennas [5], loading of slots and notches in the radiating patch [6][7][8][9].The incorporation of suitable dimensions of slot on the circular patch antenna does not introduce any mode but reduces the second order mode/resonance frequency.Thus, along with fundamental mode, such perturbed antennas show dualband as well as wideband behavior [10][11][12].Similar properties are also observed in annular ring patch antennas.

II. ANTENNA DESIGN AND ITS EQUIVALENT CIRCUIT
A two layered notch loaded ARMA configuration is shown in Fig. 1 and further a superstrate is used to protect the radiating patch.Two rectangular notches of dimensions N d × N w are etched in the annular ring patch having inner and outer radii 'a' and 'b' respectively.In this analysis, for some calculation purpose, it is assumed that annular ring patch with inner 'a' and outer radii 'b' is equivalent to square ring patch with inner width '2a' and outer width '2b' (Fig. 1).It is because many characteristics of square ring patch are similar to annular ring patch [13][14].Annular ring patch antenna is parallel LCR resonator for one resonant mode and the equivalent circuit can be given as shown in Fig. 2a.The expression for the resistance R 1 , inductance L 1 and capacitance C 1 can be given as [5,15].When two notches are etched in the ring patch with respect to feed point, the current length increases around the notch and hence the additional inductance ΔL and capacitance ΔC appear in the antenna structure which modify the initial equivalent ring circuit as shown in Fig. 2 b.Now the equivalent circuit for Notch loaded annular ring


Ground Plane notch loaded ARMA can be given by adding a coupling capacitance (C C ) between two resonant circuits (Fig. 2c).Therefore, the present antenna shows a dual nature because both the resonant circuits give different resonant frequencies.The input impedance of the antenna can be calculated from the equivalent circuit shown in Fig. 2c. here, The additional inductance (ΔL) and capacitance (ΔC) can be calculated by [16][17] where, C C is the coupling capacitance and given by [18] 2 here Q 1 and Q 2 are the quality factors of both the resonators.The resonance resistance (R 2 ) of the modified configuration of the ARMA can be calculated from [19].In the proposed antenna three layers of dielectric substrates are used, the effective dielectric constant of the structure can be calculated from [20].The values of reflection coefficient and return loss can be calculated as: where Z 0 = characteristic impedance of coaxial feed (50  ) Return loss = -20 log 10 (  ) The radiation pattern for the antenna can be given by assuming it as conventional annular ring antenna [21].
Here r is the distance of an arbitrary far field point, k 0 and k nm are the propagation constants in free space and in dielectric medium in TM nm mode respectively.The return loss for different values of notch depth is calculated using equation ( 6) and shown in Fig. GHz) for upper side and 128 MHz (1.781-1.653GHz)for lower side respectively.

Parameters
The higher resonant frequency (f H ) shifts from 3.13 GHz to 2.66 GHz and lower resonant frequency (f L ) shifts from 1.84 GHz to 1.73 GHz for the increasing value of notch depth (N d ).The similar effect is observed when notch width (N w ) increases (Fig. 5).From Fig. 6 it is observed that the frequency ratio f L /f H is inversely proportional to the notch depth and notch width.It is noted that the effect of notch depth on both the resonant frequencies is more significant as compared to notch width.Theoretical results obtained by the cavity model are compared with the IE3D simulated results [22] and the result obtained by ANN method [23].The results predicted by theory are in good agreement with the simulated as well as ANN results.However, some deviation in the theoretical result is seen because the analogy between square ring and annular ring differs in the patch area which causes the shift in resonance frequency.For a given dimension the area of an annular ring is smaller than square ring due to which both the resonant frequencies of the square ring move towards lower side as shown in Fig. 7.The radiation pattern of the antenna is calculated using equations ( 7) and (8) at lower (1.75 GHz) and upper (2.74 GHz) resonance frequencies.The results are also compared with the simulated results as shown in Fig. 8 (a and b).It is observed that 3dB beam width (66 0 ) at lower resonant frequency is greater than the beam width (32 0 ) at upper resonant frequency.It is due to (i) incorporation of the notches in ring patch (ii) higher ratio of inner and outer radius of annular ring and (iii) some assumptions in the theory which change the broadside nature of the radiation pattern and hence the symmetry of the radiation pattern deviates at upper resonant frequency.The sidelobes in radiation pattern at upper resonance frequency can be reduced by optimizing the notch dimensions as shown in Fig. 9.
The antenna gain obtained at upper and lower resonace frequencies are 4.25 dB (at 2.74GHz)and 6.6dB (1.75 GHz) respectively (Fig. 10).Variation of radiation efficiency as a function of frequency is shown in Fig. 11.From the figure it is clear that at upper and lower resonance frequencies the efficiency of the proposed antenna is 75% and 80% respectively .

Fig. 1
Fig.1 Configuration of proposed antenna

Fig. 2 Fig. 3
Fig. 2 Equivalent circuit of (a) ARMA (b) notched ARMA (c) Modified notched ARMAThis dual nature of antenna can also be explained by the current distribution on the ring patch obtained by the IE3D simulation software.Since etching a notch in the ring patch not only miniaturizes the antenna size but also reduces the resonance point of higher (TM 12 ) mode towards dominant (TM 11 ) mode (Fig.3) and hence a dual band antenna response is observed.
Values Dielectric constant of material used for thickness h 1 =6.1 mm =1.03 Dielectric constnat of material used for thickness h 2 =6.05 mm =3.5 Dielectric constant of material used for thickness h 3 =1.1 mm =1.04 Inner radius of the ring (a) 12.05 mm Outer radius of the ring (b) 36.10 mm Length of the notch (N d ) 15mm Width of the notch (N w ) 3.0 mm Feed location (x 0 ,y 0 ) 27.0,0 mm

Fig. 4 Fig. 5
Fig.4 Variation of return loss with frequency for different notch depth (N d )

Fig. 6 Fig. 7
Fig.6 Variation of frequency ratio with different notch depth (N d ) and notch width (N w )

Fig. 9
Fig. 9 Variation of radiation pattern at upper resonace frequency for different values of notch depth (N d )

Fig. 10 Fig. 11
Fig. 10 Variation of Gain as a function of frequency Therefore, in this paper, a dual band ARMA has been studied in which two notches are incorporated in the radiating patch with respect to the feed point.Circuit theory concept is used to analyze the various antenna characteristics such as impedance bandwidth, return loss,gain and radiation pattern.