Gap Coupled Dual-Band Petal Shape Patch Antenna for WLAN / WiMAX Applications

A compact gap coupled dual-band patch antenna is proposed for WLAN and WiMAX applications. Two resonating frequencies at 3.6 GHz and 5.2 GHz with a frequency ratio of 1.40 (theoretical), 1.45 (simulated) and 1.48 (measured) are observed. The frequency ratio depends on the thickness of substrate and gap length between the fed and parasitic patches. The impedance bandwidth at lower resonant frequency is 23.7 % (theoretical), 3.9 % (simulated) and 8.7 % (measured) and at upper resonant frequency it is 23.5 % (theoretical), 4 % (simulated) and 9.2 % (measured). Simulated gain of the patch antenna is 1.6 dBi at lower resonant frequency and 4.2 dBi at upper resonant frequency. Voltage Standing Wave Ratio (VSWR) remains below 1.2. The electric and magnetic field radiation patterns at both the resonating frequencies clearly depict that the co-polarization is higher than the cross polarization. Experimental return loss (|S11|), VSWR, input impedance and group delay are in close agreement with theoretical and simulated (by High Frequency Structure Simulator (HFSS) Software) results.

The shape of the antenna is intuitive however the physical parameters can be altered and optimized to operate in a particular range of frequency.In order to reduce volume, planar area and circuit complexity, two single band antennas were replaced by dual-band micro-strip patch antenna [9].Recently a dual-band monopole antenna with double spurline for PCS (Personal Communication System) and Bluetooth applications [10], and a miniaturized dual-band antenna for WLAN applications [11] have been reported.
Micro-strip patch antennas have gained special attention in the field of WLAN, Wi-Fi, WiMAX and satellite communications.Numerous designs covering the aforesaid applications and its analysis thereof have been reported [12], [13], [14], [15] and [16].Some of the inherent drawbacks of the micro-strip antennas are its narrow bandwidth, low gain and low radiation efficiency [17] and [18].To improve the gain, bandwidth and to make antenna multi-resonating, a number of techniques such as loading of notches and slots of different shape and size on the patch, posting a shorting pin on the radiating patch and introducing a gap between patches are reported [19], [20], [21], [22], [23], [24], [25], [26], [27], [28] and [29].The purpose of introducing a slot or notch is to reduce overall area of the patch.Further, introduction of a slot and a notch changes the inductive and capacitive behavior of the distributed element and the lumped element equivalent and theoretical analysis becomes more complex.In the present case, we achieve a fairly compact antenna without slot or notch.
Multi-band antenna designs are preferred as they can be easily embedded in MMICs.The researches on some alternative techniques to enhance the bandwidth are going on at a fast pace [30].The antennas reporting improvement in impedance bandwidth by means of different techniques suffer from low gain, poor radiation pattern, and in the absence of theoretical details and/or experimental verification, a proper justification of the obtained results is not possible.In the present work, the shape of the antenna is conceived and created by combining two different shapes, viz.square and semi-circle.As shown in Fig. 1(a), the square patch (shown by dotted line) is surmounted by the semi-circular patches on each side of the square patch.The entire structure is separated along the xaxis with a gap of 1 mm. Figure 1(a) forms a structure of a gap coupled petal shape antenna.A comparative overview of different antenna structures is presented in terms of patch volume, patch area, substrate material, impedance bandwidth and gain in Tab. 1.
The proposed antenna (cf.Fig. 1) is analyzed using the concepts of cavity model and circuit theory.The parametric analysis has been performed using HFSS software by ANSYS and the simulated results have been validated by experimental and theoretical results.The proposed structure has been simulated and optimized with and without parasitic element.Copper shorting pin is inserted between the ground plane and the radiating patch to enhance the bandwidth and gain of the proposed antenna.We propose an antenna with minimum volume and area as compared to other antennas reported in Tab. 1.A maximum reduction of 91.46 % in volume and 78.2 % in patch area is achieved in the present work as compared to the works reported in references in Tab. 1.The percentage reduction has been calculated taking the volume and patch area of the proposed antenna as reference values.
The antenna is fabricated on a FR-4 epoxy substrate (relative permittivity of substrate ( r = 4.4) and loss tangent (tan δ = 0.02)) in the laboratory.The VSWR, return loss (|S 11 |), group delay and input impedance have been experimentally measured by vector network analyzer (VNA) E5071C.The parameters such as VSWR, radiation pattern, antenna gain, frequency ratio and surface current distribution determine the performance of proposed antenna which is presented in the subsequent sections.

Antenna Design and Theoretical Analysis
The  The rectangular (L p × W p ) mm 2 micro-strip patch antenna is viewed as a parallel combination of resistance (R), inductance (L) and capacitance (C).The values of these elements can be calculated according to [37]: where h is thickness of the substrate, X 0 is X- In Eq. ( 4), c is the velocity of light in m•s −1 , Q is the quality factor, 0 is the permittivity of free space, e is effective permittivity for W p /h ≥ 1 and r is the relative permittivity of the substrate material.The effective permittivity is given according to [38]: The antenna comprises of two identical (fed and parasitic) resonating patches by proper adjustment of gap 'g' between them.It has been already reported [38] that a semi-circular disc can be transformed and made equivalent to a rectangular patch.The proposed antenna is transformed to its equivalent rectangular patches as shown in Fig. 3, for simplifying mathematical analysis.Equivalent circuits of the transformed driven and the parasitic patches are shown in Fig. 4   formed equivalent rectangular patches are deduced in the following manner: In Fig. 3(a), area of each half semi-circular patch portion-2 and 4 and the area of the removed portion below the patch portion-2 and 4 is equal to 1 4 πr 2 and g 2 r respectively.The resultant area (A) of the patch portion-2 and 4, therefore, is given by The area (A) of the transformed equivalent rectangular patch portion-2 and 4 (cf.Fig. 3(b)) is equal to where W r = r − g 2 is the transformed width and L c is the transformed length of the rectangular patch portion-2 and 4 (for both fed and parasitic patch).The semi-circular patch portion-3 is also transformed to its equivalent rectangular patch and the area is given as where L p is the transformed patch length and W c is the width of the rectangular patch of semicircular portion-3 (for both fed and parasitic patch).The proposed (a) Equivalent circuit diagram of the proposed antenna.The equivalent circuit and modified equivalent circuit of proposed antenna are shown in Fig. 5(a) and Fig. 5(b) respectively.The expression of gap capacitance C g and plate capacitance C s of the micro-strip patch are calculated according to [39]: where C L is the terminal capacitance of the open circuited conductor, given by where C ll is the conductor extension length: Z 0 -characteristic impedance.
Also the input impedance of the proposed antenna of Fig. 5(b) can be given as: where: By introducing the shorting pin on the patch, a parallel inductance L s is added to the whole patch and the equivalent circuit is modified for the proposed antenna as shown in Fig. 5(a).The inductance value of shorting pin is calculated after [40] and is given by Eq. ( 19): where: d is diameter of the shorting pin, E is Euler's constant = 0.5772, η 0 = 120π.
Z 2 and Z 3 as shown in Fig. 5(b) are given by the following: Z p is the impedance of fed patch (cf.Eq. ( 18) and Eq. ( 21)) while Z pp is the impedance of parasitic patch and are given as: Using the above-mentioned equations, the total input impedance of the proposed antenna is calculated and the other antenna parameters such as reflection coefficient, VSWR and return loss are:

Results and Discussion
The distributed surface current density for the proposed gap coupled patch antenna at the lower (3.6 GHz) and upper (5.2 GHz) resonating frequencies, respectively are shown in Fig. 6(a) and Fig. 6(b).It has been observed that at lower resonant frequency, the parasitic patch is energized by the driven patch and maximum current is flowing from right to left along the coupled edge.Parasitic patch is radiating at a lower resonant frequency only, whereas at upper resonating frequency only the driven patch is radiating.Maximum current is flowing along the left and the right edges of the fed patch at higher frequency along with the y-axis.Surface current density and the current direction observed at resonating frequency of 3.6 GHz (cf.Fig. 6(a)), suggest [17] that the dominant mode is TM 10 .Similarly, at resonating frequency of 5.2 GHz (cf.Fig. 6(b)) the current direction indicates that the dominant mode is TM 20 [17].
On observation of the results of Fig. 10 and Fig. 6(a), we infer that the lower resonating frequency (3.6 GHz) remains unchanged with the variation of gap length g and a maximum simulated surface current distribution is observed as 209 A•m −1 .With the change in the gap length, the lower resonating frequency is marginally shifting (cf.Fig. 10), therefore, the dominant mode (TM 10 ) for all the gap lengths will remain unchanged.With the increment of 0.5 mm in gap length (from 0.5 mm to 1.0 mm and from 1.0 mm to 1.5 mm) we observe an increasing shift of 100 MHz / 0.5 mm (cf.Fig. 10) in the resonating frequency.On perusal of current distribution diagrams Fig. 6(b), Fig. 6(c) and Fig. 6(d), it is evident that the maximum surface current densities (shown as red in Fig. 6) are 120 A•m −1 (for g = 0.5 mm, f r is 5.2 GHz), 170 A•m −1 (for g = 1.0 mm, f r is 5.3 GHz), 178 A•m −1 (for g = 1.5 mm, f r is 5.4 GHz).With the change in gap length and resonant frequencies, we observe a change in magnitude of the current density but no change is observed in the direction of the current, hence, it can be safely concluded that the dominant mode is TM 20 [17].
A large impedance bandwidth with good return loss is desirable for an efficient transmission/reception of the signal in the given frequency band.A monotonically increasing behavior of impedance bandwidth is observed in Fig. ement circuit (cf.Fig. 5(a) and Fig. 5(b)) is shown in Fig. 7 and Fig. 8.A significant difference between the simulated and theoretical, measured and theoretical bandwidths is observed from Fig. 7 and Fig. 8.The reason of this difference is attributed to the difference in shape and size of the rectangular and petal shape patches.As only the area in the transformed rectangular patch is conserved, both the patches (rectangular and petal shape) produce different current distribution patterns, this causes the other antenna parameters like impedance bandwidth, radiation pattern, gain and radiation efficiency to vary with shape and size.
On the basis of above discussion, it can be safely concluded that it is not possible to compare the different antenna parameters obtained by means of theoretical analysis of lumped element circuit and obtained by simulation of actual antenna structure or experimentally.The return loss plot obtained from theoretical analysis (transformed patch analysis) is used to validate only the resonant frequencies of the designed structure [41].Further, assumptions involved in theoretical analysis fail to correctly predict all other antenna parameters (except resonant frequency) including bandwidth [38] and [40].
We report a better impedance bandwidth in the present work (8.7/9.2 %) than antenna with Hshape (4.8/3.8 %), W-shape (5.28/2.77%), V-shape (3.2 %), E-shape (3.9/7.5 %) and less than L-shape (16.9/32.9%) and F-shape (26.8/11.4%).However, the L-shape and F-shape antennas occupy a larger volume of 59.57 % and 58.85 % and patch areas of 62.1 % and 58.9 % respectively as compared to the proposed antenna.The large impedance bandwidth in L-shape and F-shape antennas is due to use of micro-strip line as feed line.A single band is observed in case of the fed patch only, i.e. without parasitic patch, whereas for the proposed structure, i.e. with parasitic patch, two resonating frequencies are observed (cf.Fig. 9).Current distribution in parasitic patch is responsible for the presence of lower resonating frequency and is confirmed by the observation of theoretical and simulated return loss curve for antenna with parasitic patch (cf.Fig. 9).The result observed in the Fig. 9 is in conformity with the other reported results for structures having only fed patch, i.e. without parasitic patch and with parasitic patch [38].
Effect of gap length g is depicted in Fig. 10 by means of return loss versus frequency variation.A marginal change is observed at the lower resonating frequencies as the gap length is increased whereas with the in- crease in the gap length we observe (cf.Fig. 10) a shift in resonant frequency.The reason for shift in resonating frequency is because the total gap capacitance is the function of the gap length (cf.Eq. ( 9), Eq. ( 10), Eq. ( 11), Eq. ( 12), Eq. ( 13), Eq. ( 14), Eq. ( 15) and Eq. ( 16)), which changes exponentially with change in resonating frequency.An optimal gap length of 0.5mm is chosen so that the patch area of the antenna remains conserved and exponential shift of resonating frequency at higher frequencies can be avoided.
The variation of return loss with frequency for different values of substrate thickness h in the case of the proposed antenna is shown in Fig. 11.Antenna return loss behavior with substrate heights h = 0.6 mm, 1.6 mm and 2.6 mm are simulated.FR-4 glass epoxy substrate with a height of 1.6 mm is chosen for prototype as it is easily and commercially available.Further, as the height of the antenna is increased (from 1.6 mm to 2.6 mm), the overall volume will increase (by 62.5 %) which will make the antenna unsuitable to be embedded in sleek and small devices.While when the height of the substrate is reduced (from h = 1.6 mm to 0.6 mm), the return loss is not sufficient and it resonates only at a single frequency (5.4 GHz) making the antenna unsuitable for the desired application.For h = 2.6 mm a marginal shift towards a lower frequency region at lower resonating frequency and a shift of approximately 210 MHz towards the lower frequency region of higher resonating frequency is observed from the reference substrate height (h = 1.6 mm).Increment and decrement in the height of the substrate affects the capacitance C (Eq. ( 1)), i.e.C decreases with increase in height h which in turn increases R and L, this alters the total operating frequency of the antenna.Further, the alteration in substrate height shifts the impedance loci and is the reason for the shift in resonant frequency.As observed in Fig. 12, frequency ratio varies with the change in substrate height and gap length.For the proposed antenna the gap length is 0.5 mm, substrate height is 1.6 mm, and the simulated frequency ratio is 1.45.Increase in gap length increases the frequency ratio, whereas a similar behaviour is not observed when the substrate height is increased.A percentage difference of 2.6 % between experimental and simulated frequency ratio, 3.4 % between simulated and theoretical frequency ratio and 6.0 % between experimental and theoretical frequency ratio is observed.Percentage difference between simulated and experimental frequency ratio is well within the permissible limits of error.As discussed above due to the difference in shape and size of the simulated and theoretical structures a percentage difference of 6 % in frequency ratio is observed.
A simulated gain of an antenna with shorting pin, without shorting pin and without parasitic patch is il- lustrated in Fig. 13.After inserting the shorting pin on the parasitic patch it is observed that the gain remains constant (1.6 dBi) at the lower resonating frequency while gain is increased from -4 dBi to 4.2 dBi at upper resonant frequency.For a shorted antenna we observe an enhanced gain as compared to the antenna without parasitic patch.In the present work, we report a better-simulated antenna gain (4.2 dBi) at higher resonating frequency than antennas with Hshape (3.9 dBi) and F-shape (2.89 dBi).The gain of the W-shape antenna at higher resonating frequency is equal to the antenna gain obtained in the present work.The reason of better antenna gain at lower resonating frequencies for H-shape and W-shape is attributed due to the substrate material (foam for H-shape and RT Duroid and foam for W-shape) and height (4 mm both for H-shape and W-shape antennas) of the substrate.
The resonant frequency changes with the change in the substrate material and its height.It is well established that the gain increases as the height of the substrate increases.
Radiation pattern (co-polarization and crosspolarization) in the XZ-plane (ϕ = 0 • , E-plane) and YZ-plane (ϕ = 90 • , H-plane) of the proposed antenna for both the resonating frequencies is observed in Fig. 14.There is sufficient difference between copolarization level and cross-polarization level (in dB) in both E-plane as well as H-plane.The radiation pattern in E-plane for 3.6 GHz and H-plane for 5.2 GHz shows omni-directional behavior while good broadside radiation pattern behavior is observed in H-plane for 3.6 GHz and E-plane for 5.2 GHz with desirable low cross-polarization levels.
Theoretical, simulated and measured plot of VSWR versus frequency is shown in Fig. 15.A VSWR less than 1.2 is observed in each case which is suggestive of good impedance matching.The antenna is excited by a coaxial probe feed of 50 Ω characteristic impedance.To excite the patch on a given frequency, impedance matching (impedance of the antenna is same as characteristics impedance) is required between the patch and connector at the given frequency.Theoretical, simulated and experimental input impedance values are presented in Fig. 16.At lower resonant frequencies the input impedances are 50 Ω (theoretical), 47.9 Ω (simulated) and 44.3 Ω (experimental) while at higher resonant frequencies input impedances are 49.3Ω (theoretical), 45.1 Ω (simulated) and 34.5 Ω (experimental).Similar nature of curves is observed in case of theoretical, simulated and measured VSWR and input impedances (cf.Fig. 15 and Fig. 16).This indicates that the theoretical, simulated and experimental resonating frequencies can be correctly predicted with small change in impedance and VSWR.However, it is difficult to predict other antenna parameters theoretically.
The overall radiating mechanism of the patch antenna is least affected by the marginal shift in the lower and upper resonating frequencies and is established by the fact that the nature of theoretical, simulated and experimental curves is similar (cf.Fig. 7, Fig. 9, Fig. 11, Fig. 15 and Fig. 16).
The marginal impedance mismatch is caused due to approximation in calculations, mathematical instability involved in parameter calculation by the software, introduction of fringe capacitance and mechanical tolerances in the fabrication of prototype antenna.The least count errors of the measuring instruments are also the cause of variation in measured and simulated values.
A marginal variation between theoretical, simulated and measured lower resonating frequencies is observed in Fig. 15 and Fig. 16.The percentage variation between theoretical, simulated and measured lower resonating frequencies (cf.Fig. 15 and Fig. 16) is similar to the variation observed in Fig. 7.A more pronounced variation between theoretical, simulated and measured higher resonating frequencies is observed in Fig. 15 and Fig. 16 which are similar to that of the variation observed in Fig. 7. VSWR and return loss measurements provide the similar nature of information and the same is established by the observation of Fig. 7 and Fig. 15.Resonant frequencies as observed from Fig. 7, Fig. 15 and Fig. 16 are confirmed from these measurements and all the results validate each other.
As reported recently [29], less than 0.5 ns of group delay variation is desirable for efficient transmitting antenna.Identical or symmetrical patches exhibit good group delay response.As shown in the Fig. 1(a), the fed patch and parasitic patch are identical.Therefore, a good group delay response is expected and informs about the degree of distortion in transmitted/received pulses [42].
Figure 17 depicts the group delay response of the proposed antenna and it is observed that the simulated and measured group delay variation for proposed antennas is less than 0.5 ns for the entire frequency range.
Percentage radiation efficiency of antenna with and without parasitic patch is illustrated in Fig. 18.More than 70 % radiation efficiency is observed for both the antennas.Enhanced efficiency of 9.74 % (3.6 GHz) and 6 % (5.2 GHz) in the case of antenna with parasitic patch is observed as compared to antenna without parasitic patch.

Conclusion
In the proposed antenna structure, we observe a fairly large reduction in overall patch volume and area with an enhanced impedance bandwidth as compared to other reported antennas of H, V, W and E-shapes.The frequency ratio of antenna is sensitive to the change in gap length between parasitic and fed patch and it varies proportionally with gap length.Change in gap length does not affect the lower resonant frequencies whereas we observe at frequency shift of 100 MHz towards higher side with every 0.5 mm increase in gap length.Adding the shorting pin into the parasitic patch, a dual-band (3.6/5.2GHz) operation and enhancement in overall gain is observed.The low crosspolarization levels in both E-plane and H-plane make the structure suitable for dual-band operation for wireless applications such as WLAN/WiMAX.
Front view of the geometrical structure of the proposed antenna.Geometrical side view of the proposed antenna.(c)Front view photograph of the fabricated antenna.

Fig. 1 :
Fig. 1: (a) Front view of the geometrical structure of the proposed antenna, (b) geometrical side view of the proposed antenna and (c) front view photograph of the fabricated antenna.
geometrical top view, side view and the fabricated top view of the proposed micro-strip patch antenna are shown in Fig. 1(a), Fig. 1(b) and Fig. 1(c), respectively.Four semicircles are surmounted on each side of a square patch creating a petal shape and a rectangular (D × g) mm 2 slot is removed from the patch along the x-axis to divide it into two parts, one being a fed patch and other being a parasitic patch, resulting into the proposed antenna.The patch placed close to the fed or driven patch gets energized through the suitable radiating coupling is termed as parasitic patch.Equivalent T or π circuit represents an arbitrary discontinuity at the junction of two patches [36] as shown in Fig. 2(a) and Fig. 2(b).The radiating patch antenna has been excited by the 50 Ω coaxial connector.Design (a)   and Fig.4(b), respectively.Physical dimensions of both the patches are same due to their symmetrical structure.Therefore, the equivalent circuits, as well as their elemental values, are same.Dimensions of trans-Half portion of the proposed antenna.
Transformed equivalent rectangular patch of the structure of Fig.3(a).

Fig. 3 :
Fig. 3: (a) Half portion of the proposed antenna and (b) transformed equivalent rectangular patch of the structure.
Modified equivalent circuit of Fig. 5(a).

Fig. 5 :
Fig. 5: Equivalent circuit diagram of the (a) proposed antenna and (b) modified equivalent circuit.

Fig. 9 :
Fig. 9: Simulated and theoretical return loss |S 11 | of with and without parasitic patch antenna.

Fig. 10 :
Fig. 10: Variations of return loss |S 11 | with frequency for different values of gap g.

Fig. 17 :
Fig.17: Group delay response of the proposed antenna.

Fig. 18 :
Fig. 18: Radiation efficiency of antenna as a function of frequency.
Tab. 1: An overview of antenna shape, volume, patch area, resonating frequency, impedance bandwidth and gain.
degree in 2008 from University of Allahabad.He joined as Lecturer in the Department of Electronics and Communication, University of Allahabad in 1996, became Sr. Lecturer in 2002, Reader in 2007 and Associate Professor in 2010.He has received German Academic Exchange Service Fellowship (DAAD) in the year 2003.He has worked for his Ph.D. research work during DAAD fellowship in the University of Potsdam, Germany from June 2003 to December 2004.He again visited University of Potsdam in the year 2008 under re-invitation program of DAAD.His area of research is charge storing polymers, polymer electronics, photo stimulated charge profile measurements, thermal diffusivity of polymers, microwave and RF device and circuit simulation and its applications.E-mail: rsingh68@allduniv.ac.in, rsingh68@gmail.com