A Compact Wideband Patch Antenna Loaded by Interdigital Capacitor with Equivalent Circuit Model

In this paper a wideband microstrip patch antenna (MPA) using aperture coupling feeding technique with bandwidth (BW) of 28% is designed at first. Afterwards for the pupose of reducing the size of the radiating element, the composite right/left hand (CRLH) concept is used by implementing an interdigital capacitor (IDC) as series left hand component in the antenna. The slot in the ground plane acts as a left hand parallel inductor. Through this technique, three operation modes of CRLH antenna is excited and by appropriate adjusting of the IDC parameters, closing and mixing of resonant frequencies are achieved. Size reduction in the order of 15.5% and 6.2% in the patch and slot dimensions compared to the initial designed antenna is obtained respectively. The equivalent circuit model of the final designed antenna is presented and simulated. The final designed antenna is fabricated and tested.


I. INTRODUCTION
The demands for compact, wideband and portable transceiver systems are the consequence of increasing development of modern wireless communication.Since antenna is an important part in transceiver systems with limited space in many applications, many efforts have been done to reduce the size of antenna [1].One of the limitations of MPA is its narrow BW which is in the order of a few percent.Several techniques have been introduced for widening the BW of MPA including stacked patch, proximity coupling, multimode techniques, implementing variations in the ground of the antenna by defected ground structures (DGS) and changing shape of the patch [1], [2].In this study, aperture coupling feeding technique is used for BW increasing which was first introduced by Pozar in 1985 [3]. Several advantages of this method are: isolation of feed from radiating element, capability of using different substrates for feed and patch with different thickness and permittivity which lead to reduction of surface waves in the feed substrate and also antenna BW enhancement [3].As it was mentioned, besides being wideband, size reduction is an important subject in nowadays communication systems.One way for size reduction is the utilization of metamaterials.Metamaterials are artificially structured materials providing electromagnetic properties not encountered in the nature.These materials are also called left handed materials (LHMs) due to the left handness of electric, magnetic field and wave vector.Some of the other various specifications of LHMs are: reversal of Doppler effect, inverse Snell's law, changing of convergence and divergence effect in incidence of wave to concave and convex lens [4], [5].Also by using LHMs concept, size reduction in the radiating element of the antenna is done [5]- [7].Through using metamaterials, an antenna with compact size, high efficiency and proper BW can be obtained.In this article, at first step, a wideband aperture coupled MPA is designed.Then an IDC as a left hand series capacitor is implemented in the patch [8]- [12].The slot in the ground plane is a left hand parallel inductor which together with the IDC offers a CRLH microstrip antenna.This is the main feature of this antenna.In the other works the left hand inductor is imposed to the antenna by using microstrip line [13], cutting CSRR in the ground [10], chip [14] or post-wall [11], [12], [16] but in this article the slot in the ground inherently acts as a resonator and a left hand inductor simultaneously.In [10], through implementing an IDC in radiating element and a complementary split ring resonator in the ground plane of the antenna, a CRLH antenna has been proposed with BW of 6.8%.In [16], a CRLH antenna has been designed by using surface integrated waveguide (SIW) as distributed left hand inductors and an IDC as series left hand capacitor.The -10 dB impedance BW of this antenna is 1.52%.In [15], a two arm transmission line metamaterial antenna with the BW of 3% has been proposed.Further size reduction of antenna has been achieved in [15] in comparison with those in [10], [16].In both of the antennas have been investigated in [15] and [16], via is used in the structure.But a single layer vialess CRLH antenna, using coplanar waveguide feeding technique has been offered in [17] with the BW of 6.8%.In our work a three layer compact CRLH antenna with the BW of 28% is designed without via.II.PROPOSED DESIGN Among different feeding methods of MPAs, aperture coupling feeding technique is used in the designing of initial antenna because of several advantages which was mentioned in section I.
Extended BW is the most important reason for choosing this kind of feeding method in this paper.

A. Wideband aperture coupled MPA
We first designed an aperture coupled MPA without IDC.According to Fig.

B. Inserting the IDC in the antenna
In the next stage for improving the features of the antenna, an IDC is implemented in the patch (Fig. 2).The effect of variations of capacitor parameters on antenna characteristics are shown in Fig. 3  (Fig. 3).11 S of this antenna is shown in Fig. 3(a).As it can be seen, although there is some degradation in return loss of the original antenna after inserting capacitor in it, but a new resonant frequency is added.Referring to Fig. 3 it should be noted that when each of the IDC parameters is varied, the other parameters of the antenna and IDC remain constant.  .Then through an optimized IDC which is inserted in the patch, size reduction is achieved.After several simulations, we reach an optimized patch which it's 11 S is compared with the previous designs in Fig. 6.As it is shown in Fig. 6, after inserting the IDC, there is a small shifting in the first resonance, but after compacting of the radiating element, the shifting is more. .By this method we achieved to 15.5% size reduction for the patch and 6.2% for the slot.Displacement of the IDC imposes a slight mismatch in the middle of the BW which can be compensated by tuning the stub length.11 S of final designed antenna and the fabricated  I.

III. EQUIVALENT CIRCUIT MODEL
In this section, an equivalent circuit model of final designed antenna (compacted antenna) with the IDC is presented.According to Fig. 8, the model is consisted of input transmission line (TL), first coupling transformer, parallel LC tank which is equivalent to the slot, second coupling transformer and patch impedance [18].The patch impedance is comprised from lower and upper parts.The upper part of the patch is divided into two TLs which the IDC is inserted between them.It is necessary that: , , , , C L C N N can be calculated by the formulation offered in [19]- [20].The values of the lumped elements and the other parameters in the equivalent circuit model are: , 0.9 , 0.384 , 3.42 , 2 It should be mentioned that through using formulas, initial values of lumped elements are calculated then for better compatibility of circuit model simulation results with full wave electromagnetic counterpart, tuning of elements values is necessary.The simulation result of circuit model is depicted in Fig. 9.

IV. MEASUREMENT RESULTS
Final designed antenna is fabricated on ultaralam2000 printed circuit board (PCB).The patch and the feed line are implemented on two separate PCBs.The air gap between two layers is implemented by a frame of Teflon with loss tangent of 0.001.Fig. 11 shows the fabricated antenna.The return loss of the antenna is measured by 8510C network analyzer.There is a good agreement between measurement and simulation result of final designed antenna.

V. CONCLUSION
A wideband aperture coupled MPA with the BW of 28% has been designed at first.Then through inserting an IDC and by optimum tuning of its physical dimensions and location, size reduction of the patch and the slot in the order of 15.5% and 6.2% is achieved respectively.Effects of variation of IDC parameters on the antenna return loss are studied in detail.The IDC and the slot in the ground plane offered a CRLH antenna which allows more size reduction whereas the antenna remains wideband.
To obtain better insight into performance of the antenna, a circuit model is developed.The prototyp e of the antenna has been fabricated and there is a good agreement between circuit and full wave simulation with measurement result.
) and third layer above the patch which is similar to the feed layer.Air gap is selected as the patch substrate to increase the BW of the antenna.The return loss and the normalized radiation pattern of this antenna are shown in Fig.1(c) and (d).The dimensions of the antenna after optimization have been listed in table I.The BW of the antenna is 28% from 2.64 GHz to 3.5 GHz ( 11 S ≤ -10 dB).Electromagnetic simulations have been done by a full wave finite element based simulator HFSS13 and circuit analyses have been performed by Microwave Office10 software.677 ___ xz-plane ----yz-plane

Fig. 2 . 1 n
Fig. 2. Aperture coupled MPA structure with IDC.According to Fig. 3(a) by decreasing 0 a from 1mm to 0.25 mm the third resonance is shifted downward whereas 1 a and 2 a are constant.The third resonant frequency is equivalent to

Fig. 3 .
Fig. 3. Simulated return loss for different IDC parameters.(a) with 0 a variations, (b) with 1 a variations, (c) with 2 a

Fig. 6 .
Fig. 6.Simulated return loss of initial design antenna, with optimum IDC and after size reduction.

Now 11 S
of the compacted antenna must be shifted downward by changing the IDC parameters.Finally we set 2 2 a mm  and move IDC toward the radiating edge of the patch.As it is demonstrated in Fig. 7, 11S is shifted downward by this technique.After size reduction, the dimensions of the patch are:

Fig. 7 .
Fig. 7. Simulated return loss for different displacement of IDC

Fig. 8 .
Fig. 8. Equivalent circuit model of the final designed antenna.

Fig. 10 .Fig. 11 .
Fig.10.Simulated characteristics of final designed antenna.(a) Gain (dBi), (b) Normalized radiation pattern (dB) and 4. The IDC which represents a left hand series capacitor is inserted in the center of upper semi part of the patch.The dimensions of the capacitor in the first effort are as follow:

Table I .
Dimensions of the initial and final designed antenna parameter