A Thin, LowProfile Antenna Using a Novel High Impedance Ground Plane
Introduction
The size of the antenna for a given application doesn’t depend purely on the technology but on the laws of physics where the antenna size with respect to the wavelength has the predominant influence on the radiation characteristics. With modern day communication devices becoming smaller and lighter, demand for lowprofile antenna designs is greater than ever [1]. One way of realizing a lowprofile antenna design is to use a high impedance ground plane in place of the conventional metallic ground plane [27]. Metallic plates are used as ground planes to redirect the back radiation and provide shielding to the antennas. By nature, the conventional ground planes that are perfect electric conductors (PECs) exhibit the property of phase reversal of the incident currents that result in destructive interference of the original antenna currents and the image currents. To overcome this effect, antennas are to be placed at a height of quarter wavelength above the metallic ground plane making the size of the antenna bulky at low frequencies. To reduce the size of the antenna, we need a ground plane that is dual of the conventional PECs, in other words we need a PMC (perfect magnetic conductor). But how can we realize a PMC that is not available in nature? The answer to this problem is provided in the form of high impedance surfaces (HISs) which can essentially be considered as artificial magnetic conductors [8, 9]. HISs are popular for their widespread applications in reflectarray antennas, lowprofile antennas, electromagnetic absorbers and polarizers [1013]. These surfaces exhibit unique properties like the inphase reflection of incident waves and the suppression of the surface waves. Different antenna parameters like the gain, impedance and the size can be enhanced by incorporating the HISs into the antenna structures. The design of the HISs can be optimized to tailor their electromagnetic properties depending on the operational requirements. Computer aided design tools have enabled the solution of complex problems by means of numerical optimization algorithms [14, 15]. A large number of optimization methods are presently available for solving electromagnetic problems. Deciding the most appropriate method for a given problem however is a nontrivial task and depends on the factors like the number and range of the varying parameters, the goal of the optimization, the model size and the resources available.
The twodimensional (2D) arrays of periodic resonant elements (printed or complimentary slot) interact with electromagnetic waves within certain frequency band(s) and can be characterized as frequency selective surfaces (FSSs). Fig. 1, Fig. 2, and Fig. 3 show different FSS elements from the literature where each design has its own advantage over the other.
(a) Dual band 
(b) Triple band 

Figure 1: Multiband perturbed FSS structures [16] 
(a) Rectangular loop 
(b) Circular loop 
(c) Jerusalem cross 
(d) Rectangular patch 
Figure 2: Dualpolarized FSS elements 
(a) Tripole 
(b) Rectangular patch 
Figure 3: Fractal FSS elements 
The multiband dipole structures are polarization dependent, the symmetric designs are dualpolarized and the fractal structures are compact designs. The HIS is realized by printing the periodic array of FSSs over a metal backed dielectric substrate. It is important to optimize the performance of HIS over the frequencies of interest. It is observed that the characteristics of the FSS and HIS follow each other and this correlation can be exploited to speed up the optimization process by carrying out the design in two steps:
 Optimize the freestanding FSS,
 Realize the HIS by printing the optimized FSS on a metal backed dielectric substrate.
Even though there is growing demand for wideband antennas, a narrowband design has its advantages in cordless and wireless phone applications that operate at 49 MHz, 900 MHz, 2.4 GHz and 5.8 GHz. Interference from adjacent frequency bands can be avoided by using narrowband antennas that operate only around the frequency of interest. This article describes a novel FSS structure that is optimized for steep behavior of the reflection coefficient. The FSS unit cell is the combination of the Jerusalem cross and the three step fractal patch as shown in Fig. 4.
(a) Unit cell 
(b) FSS structure 
Figure 4: Combination of Jerusalem cross and threestep fractal patch 
The reflection characteristics of the FSS structure are explored in designing a HIS that can be used as a potential substrate for antennas in cordless phone applications to reduce cross talk. The performance of the HIS substrate is demonstrated with a 5.8 GHz lowprofile monopole (quarter wavelength) antenna with a 0.07 λ dielectric thickness. The monopole is first analyzed as a wire structure and then this design is translated to a printed format.
FSS Design and Optimization
The operation of the FSS structure depends on the resonance of the unit cell. The periodic array of the unit cell interacts with the electromagnetic wave and resonates at certain frequencies where it acts as a band stop filter with total reflection of the incident plane wave as shown in Fig. 5.
(a) Reflectivity behaviour 
(b) Current distribution on the unit cell 
Figure 5: Performance characterization of the proposed FSS 
The initial design of the FSS structure with broad band characteristics is optimized for sharp narrow band characteristics. Commercial software FEKO [22] is used for the analysis of the FSS structure using two different optimization methods: Simplex NelderMead and the Particle Swarm Optimization (PSO) [20].
Simplex (NelderMead Method):
The simplex NelderMead algorithm is a local or hill climbing algorithm in which the final optimum relies strongly on the starting point. The term simplex refers to the geometric figure formed by a set of N+1 points in an Ndimensional space. The basic idea of the simplex method is the comparison of values of the combined optimization goals at the N+1 points of the general simplex (where each point represents a single set of parameter values) to facilitate the movement of the simplex towards the optimum point during an iterative process. The movement of the simplex is achieved using three operations: reflection, expansion, and contraction.
Particle Swarm Optimization (PSO):
Particle Swarm Optimization is a global search algorithm which is a population based stochastic evolutionary computation technique based on the movement and intelligence of swarms found in nature. The mechanism of PSO can be best described using the analogy of a swarm of bees in a field whose goal is to find the highest concentration of flowers where each bee represents a set of parameter values. Every bee has information about the position of flower abundance based on its own experience (local best) and the position of maximum flower abundance based on the experience of all the other bees (global best). Based on the weights given to individuality or peer pressure a bee flies in a direction, between the positions of the local and the global bests. Once the flying is done, the bee conveys the new found information to all the other bees which then adjust their positions and velocities. With this constant exploring and exchange of information, all the bees are eventually drawn towards the position of highest concentration of flowers.
The possible optimization parameters/variables in the proposed FSS unit cell are the dimensions of the Jerusalem cross arms and the fractal patch. An optimization mask was used to specify the optimization goal as shown in Fig. 6.
Figure 6: FSS reflectivity behaviour, original and the desired (goal of optimization) 
Being a local optimizer, the convergence of the Simplex algorithm is much faster compared to the global optimizer PSO. But, unlike the global optimizer PSO, the success of the Simplex depends on the starting point that carries the disadvantage of converging at a local minimum. From Fig. 7, it is clear that the global optimizer PSO was able to approximate the mask more closely compared to the simplex but at the cost of huge runtime (see Table1 for runtimes).
Figure 7: Comparison of the simple and PSO algorithms 
To improve the chances of reaching the global minimum without compromising on the speed of convergence, PSO is hybridized with Simplex where the global optimizer will be used to find the starting point for the local optimizer. The hybridized method has improved the speed of the optimizer without compromising on the ability to reach the global goal. In this process the local optimizer was started after 100 iterations of the global optimizer. The local optimizer simplex converged to the global minimum in 154 iterations as shown in Fig. 8, reducing the runtime by 95%.
Figure 8: Comparison between PSO and SimplexPSO hybrid optimization 
Table1, describes the number of iterations and the time taken for each optimization algorithm to converge on a 2 GHz, EM64T Linux machine that has 2 physical CPUs with 4 cores per CPU.
Optimization algorithm 
No. of iterations 
Time taken (hours) 


PSO  5000  900 

Simplex  179  32.2  
NelderMead 
100+154 
45.7 

Table 1: Optimization performance 
HIS Design and Validation
The optimization completes the first step in the realization of artificial magnetic conductor taking the design process to the next stage where the optimized FSS structure shown in Fig. 9 (b) is printed on a metal backed dielectric substrate. The design parameters of the HIS shown in Fig. 10 are given in Table2, where λd denotes the wavelength inside the dielectric at 5.8 GHz.
(a) Initial unit cell 
(b) Optimized unit cell 

Figure 9: FSS unit cell geometry 
Figure 10: HIS realized with optimized FSS 
Periodicity of the unit cell  7.6 mm 

Dielectric constant of the substrate 
εr = 2.2 

NelderMead 
3 mm = 0.07 λd 

Table 2: HIS design parameters 
The reflectivity characteristics of the HIS ground planes realized using the unoptimized and the optimized FSS structures reveals the correlation between the FSS and the HIS. The HIS realized with optimized FSS reduced the bandwidth of the unoptimized design by 7% as shown Fig. 11, where the bandwidth is defined for the phase of the reflection coefficient varying between +90 and 90 degrees.
Figure 11: Reflectivity characteristics of HIS realized with unoptimized and optimized FSS 
Unlike the conventional PEC ground planes, antennas can be placed very close to the surface of the HIS ground plane resulting in a lowprofile design [21]. The performance of the lowprofile design is tested with a quarter wave (at cordless frequency of 5.8 GHz) monopole antenna with the HIS ground plane and a metal backed dielectric substrate of same thickness as shown in Fig. 12.
(a) Monopole antenna on HIS groundplane 
(b) Monopole on metal backed dielectric substrate 
Figure 12: Design comparisons 
Fig. 13 validates the performance of the HIS ground plane with low return loss and an improvement of 7.5 dB in the Gain over the metal backed dielectric substrate.
(a) Return loss of monopole 
(b) Monopole antenna gain 
Figure 13: Antenna performance at 5.8 GHz (Elevation phi=0) on HIS and dielectric substrates 
Planar Antenna
Antennas are generally preferred in a printed format so that they can be made flush with the surrounding environment. Printed planar antennas also have the advantage of being cheap and more convenient to manufacture and lend themselves more easily to mass production than nonprinted antennas. For these reasons we transfer our design from the protruding cylindrical monopole structure to one involving a planar printed monopole.
The wire monopole (modeled as a cylinder) is transformed to the printed monopole using the well known formula , where ‘a’ is the radius of the cylinder and ‘w’ is the width of the strip. This strip monopole is located at the same height as the axis of the cylindrical monopole to keep the electromagnetic relationship between the High Impedance Surface (HIS) and the monopole intact. It is not desirable that the gap between the strip monopole and the top surface be left as freespace as this leaves the monopole vulnerable to damage and also defeats the purpose of ease of manufacture. In order to avoid these problems we fill this space with a dielectric superstrate (relative to the HIS) that has the same dielectric properties as the substrate. Fig. 14 (a) shows the printed monopole antenna on top of the newly added dielectric layer. The HIS is located at the boundary of the dielectric layers and can be seen in the wire frame view. Fig. 14(b) displays the coaxial cable feeding mechanism in a cutplane view. A TEM mode is excited from an end of the cable whose outer conductor terminates at the ground plane and inner conductor extends further through the substrate to excite one end of the monopole.
(a) HIS groundplane between substrate layers 
(b) Coaxial feed for the monopole 
Figure 14: Geometry of a printed monopole antenna with HIS groundplane 
Replacing the air layer with a dielectric substrate alters the electrical length of both the monopole and the HIS, thereby moving the resonant frequency away from the desired value of 5.8 GHz. To retune the antenna back to 5.8 GHz we scale the monopole by a factor of and the HIS by a factor of . It should be pointed out that although the scaling brings the resonance very close to 5.8 GHz; some finer adjustments of these factors is required to make the resonance fall exactly at 5.8 GHz. Fig. 15 compares the S11 of the planar design with the previous nonplanar design and the nonHIS substrate. From the graph we note that the planar design leads to an increase in the return loss bandwidth (defined as being lower than 10dB). Due to the improved impedance match at our center frequency we find that the gain of the antenna is increased from a value of 5.35 dB (nonplanar monopole) to a value of 7.73 dB (planar monopole). Fig. 16 illustrates this behavior and shows the gain pattern in the elevation plane (XZ).
Figure 15: Comparison of return loss for printed monopole antenna 
Figure 16: Monopole antenna gain for the planar and nonplanar antennas at 5.8 GHz 
Effect of the Substrate Length and Width
As overall size of the antenna including the HIS ground plane is important for use in compact mobile devices, we also studied the effect of substrate length and width on the impedance characteristics of the antenna. Fig. 17 shows the variation in return loss due to decrease in substrate size. It can be seen that decrease in substrate size narrows the impedance bandwidth. Substrate size can be used to control the impedance bandwidth.
Figure 17: Effect of the substrate size 
Conclusions
A novel FSS structure is designed by combining the fractal and the Jerusalem cross elements. The resultant structure provides more flexibility in controlling the reflection coefficient behavior. The efficiency of the optimizers can be increased by hybridizing the local optimizer with the global optimizer, which is demonstrated in the case of the proposed FSS structure. The narrowband HIS realized from the optimized FSS can be used in designing lowprofile antennas. The lowprofile monopole antenna on the HIS ground plane with a substrate thickness of 0.07 λd improves the gain of the antenna by 7.5 dB. Further improvement to the antenna can be made by transforming the design into a planar antenna which increases the gain from 5.35 dB to 7.73 dB. It is found that doing so increases the return loss bandwidth of the antenna. A study of the substrate size shows that a reduction in size causes the antenna to become narrow band but at the cost of the resonance null depth.
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