An Analytical Approach for Design of Microstrip Patch (MsP)

Received Mar 14, 2018 Revised Jul 17, 2018 Accepted Aug 5, 2018 A reliable configuration of electromagnetic interactions for antenna design can yield an effective Microstrip patch (MsP) antenna. During its design, the antenna arrays involve issues with parameters (i.e., space, dimension, shape) adjustment. This problem can be tackled with an analytical approach which can help to bring better idea to design the antenna aaray. However, the realistic designs of antenna array are quite expensive while extracting computational accuracy. Thus, to have low cost computational accuracy various meta-heuristic (generic algorithm, partical swarm optimizarion) approaches are used and are considered as effective one in handling the pattern synthesis problems. Howeever, the use of meta-heuristic approaches demands thousands of functions to analyze the antenna design. This manuscript introduces an analytical approach for MsP antenna desing using MATLAB that brings optimization in handling the side lobes and optimizing the reflection as well as radiation responses. The outcomes of the design were analyzed with respect to reflection, radiation coefficients, side lobes and found effective at 10GHz as per computational cost is concern. Keyword:


INTRODUCTION
The Microstrip Patch (MsP) antenna arrays design demands a reliable electro-magnetic interactions (EmI) within antenna array structures to provision the requirements of the antenna design induced by array radiations and reflection responses [1]. The electro-magnetic interactions are consists of element environment, element coupling, substrate finite size, feeding impact etc. Such impacts can only be reliably accounted for design process through typically discrete, full-wave, electro-magnetic simulations mainly by using complete antenna array module [2].
The antenna array design involved with issues elements dimensions adjustment, array shape adjustment, array spacing adjustment, feeding location adjustment etc. In that regard, a mathematical approach can be considered as effective for significant way of antenna array design [3]. The real time implememtation of mathematical approach can leads to higher cost in antenna array design as it takes of more number of simulations iterations in array model [4]. The meta-heuristics mechanisms such as particle swarm optimization [5]; genetic algorithms [6] are outcomes with significant results which can handle the pattern synthesis issues [7]. The limitation of meta-heuristic mechanisms is that it needs thousands of functions for antenna design analysis. Hence, this paper aims to perform the accurate design of MsPantrnna by using an analytical approach for pattern synthesis. Finally, the design analysis is performed by considering the parameters like radiation, reflection coefficients, operating frequency and minimization of side lobes. The paper is organized with sections like reveiew of existing works (in section 2), design and implementation of proposed system (in section 3), results and analysis (in section 4) and conclusion (in section 5). (1) Further, the center localization of the patch (Px, Py) is computed by using equation 4.
Py =∑((Spi + ( )), i=2 Based on these coordinates, a rectangle is plotted and for the same rectangle, patch center is determined.
The distance for right angled triangle (x t ) is obtained by using equation 8.
Then slot aperture of metal ground is calculated for both the Xpath and Ypath using equation 9.
Finally the labeling of the plot is done and outcome of the topology is shown in the Figure 3.
i.e., λ = c/fc (10) The array size along with elevation and azimuth direction can be obtained by required beam width. For the half wavelength spacing, the number of elements along with certain direction can be given as; NR or NC = b Sin 2 (11) In equation 11, the value of b  represents the beam width along that direction. The other parameters (Op) like azimuth cutoff and elevation cut off can obtain by following equation.
Op = NR_NC(c, fc [d1, d2, w1, u1, v1, v2, wc, wo]) (12) Then, the uniform rectangular array (URA) is considered as the integration of two separable uniform Line arrays (ULA) and designed the windows for both the elevation and azimuth direction through digital filer design methods. Then the URA developed by identical sensor elements can be given as: i.e., URA = Is ([ In equation 13, Is indicates the identical sensor element. On assigning the weights to the array following equation 14 is obtained. i.e., Aw Ew nURA   (14) Where nURA indicates the new URA, Ew indicates the elevation weight and Aw represents the Azimuth weight. Later the comparison among the new URA and previous URA. In antenna technology the side lobes are the local maxima or lobes of the far field radiation pattern which are not the main lobes. Here, the side lobe level of the new URA is compared with the previous design. However, the new URA does not meet the requirements and hence trial and error method is applied to NR and NC parameters.
i.e., NR = NR+ NC = NC-Then obtained values of NR and NC are updated to get the optimized design results.

RESULTS ANALYSIS
For design of MsP antenna MATLAB is used and obtained results on execusion. The performance analysis of the design is compared with existing method. The following Figure 4, illustrates the beam pattern for looks directions ranging from <-30 0 to 0 0 azimuth and elevation degrees and maintains null at -40 0 .

Figure 4. Beam pattern for azimuth and elevation degree
The array synthesis is represented in Figure 5 with respect to topology 1, 2, 4 and optimal topology by considering bandwidth. Here, the topology 1 array is just crossing the required bandwidth of patterns of topology 2, 4 and optimal topology. However, the side lobes of patterns bandwidth is higher that of desired pattern. This kind of side lobes can be optimized by utilizing windowing operations to array. If URA is the combination of two different uniform linear arrays (ULA), then thedesign of window can be performed separately in both elevation and azimuth directions by utilizing filter designing models. The Figure 4 gives the side lobe level compared with different topologies and is found that side lobe level of optimal topology is less than topology 1, topology 2 and topology 4. The 3D radiation patterns are composed of symmetries for both azimuth and elevation cuts. Hence, the patterns are acquired through URA. The Figure 6 indicates that no energy is radiated in reverse to back of array in which the bandwidth and side lobe level of synthesized pattern are resulted with desired specification and is considered as 3D pattern synthesis. The Figure 7 represents the MsP antenna over the frequency band. In this, the resistance and reactance varyas frequency varies. This variation can be seen that the reactance value is negative before the resonance and the same value is positive after the resonance and this reactance is considered as"series resonance". If impedance curve varies from positive to negative reactance and is considered as "parallel resonance". Both the resistance and reactance are fully different as resistance which is not depend on frequency while reactance does. The resistance does not cause phase shift while reactance causes phase shift of 90 0 among voltage and current. In Figure 7, resistance remains at positive value and reactance stays at negative value during resonance and reaches positive after resonance. The antenna reflection coefficient is shown in Figure 8 which is the relative fraction of the incident Radio frequency (RF) power and is reflected back because of impedance mismatch. The impedance mismatch is the difference among the antenna input impedance and the transmission line characteristic or reference impedance. The reflection coefficient is represented as operating bandwidth of antenna. The antenna bandwidth is the frequency band on which the magnitude of reflection coefficient < -10dB. The active reflection coefficients analysis with four different topology are compared corresponding to frequency are shown Figure 9, where optimal topology acquired positive value than other topology1, topology2 and topology4. Figure 9. Active reflection coefficient Vs frequency The Figure 10 represents the array side lobe level for different methods. The side lobes are the far field radiation pattern and are not considered as main lobes. The side lobe level increases with decreases in the bandwidth. In order to get a significant array pattern, the side lobe level value must be higher. From the Figure 10, it is found that the optimal topology, topology1, topology 2and topology 4exhibits 24.3109, 16.8963, 18.7218, and 21.0294 respectively. Thus, the optimal topology acquires lower antenna cost with higher value of side lobe level.

CONCLUSION
This paper introduces ananalytical approach to perform the simulation of linear MsP antenna design. The results of the design were considered with respect to beam patterns synthesis, design pattern (3D) syntehesis, antennaperformance over frequency band, and analysis offrequency with respect to magnitude, active reflection coefficient Vs frequency and Side lobe levels for different methods. The outcomes of the approach allow significantly controlling both the radiation as well as reflection coefficient through the element geometry design and identical sensor element. The analytical approach come up with minimized the cost of antenna to low side lobe level corresponding to some EMI of array antenna.