International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 12 Issue: 04 | Apr 2025
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Fringing Field Effect on Patch Perimeter and Simple Co-related Design Formulae for Microstrip Antennas of Various Patch Shapes S. K. Bhatnagar 104/97, Vijay Path, Mansarovar, Jaipur – 302020, India Formerly at Swami Keshvanand Institute of Technology, Management and Gramothan, Jaipur, India ---------------------------------------------------------------------***------------------------------------------------------------------rectangular shape a formula for effective dielectric constant is in wide use that requires width of the rectangle physical dimensions of a microstrip antenna patch of any (W) while the exercise is for estimating width W and shape. A universal model (can be used for any patch shape) length L of the rectangle. So a temporary value of W is has been proposed for virtual extension in patch perimeter calculated by assuming the effective dielectric constant to due to fringing fields in such antennas. The new model be average of the substrate dielectric constant ( r) and of contains terms that are specific for geometrical shape of the the air. The purpose is to minimize the mismatch between patch. From this model, simple design formulae have been the designed and measured (empirical) values of derived for various shapes of the microstrip antenna patch. resonance frequencies. These concepts gave results Additionally it is very simple and straight forward to use. reasonably accurately. For increasing the accuracy the The model eliminates need to transform one shape into concept of “dynamic effective dielectric constant” was another for estimating patch dimensions. New formulae do brought-in. Analytical expressions were developed for not require “curve fitting of data” or computation of rectangular shape. Other shapes were converted into “effective dielectric constant” or “dynamic dielectric equivalent rectangular patches and analyzed. The area of constant”. The novelty of this paper is that for developing equivalent rectangular/circular shape was taken to be mathematical model for microstrip antennas, first a theory equal to the area of patch under consideration [1-10]. Yet, is propounded, formulae derived and then the results of the some researchers considered equivalent patch by keeping formulae are compared with empirical data to validate the the perimeter of constant size between the two shapes formulae. Usually empirical data is plotted in the form of [11-13]. The formulae became more and more complex curves. Design models are then developed and fine tuned and difficult to solve. Artificial Neural Network (ANN) using curve fitting techniques. An expression has been models have been developed to match the results obtained proposed for estimating the constant of proportionality in by curve fitting formulae. The unknown coefficients of the the new model. The proposed theory also results in formulae model are determined by using genetic algorithm/ neural for (i) the ratio of fringing area to physical area, (ii) the network. The ANN networks are trained to output desired ratio of extension in patch perimeter to physical perimeter results. Models are created (weights are assigned) to and also (iii) ratio of extension in critical dimension to obtain the results that the author desires. This process led physical critical dimension of the patch for different shapes. to different formulae for every shape of the patch. There is Key words: Design formula, Electrical thickness of hardly any correlation between them. Attempts have been substrate, Fringing field area, Microstrip antenna, Patch made to generalize the solution for microstrip antenna [2, 8, 14, and 15]. Even in these publications the discussion is perimeter, Patch dimensions, Resonant frequency focused on rectangular, circular and triangular shapes 1. INTRODUCTION only. Elliptical and arbitrary shapes are rarely considered. Multilayer perceptrons network with 3 learning When microstrip antennas were designed using halfalgorithms have been used [2]. The process of using ANN wavelength formulae there was a mismatch between is cumbersome for simultaneous solutions for different designed and experimental values of the resonant patch shapes. In any ANN approach as the number of frequency. This has been attributed to fringing fields in shapes (and therefore models) increase, the complexity of antenna. To account for this mismatch the concept of ANN increases. Auto-metric Graph Neural Network has “extension in physical length” was introduced. Other been used for prediction of microstrip antenna dimension researchers introduced the concept of “effective dielectric [16]. Characteristic Mode Analysis [17] and Machine constant”. Yet others used both the concepts. Dielectric Learning approaches [18, 19] have also been used for the constant of the antenna structure is an important same purpose. [15] has considered non-uniform fringing parameter and its treatment varies from researcher to around vertices and edges. There is a need for simple researcher. Dielectric constant, effective dielectric formulae that quickly estimate dimensions of regular or constant and dynamic dielectric constant all have been irregular shaped microstrip antenna patch. This paper used in attempting to match one’s theory with aims at developing simple formulae for estimating the experimental results of someone else or of oneself. For the critical dimension of the patch and correlating the
Abstract - This paper presents a leap forward for finding
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