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The microstrip antenna with a symmetrical rectangular radiator and four teeth is described. The influence of the base geometric parameters of the antenna on the bandwidth at the base frequency was studied. The following geometric parameters of the antenna are selected: the length and the width of the radiator, the depth of cuts, the thickness of the substrate, the length of the ground plane and the width of the feed line. The regression analysis was carried out and the mathematical model describing the dependence of the bandwidth on the length and the width of the radiator and the depth of the cuts was developed. The root-mean-square error and the relative absolute error of the model were calculated. The graphs of the bandwidth dependences on the geometric parameters are presented.
It was established that the decrease of the bandwidth values is associated with an increase of the radiator width and the substrate thickness. It was shown that a slight influence on the bandwidth are made by the changes of the radiator length and the depths of the cuts only in the case when the radiator width is much smaller than its length. The proposed formula describing the relationship of the bandwidth with the geometric parameters of the antenna can be used to design a four-tooth antenna with wide bandwidth.
Nowadays microstrip antennas are among the most common and widely used types of antennas . The most studied of them are microstrip antennas with rectangular and other radiators of simple geometry [1, 2]. However, the narrow bandwidth restricts the use of such antennas. There are various methods for this problem solution [3-6]. The bandwidth can be widened by adding the cutouts to the radiator. For example, the slots in the form of the letter L , H and U , the letter E  and even their combinations  are used. The ground plane is changed [11-14], as well as other methods [15, 16] are used, including the use of metamaterials [17, 18]. Due to these and other optimization approaches, the antennas not only increase the bandwidth, but also improve other characteristics of the antennas.
One of the promising areas is the creation of so-called tooth antennas (the antennas with the cutouts on the sides of a rectangular radiator). For example, in  such an antenna is described with the cutouts only on one side, and the symmetrical tooth antenna was studied in . In , it is considered tooth antennas with stepped radiating elements, and microstrip patch antenna with seven operating ranges is presented in .
However, the process of any antenna design that has certain electrodynamic characteristics is quite long and time consuming. One of the promising approaches is the use of regression models describing the relationship between the electrodynamic characteristics of an antenna and its geometry . Using these relationships, you can determine an approximate shape of an antenna immediately, which will be well matched in a given frequency range. This approach facilitates the antenna design process and allows to obtain a well-matched antenna in a shorter period of time.
In this paper we consider the antenna with a symmetrical four-tooth radiator. The influence of the radiator geometry on the antenna bandwidth is shown. The regression model is designed that describes the relationship of the bandwidth at the base frequency with the geometric parameters of the radiator. The influence of the substrate thickness, ground plane dimensions, radiator scale and the width of the feeding line on the bandwidth are analyzed. Graphs showing the dependence of the bandwidth on tunable antenna parameters are presented.
The microstrip antenna with the radiator of symmetrical four-tooth shape is considered. The dependencies of the bandwidth at the base frequency on geometric parameters of the radiator and other antenna parameters were studied. The regression model is developed for the bandwidth. The behavior of the bandwidth is analyzed when other parameters of the antenna are changed.
The obtained regression model (together with the regression model for the base frequency) can be used to find the maximum values of BW at given constraints on the radiator parameters. After the obtaining of the radiator dimensions, it is possible improve the bandwidth by the corresponding change of other antenna parameters.
The work is performed according to the Russian Government Program of Competitive Growth of Kazan Federal University.
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