## 3 The Three-Dimensional UWB Antenna: Geometry, Computer Model, and Matching Parameters  
The geometry and matching characteristics of the antenna were presented in work [23]. A somewhat unusual compact geometry of the antenna, the simplicity of its power supply unit design, the wide matching band, the presence of a stable phase center in this band, and the stability of a group signal delay under the conditions of pulse excitation suggest the need for a more detailed study of not only the matching quality of the antenna but also its bandwidth and, finally, radiation features. The antenna design and the underlying physical considerations are described in [23]. Since the publication of this work, the antenna manufacturing technology has been improved. For the best reproduction of its geometric parameters, the antenna model is printed on a FlyingBear model Ghost 6, 3D printer. PLA is used as plastic. This plastic is less susceptible to external influences. The printing was carried out with the entire model completely filled. The antenna itself, with a rectangular platform for attaching the connector, is made of brass using the investment casting method using a disposable shell gips around the plastic model. As the temperature rises, the sample melts and is removed, and brass is poured into the resulting cavity, forming a casting with high accuracy. In its natural form, an antenna with an SMA connector is shown in Figure 1. The flat conductor forming the antenna has a constant width along 2/3 of its length, and is wedge-shaped along 1/3 of its remaining length with the rounded top having a radius of 1.5 mm. The width of the strip conductor of constant width is equal to 16 mm, and its thickness is 2.0 mm. The greatest linear antenna size is 42 mm. The computer antenna model and the dependence of its reflection coefficient \(S_{11}\) calculated on its basis using the software package CST Microwave Studio Suite (vS2 2024 Golden) are shown in Figures 1 and 2, respectively. As can be seen from Figure 2, the antennas matching band at a level of \(-10\) dB is \(11\) GHz. Hence, the antenna by its matching band belongs to the class of ultra-wideband antennas. Naturally, the question arises: what ensures such high matching quality? It is unlikely that a meaningful answer can be given to this question without studying the antenna radiation features. Characteristic Modes of the Three-Dimensional UWB Antenna--The Main Attributes in Understanding Its Radiation Characteristics  
In the initial stage of research, it is expedient to establish the characteristic modes significant in the given frequency band, to determine their resonant frequencies, and to establish in what frequency ranges they are inductive or capacitive. Within the framework of the TCM, the main antenna characteristics can be most fully described by the frequency dependences of the characteristic angles of the modes and their modal significance. These dependences were obtained for the snail-shaped antenna using instruments of the integral equation solver and multilayer solver integrated into CST Microwave Studio Suite. Since calculations were performed in a wide frequency band (\(2\dots\) \(10\) GHz), special measures were undertaken to take into account all significant modes in the specified band, including determination of the significant modes in the sampled frequency range, determination of the significant modes in the entire frequency range from several starting frequencies of the examined range. Particular care was taken to ensure continuous tracking modes. The matter is that in a number of the well-known computer products containing instruments for finding the characteristic modes, automatic mode tracking is envisaged. However, in the literature, it was reported that in actual calculations, tracking failures sometimes occur,  
Figure 1: Snail-shaped Antenna (**left**). Computer model of the snail-shaped antenna (**right**). Figure 2: Frequency dependence of the reflection coefficient \(S_{11}\).