A Series of Frequency Shift Antennas Based on Shape Blending

In this paper, an automatic antenna design method based on the shape blending algorithm is proposed. ,e algorithm is used to construct the shape of the wide slot of a CPW-fed antenna. Firstly, two basic shapes are chosen as the initial shape and the target shape.,e shape blending process is then applied on them to get a series of shapes, which are used as the geometry structure of the wide slot. In this way, a series of CPW-fed wide slot antennas are obtained. And they have similar but gradually changing characteristics. ,e bandwidth ranges are 8.00–9.24 GHz, 7.95–9.05 GHz, 7.05–8.55 GHz, 6.95–8.13 GHz, and 6.55–7.50 GHz, respectively. ,e overall size of the antenna is 26mm ∗ 20mm ∗ 0.6mm. Experimental results show that the resonant frequencies vary (via translation) with the change of slot shape in a specific frequency band. ,e experiments also validate that the antennas have omnidirectional radiation characteristics. ,e radiation gains and aperture efficiencies of the antennas are about 3.8–5.5 dBi and 57.7–83.0% at their centre frequencies, respectively. ,e experiment results show that the proposed antennas could be used in C-band and X-band radar applications.


Introduction
In recent years, with the rapid development of new smart wireless communication systems and technologies, the requirements for wireless transmission are becoming more and more stringent. As an important part of wireless communication systems, antennas have an impact on the performance of the entire system [1]. e CPW structure feed-printing slot antenna adopts a coplanar waveguides transmission line structure for feeding; it has the advantages of ultra-wide bandwidth, small volume, and conformal design [2][3][4]. For antennas with CPW structure, there are two traditional design methods: one is to improve the impedance bandwidth or gain of the antenna by changing the geometry of the radiation patch, e.g., designing the radiation patch to be circular, square, diamond, or trapezoidal; the other is to improve the impedance bandwidth of the antenna via the geometry of the slot structure, e.g., rectangle [5], circle [6], and hexagon [7]. By embedding p-i-n diodes to the bow-tie arms, the electrical length of the antenna is changed and the resonance frequency is changed [8]. By controlling the feeding phase, different resonance frequencies are generated [9]. And the resonant frequency is moved by adding different numbers of stubs [10].
However, these methods are all aimed at specific types of antennas and changing the antenna structure through experience to produce different resonance points or make the resonance points moving. e method proposed in this paper can be applied to many kinds of antennas. At the same time, this method does not need the designer's professional knowledge. And it can be widely popularized.
is work breaks through the traditional design method and uses a shape blending algorithm to design and optimize the slot shape of the antenna to obtain a series of antennas whose resonant frequency varies with the shape of the slot geometry in a specific frequency band.
is is of great significance to the design of antennas with specific resonant frequencies. Using this method, we designed and fabricated a series of antennas with dimensions: 26 mm * 20 mm * 0.6 mm. Test results show that with the change of the slot shape, the resonant points of these antennas shift in the characteristic frequency band; these antennas have stable gain and good directional radiation characteristics.
e second section of the paper describes the shape blending algorithm. e third section shows a series of antennas obtained by an algorithm that varies the resonant frequencies as the slot changes. In section four, the results of the antenna are presented and discussed. Finally, the work is summarized.

Shape Blending Algorithms
Shape blending is also called graphic deformation. As an application of computer vision, image deformation has attracted much attention in recent years. Its application scope has gradually expanded from the computer field to the

Initial shape
Target shape     International Journal of Antennas and Propagation industrial field [11]. Shape fusion is the fusion of initial shape and target shape to produce a series of shapes. e resulting shape has the characteristics of both the initial shape and the target shape. As shown in Figure 1 [12], it shows the contour fusion process from a Volkswagen to a Porsche. Several blended contour shapes are obtained during the fusion process. ere are two key steps in the shape blending algorithm. e first step is to establish the corresponding relationship between the initial shape and the target shape.
is relationship is established on the elements of two shapes (such as vertices and edges). It is called the corresponding problem. e second step is to determine the trajectory of the corresponding elements, which is called the trajectory problem. In this paper, the shape blending algorithm is used to optimize the slot shape of the antenna. e cross shape is selected as the initial shape, and the rectangle is taken as the target shape, which is shown in Figure 2. e selection of feature points is especially important after determining the initial and target shapes. e feature points are selected and paired by the Ray firing method. e cross and the square are placed in the same coordinate system so that their centres coincide at the origin. 16 feature points A1-A16 are selected on the cross shape, and then 16 rays are, respectively, formed by connecting with the origin, and the 16 rays and the square generate 16 intersection points B1-B16 as feature points of the square. e selection of feature points in this paper is shown in Figure 3.
After the feature points are determined, the trajectory problem is solved by using the simple linear interpolation method to get the fused shape C, which is expressed as the following equation: (1)

Antenna Design
In this work, only the slot shape of the antenna is fused, while the other parameters are identical. e basic geometric structure of these antennas is shown in Figure 4. e shape of the slot is represented by a frame with dimensions determined by a shape blending algorithm. e substrate thickness of the antenna is 0.6 mm, the relative dielectric constant is 4.4, the loss tangent is 0.02, and the overall antenna size is W * L. e antenna is fed via a CPW structure such that the feed line width s is 1 mm and the gap between the feed line and the ground is 0.2 mm. e specific dimensions are as follows: W � 20 mm, W1 � 16 mm, W2 � 6 mm, S � 1 mm, L � 26 mm, L1 � 21 mm, L2 � 6 mm, L3 � 4.7 mm, dw � 0.2 mm, and g � 0.2 mm. During the shape blending process, the shape of the gap is produced by varying the t parameter, as shown  in Figure 5. Physical photographs of some of the antennas in this series are shown in Figure 6.
And the design idea of this paper is as follows. Firstly, the classical antenna is selected. And the patch shape and slot shape have the greatest impact on the antenna performance. By using shape fusion algorithm to change the slot shape, the function of antenna resonance point is realized. At the same time, the advantages of this design method are as follows: (1) to a certain extent, no longer rely on the experience of engineers so that everyone can realize the movement of the resonance point of the antenna through this method; (2) this method can be applied to many types of antennas and has great advantages compared with the method which can only be used for a single type of antenna.

Results and Discussion of Antenna Parameter
Antennas with different slot shapes can be obtained by changing the value of t. As t changes, the resonant frequency of the antenna also changes. We have also made prototypes of several antennas and tested them. Several     Figure 7 comparing with the simulation return loss. And we can see that the test results and the simulation results have the same change trend. As the t parameter increases, the resonant frequency of the antenna decreases. As shown in Figure 7, as t increases, the measured return loss improves. Similarly, the resonant frequencies are getting closer to the simulation results. e antenna gains and aperture efficiencies of the series of antennas in their respective effective frequency band are shown in Figures 8(a) and 8(b). Although these antennas are omnidirectional antennas, it can be seen from the results shown that the gain of these antennas is mostly maintained above 2 dBi, with a maximum gain of 5.96 dBi.   International Journal of Antennas and Propagation e aperture efficiencies of the 5 antennas span from 16% to 89% over the whole frequency band. Figure 9 shows the current distribution of the antenna. e image shows the current direction and distribution of these antennas in a more intuitive manner. e gain is relatively stable along a particular frequency bands. e E-plane and H-plane antenna patterns of these antennas are shown in Figures 10  and 11, respectively. e FR4 material is not suitable for high-frequency signals, processing technology, or the test environments, among other factors; therefore, the measured data and the simulated data of the return loss at high frequencies are quite different. As the t changes, the resonant frequency of the antenna decreases; the measured data and the simulation data gap becomes smaller as a result. e measured and simulated patterns of these antennas are similar, as shown in Figures 10 and 11. International Journal of Antennas and Propagation Before concluding the paper, the proposed design has been compared with the existing technology. e specific results are shown in Table 1.

Conclusions
A shape blending algorithm, which can be used to steadily change the resonance point of antenna, is proposed in this paper. Compared with the conventional design method, the proposed design method does not require much on the expertise of the antenna designers. Another advantage is that a series of antennas could be obtained with just one design process. To verify the proposed method, five prototypes have been designed, fabricated, and tested. e experiment results show that by changing the blending coefficient value t, the resonant points vary accordingly, which are 8.62 GHz, 8.38 GHz, 8 GHz, 7.6 GHz, and 7 GHz, respectively, while keeping the absolute bandwidth fixed, around 1.2 GHz. e overall size of the antennas is all 26 mm * 20 mm * 0.6 mm. e antennas also demonstrate stable gain and omnidirectional radiation characteristics. e radiation gains and aperture efficiencies of the antennas are 3.8-5.5 dBi and 57.7-83.0% at their centre frequencies, respectively. erefore, the proposed antennas could be applicable for C-band and X-band, offering good gains and efficiencies through the working frequency bandwidths.

Data Availability
e data used to support the finding of this study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest regarding the publication of this paper.