# Progress on Single-Feed Quality Wideband Linear Wire Array
## 3 Driven Element
### Impedance Characteristic  
Figure 1 shows the basic forms of loop antennas, slot antennas, and loop-slot antennas, where the blue parts represent metal, and the red arrows represent the lumped ports. The WHEMS antenna has a loop structure and can be classified as a loop, slot, or slot loop antenna, but it has a unique feeding structure and characteristics that differ from those of a typical loop antenna [29]. A slot antenna is typically characterized by a large ground plane [30], while a slot loop antenna is made up of two separate, unconnected pieces of metal [31]. The novel slot antenna has an irregular geometrical design, new materials, and a co-planner waveguide feeding mode [32; 33]. Figure 1 illustrates examples of typical loop, slot, and slot loop antennas, while Figure 2 shows the WHEMS antenna [19].  
Figure 3 shows the basic form and parameters of the WHEMS antenna, where the part in blue is metal. The WHEMS antenna can be regarded as two parallel end short-circuited lossy transmission lines, and the radiation can be equivalent to the loss of the transmission line. The input impedance of the WHEMS antenna is derived belo  
Figure 1: Schematic diagrams of (**a**) loop antenna, (**b**) slot antenna, and (**c**) slot loop antenna.  
arm of the WHEMS antenna here is infinitely thin. The lossless characteristic impedance \(Z_{0}\) of the linear WHEMS antenna is shown in Equation (1):  
\[Z_{0}=120(\ln\frac{L\cos\alpha}{d/2}-1). \tag{1}\]  
Lossy characteristic impedance is given by Equation (2):  
\[Z_{c}=Z_{0}(1-j\frac{\sigma}{\beta}). \tag{2}\]  
Equation (3) is the loss factor:  
\[\sigma=\frac{R}{2Z_{0}}=\frac{2R_{s}}{Z_{0}L(1+\cos\alpha)(1+\frac{\sin\beta L (1+\cos\alpha)}{\beta L(1+\cos\alpha)})}. \tag{3}\]  
Among these, the loss resistance, that is, the radiation resistance of the antenna, can be calculated using Equation (4):  
\[R_{s}=\frac{1}{2l_{0}^{2}}\sqrt{\frac{\mu}{\varepsilon}}\int_{0}^{2\pi}\int_{ 0}^{\pi}\left|H_{\phi}\right|^{2}r^{2}\sin\theta d\theta d\phi. \tag{4}\]  
The \(H_{\phi}\) is given in [19]. Therefore, the input impedance of half a WHEMS antenna is shown in Equation (5):  
\[Z_{in}/2=Z_{0}\frac{sh2\sigma l+\frac{\sigma}{\beta}\sin 2\beta l}{ch2\sigma l +\cos 2\beta l}+Z_{0}\frac{\sin 2\beta l-\frac{\sigma}{\beta}sh2\sigma l}{ch2 \sigma l+\cos 2\beta l}. \tag{5}\]  
Assuming that \(\alpha=60\) deg and when \(f=f_{0}\), \(\beta l=2\pi\), the input impedance of the linear WHEMS antenna can be calculated according to Equations (1)-(5), as shown in Figure 4. The following can be gleaned from the figure:  
Figure 3: Basic form of a WHEMS antenna.  
Figure 2: (a) A photo of the prototype, (b) a partial perspective front view, and (c) a partial perspective front view of the WHEMS antenna from [19].  
The WHEMS antenna theoretically has infinite bandwidth, and the module value of input impedance gradually converges to half of the characteristic impedance of half the WHEMS antenna with the increase in frequency;
2. The first matching resonant point of the WHEMS antenna is at the first parallel resonant point, that is, when half the WHEMS antenna is equivalent to a half-wavelength short-circuit transmission line. At this point, half the WHEMS antenna has a perimeter of one wavelength.