# A Compact Sub-GHz Wide Tunable Antenna Design for IoT Applications
## 2 Design Details
### Antenna Operation  
Slot-based FR antennas gain more attraction as they are low-profile planar structures, easy to integrate, and able to operate in wide frequency bands. In the literature, open and closed-ended slot designs were investigated and reported. The closed ends or short-circuited slot antenna can be modeled as \(\lambda/2\) transmission line which corresponds to its fundamental frequency of resonance [39]. These antennas may be loaded with capacitive  
Figure 1: Proposed antenna (**a**) Top view (**b**) Bottom view (All dimensions are in millimeters, mm).  
Figure 2: Fabricated antenna (**a**) Top view (**b**) Bottom view (dimensions are in millimeters, mm).  
reactance. The antenna resonance can be optimized over a wide frequency band. The rectangular slot antenna fundamental resonance frequency is given by the following [40]:  
\[f_{r}=\frac{c}{(l_{m}+w_{m})}\ \times\frac{c}{4\ f_{res}\ \sqrt{\frac{c_{r}+1}{1.5\pi_{r}}}} \tag{1}\]  
\[l_{m}=l_{1}+l_{2}+4l_{3}+2l_{4}+2l_{5}\text{, }w_{m}=4w_{1}+4w_{2}+w_{3}+w_{4} \text{, }c\text{ is the speed of light in free space, }c\text{r is the relative permittivity of the substrate,}f_{r}\) is the modified rectangular antenna's fundamental resonance frequency, and the term (\(l_{m}+w_{m}\)) is the mean circumference of the meandered rectangular ring slot antenna. In the proposed design, the effective mean circumference can be an estimate of several rectangular slots that determine the overall fundamental resonance frequency.  
The meandered loop-slot structure was reactively loaded using a varactor diode (\(D_{o}\)), as shown in Figures 1 and 2. The varactor diode was utilized to vary the slot-line capacitance at a certain point. As a result, it helped in bringing the resonance frequency down to the lower band. The reactive loading is a non-uniform operation, and it can be determined using the location of the varactor diode (\(L_{v1}\)), its capacitance value \(C_{v}\) and the impedance (\(Z_{o}\)) of the slot line structure. The resonance frequency of the reactive loaded slot can be determined using the transmission line equivalent circuit model as given in the following [41]:  
\[\tan(\beta\ L_{t})+\tan(\beta\ (L_{t}-L_{v}))-\omega C_{v}Z_{in}\tan(\beta\ L_{1}) \tan\beta\ (L_{t}-L_{v})=0 \tag{2}\]  
where \(L_{t}\) is the total length of the slot (\(L_{t}=l_{m}+w_{m}\)), \(\beta\) is the propagation constant. This constant depends on the frequency of operation \(L_{v}\) is the distance of diode placement from the feedline, \(C_{v}\) is the varactor diode capacitance, and \(\omega\) is the angular frequency. The reactively loaded slot antenna resonance frequency can be numerically determined by solving Equation (2). The resonance frequencies obtained for the optimized design using HFSS were also compared with theoretical values based on Equation (2). The two results (theoretical, HFSS-based) obtained are (750 MHz and 764 MHz), (826 MHz, 836 MHz), (901 MHz, 885 MHz), (981 MHz, 964 MHz), (1052 MHz, 1029 MHz). A small variation in values is observed. Thus, the mathematical expression derived is useful to obtain an insight into the effective reactive loading of the slot antenna structure.  
Figure 3 shows the equivalent circuit model of the proposed meandered loop-slot antenna. The series combination of a microstrip feedline (series \(L_{t}C_{f}\) circuit) and an \(RLC\) resonating circuit that represents the loop-slot radiating structure is shown in Figure 3a.  
Figure 3: Equivalent circuit model (**a**) Meandered loop-slot with feedline (**b**) Varactor diode (**c**) Complete circuit model.  
The varactor diode equivalent circuit and the complete antenna design equivalent circuit model are shown in Figure 3b,c, respectively [42]. The antenna equivalent circuit model analysis assists in gaining a better understanding of the proposed antenna design multi-band operation, the slot reactive loading, and FR antenna operation. ADS can be used to obtain the antenna circuit element values and the antenna reactive loading parts can be extracted by using the S-parameters [43].