# Dual-Band Single-Layer Fractal Frequency Selective Surface for 5G Applications
## 4 Design Parameters and Guidelines
### Unit Cell Size \(w\) and Central Element Width \(t\)  
As explained in the first part of this section, the two parameters that allow the most consistent flexibility in adjusting for frequency and bandwidth, are \(w\), and to a lesser extent, \(t\). \(w\) stands for the size of the element and is measured from the top of the bow tie to the bottom. \(t\) is defined as the width of the central metal strip and has a limited range. The size parameter \(w\) is investigated from 70 to 100 mm. In this interval, the frequency shifts follow a linear relationship. The range for \(t\) goes from 0.5 to 2.8 mm. Its lower limit is due to the physical design limitations of a copper trace width. The upper limit is in place so that the different bow ties will not end up touching each other. These two intervals were used to carry out a parameter sweep in the CST Microwave Studio. The results from these simulations were then analyzed to derive equations for the frequency and bandwidths of the two attenuation bands. Using Python, the results were plotted on four different graphs as point clouds, as can be seen in Figure 8.  
From the previously mentioned plots in Figure 8, it is clear that there is some linear relationship for the center frequencies as well as the bandwidths. These linear relationships lead to the following four equations (Equations (1)-(4)), derived using linear regression. The precision (p), as calculated by the algorithm, for these equations is also given. These numbers are only valid in the simulation intervals. Outside these intervals, the curves start to diverge from the planes with increasing and decreasing \(w\) values. Equation (1) is a good starting point to adjust the first notch. It is valid from 750 MHz to 1150 MHz. It can be noted that an increase in overall size \(w\) has a large effect on the resonance: although \(t\) weights more, it denotes the width of the central metal strip, and it is not possible to vary by a lot. \[f_{low}\;[\mathrm{GHz}]=0.0434t\;[\mathrm{mm}]-0.0134w\;[\mathrm{mm}]+1.9238 \qquad p=98.939\;\% \tag{1}\]  
Figure 7: Frequency response of the final design. The second equation has a wider useful interval, from 3.4 GHz to 4.3 GHz. This means that the same change in \(w\) yields a more drastic frequency shift in the second resonance band than in the first lower one. \(t\) in comparison seems to have less effect when the equations are looked at more closely; \(t\) has about 50% less effect on the low band center frequency position than the high-frequency center band position. The precision of both Equations (1) and (2) is both high and similar. This means that both can be a good starting point for designing a similar design around 800 MHz and 3.5 GHz. \[f_{high}\left[\mathrm{GHz}\right]=0.0249t\left[\mathrm{mm}\right]-0.0443w \left[\mathrm{mm}\right]+7.3136\qquad p=98.626\ \% \tag{2}\]  
When the design requirements are taken into account, the frequency response needs to have at least a bandwidth of 400 MHz around the center frequencies at the \(-10\) dB level. The center frequency for the lower band varies around 800 MHz, and not the predetermined 700 MHz. Because of the larger bandwidth, the suppression of reflectivity is still \(-10\) dB at 700 MHz, and the total width around 700 MHz is more than sufficiently damped. In Figure 8c, the bandwidth variation interval is visible on the z-axis and ranges from 1.3 GHz to 2 GHz. This is wide enough and can be effectively tweaked with Equation (3). The influence of \(t\) on the bandwidth is this time higher than the influence of \(w\). This can be interesting for some applications. For example, one can achieve a high bandwidth and low first frequency band by using a high \(w\) value and high \(t\) value. The precision of this equation is again relatively high, with more than 98% accuracy. \[BW_{low}\left[\mathrm{GHz}\right]=0.1312t\left[\mathrm{mm}\right]-0.0175w\left[ \mathrm{mm}\right]+2.7797\qquad p=98.267\ \% \tag{3}\]  
The last equation is an interesting one.