# Validation of an RF Image System for Real-Time Tracking Neurosurgical Tools
## 2 Materials and Methods
### System Hardware
#### 2.1.1 Antenna Design and Standard Characterization in the Frequency Domain  
The main drawback of Vivaldi antennas is their physical size, which is considerably large. This may pose a limit for its use in this type of imaging system, where a reduced size for the antennas is desirable. Vivaldi antennas are based on an exponential-profile radiating slot that features the same characteristics regardless of the frequency, so the bandwidth is theoretically infinite. In the design process, the size of the initial and final aperture is selected depending on the targeted frequency range of operation, being the size of the small aperture a half wavelength of the highest frequency and vice-versa. This aspect is especially important when determining the minimum operating frequency, that limits the size of the antenna. We, therefore, adapted the design to the above-mentioned frequency requirements. The feeding of the antenna is implemented with a microstrip transmission in the bottom face. For the impedance matching to 50 \(\Omega\) throughout the entire frequency range, an open-ended radial stub transmission line is used with some transmission line sections with variable width [25]. Figure 2 shows a picture of the Vivaldi-like designed antennas, including the top and bottom layers.  
The proposed antennas are a modification of classical Vivaldi antennas. To overcome the size restrictions, the final size was reduced by truncating the exponential profile of the slots and by modifying the geometric shape of the antenna aperture. This modification  
Figure 2: Designed Vivaldi-like antennas: top (**left**) and bottom (**right**).  
was made by optimizing the dimensions of the new aperture by simulations with ANSYS HFSS and Keysight EMPro software, so that the smallest antenna size is obtained while the frequency-domain performance of the antenna is unaltered. The main effect of this size-reduction process is the bandwidth decrease. In the design process, we pursued the best antenna characteristics between 0.1 and 6 GHz, according to the target frequency range. Additionally, three director elements were added in the antenna aperture region (see Figure 2) with the aim to increase the directivity of the antenna by concentrating the radiation pattern in the aperture's direction. The final size of the antenna is 70 \(\times\) 68 mm\({}^{2}\), which means a size reduction of more than 4 times in comparison with a standard Vivaldi antenna with the same frequency characteristics. Finally, the antenna was printed onto a 1.52-mm-thick piece of FR4 substrate (with dielectric constant of 4.4 and loss tangent of 0.02) following a photolithography and chemical etching process.  
One of the antennas was placed inside an anechoic chamber to carry out a standard characterization. Firstly, the return losses were characterized by means of the scattering parameter \(S_{11}\). The results of both the simulated and measured response are plotted together in Figure 3. An acceptable agreement can be seen, thereby validating the design, optimization, and implementation processes. The experimental operating frequency range of the antenna is from 1.2 to 5 GHz (for \(S_{11}<-10\) dB), which means 123% bandwidth for a central frequency of 3.1 GHz; thus, confirming its wideband nature. Secondly, the antenna radiation patterns were measured by employing a horn antenna as a reference. The measurement characterization of the antenna in terms of the E-plane and H-plane radiation diagrams at specific frequency points can be seen in Figure 4. It is worth noting that the designed antenna has a higher directivity in the E-plane (the aperture plane), especially at higher frequencies. Following these steps, the 16 involved antennas were characterized, obtaining well-high identical results.