# Switchable Broadband-to-Tunable Narrowband Magnetic Probe for Near-Field Measurements
## 2 Magnetic Probe Design  
The proposed magnetic probe consists of four stick-up layers; the first and fourth layers are employed as shielded ground layers for isolation purposes, the second layer stands for the strip loop and transmission line, and the third layer is dedicated to maintaining the symmetry of the structure. This probe is based on an FR-4 substrate with a relative permittivity of \(\varepsilon_{r}=4.3\) and a loss tangent \(\tan\delta=0.025\). Figure 2 shows the geometrical shape of the probe's layers, while the dimensions are illustrated in Figure 3.  
The structure of the proposed probe in the typical case (broadband response) can be represented by a Loop Gap Resonator (LGR), as shown in Figure 4. The resonance frequency of the LGR is based on the capacitor of the gap and the loop's inductor, which can be calculated mathematically using Equation (1) [29]. Figure 3: Front view of the magnetic probe with all dimensions. Figure 2: Magnetic probe layers: (**a**) Top layer (ground); (**b**) detailed view of the stripline layer; (**c**) detailed view of the symmetry-maintaining layer; (**d**) bottom layer (ground). \[C = \varepsilon_{0}\frac{w\,l}{n\,t}, \tag{1}\] \[L = \mu_{0}\frac{\pi r^{2}}{l}. \tag{2}\]  
Since,  
\[f_{0}=\frac{1}{2\pi\sqrt{LC}}. \tag{3}\]  
Substituting (1) and (2) in (3) yields:  
\[f_{0}=\frac{v_{0}}{2\pi r}\sqrt{\frac{n\,t}{\pi\,w}}, \tag{4}\]  
where \(n\) is the number of gaps in the loop, \(w\) is the strip width in mm, \(r\) represents the probe's radius in mm, and \(t\) is the gap width in mm and equal to (\(2\times r_{\text{{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{\it{ \it{\it{ \it{  {                    }}}}}}}}}}}}\)). The theoretical resonance frequency of the LGR is computed by substituting the probe's parameter values in Equation (4), where \(w=0.56\) mm, \(r=1.7\) mm and \(t=0.5\) mm. Consequently, the theoretical result of the resonance frequency coincided with the simulated S11 parameter obtained from the CST EM Microwave Studio [30], where \(f_{0}=\frac{3\times 10^{8}}{2\pi\times 1.7\times 10^{-3}}\sqrt{\frac{0.5 \times 10^{-3}}{\pi\times 0.56\times 10^{-3}}}=14.9\) GHz. The simulated reflection coefficient is shown in Figure 5, while the overall dimensions of the proposed probe are listed in Table 1.  
Figure 4: Magnetic probe layers: (**a**) proposed probe; (**b**) loop gap resonator. Figure 4.0 Reflection coefficient versus frequency of the LGR. Figure 6 presents the surface current distribution of the designed LGR probe in 2D and 3D views, which is an essential criterion to gain deep insight into the broadband probe's resonance behavior. It can be seen that the power flows from the port toward the loop through the transmission line, then moves to the other side through via-1 and back to complete the open circle, as evidenced by the black arrows. The S11 parameter describes the electrical characteristic of the antenna, and determines its impedance bandwidth. Furthermore, both the S11 parameter and S21 parameter are critical factors in evaluating the magnetic probe characteristics; the S21 parameter measures the strengths of the magnetic field and the electrical field in the vertical and horizontal directions, respectively. At the same time, the S11 parameter describes the resonance characteristics of the magnetic probe. Unlike the antenna, the magnetic probe operation bandwidth is computed by taking the \(-3\) dB value of the reflection coefficient curve [31]. Figure 7 shows the simulated S-parameters of the proposed magnetic probe with a 2 mm height above the trace of the microstrip reference board. It can be seen that this probe has high sensitivity (as S21 \(>-27\) dB) in the 1 GHz to 3.4 GHz band, and starts losing its sensitivity (as S11 \(<-3\) dB) beginning at 3.5 GHz and beyond. The proposed broadband magnetic probe has been fabricated and tested with the help of a Network Analyzer, a Directional Coupler, and a reference board, as shown in Figure 8b.