## 3 Probe Design and Calibration  
When using a probe antenna on an unmatched impedance termination, the antenna input impedance should also be known, typically by measuring its input reflection coefficient. Calibrating such an antenna also requires gain measurements. Since the antenna will be placed on a metallic drone body, the effect of the drone body should also be investigated. An electrically short antenna is expected to have a low realized gain, and the measurements \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Electrically Short,** & **Electrically Short,** & **Electrically Small** \\  & **Straight Dipole** & **Folded Dipole** & **Loop** \\ \hline Radiation resistance & Less than 2 \(\Omega\)1  & Less than 0.3 \(\Omega\)1  & Less than 0.3 \(\Omega\)1  & Less than 0.3 \(\Omega\)1  \\ \hline Input reactance & Capacitive, & Inductive, & Inductive, & Inductive, \\ (7-30 MHz) & \(-\)10,000 to \(-\)2000 \(\Omega\) & 100 to 500 \(\Omega\) & 100 to 500 \(\Omega\) \\ \hline \hline \end{tabular}
\begin{tabular}{c c c} \hline \hline \multirow{4}{*}{Pattern stability over the frequency range of interest} & \multirow{4}{*}{High} & High, but dual-mode: & \\  & & loop mode at lower & \\  & & frequencies, dipole & \\  & & mode at higher & \\  & & frequencies & \\ \hline \hline \multirow{4}{*}{Mechanical stability} & Good, when attached & Good, when attached & Good, when attached \\  & tangentially to the & horizontally to the & horizontally to the \\  & drone body & drone body & drone body \\ \hline Radiation below & Constant over the & Slightly variable over & \\  & the drone & frequency band & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison between different types of electrically small probes. are performed very close to the antenna under test; consequently, the effect of most of the environing objects on the accuracy would be negligible. The two-antenna method [16; 30] can be adapted to characterize such a probe by successively pairing two identical probes as follows: both on dielectric tripods, the first on a dielectric tripod and the second attached to the drone (Figure 2). The gain can then be found by taking into consideration the input impedance variation [31] as follows  
\[G_{\text{probe off drone}}=\sqrt{\left(\frac{4\pi r}{\lambda}\right)^{2}\frac{R_ {0}}{R_{a2\text{ off drone}}(f)}\frac{\left|S_{21\text{ off drone}}\right|^{2}}{ \left|1-S_{22\text{ off drone}}\right|^{2}\left(1-\left|S_{11}\right|^{2} \right)}}\, \tag{1}\]  
\[G_{\text{probe on drone}}=\frac{1}{G_{\text{probe off drone}}}\bigg{(}\frac{4\pi r }{\lambda}\bigg{)}^{2}\frac{R_{0}}{R_{a2\text{ on drone}}(f)}\frac{\left|S_{21 \text{ on drone}}\right|^{2}}{\left|1-S_{22\text{ on drone}}\right|^{2}\left(1- \left|S_{11}\right|^{2}\right)}. \tag{2}\]  
Since \(S_{22}\) and \(R_{a2}\) are not essentially impacted by the drone body proximity, the following results:  
\[G_{\text{probe on drone}}=G_{\text{probe off drone}}\frac{\left|S_{21\text{ on drone}}\right|^{2}}{\left|S_{21\text{ off drone}}\right|^{2}}. \tag{3}\]  
As probes, we considered a pair of \(1\) m long dipoles (Figure 3); we chose a folded configuration, as explained in Section 2. Such a dipole is electrically short over the entire HF band; as a result, the impact of the common mode currents on gain measurements is quite high [32]. One-to-one baluns were used as part of the antenna in order to reduce the effect of the common mode currents, and thus the antennas will be characterized including the transformers. The same balun will be used with the probe on the drone as well. When used as a probe on a drone, the folded dipole has no feeder, and therefore the common mode current would not impact on the radiation pattern as it does when measuring the probe gain. Conversely, the current would close through the ground of the on-drone data-acquisition circuitry and may therefore induce erratic operation. In Section 4, we will thoroughly analyze the effect of the balun in terms of input impedance and losses. Figure 3: Folded dipole as a probe.