# The Analysis of Experimental Deployment of IGLUNA 2019 Trans-Ice Longwave System
## 2 Transmitting Antenna Design and Parameters
The first repair of the surface antenna--performed by cable braiding--increased  
Figure 2: A simplified floorplan of the Glacier Paradise premises inside the Klein Matterhorn glacier, with the 270 kHz antenna cable installed. its resistance to 4.1 \(\Omega\); the second repair, employing a pair of banana plugs from the already dismantled glacier antenna system, increased the resistance of the antenna to 4.4 \(\Omega\). This clearly indicates that despite the fact of extreme (in relation to the Earth's surface) environmental conditions, the resistances and inductances of such antenna systems are not severely affected and remain mostly unchanged. Figure 4: Averaged values of the antennas’ inductances. Figure 3: Measured inductances of the glacier- and surface loop antennas. Measured inductances and resistances of both antennas allowed the calculation of the \(Q\) factors using a conventional formula for RLC circuit as the inversion of the coefficient describing the damping of the oscillations [13]:  
\[Q=\frac{2\pi fL}{R} \tag{1}\]  
where\(f\) is the circuit's operating frequency (Hz); \(L\), inductance (H); and \(R\), resistance (\(\Omega\)). The approximate impedances \(Z\) for the respective days of operation have been calculated using a formula for a series circuit [13], as the deployed antennas operated as \(RL\) in-series loops of the transmitters' drain circuits [7,13]:  
\[Z=\sqrt{R^{2}+4\pi^{2}f^{2}L^{2}} \tag{2}\]  
with the total resistance of the circuit approximated by the dominant DC resistance; the accurate calculation of the total resistance for large and highly irregular loops requires different and much more complex methods than for small loops [10] (including the precise definition of the antenna's surroundings, which in this case were neither simple nor constant). The calculated \(Q\) factor values and approximate impedances for 270 kHz are shown on Figures 6 and 7. The changes of the Q factor, related to the changes of the inductances, show convergence to the value of \(\sim\)210 this, when used to calculate the available bandwidth for the A3E type of emissions, gives only bandwidth (BW) = \(\sim\)1.4 kHz too low value for a recognizable voice/telephony modulation. The actual parameters of the antennas--the DC resistances, inductances and the \(Q\) factors, respectively--were affected by the modulation transformers, which became the in-series parts of the antenna circuits, allowing a sufficient increase of the bandwidth obtained during the experiments' operation to allow sound/voice transmissions (see Section 4). Figure 5: The measured DC resistances of the antennas. Both antennas remained as untuned (no external capacitor) high-impedance circuits [4], with approximate impedance values of nearly a half of the input impedance of a high-power longwave transmitter's power stage [14]: \(\sim\)773 \(\Omega\). As the antennas possessed the length of quarter-wave values for 270 kHz (278 m), the analytic definition of their radiation resistance becomes complicated, especially with the inclusion of their actual shape after laying down in and on the glacier, and random objects and systems present on the surfaces of their 'cores'. However, if such antenna is considered to be a singular loop of a flat coil, using  
Figure 6: The calculated Q factors of the inside-glacier- and surface antennas. Figure 7: The calculated approximate impedances of the inside-glacier- and surface antennas. the measured inductance values respective specific magnetic permeabilities \(\mu_{r}\) of the surrounding medium can be calculated by using the adaptation of the formula given in [15]:  
\[L=\mu_{0}\mu_{r}\frac{r}{2}\Psi_{z\Lambda} \tag{3}\]  
where \(\mu_{0}=4\pi\cdot 10^{-7}\) H/m (magnetic permeability), \(r\) is the radius of the antenna (assuming circular shape: 44.245 m) and \(\Psi_{z\Lambda}\), the magnetization flux (here equal to 20 [15]).