# Icing Mitigation by MEMS-Fabricated Surface Dielectric Barrier Discharge
## 3 Electrical Characterization  
### Setup  
A Chroma (Model 61603) wave function generator and a high-voltage custom-built transformer (Bremer Transformatoren GmbH) provided the sinusoidal high-voltage with a frequency f of 1 kHz for the SDBDs, see Figure 5. The high-voltage was measured using a Tektronix P6015A 1:1000 high-voltage probe. WIMA FKP1 capacitors were utilized to measure the charge transferred in the SDBDs. The exact value of the measurement capacitance was determined with a GW Instek (Model LCR- 817) LCR-meter at the measurement frequency 1 kHz. For the glass and the FR-4 samples a 32.74 nF measurement capacitor was used and due to a larger capacitance of the zirconia SDBD a 151.45 nF measurement capacitor was used there. The voltage drop across the capacitor was measured by a dual wire and connected via BNC to the Rohde & Schwarz RTO2034 oscilloscope, which averaged the charge-voltage plot of the samples over 200 high-voltage cycles. The charge-voltage characteristics were integrated by a python3 script to obtain the dissipated power of the SDBDs. For further details on the technique of power measurements see [40,41] and references therein.  
Additional experiments were carried out to estimate the power loss in the dielectric. For this purpose, the high-voltage electrodes were covered by a conductive copper tape above the area of the ground electrode and were then embedded in flowable silicone (Dow Corning 3140 RTV). This additional insulation suppresses the plasma formation at all electrodes. In the following these samples are further called \"capacitor samples\" and are sketched as configuration 2 in Figure 5. Both configurations were operated at ambient air and room temperature.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \multicolumn{1}{c}{} & \multicolumn{4}{c}{**Substrate Properties**} & \multicolumn{4}{c}{**Electrodes**} & \multicolumn{4}{c}{**i**CORE**} \\ \hline \multirow{2}{*}{**Name**} & \(\sigma\) & \multirow{2}{*}{\(\epsilon_{r}\)} & \multirow{2}{*}{\(\Theta\)} & \multirow{2}{*}{**tan**\(\delta\)} & \(d_{diel}\) & \multirow{2}{*}{**Method**} & \(d_{el}\) & \multirow{2}{*}{**Metal**} & \(V_{rms}\) & \(P/L\) & \(v\) & \(T\) \\  & [**\(\mu\)m**] & & & & & [**\(\mu\)m**] & & [**\(\mu\)m**] & & [**kV**] & [**W**/ m] & [**m**/ s] & [**\({}^{\circ}\)C**] \\ \hline FR-4 & 0.70 & 5.5 & 106\({}^{\circ}\) & 0.008 & 500 & PCB & 35 & Cu/Au & 5.4 & 7.2 \(\pm\) 0.5 & 50 & \(-\)17 \\ Borofloat glass & 0.02 & 4.3 & 99\({}^{\circ}\) & 0.011 & 500 & MEMS & 0.26 & Cr/Ni & 5.4 & 7.2 \(\pm\) 0.5 & 27 & \(-\)18 \\ Zirconia & 0.15 & 28.3 & 68\({}^{\circ}\) & 0.015 & 150 & MEMS & 0.2 & Ti & 2.0 & \(\sim\)20 \({}^{\ast}\) & 30 & \(-\)20 \\ \hline \end{tabular}
\end{table}
Table 1: Overview of the measured materials, the measured surface roughness (\(\sigma\)), the dielectric constant (\(\epsilon_{r}\)), the contact angle (\(\Theta\)), the loss tangent (\(\delta\)), the used substrate/dielectric thicknesses (\(d_{diel}\)), the manufacturing processes (method), the electrode thickness (\(d_{el}\)) and the electrode material. The table also shows the icing wind tunnel parameters at which the experiments were conducted, namely the operation Voltage (\(V_{rms}\)) of the SDBD and its measured power scaled to the electrode length (\(P/L\)), the applied air speed (\(v\)) and the temperature (\(T\)). \({}^{\ast}\) estimated from measurements at ambient air.  
Figure 5: Measurement setup for the plasma power and the estimation of the dielectric losses. Configuration 1 is a sketch of the SDBD sample. Configuration 2 represents the capacitor setup.