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3. PROPERTIES OF MICRO-DISCHARGES 3.B. ERROR ANALYSIS IN CHARGE MEASUREMENT cycles at typical DBD frequencies, the gas composition should change as the diffusion is very slow. 3.B Error analysis in charge measurement In the method used to measure charge transferred by one filament, contribution from the background capacitive signal is neglected assuming it to be insignificant. As has been explained in section 3.3.4, the voltage remains constant when the filament is discharging. Which implies that the background sinusoidal signal can be expected to be constant. Even if the voltage is assumed not to stay constant, because of small discharge area, the error due to the background signal can be estimated by estimating how much the background signal can contribute to the actual measurement itself. Charge measured by the Lissajous capacitor as a capacitive response to the applied sinusoidal voltage in the absence of a filament is given by equation 3.22 Q = Q0sin(2πt + φ) (3.22) T The maximum rate of change for a sine function is where it crosses zero where it can be approximated as In a 200 ns window the maximum change in Q will be 2π200 × 10−9 Q ≈ Q0(2πt + φ) T (3.23) (3.24) (3.25) ∆Q≈Q0 ∗ 44×10−6 ∆Q ≈ Q0 20 The amplitude of the charge signal (Q0) varied from 4.3 nC to 6.7 nC in the experi- ments, which will give a worst case scenario of 50 % error in the charge transferred due to first filament if it occurs at the zero crossing of voltage cycle. However, most of the filaments do not occur at the zero crossing and at higher pressure, the amplitude of charge also decreases which improves the precession. Also, second and later filaments in a half cycle occur further from zero crossing which will improve the accuracy. A more robust way to estimate error is to simulate a sine curve using matlab (software used to analyze all the electrical data) and use it to find the change in sine function for 100 ns at the origin and twice that amount gives the change in sine function for a time window of 200 ns. It has been found that a sine function with a frequency of 22.5 70PDF Image | Understanding CO2 containing non-equilibrium plasmas
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