Rise Time and Peak Current Measurement of ESD Current from Air Discharges with Uncertainty Calculation

Abstract

The greater number of electrostatic discharges (ESDs) that occur in nature is by air rather than by contact. However, due to low reproducibility in the current of air discharges, the IEC 61000-4-2 defines that the current’s calibration of an ESD gun must be made only for contact discharges. In the work presented here, there is an attempt to improve the poor reproducibility of air discharges by a significant observation derived from ESD measurements and, more specifically, the relationship between the rise time and the peak current for every ESD gun. This fact validated in this paper from current measurements of two different ESD guns will help all who are involved in ESD measurements in EMC laboratories by reducing the existing uncertainty in measurements of air discharges.

1. Introduction

Electrostatic discharge (ESD) is defined as the sudden release of energy between two objects when they come into contact; it is a physical phenomenon that is intertwined with many different aspects in many scientific fields [1,2]. It combines high voltages with charging voltages that are usually a few kV, electronics; the discharge current destroys high tech electronic equipment [3,4,5,6,7,8,9,10,11], and of course electromagnetic field and electromagnetic compatibility [12,13,14,15,16,17,18,19,20,21,22,23], vulnerable equipment that must be shielded against the transient electromagnetic fields (the phenomenon lasts only a few ns) coming from the ESD event and the severe consequences of the ESD current, which may reach some Amperes.

Due to the high importance of the phenomenon in everyday human activity involving high tech equipment (PCs, cellar phones, laptops, tablets, etc.), ESD immunity testing specifies the IEC 61000-4-2 [24]. This Standard prescribes the calibration procedure of the ESD generators (or guns) that simulate the real ESD current, which must be made only for contact discharges. This happens due to the high reproducibility of contact discharges in addition to air discharges, in which the peak current may differ from one discharge to another due to the different arcs that are produced [25,26,27,28,29]. It is also the simplest case to examine in an uncertainty evaluation budget. Certainly, it has to be mentioned that air discharges can have major electromagnetic impacts on equipment due to the higher peak current and faster rise times compared to the ones of contact discharges. This is due to the fact that many factors, such as test voltage, approach speed, electrode surface conditions, and climatic conditions, have a significant impact on the test results [30,31,32,33,34,35].

The conditions that preexist before air discharges occur have been analyzed in various studies. In [36], the pre-charge conditions before the formation of the electric arc and for various gases are studied in depth. In [37], a new technique combining the surface and avalanche process during air discharges in short gaps is proposed. In [38], the effect of the shapes of metal electrodes on ESD current and radiation noise is discussed. In [39], the results indicated that as temperature decreases, or pressure increases, the electrostatic breakdown voltage increases, while in [40], the approach speed on spark length during air discharges with different temperature and humidity is examined. In a recent study [41], a model is constructed to make both the varied plasma velocities reported in the literature understandable, and also make predictions about the arc radio-frequency interference, contamination produced by the arcs, and the total charge in an arc possible.

The spark formation has been studied extensively [25]. Air discharges that accompany a spark are severer than contact discharges and play a significant role in the malfunction of electronic devices. However, they have not been quantitatively evaluated and the IEC Standard [24] is mainly focused on air discharges. In the current work, measurements of the discharge current during air discharges for the Pellegrini target placed in the center of a grounded metal surface (1.5 × 1.5 m²) have been conducted and the relationship between the peak current and the rise time is investigated with respect to the uncertainty of the measurements and the possibility of improving the testing reproducibility. It was proved that that the ratio of the peak current (I_p) to the charging voltage (U_c) has a good exponential relationship with rising time, although the experimental conditions cannot be exactly the same at each air discharge.

2. The IEC 61000-4-2

The Human Body Model (HBM) pulse that an ESD gun has to produce is depicted in Figure 1, according to IEC 61000-4-2 [24]. The rise time (t_r) of the discharge current is 0.8 ns (±25%), and its amplitude is determined by the ESD gun’s charging voltage. There are four parameters of the ESD current: The rise time (t_r), the peak discharge current (I_p), the current at 30 ns (I₃₀), and the current at 60 ns (I₆₀). These two current values I₃₀ and I₆₀ are determined for a period of 30 ns and 60 ns, respectively, commencing at the time point when the current equals 10% of the peak current, as shown in Figure 1. The limits of these parameters, as shown in

Table 1. Waveform parameters of the ESD current for contact dicharges.

Level	Charging Voltage (kV)	Ip (A)	Accepted Deviation	tr (ns)	Accepted Deviation	I30 (A)	Accepted Deviation	I60 (A)	Accepted Deviation
1	2	7.5	±15%	0.8	±25%	4	±30%	2	±30%
2	4	15				8		4
3	6	22.5				12		6
4	8	30				16		8

, are solely valid for contact discharges.

In the current Standard, the air discharge method is defined as the method where the charged electrode of the test generator moves towards the Equipment under Test (EUT) until it touches the EUT. Additionally, in the case of air discharge testing, the climatic conditions shall be within the following ranges: (a) For the ambient temperature: 15 °C to 35 °C; (b) For the relative humidity: 30% to 60% and (c) For the atmospheric pressure: 86 kPa (860 mbar) to 106 kPa (1060 mbar). Additionally, it defines that during air discharges the ESD generator shall approach the EUT as fast as possible, while the applied charging voltages are the same to the contact discharges, as shown in Table 1, with voltages up to 15 kV.

3. Test Setup

Figure 2 shows the test setup for the measurement of the ESD current from air discharges. Two ESD guns were used, the Schaffner’s NSG-433 and the NSG-438. The target was placed in the center of a metallic grounded plate with dimensions 1.5 × 1.5 m², 70 cm above the ground and it was connected with a 2.5 GHz wide band oscilloscope through a coaxial cable of 50 Ohms. Two charging voltages of 2 kV and 4 kV were applied for each gun. For every charging voltage, twenty measurements of air discharges were conducted.

During the experiment, a high-speed scenario is simulated, since the approach speed is kept constant at around 0.5 m/s. In order for the measurement set-up to be unaffected by surrounding systems, the experiment was conducted in an anechoic chamber. The temperature, the relative humidity and the atmospheric pressure were measured and found in the ranges 21 ± 2 °C, 45 ± 5% and 1000 mbar ± 5%, respectively. The charging voltages for both the two ESD guns were 2 kV and 4 kV.

The pre-charge level can be derived with a very good approximation from the breakdown field between two parallel plates, as shown below [36].

$$V=B·p·d·\left(C+\ln \left(p·d\right)\right)$$

(1)

In (1), B and C are parameters dependent on the composition of the gas, p is the gas pressure, and d is the distance between the plates. For air, B = 365 V/(cm·Torr) and C = 1.18.

It is known that the position of the ground strap affects the falling edge of the current’s waveform. In order to minimize the uncertainty of this fact, the ground strap was at a distance 1 m from the target as the Standard defines and the loop was as large as possible

4. Uncertainty in Measurements

4.1. Short Introduction to Uncertainty

Today it is not only of great importance that the instruments we use to measure can do so correctly, but “how” correctly they measure is also essential. The processes around the subject of measurement have led to the acceptance of a single mechanism for the quantitative assessment of the quality of measurement called uncertainty [42,43,44,45]. Uncertainty is defined as “a parameter associated with the result of a measurement, which characterizes the dispersion of values that could reasonably be attributed to the measured quantity” [43].

The meanings of error and uncertainty are often confused. The term uncertainty is usually compared to the term error, which has long been used to characterize the deviation of a measurement from the true value of the measured quantity. Error is defined as “the difference between the result of a measurement and a true value of the measured quantity”. From the above definition, what should be emphasized is the use of the indefinite article “a”. The reason is that there may be more than one value compatible with the definition of the measured quantity and that we cannot know what the “true” value is. In theory, the true value could only be the result of a perfect ideal measurement. The result of a measurement characterized by negligible uncertainty can be referred to as a “conventional true value”.

From the above, it becomes clear that the error has no particular practical utility since it is based on a deterministic view of things. Thoughtfulness is what prevails in measurements. Error refers to a point (value), while uncertainty refers to a range of values. Figure 3 and Figure 4 further help to clarify the two meanings.

4.2. Calculation of Uncertainties

In general, measurement uncertainty is made up of many components that can be divided into two types based on how they are calculated. Type A uncertainty is assessed using statistical analysis of an observation series, whereas Type B uncertainty is calculated using any available information about the variability of the measured quantity, such as calibration certificates, previous measurements, measuring equipment specifications, the operational procedure, and the subjective judgment of the person performing the measurements [44].

In this work Type A uncertainty is calculated as the repeatability of the measurements, as shown in the following Equation (2):

$$U_A=\frac{S_A}{\sqrt{n_A}}=\sqrt{\frac{1}{n_A\left(n_A-1\right)}{\displaystyle \sum _{i=1}^{n_A}}{\left(x_i-x_m\right)}^2}$$

(2)

where n_A is the number of the air discharges, x_i is the measured value, x_m is the mean value of n_A measurements and s_A is the standard deviation from the mean value.

After the Type A uncertainty calculation, we must proceed with the calculation of Type B uncertainty, knowing the distribution that each source of uncertainty follows and which is given by the following equation:

$$U_B=\sqrt{{\displaystyle \sum _{i=1}^N}{U}_{B_i}^2}=\sqrt{{\displaystyle \sum _{i=1}^N}{\left(\frac{S_{B_i}}{k_i}\right)}^2}$$

(3)

where, s_B is the limit value of source i, and k_i is the coverage factor of the corresponding distribution.

The combined standard uncertainty U_C and the expanded uncertainty U are given by Equations (4) and (5).

$$U_C=\sqrt{U_A^2+U_B^2}$$

(4)

$$U=k{U}_C$$

(5)

The coverage factor k for a coverage probability of 95% is 2.

5. Results and Discussion

5.1. Measurement Results

Figure 5 depicts typical waveforms of air discharges for the two different ESD guns using the experimental setup described before. It is obvious that these two current waveforms differ. The peak current of the NSG-433 gun is higher than the one of NSG-438, with an average value higher than the one of the second gun. This happens because these current waveforms are referred to air discharges, where there is a great difference in the values of t_r and I_p, as can be seen in the following

Table 2. Rise time and peak current measurements for two different ESD guns and for two different charging voltages.

Measurement Number	NSG-433				NSG-438
	+2 kV		+4 kV		+2 kV		+4 kV
	tr (ns)	Ip (A)	tr (ns)	Ip (A)	tr (ns)	Ip (A)	tr (ns)	Ip (A)
1	0.321	13.02	0.745	13.84	0.712	5.75	0.405	14.55
2	0.652	7.75	0.331	22.09	0.546	6.51	0.651	12.25
3	0.263	14.52	0.514	17.09	0.649	6.15	0.688	11.95
4	0.710	7.52	0.899	12.96	0.736	5.65	0.501	13.22
5	0.425	10.52	0.621	14.92	0.569	6.45	0.602	12.75
6	0.795	7.12	0.428	19.23	0.812	5.41	0.897	10.35
7	0.534	9.05	0.736	14.75	0.479	7.02	0.304	16.95
8	0.770	7.22	0.568	16.50	0.726	5.71	0.229	19.61
9	0.812	6.85	0.339	21.05	0.401	7.79	0.235	19.33
10	0.642	8.01	0.632	14.85	0.461	7.23	0.440	14.02
11	0.569	8.65	0.531	16.54	0.527	6.65	0.533	12.69
12	0.628	8.25	0.726	14.82	0.498	6.98	0.510	12.93
13	0.669	7.62	0.667	15.27	0.432	7.52	0.691	11.86
14	0.658	7.65	0.643	14.41	0.358	8.25	0.789	11.08
15	0.519	9.25	0.459	18.05	0.594	6.35	0.582	12.10
16	0.612	8.44	0.549	17.9	0.698	5.85	0.599	11.93
17	0.556	8.94	0.605	15.05	0.512	6.71	0.690	11.89
18	0.435	10.35	0.705	14.85	0.579	6.39	0.612	12.61
19	0.259	14.56	0.639	14.44	0.412	7.67	0.609	12.65
20	0.736	7.25	0.249	29.35	0.615	6.21	0.555	12.28
Average Values	0.578	9.13	0.579	16.90	0.566	6.61	0.556	13.35
Standard deviation	0.166	2.35	0.160	3.78	0.126	0.79	0.172	2.49
Uncertainty Type A	0.037	0.53	0.036	0.85	0.028	0.18	0.038	0.56
Relative Uncertainty Type A (%)	6.433	5.77	6.170	5.00	5.000	2.66	6.898	4.18

. The electric arc in air discharges is very difficult to reproduce in every air discharge, although it was with great effort that we attempted to ensure that the conditions were similar for the two ESD guns from air discharge to air discharge.

In Table 2 below and in Figure 6 and Figure 7, twenty different measurements of the rise time and the peak current for air discharges for the two different ESD guns and for two different charging voltages (+2 kV and +4 kV) are presented. In the same Table, the average values, the standard deviation and the uncertainty (type A) of these measurements are also included.

In the following Figure 8 and Figure 9 the relationship between the peak current to the charging voltage (I_p/U_c) and the rise time for the two different ESD guns and for air discharging are presented. It is obvious that I_p/U_c has a good exponential relationship with rising time, although there are different conditions in the experiment. This proves that I_p, t_r and U_c have a relation independently to the approach speed which is:

$$\frac{I_p}{V_C}{t}_r^a=c$$

(6)

where c is a number depending on the constructional details of the ESD gun and α an index depending on the experimental conditions and the ESD gun type. Making the best fitting exponential curve the measured data of the two ESD guns α = 0.66 and c = 0.0031 for the NSG-433 ESD gun, while for the NSG-438 α = 0.52 and c = 0.0024.

5.2. Uncertainty Calculations

The average values and uncertainty Type A of the peak current (I_p) and the rise time (t_r) are presented in Table 2. The combined standard uncertainty and the expanded uncertainty of I_p and t_r are calculated in

Table 3. Combined Standard Uncertainty for I_p.

	Contributor	Distribution	Value (%)				Devisor	ui (%)				${\mathit{u}}_{\mathit{i}}^2 (\%{)}^2$				Source
			NSG-433		NSG-438			NSG-433		NSG-438		NSG-433		NSG-438
			2 kV	4 kV	2 kV	4 kV		2 kV	4 kV	2 kV	4 kV	2 kV	4 kV	2 kV	4 kV
Type A	Repeatability	Normal	5.77	5.00	2.66	4.18	1	5.77	5.00	2.66	4.18	33.29	25.00	7.08	17.47	Table 2
Type B	Vertical reading of oscilloscope’s indication	Normal	0.82				2	0.41				0.17				Certificate of calibration
	Measuring chain Pellegrini target-attenuator-cable	Normal	1.04				2	0.52				0.27				Certificate of calibration
	Chain to oscilloscope failure	U shaped	1.08				$\sqrt{2}$	0.76				0.58				Certificate of calibration
	Approach to the target	Normal	1.00				2	0.50				0.25				Experience of the Lab
	${\mathit{U}}_{\mathit{C}}^{\mathbf{2}}$											34.56	26.27	7.66	18.74
	Combined Standard Uncertainty UC (%) Equation (4)											5.88	5.13	2.77	4.33
	Expanded Uncertainty (for k = 2) U (%) Equation (5)											11.76	10.26	5.54	8.66

and

Table 4. Combined Standard Uncertainty for t_r.

	Contributor	Distribution	Value (ps)				Devisor	ui (ps)				${\mathit{u}}_{\mathit{i}}^2 (\mathbf{ps}{)}^2$				Source
			NSG-433		NSG-438			NSG-433		NSG-438		NSG-433		NSG-438
			2 kV	4 kV	2 kV	4 kV		2 kV	4 kV	2 kV	4 kV	2 kV	4 kV	2 kV	4 kV
Type A	Repeatability	Normal	37.20	35.74	28.29	38.36	1	37.20	35.74	28.29	38.36	1383.84	1277.35	800.32	1471.49	Table 2
Type B	Peak value reading	Normal	50.00				2	25.00				625.00				Uncertainty of Peak Value 3%
	Time I90 reading	Rectangular	25.00				$\sqrt{3}$	14.43				208.23				Oscilloscope’s sampling rate 20 Gs/s
	Time I10 reading	Rectangular	25.00				$\sqrt{3}$	14.43				208.23				Oscilloscope’s sampling rate 20 Gs/s
	Vertical reading of oscilloscope’s indication	Normal	30.00				2	15.00				225.00				Certificate of Calibration
	Measuring chain cable—Attenuator—Pellegrini target	Normal	30.00				2	15.00				225.00				Certificate of Calibration
	${\mathit{U}}_{\mathit{C}}^{\mathbf{2}}$											2875.3	2768.81	2291.78	2962.95
	Combined Standard Uncertainty UC Equation (4)											53.63	52.62	47.87	54.43
	Expanded Uncertainty (for k = 2) U Equation (5)											107.26	105.24	95.74	108.86

, respectively.

5.3. Results Discussion

The measurement evaluation process heavily relies on the uncertainties. The accuracy of the measurements may be severely compromised, and any argument based on experimentation may suffer if the uncertainty levels are too high. While the parameters that were kept constant (temperature and humidity) were not considered to participate in the uncertainty values, the uncertainty calculation method of ESD current parameters took into consideration some uncertainty sources that may interfere with the results. Special consideration was given to the arc and, therefore, the ESD guns were approaching the target quickly enough as an effort to maintain a modest and constant arc length.

Type B uncertainty has a very small contribution to the overall uncertainty for the peak current. In addition, for the rise time, Type B uncertainty is comparable to the Type A uncertainty. The values of the uncertainties are higher than the ones suggested in [24] for the ESD current parameters. This is not surprising since air discharges (through the arc) cannot be repeated in the same way each time. However, in the previous paragraph and from the measurement analysis, it was found that no matter the charging voltage or the approaching speed, there is a relationship between the rise time and the peak current as it is described in Equation (1) and it is unique for each ESD gun. This improves the reproducibility of the air discharges, and it can be used in further analyses and examinations of the complicated phenomenon of ESD air discharges. Air discharges are used during ESD tests in order to check that the ESD gun produces a proper current waveform; this is a way to make a short verification of the gun. A laboratory technique could be developed during the verification of ESD air discharges ensuring their reproducibility, since there exists a steady relationship between t_r and I_p.

Previous laboratory measurements could be quite helpful. The standard deviation would be less as the number of measurements increases and assuming a normal distribution. Given a normal distribution and an increase in the number of measurements utilizing our measurement system, the standard deviation would decrease as the number of measurements increased. As the overall uncertainty might be reduced even further, measurement data could be given with more assurance.

6. Conclusions

In this work, we dealt with the task of uncertainty calculation of the rise time and the peak current for air discharges and for two different ESD guns. A calculation method of these uncertainties was proposed, taking into consideration two types of uncertainty: Type A and Type B. The proper equipment and experimental setup were also described, helping to capture the current waveform satisfactorily and maintain low levels of uncertainty.

Updated restrictions for the ESD parameters have to be studied, since measuring instruments become faster and the unknown features of the air discharge phenomenon are lowered. It should be considered for future work to lessen the uncertainty, possibly by using a measurement device with a higher bandwidth. Additionally, a correlation between the rise time and the peak current for each ESD gun was found and it could be used in the future reproducibility of ESD guns during air discharges, which could be included in the next IEC revision [24].