Simulation Modelling Practice and Theory 15 (2007) 1089–1102 www.elsevier.com/locate/simpat

Estimation of the electromagnetic field radiating by electrostatic discharges using artificial neural networks L. Ekonomou a, G.P. Fotis

b,*

, T.I. Maris c, P. Liatsis

d

a

Hellenic American University, 12 Kaplanon Str., 106 80 Athens, Greece National Technical University of Athens, School of Electrical and Computer Engineering, High Voltage Laboratory, 9 Iroon Politechniou Street, Zografou, 157 80 Athens, Greece c Technological Educational Institute of Chalkida, Department of Electrical Engineering, 334 40 Psachna Evias, Greece City University, School of Engineering and Mathematical Sciences, Division of Electrical Electronic and Information Engineering, Information and Biomedical Engineering Centre, Northampton Square, London EC1V 0HB, United Kingdom b

d

Received 28 December 2006; received in revised form 11 March 2007; accepted 1 July 2007 Available online 20 July 2007

Abstract An artificial neural network (ANN) model and more specifically a feedforward multilayer network, which uses the powerful backpropagation learning rule, is addressed in order to estimate the electric and magnetic field radiating by electrostatic discharges (ESDs). Plenty of actual measurements, carried out in the High Voltage Laboratory of the National Technical University of Athens are used in training, validation and testing processes. The developed ANN can be a necessary tool for laboratories involved in ESD tests, either facing a lack of suitable measuring equipment or for laboratories which want to compare their own measurements. This is extremely useful for the laboratories involved in the ESD tests according to the current IEC Standard [International Standard IEC 61000-4-2: Electromagnetic Compatibility (EMC), Part 4: Testing and measurement techniques, Section 2: Electrostatic discharge immunity test, Basic EMC Publication, 1995.], since the forthcoming revised version of this Standard will almost certainly include measurements of the radiating electromagnetic field during the verification of the ESD generators. The authors believe that the proposed ANN will be extensively used, since the produced electromagnetic field radiating by electrostatic discharges, can be calculated very easily and accurately by simply measuring the discharge current.  2007 Elsevier B.V. All rights reserved. Keywords: Artificial neural networks (ANN); Electrostatic discharge (ESD); Electromagnetic field; International standard; IEC 61000-4-2

1. Introduction Electrostatic discharge (ESD) is a constant threat for electronic or integrated circuits. Therefore, the International Electrotechnical Committee (IEC) prescribed the standard 61000-4-2 [1] in order to define a procedure, which must be followed immunity the tests on electrical or electronic equipment against electrostatic *

Corresponding author. Tel.: +30 6937748770; fax: +30 210 772 3504. E-mail address: [email protected] (G.P. Fotis).

1569-190X/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2007.07.003

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discharges. However, during these tests an equipment under test (EUT) may pass with one generator and may fail with another for the same charging voltage and for the same discharge current. Similar results can be observed for the same generator as well, since an EUT may pass the test with one orientation of the ESD generator and fail with another. In order to investigate this peculiar fact, the produced electromagnetic field by the ESD generators was measured. Wilson and Ma [2] were the first, who simultaneously measured the current and the electric field during electrostatic discharges at a distance of 1.5 m, using a broadband, TEM horn antenna. Many researchers have conducted measurements of the electromagnetic fields associated with an ESD event. Pommerenke [3] measured the electric and the magnetic field at distances between 0.1 and 1 m, for both air and contact discharges. He found that the magnitude of the magnetic field strongly depends on the 1/R factor (where R is the distance from the point where the ESD occurs). He also found that after a period of decrease, the magnitude of the electric field increases. In [4,5] measurements of the produced electromagnetic field during electrostatic discharge at the calibration setup have been carried out, proving that the field measurement is a challenging task and its results may vary depending on the field probes and the measurement system. Measurements of the radiating magnetic [6] or electric field [7], when the current transducer (Pellegrini target) is mounted on the center of a grounded metal plane proved that different generators produce different electromagnetic fields and also that each individual generator produces different electromagnetic fields depending on its orientation to the EUT. The main conclusion of this work for the radiating electromagnetic field produced by the ESD generators is that the produced electromagnetic field must be also measured during the verification of the ESD generators. It is almost certain that the next revision of the Standard [1] will include measurements of the electromagnetic field, produced by the ESD generators, during the verification. However, these measurements require the use of specific magnetic and electric field sensors, which are extremely complicated in construction and in use and certainly of high cost. In this paper, an artificial neural network (ANN) is addressed in order to estimate the electric and the magnetic field radiating by electrostatic discharges. ANNs have seen increased usage in recent years in various fields such as finance [8,9], medicine [10,11], industry [12,13] and engineering [14–17], due to their computational speed, their ability to handle complex non-linear functions, robustness and great efficiency, even in cases where full information for the studied problems is absent. Actual electromagnetic field measurements, radiated by electrostatic discharges and carried out in the High Voltage Laboratory of the National Technical University of Athens, are used in order to train, validate and test the proposed ANN. The developed ANN can be a necessary tool for laboratories which are facing either a lack of suitable ESD test equipment or for laboratories which want to compare results to their own measurements. The authors believe that the proposed ANN will be broadly useful, since the electromagnetic field produced by electrostatic discharges, can be calculated very easily and accurately by simply measuring the discharge current, during the verification of the ESD generators according to the current Standard [1].

2. The IEC 61000-4-2 According to IEC 61000-4-2 [1] an ESD generator must produce a human body model (HBM) pulse as it is shown in Fig. 1. The pulse of Fig. 1 is divided into two parts: a first peak called the ‘‘initial peak’’, caused by the discharge of the hand, where there is the maximum current and a second peak, which is caused by the discharge of the body. The rise time (tr) of the initial peak is between 0.7 ns and 1 ns and its amplitude depends on the charging voltage of the ESD simulator. According to the specifications of the standard for the verification of ESD generators there are four parameters whose values must be confined by certain limits. These parameters are: the rise time (tr), the maximum discharge current (Imax), the current at 30 ns (I30) and the current at 60 ns (I60). As is shown in Fig. 1 these two current values are calculated for a time period of 30 ns and 60 ns, respectively, starting from the time point, when the current equals to 10% of the maximum current. The limits of these parameters are shown in Table 1 and are valid for contact discharges only.

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Fig. 1. Typical waveform of the output current of the ESD generator [1]. Table 1 Waveform parameters Voltage (kV)

Imax (A)

Rise time (tr) (ns)

Current at 30 ns (A)

Current at 60 ns (A)

2 4 6 8

6.75–8.25 13.50–16.50 20.25–24.75 27.00–33.00

0.7–1 0.7–1 0.7–1 0.7–1

2.8–5.2 5.6–10.4 8.4–15.6 11.2–20.8

1.4–2.6 2.8–5.2 4.2–7.8 5.6–10.4

3. Measurement system 3.1. Experimental setup The experimental setups for the measurement of the magnetic field and the electric field are shown in Figs. 2 and 3, respectively. The current and field (electric or magnetic) produced by contact discharges for various charging voltage levels were measured simultaneously, by the 4-channel Tektronix oscilloscope model TDS 7254B, whose bandwidth ranges from dc to 2.5 GHz. The ESD generators used were the NSG-433 and the NSG-438 of Schaffner. The positioning of the high voltage cable was kept constant during the experimental procedure. In order for the current to be measured, a resistive load was used, as the IEC [1] defines and it was placed on the center of a 1.5 m · 1.5 m horizontal metal plane, which was placed 70 cm above the ground. The sensors that were used for the experiment were ground based field sensors with active integration developed by Pommerenke [18]. They were placed at various distances (20, 35, 50 and 65 cm) from the discharge point on the metal plane and in three perpendicular directions (direction A, direction C and direction D) as it can be seen in Fig. 4. Measurements in direction B were not conducted due to the interference of the ground strap of the ESD generator. 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 on the measurement of the magnetic field, the ground strap was at a distance of 1 m from the target as defined in [1] and the loop was as large as possible. 3.2. Experimental results Figs. 5 and 6 depict representative H-field and E-field waveforms in relation to the discharge current for the first 200 ns, respectively, when the field sensors are placed at a distance of 20 cm from the discharge point in direction A.

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Fig. 2. Experimental setup for the measurement of the magnetic field.

Figs. 7 and 8 depict the peak H-field and E-field, respectively, for charging voltage of +2 kV in direction A for the NSG-438 ESD generator. It is obvious that each generator produces different electromagnetic field. Figs. 9 and 10 show the comparison between the peaks of the absolute value of the magnetic field and for the electric field for all three directions proving that the produced electromagnetic field differs depending on the orientation of the ESD generator. 4. Artificial neural networks Artificial neural networks also known as neurocomputers, parallel distributed processors or connectionist models are devices that process information. The main purpose of ANNs is to improve the capability of computers to make decisions in a way similar to the human brain and in which standard computers are unsuitable [19]. ANNs typically consist of a large number of processing elements called neurons or nodes bonded with weighted connections. A single neuron by itself usually cannot predict functions or manage to process different types of information. This is because an ANN gains its power from its massively parallel structure and interconnected weights. There are plenty of ANN architectures that have been proposed, but the most popular and effective is the architecture called feedforward multilayer network. Feedforward is called because all the connections either go from the input layer to the output layer, from the input layer to the hidden layer, or from the hidden layer to the output layer [20]. An example of a feedforward multilayer network is shown in Fig. 11 and consists of three main layers. The output layer corresponds to the final output of the neural network. The external inputs are presented to the network through the input neurons. Finally, there are the hidden layers, where the outputs of a hidden layer are the inputs to the following layer.

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Fig. 3. Experimental setup for the measurement of the electric field.

ANNs have the ability of learning by adaptively adjusting their weights using a training algorithm. Ideally, the learning process will adjust the weights of the ANN such that when a given input is presented to the network, the desired output is produced. The learning process starts by presenting the inputs to the network. The set of all the training data is called the training set. The weights are adjusted and the network is expected to produce a particular output for each input. The sum of all weighted inputs represents the neuron transfer function. The set of the desired outputs is called the target set. Each presentation of the training set to the network is called an iteration or epoch. One of the most popular and powerful learning algorithms used to train feedforward multilayer networks is the backpropagation [21]. The algorithm has two phases, the forward phase and the backward phase. In the forward phase, the input data are presented to the network and the outputs of the hidden layer are given as inputs to the proceeding layer. This process is continued until the final output is computed. In the backward phase, the error signal is calculated and propagated backwards to adjust the weights such that the sum of the squared error is minimized. The mathematical complexity and the time requirements of the algorithm increase by increasing the number of neurons in the hidden layers. Thus, each ANN is determined according to its architecture, the transfer function and the learning algorithm [22]. 5. Design of the proposed ANN The goal of this work is to develop an ANN capable of accurately estimating the electric and magnetic fields radiated by ESD generators. A feedforward multilayer network and the backpropagation learning algorithm

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Fig. 4. The measurement points where the field sensors were placed.

Fig. 5. ESD current and H-field for the NSG-438 ESD generator at 20 cm from the discharge point, in direction A (charging voltage = +2 kV).

have been selected for this purpose. Seven parameters that play an important role in the estimation of the electric and magnetic field radiating by electrostatic discharges are considered as the inputs to the neural network, while as outputs the peak value of the electric and the peak value of the magnetic field are considered. These data, which are presented in Table 2, constitute actual data recorded during measurements carried out in the

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Fig. 6. ESD current and E-field for the NSG-438 ESD generator at 20 cm from the discharge point, in direction A (charging voltage = +2 kV).

Fig. 7. Peak of H-field for various distances from the discharge point in direction A, using the NSG-433 and NSG-438 ESD generators.

High Voltage Laboratory of the National Technical University of Athens [6,7], using the method and the measurement system presented in Section 3. More specifically several hundreds of measurements have been performed using the two different already mentioned ESD generators, i.e. the NSG-433 and the NSG-438 produced by Schaffner. This extensive number of measurements is due to the many parameters. The input parameters were: the generator’s charging voltage (U) (±2, ±4, ±6, and ±8 kV), the distances (d) from the discharge point on the metal plane (20, 35, 50, and

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Fig. 8. Peak of E-field for various distances from the discharge point in direction A, using the NSG-433 and NSG-438 ESD generators.

Fig. 9. Peak of H-field for the NSG-433 ESD generator for three perpendicular directions on the horizontal plane (charging voltage = +2 kV).

65 cm), the three perpendicular directions (dir) (direction A, direction C, direction D) (Fig. 4) and the current waveform parameters which are the rise time (tr), maximum discharge current (Imax), current at 30 ns (I30) and current at 60 ns (I60), where their different values are presented in Table 1. The output parameters of the ANN were the peak value of electric field (Emax) and the peak value of magnetic field (Hmax). These several hundreds of measurements, for each one of the two generators, constitute combinations of all the above parameters.

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Fig. 10. Peak of E-field for the NSG-433 ESD generator for three perpendicular directions on the horizontal plane (charging voltage = +2 kV).

Σ

f

Σ

f

Σ

f

Σ

f

Σ

f

Σ

f

Σ

f

Σ

f

Σ f Input neurons of source First hidden nodes layer

Second hidden layer

Layer of output neurons

Fig. 11. An example of a feedforward multilayer network.

Table 2 Artificial neural network architectures Input variables – – – – – – –

Charging voltage (U) Rise time (tr) Maximum discharge current (Imax) Current at 30 ns (I30) Current at 60 ns (I60) Distance (d) Direction (dir)

Output variables – Peak value of the electric field (Emax) – Peak value of the magnetic field (Hmax)

The structure of the developed network i.e. the number of hidden layers and the number of nodes in each hidden layer, was decided by trying several varied combinations in order to select the structure with the best generalizing ability amongst the all tried combinations, considering that one hidden layer is adequate to distinguish input data that are linearly separable, whereas extra layers can accomplish non-linear separations [23,24]. This approach was followed in this work, since the selection of an optimal number of hidden layers

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and nodes for a feedforward network is still an open issue, although several papers have been published in these areas. As it is mentioned earlier each ANN is also determined according to the transfer function and the learning algorithm that it uses. In this work three different transfer functions (the hyperbolic tangent sigmoid, the logarithmic sigmoid and the hard limit) and three different training functions of the backpropagation learning algorithm (the Gradient Descent, the Gradient Descent Momentum with an Adaptive Learning Rate and the Levenberg–Marquardt), were examined in order to be selected this one, that contributes to the best ANN’s generalizing ability. 6. Training, validation and testing processes The proposed ANN was trained using the MATLAB Neural Network Toolbox [25]. 2304 of each input and output data, were used to train and validate the artificial neural network. These data refer to measurements conducted with both ESD generators (NSG-433 and NSG-438), in every possible combination of: (a) generator’s charging voltage (8 different charging voltages), (b) distance from the discharge point on the metal plane (4 different distances), (c) perpendicular direction (3 different directions) and (d) current waveform parameters (12 different sets of current waveform parameters). In each training iteration, 20% of random data (431 data sets) were removed from the training set and a validation error was calculated for these data. The training process was repeated until a root mean square error between the actual outputs (peak value of electric field, peak value of magnetic field) and the desired outputs reach the goal of 0.5% or a maximum number of epochs (it was set to 15,000), is accomplished. Finally, the estimated values of the electric and magnetic fields were checked with the values obtained from situations encountered in the training, i.e. the 2304 values, and others which have not been encountered (additional sets of input and output data, except the 2304, were used). It must be mentioned that although in [26] it is proved that any non-linear function can be approximated by a feedforward neural network with one hidden layer without any minimum convergence time guarantee, in this work ANNs with more than one hidden layers are examined to study the convergence rate for the particular problem of the electric and magnetic estimation. In order to be found the best architecture for the network (i.e. the backpropagation training function, the transfer function, the number of hidden layers and the number of neurons in the hidden layers that give the minimum root mean squared error [27]), a feedforward multilayer network has been used, each one of the three different training functions and transfer functions were tried and sets of scenarios were taken with inner change of hidden layers (1, 2, 3 or 4) and number of neurons in each hidden layer (2–30). After extensive simulations with all possible combinations of the 3 training functions, the 3 transfer functions, the 1–4 hidden layers and the 2–30 neurons in each hidden layer it was found that the ANN with 2 hidden layers, with 19 and 14 neurons in each one of them, with the Levenberg–Marquardt training function and the hyperbolic tangent sigmoid transfer function has presented the best generalizing ability, had a compact structure, a fast training process and consumed lower memory than all the other tried combinations. The mean square error was minimized to the final value of 0.005 within 12,767 epochs. Table 3 presents the training data of the best 10 designed ANN models which have presented the best generalizing ability among all the others designed. Table 3 Training data of designed ANN models Number

Structure

Training function

Transfer function

Epochs

Train error

Validation error (%)

1 2 3 4 5 6 7 8 9 10

7/19/14/2 7/12/23/2 7/11/8/15/2 7/6/21/19/2 7/23/14/9/2 7/17/28/21/2 7/13/20/2 7/24/16/2 7/18/12/2 7/21/26/10/2

Leven.–Marq. Leven.–Marq. Gr. des. m. ad. l. Grad. descent Grad. descent Grad. descent Leven.–Marq. Leven.–Marq. Gr. des. m. ad. l. Gr. des. m. ad. l.

Hyp. tang. sigm. Log. sigm. Log. sigm. Hyp. tang. sigm. Log. sigm. Log. sigm. Hard limit Log. sigm. Log. sigm. Hyp. tang. sigm.

12,767 15,000 13,391 15,000 14,501 15,000 15,000 15,000 12,733 15,000

0.005 0.008 0.005 0.006 0.005 0.013 0.018 0.009 0.005 0.021

5.437 6.922 10.065 9.753 8.376 11.343 20.837 11.838 12.291 23.620

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7. Results The trained ANN for the estimation of the electric and magnetic field radiating by electrostatic discharges have been applied to forty-eight different case studies (different charging voltage of the generator, distance from the discharge point on the metal plane, direction in which the measurement is conducted and current waveform parameters), which were not part in the training, validation and testing processes and are shown in Table 4. Table 4 Measured electric and magnetic field versus artificial neural network’s results Number

Varying parameters U (kV)

tr (ns)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

+2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 +2 2 2 2 2 2 2 2 2 2 2 2 2 +4 +4 +4 +4 +4 +4 +4 +4 +4 +4 +4 +4 4 4 4 4 4 4 4 4 4 4 4 4

0.73 0.79 0.75 0.76 0.79 0.78 0.81 0.77 0.74 0.71 0.70 0.72 0.71 0.79 0.73 0.74 0.75 0.76 0.72 0.71 0.70 0.73 0.74 0.76 0.72 0.70 0.71 0.73 0.71 0.70 0.71 0.72 0.70 0.73 0.71 0.70 0.71 0.71 0.72 0.75 0.76 0.73 0.72 0.71 0.72 0.74 0.75 0.76

Emax (kV/m) Imax (A)

I30 (A)

I60 (A)

7.02 6.99 6.87 7.13 7.30 7.19 7.22 7.21 7.35 7.41 7.27 7.09 7.03 7.02 7.03 7.06 7.09 7.12 7.13 7.15 7.09 7.06 7.09 6.95 14.62 14.78 14.73 14.69 14.75 14.79 14.76 14.82 14.84 14.90 14.75 14.71 14.69 15.42 14.73 14.75 14.70 14.52 14.80 14.99 14.67 14.70 14.91 14.93

3.69 3.72 3.65 3.68 3.72 3.91 3.65 3.98 3.76 3.59 3.66 3.69 3.72 3.85 3.65 3.93 3.82 3.91 3.94 3.99 4.02 3.96 3.97 3.85 6.88 6.79 6.78 6.55 6.81 7.06 7.15 6.98 6.31 6.64 6.91 6.76 7.52 7.26 7.30 7.13 7.01 7.28 7.39 7.19 7.15 7.19 7.32 7.44

2.46 2.49 2.43 2.41 2.58 2.51 2.46 2.38 2.35 2.46 2.42 2.41 2.52 2.49 2.43 2.41 2.49 2.46 2.41 2.43 2.41 2.35 2.34 2.33 5.33 5.14 6.06 5.54 5.09 5.14 5.65 5.18 5.66 5.47 5.78 5.41 5.81 5.14 5.66 5.59 6.05 5.96 5.76 5.48 6.06 5.97 5.69 5.99

d (cm)

D

Measured

20 35 50 65 20 35 50 65 20 35 50 65 20 35 50 65 20 35 50 65 20 35 50 65 20 35 50 65 20 35 50 65 20 35 50 65 20 35 50 65 20 35 50 65 20 35 50 65

A A A A C C C C D D D D A A A A C C C C D D D D A A A A C C C C D D D D A A A A C C C C D D D D

5.19 4.10 2.40 2.32 5.12 3.49 2.39 2.60 5.67 4.04 3.07 3.54 5.98 4.09 2.64 5.84 3.33 2.30 2.50 5.89 4.03 2.94 3.41 2.74 11.60 7.28 4.80 4.61 9.61 6.56 4.73 5.21 10.67 7.45 5.42 6.19 12.38 8.31 5.12 4.12 12.07 6.17 4.57 4.77 12.12 7.63 5.45 7.41

Hmax (A/m) ANN 5.61 4.49 2.31 2.55 5.72 3.59 2.21 2.44 5.99 4.19 3.16 3.69 6.13 3.95 2.41 6.19 3.02 2.06 2.31 6.19 4.23 3.15 3.21 2.56 12.51 7.35 4.59 4.55 9.75 6.73 4.93 5.35 11.25 7.95 5.95 6.03 11.45 8.59 5.03 4.25 12.47 6.75 4.19 4.75 12.95 7.95 5.55 7.55

Measured 2.61 2.05 1.32 1.33 2.91 1.62 1.37 0.98 2.76 1.62 1.63 1.02 2.85 1.79 1.21 1.02 2.93 1.82 1.28 1.06 2.97 2.11 1.47 1.24 3.32 2.96 2.31 2.55 3.44 2.79 2.35 1.68 3.34 3.08 2.67 2.00 3.31 2.89 2.27 2.80 3.36 2.82 2.26 1.52 3.29 2.82 2.64 2.10

ANN 2.85 2.23 1.49 1.29 2.99 1.69 1.22 0.76 2.93 1.75 1.44 1.25 3.05 1.62 1.03 1.23 3.14 1.71 1.13 1.25 3.15 2.31 1.32 1.02 3.86 2.99 2.13 2.40 3.58 2.95 2.56 1.95 3.96 3.48 2.95 1.90 3.05 2.97 2.10 2.95 3.59 2.99 2.09 1.50 3.56 2.90 2.77 2.25

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Relative error between measured and calculated Hmax values 25.00%

Relative error (%)

20.00% 15.00% 10.00% 5.00% 0.00% -5.00% 0

10

20

30

40

50

-10.00% -15.00% -20.00% -25.00% Number of data set

Fig. 12. Relative error for the Hmax between measured and calculated using the ANN values.

Relative error between measured and calculated Emax values 15.00%

Relative error (%)

10.00% 5.00% 0.00% 0

10

20

30

40

50

-5.00% -10.00% -15.00% Number of data set

Fig. 13. Relative error for the Emax between measured and calculated using the ANN values.

Histogram of the relative error for Hmax 25.00%

Relative error (%)

20.00% 15.00% 10.00% 5.00% 0.00% -5.00% 1

4

7

10 13 16 19 22 25 28 31 34 37 40 43 46

-10.00% -15.00% -20.00% -25.00% Data set

Fig. 14. Histogram of the relative error between actual measured and ANN’s results for the Hmax. (The mean value is 3% and the deviation is 1%).

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Histogram of relative error for the Emax

Relative error (%)

15.00% 10.00% 5.00% 0.00% -5.00%

1

4

7

10 13 16 19 22 25 28 31 34 37 40 43 46

-10.00% -15.00% Data set Fig. 15. Histogram of the relative error between actual measured and ANN’s results for the Emax. (The mean value is deviation is 0%).

1% and the

The produced ANN results, which are presented in Table 4, have been compared to actual values of electric and magnetic field (which are also presented in Table 4), measured during experiments performed in the N.T.U.A.’s High Voltage Laboratory for exactly the same parameters. The results obtained using the proposed ANN are very close to the actual measured ones, something which clearly implies that the proposed ANN method is well working and has an acceptable accuracy, since the measured maximum electric and magnetic field strengths are close enough to these calculated by the designed ANN model. Figs. 12 and 13 present the percentage error between actual measured and ANN’s results. In Figs. 14 and 15 histograms of the relative error between actual measured and ANN’s results for the (Hmax) and (Emax) are presented. It must be mentioned that the developed ANN can be applied without restriction to any commercial available ESD generator by just measuring the ESD current during the verification of the ESD generators. The developed ANN will be a useful tool for all the laboratories involved in ESD tests, since they will be able to conduct the verification of the ESD generators by simply measuring the ESD current. The produced electromagnetic field, which will be included in the next revision of the Standard [1] will be calculated by the proposed ANN. 8. Conclusions In this paper, an artificial neural network (ANN) is addressed in order to estimate the electric and magnetic field radiating by electrostatic discharges. The results of the developed ANN model proved its accuracy, since they are very close to the actual measured ones, something which clearly implies that the proposed ANN method is well working. With the proposed ANN method, the produced electromagnetic field radiating by electrostatic discharges, can be calculated easily and accurately by measuring the discharge current. This will be extremely useful for the laboratories involved in the ESD tests since they will be able to conduct the verification of the ESD generators, after the revision of the current Standard in which measurements of the electromagnetic field will be compulsory. Acknowledgement The authors thank Professor David Pommerenke of the Missouri-Rolla University in the USA for the field sensors he lent to them in order to measure the electric and the magnetic field. References [1] International Standard IEC 61000-4-2: Electromagnetic Compatibility (EMC), Part 4: Testing and measurement techniques, Section 2: Electrostatic discharge immunity test, Basic EMC Publication, 1995.

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