NUMERICAL CALCULATION OF ESD

Transcription

1 NUMRICAL CALCULATION OF SD R. Jobava D. Karkashadze R. Zaridze Ph. Shubitidze D. Pommerenke M. Aidam Tbilisi State University Republik of Georgia Technical University Berlin Germany tel: fax: insteinufer 11, Berlin Technical University Munich Germany Abstract A non linear time domain method of moments algorithm is presented. It allows the calculation of transient fields of SD from bodies of revolution. The arc is taken into account. Results are validated by measurement of currents and fields. Transient field data are presented in a form to enhance the understanding of the process of SD and are applied to a problem of in-circuit coupling. 1 Introduction Transient fields of SD cause malfunctions in electronics. To determine the severeness of SD, numerical calculation methods are very helpful [4,9,2]. Such methods can be used to determine' the coupling into a circuit or the penetration of fields through a slot [6,7,8,9]. To predict possible malfunctions the transient fields must be known in the near and the far zone. A numerical calculation must take into account all important parameters of SD, such as: - Geometry of the structure, - Charging voltage and the voltagekapacitance change due to the approach, - arc length in the moment of discharge. Actual SD involves an arc. Due to the dominant influence of the arc length on the current rise [4] the modelling must include the arc. This can be done only in the time domain. Presently, the only SD field calculation method which includes an arc model is limited to thin wire dipole like structures [4]. Most real structures are voluminous. As the radiation of a voluminous object is by far more intense, such structures were investigated. The paper is structured the following way: Section two provides a general picture of the method used. The validation of the results is shown in section 3. Section 4 presents results for the near and the far field. An application to an MC problem is given in section Numerical method Different methods can be used for time-domain field calculation; such as: - Finite differences time domain FDTD - Transmission line method TLM - Method of moments MOM The main advantage of the MOM is the fast calculation and the small amount of memory needed. This is due to the fact that only the surface needs to be discretisized. The electromagnetic fields of a voluminous body can be obtained from the tangential fields on its surface by integration. The surface fields obey the integral equation for magnetic field MFI or the integral equation for electric field FI [ 10,13,11,12,14]. These equations can be solved numerically. For voluminous objects the MFI is advantageous [14,11]. To perform the numerical integration, the surface of the body is divided into patches. A constant field value on each patch is used in the calculation for simplification. The values are determined by the incident field and the properties of the body. In fig. 1 the geometry of the problem solved is described. OSISD SYMPOSIUM

2 Fig. 1: w spheroid 50 mm x 310 mm semi axes v$ first patch arc length mm ground plane I. Geometiy used: Spheroid of 31 cm x 5 cm semiaxes discharging to a groundedplane. For the solution of the integral equations a technique proposed by Bennett, Miller and others [ 1 1,12,13,I4,15] was used. This method is based on the fact that waves propagate with a finite speed. If the timelspace step and the patch size are well chosen, fields can be expressed by current values of the surrounding patches which already have been calculated [1,12,13], i.e. a time step algorithm can be programmed. The coupling of the arc to the body is done the following way: A channel with a time-dependent conductivity o(t) in the gap is assumed. Therefore we have to use: T(t) = o(t) (sey(t) + I?bbody(t)) in the channel and body size. But the electric field in the gap must be known accurately as the highly non linear arc current depends on its value due to the ionization processes modelled. 3 Validation of the alaorithm The program was tested the following ways: - Field inside the body Inside the perfectly conducting body the field should be zero. - Literature data The MFI algorithm was compared to literature data (linear scattering problems) [12,16] and to analytical results for a spheroid [ Static value It was tested if the calculated electric field approaches the negative value of the electrostatic field for long calculation times. - Measured data Currents and fields were compared to measured data. 3.1 Current compared to measurement While the current on the body can hardly be measured, the discharge current can. Measured data compared to calculations show the usability of the method, fig. 2 MFI on the surface of the spheroid. Where sey is the electric field in the spark channel caused by the spark current and body is the electric field in the channel caused by the currents on the discharging body. The arc models by Rompe and Weizel [ 181 and the model by Mesyats [ 191 are usable for SD as they can reproduce the influence of the arc length on the current rise [4]. Presently our algorithm is limited to perfectly conducting bodies of revolution. Tested geometries are the spheroid shown in fig. 1, a cone with a semi-sphere cap and a cylinder with two semi-sphere caps. The coupling between the arc and the body is the most critical part. This is due to the small gap. The gap size is only 1/1000 of the OS/SD SYMPOSIUM Y Y I- I Simul. U , I time [ns] J I

3 Fig. 2: Discharge current of the spheroid for 5 kv at different arc lengths compared to measurement, spheroid, 31 x 5 cm semiaxes, current measured with approx. 4 GHz bandwidth. The current changes from approx. 18 A to more than 50 A if the arc length is reduced in spite of the same initial voltage. Greater deviations between the measured and the calculated currents can be seen for longer arc lengths. This is due to the arc model by Rompe and Weizel [4]: The arc resistance drop is computed faster than it happens in reality for arc lengths close to the static breakdown distance given by Paschen s law [ 181. Severeness of disturbances is often not directly related to the current. Radiation and induction relate to current derivative. Therefore, an algorithm must be able to calculate the current derivative with sufficient accuracy to be usable for MC behaviour prediction. Results for current derivatives are shown in fig. 3. In general, the influence of the arc length can be reproduced by the numerical method. The differences between the measured and the calculated results are rather small compared to the overall changes. The results are suitable to access the thread of disturbances by SD. As shown in [4], the deviations at shorter arc lengths are due to of the arc model used. 3.2 Calculated fields compared to measurement From the current distribution on the body the transient fields can be calculated using integral equations [14]. Results were compared to measurements for the near and the far field, figs. 4 and I 1 : : : : : :... : >..: :. : : d 5 10 time [ns] I Fig. 3: arc length [mm] Measured peak discharge current derivative as a function of arc length for the spheroid compared to computed results. Currents measured using approx. 4 GHz bandwidth. The influence of arc length on the current derivative for constant voltage is by far greater than the influence on the current shown in fig. 2. The peak derivative values change from approx. 10 A/ns at 2.7 mm arc length and 10 kv to more than 1000 A/ns at 0.6 mm arc length. This variation happens in spite of the same voltage. It shows that the risk of a disturbance by SD can not be accessed by the charging voltage as often done Fig. 4: Magnetic field at 0.1 m distance caused by the SD of the spheroid to the ground plane. The fields were measured on the ground plane by B- dot sensors [3]. A: 10 kk 1.2 mm arc length, measurement B: IO kv, 1.2 mm arc length, calculation C: 5 kv, 0.7 mm arc length, measurement D: 5 kv, 0.7 mm arc length, calculation The calculation matches the measured fields in the near field. Field strengths reach 120 A/m at 10 kv for an arc length of 0.7 mm. Measured current risetimes where (bandwidth: 4 GHz): 10 kv 0.7 mm ns (system limit) 10 kv ns 10 kv 2.7 4ns 5 kv 0.3 mm 0.1 ns (system limit) 5 kv 0.6 mm 0.4 ns 5 kv 1.1 mm 2.5 ns Table 1: Measured current risetimes of the spheorid OS/SD SYMPOSIUM

4 Fig. 5: time [ns] Magnetic field at 1.2 m distance caused by the SD of the spheroid to the groundplane. A: IO kv, 1.2 mm arc length, measurement B: 10 kv, 1.2 mm arc length, calculation C: 5 kv, 0.7 mm arc length, measurement D: 5 kv, 0.7 mm arc length, calculation At a distance of 1.2 m the field strength still reaches 7 Alm for 10 kv and 3 Alm for 5 kv. Up to the first zero crossing the calculation matches the measurement very well. In contrast to real arc behaviour, the arc model used gives a monotone drop of the arc resistance with lime. This is the cause of the reduced accuracy of the calculation after the first current zero crossing. For MC application this is acceptable, as the highest peak values and derivative values are reached during the first impulse. As shown in fig. 2, the calculated currents at arc lengths close to Paschen's value are larger than in reality. This causes a similar effect for the transient fields, fig. 6. It could be avoided by a better arc model n 4 g o L esults 4.1 Near fields 4nalysing the spatial fields at different time steps helps to 1 inderstand important aspects during SDs e.g. near and far zone. Lines of constant magnetic field are shown in fig. 7: t = 1.7ns spheroid 30 x 5 cm semi axes i 0.1 ground plane m t = 5.lns m t = 8.511s Fig. 6: time [ns] Magnetic field at 1.2 m distance from the SD of the spheroid on the groundplane. A: 10 kv, 2.7 mm arc length, calculation B: IO kv, 2.7 mm arc length, measurement I 0.1 I OS/SD SYMPOSIUM m

5 Fig. 7: Lines of constant magneticfield during the SD of the spheroid at 10 kv and 1.2 mm arc length. Values given in A/m. At 1.7 ns the initial current wave has travelled approx. 75 % of the spheroid's length. Close to the arc the field strength reaches 46.4 A/m. At 5.1 ns the initial wave and a wave which has been caused by the reflection at the top of the spheroid superimpose causing the complex field structure shown. Proceeding on to 8.5 ns two wave fronts can be seen. The initial wave front has left the near field. The sign of the magnetic near field has changed due to the reversed current, A second wave front will be radiated soon. Although waves are radiated at every spot of the spheroid, a simplified but educational picture can be visualised by assuming just spherical waves radiated at the mayor geometric discontinuities: One radiated at the arc, the second one radiated at the top and a third radiated at the lower end of the mirror body (substituting the ground plane by a mirror body of the spheroid). The spatial field is separated into two regions: near field In the near field the field strength values are high. The field structure is complex due to superposition of radiated energy capacitively and inductively stored energy and energy which travels back to the object. The electric and the magnetic fields arc neither perpendicular nor is the ratio of theii magnitudes 377 Ohm as in the far field. far field In the far field radiated field components dominate The waves are spherical and their magnitudes drol by l/r. 4.2 Far field Results for the far field are shown in fig. 8: Fig. 8: Radiated magnetic fields at a distance of 10 m for 5 kv and 0.3 mm arc length for dflerent azimuth angles. With decreasing angle the following changes can be seen:. The plateau seen at 90" is caused by the upwards travelling current on the spheroid. The current derivative at the current front stays roughly constant until it reaches the top. The reflection at the top reduces the current derivative value due to radiation. The negative plateau has a lower value and double the length because of the virtual mirror body. At an angle of 10" two distinct peaks can be seen. The delay is 4.3 ns which is close to double the length of the spheroid. The first is caused by the wave front initiated at the arc. This wavefront reaches the observer nearly at the same time as the radiated wavefront from the top of the spheroid (Both wavefionts travel at the speed of the light upwards.) The second peak is caused by a wavefront radiated at the lower end of the mirror body. The highest peak values are not reached on the ground plane but at approx. 30". This effects circuits in a similar way as shown in figs. 10 and 11. From frequency domain it is known that electrical long antennas radiate more energy in the longitudinal direction with rising frequency. The equivalent effect in the time domain is the change of the waveform with decreasing angle. The short peaks at low angles contain more high frequency components. OSlSO SYMPOSlUM

6 5 MC - Application Once the transient fields are calculated, they can be used to investigate coupling, - into circuits, - into shielded cables, - and through slots. As an example, the coupling into a digital circuit was modelled by coupling the transient field program and SPIC. To demonstrate the possibilities of the algorithm two examples are given. Let us consider a CMOS gate input connected to a small loop placed at some distance on or above the grounc! plane. The fields induce a voltage in the loop. The voltage may disturb the circuit. As model the equivalent circuit shown in fig. 9 was used: +... PCB IC I 5v L! R Dl t Q Cgate Vind Slow CMOS circuit To model a slow CMOS circuit the following parameter values were chosen: Parameter set 1: L: 100 nh R: 200 Ohm D1 D2: spice model for ideal pn diodes Cgate: 9 PF Area: 30 mm x 30 mm rror threshold: 2.5 V at Cgate The inductance, the resistance and the input capacitance form a low pass filter with a cut-off frequency of 120 MHZ. Results for 5 kv and two different arc lengths are shown in fig. 10: - Y $ 0.8 z disturbed area, 0.3 mm arc length Fig. 9: quivalent circuit for a CMOS input coupled to a loop distance [m] Parameters are: Vind: Induced voltage calculated by: cfid = Area po. dh( t) I dt Where H(t) is the magnetic field at the point where the circuit is placed. L: Loop inductance. Fig. 10: Circuit positions at which the discharge of the spheroid at 5 kv would cause an error for the circuit shown in fig. 9 with parameterset 1. Results are for two different arc lengths: 1.1 mm: Slow rising currenbrisetime table mm: Fast rising current, risetime table 1 R: Resistance of the protection network. The disturbed volume increases with shorter arc length. Furthermore, its shape changes. As indicated in fig. 8, the D1 D2:Diodes of the protection network. disturbances caused by faster rising currents expand Cgate: Capacitance of the input gates. further at an angle of approx. 30, than on the ground The parameter values are given in the corresponding plane at 90". This spatial distribution is caused by the graphics. currents on the body. Thus, fields of SD can not be understood by just taking the arc as a radiation source. Two differently fast reacting circuits were modelled. Only a rough picture can be obtained from such an assumption OS/SD SYMPOSIUM

7 The slow rising current does not contain as much high frequency components. The spatial distribution of the disturbances is more similar to a spheroid centred at the arc. 5.2 Fast CMOS circuit The second parameter set was chosen such that the circuit is by far more sensitive to high frequency components. As usual in fast 3V CMOS the error threshold was set to 1.5 V. The loop size was reduced as it is usual in very compact fast circuits. Parameter set 2: L: 20 nh R: 200 Ohm DI D2: Cgate: Area: rror threshold: spice model for ideal pn diodes 1.5 pf 10 mm x 10 mm 1.5 V at Cgate The inductance, the resistance and the input capacitance form a low pass filter with a cut-off frequency of 700 MHz. As shown in fig. 11 the fast circuit behaves quite differently. If one compares figs. 10 and 11 it can be seen that the influence of current risetime on the disturbances is much greater for the fast circuit. This is even more pronounced if it is remembered that field strengths and their derivatives in time do not increase linearly in proximity to the object (see fig. 7). Based on these results it can be argued that for high speed electronic equipment it may be necessary to do SD tests with impulses rising faster than the 0.7 ns required by the IC test standard. This way it is possible to avoid disturbances by fast rising SD, which typically occur at low voltages or in dry conditions. Conclusion The highly non linear process of an SD of a body of revolution can be calculated by the electrodynamic method shown. Results are in good agreement with experimental data. The transient fields can be used to calculate circuit behaviour, shielding and coupling. Further work will emphasise on improved arc-body coupling and on lossy objects U 0 3 v) I -1, * I disturbed area, 1.1 mm arc length disturbed area, 0.3 mm arc length distance [m] Fig. 11: Circuit positions at which the discharge of the spheroid at 5 kv would cause an error for the circuit shown in fig. 9 with parameterset 1. Results are for two diferent arc lengths: 1.1 mm: Slow rising current, risetime see tab mm: Fast rising current, risetime see tab Acknowledaement We want to thank the Volkswagen Foundation for sponsoring this work. References P.. Wilson, A.R. Ondrejka, M.T. Ma, J.M. Ladbury, 'lectromagnetic fields radiated from SD, theory and experiment', NBS Technical Note 1314, 1988 S. Ishigami, I. Yokoshima, 'Measurements of fast transient electric fields in the vicinity of short gap discharges', MC'94, Sendai Japan, 1994, pp D. Pommerenke, 'SD: transient fields, arc simulation and rise time limit', Journal of lectrostatics 36 (1995), pp R. Zaridze, D. Karkashadze, R.G. Djobava, D. Pommerenke, M. Aidam, 'Calculation and measurement of transient fields from voluminous objects', OSSD Symp. 1995, pp M. Angeli,. Cardelli, 'Analysis of the SD current diffusion of SD current in non perfectly conducting metallic plates' Int. Symp. on MC, Sep , 1994, Rome, Italy OS/SD SYMPOSIUM

8 [7] G. Cerri, R. De Leo, V. Mariani Primiani, 'SD coupling between microstrip lines', Int. Zuerich Symp. on MC, 1995, pp [8] F. Hirtenfelder, S. Rwakasenyi, 13.S. Brown, 'Analysis of electrostatic discharge of a printed circuit board using the finite element time domain technique', Int. Zuerich Symp. on MC, 1995, pp [9] G. Cerri, R. De Leo, V.M. Primiani, M. Righetti, 'Field penetration into metallic enclosures through slots excited by SD', I Trans. on MC, Vol. 36, No.2, May 1994, pp [lo] M. Rizvi, J. LoVetri, 'SD source modelling in FDTD', Proc. I Intl. Symp. on :MC, 1994, pp [ 1 11 C.L. Bennett, 'Time domain inverse scattering', I Trans. Antennas Propagat. Vol. AP-29, pp , 1981 [ 121 A.J. Poggio,.K. Miller, 'Integral equation solutions of three-dimensional scattering problems' in 'Computer Techniques for lectromagnetics', Oxford: Pergamon Press, 1973, pp [ 131 H. Mieras, C.L. Bennett, 'Space-time integral approach to dielectric targets', I Trans. Antennas Propagat., Vol. AP-30, pp. 2-9, 1982 [I41 Bennett C. L., 'Time Domain Solution of Transient Problems. In: Lectures on Computational Methods in lectromagnetis' (d.: Harrington R. F., Wilton D. R., Butler C. M., Mittra R., Bennett C. L.), St. Cloud, SC Press, [ 151 R. Mittra, 'Integral equation methods for transient scattering' in 'Transient lectromagnetic Fields' by L.B. Felsen, Berlin: Springer Verlag, 1976, pp. 73- I26 [16] J. Mautz, R. Harrington, 'Radiation and scattering from bodies of revolution', Appl. Sci. Res. June , pp [ 171 M. Belkina, 'Radiation characteristics of the prolonged ellipsoid of rotation', lectromagnetic waves difiaction by the bodies of revolution, Moskow, 1957, pp , in Russian [ 181 Meek and Craggs, 'lectrical Breakdown of Gases', New York: J. Wiley&Sons, 1978 [ 191 G.A. Mesyats, 'Physics of pulse breakdown in gases', Moskau: Nauka Publishers, 1990, ISBN , in Russian OSISD SYMPOSIUM