TRANSFER IMPEDANCE MODEL OF MEASUREMENT PATH FOR ESD SIMULATOR CALIBRATION

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1 EMC 6 8 th INERNAIONAL WROCLAW SMPOSIUM AND EXHIBIION ON ELECROMAGNEIC COMPAIBILI, WROCLAW, 8 3 JUNE, 6 RANSFER IMPEDANCE MODEL OF MEASUREMEN PAH FOR ESD SIMULAOR CALIBRAION Janusz Baran, omasz Dróżdż, Jan Sroka 3, echnical University of Częstochowa, Institute of Electronics and Control Systems, Częstochowa, Poland baranj@el.pcz.czest.pl, drozdz@el.pcz.czest.pl 3 Schaffner EMC AG, est Systems, Luterbach, Switzerland, jan.sroka@schaffner.com Abstract: he paper deals with deriving a frequency dependent transfer impedance of a measurement path for calibration of an electrostatic discharge (ESD) simulator. he transfer impedance is derived from the scattering parameters of the calibration system components, i.e. the Pellegrini target, the cable with attenuator and the broadband oscilloscope, measured in the range from MHz to 6GHz. he frequency analysis of the whole path reveals high frequency effects neglected by the simple resistance models and makes possible reduction of the calibration uncertainty. Keywords: ESD simulator, calibration, scattering parameters, transfer impedance, two-port network. INRODUCION Electrostatic discharge (ESD) simulators (or generators) are used for testing immunity of electric and electronic equipment to electrostatic discharges and disturbances. o ensure reliability of the testing, the generators have to be calibrated, especially in terms of standardized shape of the discharge current impulse. It is ruled by the IEC standard []. he parameters that have to be preserved to ensure repeatability of the calibration are: the rise time, the peak current and the tail current after 3 and 6 nanoseconds. i [A] recorded impulse theoretical specification 3 6 t [ns] Fig.. ypical waveform of kv ESD impulse and its theoretical specification calculated with formula proposed in [] A typical waveform of the ESD impulse recorded experimentally is presented in Fig. along with "theoretical" impulse calculated on the basis of the formula proposed in []. his analytic approximation is employed in literature [,3,] and will be further used in this work. ESD Gen. Fig.. Measurement system for the ESD simulator calibration ESD Gen. target (current converter) I R cable with attenuator R U Fig. 3. Simplified DC model of the target. I discharge current, U oscilloscope input voltage (cable and attenuator neglected). Parameters measured for the target analyzed in the paper: R =.6, R =7.88R R = U /I =. he ESD simulator is tested in a system whose principal elements are shown in Fig.. he discharge hits a special current converter the Pellegrini target (see Fig.), connected to a high frequency oscilloscope by a coaxial cable with an attenuator. Earlier works, e.g. [], assumed a simple DC model of the target shown in Fig.3. However, due to the time scale of the waveforms and the target design, the high frequency features of the measurement path up to gigahertz should be also taken into consideration. Such approach makes possible better evaluation of distortions introduced in the path from the discharge current I to the oscilloscope input voltage U, and I OSC

2 Z IN Z INC Z INO I I I arget (current Cable with converter) U attenuator U Osc ESD Gen. Z R =U /I Z R C=U /I Fig.. wo-port network diagram of the ESD simulator measurement path consequently improves accuracy of the calibration which is currently based on simple resistance models. In this work we use the scattering parameters S to construct linear two-port networks with frequency dependent parameters as models of the target and cable with attenuator and calculate the transfer impedance from I to U. It is an extension of works [,3], where the transfer impedance of the target only was derived in the same way.. MODEL OF HE MEASUREMEN PAH.. Scattering and admittance parameters of the target he two-port network diagram used for analysis of the ESD simulator measurement system is shown in Fig.. he input quantities are the scattering parameters measured with a network analyzer separately for the target and the cable with 9dB attenuator. Because of the target construction it is impossible to connect to it directly the two ports of the analyzer. herefore a special adapter was used (Fig.) and the scattering matrix of the target was calculated from the measurements for adapter-target (A) and adapteradapter (AA) configurations. Fig.. Adapters (left) and the target (right) [] We assume that two identical adapters connected face to face have symmetric scattering matrices and there are no reflections. In this case the scattering matrix of a single adapter AA S A S, () AA S and the parameters of the target can be calculated as [3]: S S A A A A A S S S S. () A S A S A S he scattering parameters of the cable with the attenuator were measured directly. Because in the subsequent calculations we use the admittance parameters, the scattering parameters S have to be recalculated into using standard formulas: S S SS S S SS r, (3a) S, (3b) S S SS r r S, (3c) S S SS r r S S SS S S SS r, (3d) where the normalizing constants are assumed equal to reference impedances, in this case the impedances of the network analyzer ports, i.e. r =Z p =r =Z p =.. ransfer impedance of the measurement path he transfer impedance Z R_C =U /I (see Fig.) can be expressed as a function of the admittance parameters C of the substitute two-port network of the target and cable with attenuator connected in series: C U ZIN ZR _ C, () C I where Z IN is the target input impedance. (Index denotes the target, C the cable with attenuator, C the cascade connection of the two). he impedance Z IN can be expressed as a function of the target admittance parameters and the target load impedance Z O, which is constituted by the remaining part of the path, i.e. the cable with attenuator and the oscilloscope: U ZO Z IN, () I Z O

3 where. he admittance parameters C are calculated from the transmission matrix (ABCD parameters) A C of the substitute two-port network with equations: A A,,,. (6) A A A A Recalculation into the transmission parameters is convenient because the substitute matrix A C is a product of the transmission matrices of the cascaded components: C C C C A A A A A A A C C. (7) A A A A he transmission parameters of a two-port network are related back to its admittance parameters as follows: A, A, A, A. (8) Calculations using equations (8) have to be carried out both for the target and the cable with attenuator. he target load impedance Z O occurring in () is the input impedance of the cable: U ZO Z. (9) INC I o determine Z INC we use equation () with quantities corresponding to the cable: C ZO ZINC, () C C Z C C C C C where O and Z O is the cable load impedance which is in turn the input impedance of the oscilloscope. he impedance Z O can be calculated directly from the measured reflection parameter S of the oscilloscope: O U S ZO ZINO Z, () O p I S where Z p = is the source impedance (impedance of port of the network analyzer). 3. RESULS OF MEASUREMENS AND CALCULAIONS In the analysis we use data of the S-parameters of the Pellegrini target, cable with 9dB attenuator and oscilloscope (ektronix SCD) measured using the vector network analyzer in Schaffner EMC AG laboratory in wide frequency range from MHz to 6GHz. he measurements are given in the realimaginary part form. he S-parameters of the target, the adapters and the oscilloscope were measured for 37 frequency values and the parameters of the cable with attenuator for 69 frequencies. he greater number of measurement points in this case is dictated by necessity of more precise modeling the cable as a delay line. All the measured S-parameters data have to be interpolated to the same grid of linearly equidistant frequencies, for which the discrete Fourier transform of the discharge impulse will be further calculated. We used either simple linear interpolation or cubic splines, but in both cases the results are very similar. he DC values were obtained by extrapolation of the data towards zero frequency. Fig. 6 shows the graph of the target input impedance Z IN calculated with equation (). Looking at the real part of the impedance we can read out the low frequency resistance R IN.97, which is smaller than for the DC model from Fig.3. At about 3GHz Z IN has a high resonance peak resulting from the target construction. In Fig. 7 there are shown the frequency characteristics of the cable input impedance Z INC and the oscilloscope input impedance Z INO, obtained with equations () and () respectively. In low frequencies they are approximately standard resistances. Re(Z IN ) [] Im(Z IN ) [] Re(Z IN ) [] Im(Z IN ) [] Fig. 6. Input impedance Z IN (f) of the target Z INC Z INO Fig. 7. Input impedances: Z INC (f) of the cable and Z INO (f) of the oscilloscope Fig. 8 and 9 present the transfer impedance Z R_C of the whole considered path, calculated with equation (), versus frequency as well as the transfer impedance Z R_ =U /I of the target only. When we compare them, it is clear that large phase shift visible in Fig. 9 is introduced by the cable which works like a delay line in high frequencies. Both impedances have distinct resonant

4 peaks around 3GHz due to the target. In Fig. 8 we see that in low frequencies the reactance parts of the impedances tend towards zero so the whole path is approximately resistive with R R_C.38 (or.8 without the 9dB attenuator) and the target itself has resistance R R_.he tiny difference (.3) reveals small attenuation of the signal in the cable. hese two resistances are slightly greater than the transfer resistance of simplified DC model from Fig. 3. Re(Z R ) [] Im(Z R ) [] Z R- Z R-C Fig. 8. ransfer impedances: Z R_ (f) of the target and Z R_C (f) of the cascaded connection of the target and cable with 9dB attenuator (linear frequency scale) Z R- calculate the transform of the voltage by multiplication in the frequency domain: U ( f) ZR _ C ( f) I( f), (3) and return to the time domain using the inverse transform: u() t Re( IDF[ U( f)]). () Fig. shows the results for the considered transfer impedance model compared with the DC model. he clearly visible 8ns delay of the voltage u (t) represents the propagation time of the signal across the measurement path. he quality of the waveform at the output of the transfer impedance model depends on: ) time window o =N/f s (N number of samples, f s sampling frequency in time) of the impulse that must be wide enough to let the impulse fade and therefore avoid discontinuity artifacts in DF. Otherwise the calculated response is "non-causal" and looks like curve 3 in Fig. b for o =ns, ) spectrum range and sampling frequency. he wide spectrum range reveals high frequency features of the system (e.g. resonant peak of the target) while the greater number of frequency data shows the details of the spectrum and reduces the DF errors DC model - Z R- (f) and attenuator 3 - Z R-C (f), o =ns Z R [] Z R-C u [V] arg(z R ) [rad] Fig. 9. ransfer impedances Z R_ (f) and Z R_C (f) in magnitude-phase angle representation. DISORION OF HE ESD IMPULSE IN HE MEASUREMEN PAH Having known the frequency dependence of the transfer impedance Z R_C (f) it is possible to determine the distortion introduced by the measurement path from the specified or theoretical impulse current i (t) to the oscilloscope input voltage u (t). We transform the impulse, sampled with frequency twice as high as the upper frequency of the S- parameters data (according to the sampling theorem), into the frequency domain using the discrete Fourier transform: DF[ i ( t)] I ( f ), () a) b) u [V] 3 6 t [ns] DC model 3 - Z R-C (f), o =ns 3 6 t [ns] Fig.. he discharge impulse as voltage at the output of: - the DC target model, the target represented by Z R_ (f) loaded by the cable and oscilloscope, 3 - the path represented by Z R_C (f) loaded by oscilloscope, for time window a) o =ns and b) o =ns. Waveforms and are sketched with 9dB attenuation for better comparison

5 It is important to determine differences between the characteristic parameters of waveforms and 3 in Fig. which can be a measure of the impulse distortion neglected by the DC model in comparison with the transfer impedance model. We calculated relative differences with respect to the DC model, i.e. xdc xzr ex () xdc for the rise time, the peak value and the 3ns value for several combinations of time window and spectrum range and stated that the rise time and the peak value are most sensitive to correct choice of the time window and spectrum range which is shown in Fig.. a) b) epeak etr,, -, -, spectrum range [GHz],3,,, -, -, -,3 spectrum range [GHz] 3 6 time window [ns] 6 3 time window [ns] 3 3 he difference of the rise time (Fig. a) is small regardless of the time window when the spectrum range do not include the resonance of the target at 3GHz. In these conditions the compared models are similar. When the spectrum range includes the resonance (bars for and 6GHz) the models produce large differences, but only for short time windows. It results from discontinuity of the windowed impulse and coarse calculations of DF so these results are not reliable (see Fig. b). he difference decreases to about.% while extending the time window to ns or more which also increases the number of DF points (for ns and 6GHz N=8). he differences of the peak value (Fig. b) for longer time windows, which can be considered reliable, slightly decrease and stabilize with extending the spectrum range. he differences of the impulse magnitude at 3ns (Fig. c) and 6ns are about % and are less sensitive to the choice of frequency range and time window. It is interesting to observe how the transfer impedance model of the path affects the impulse in the frequency domain. In Fig. the power spectrum density (PSD) of the voltage u (t) obtained using Z R_C (f) is compared with that of the DC model. hey clearly differ above GHz, but this divergence is not significant because the signal power density emphasized by the resonance around 3GHz is still very low. he ratio of the difference of the impulses energy for f>ghz to the difference over the whole range is very small [ PSDu ( _ DC ) PSDu ( _ ZR )] from to 6GHz.% [ PSD( u ) PSD( u )] from to 6GHz _ DC _ ZR which means that the main reason of the divergence are different real and non-zero imaginary parts of Z R_C (f) at frequencies below GHz. hat explains why the differences of the impulse parameters shown in Fig. depend little on the frequency range if the time window is long enough., c) -e3,,, spectrum range [GHz] 3 6 time window [ns] 3 Fig.. Relative differences: a) e tr of the rise time (calculated from. to.9 of the peak value), b) e peak of the peak value, c) e 3 of the magnitude 3ns after. of the peak value, between the characteristic parameters of the DC model impulse and the transfer impedance model impulse versus frequency range f s / and time window o PSD(u ) DC model Z R-C (f) model Fig.. Comparison of the power spectrum density of voltage impulse u for the DC model and the frequency dependent transfer impedance model

6 . CONCLUSION he approach presented in the paper enables better evaluation of how the individual parts of the measurement system can affect calibration results and whether the calibration procedures currently applied are accurate enough. he investigation shows that the divergence between the transfer impedance and the DC model of the path that affects the discharge impulse specifications lies rather in slightly different gains at frequencies below GHz than in resonances at 3GHz and above, where the power density of the impulse is very low. At this stage we neglect the possible distortion of the signal inside the oscilloscope which can be modeled by an appropriate voltage transfer function. his problem was considered in [] but the analysis can be further developed. he other potential way to make the analysis more accurate is parametric modeling of the transfer impedance using an AR or ARMA model obtained from the data, because they are well suited to model line spectra. +Janusz Baran was born in Częstochowa, Poland, in 96. He received M.Sc. in electrical engineering from Częstochowa echnical University in 98 and Ph.D. from Lublin echnical University in 99. Since 986 he has been with Institute of Electronics and Control Systems at Częstochowa echnical University. His research interests include signal processing, nonlinear control and adaptive systems. omasz Dróżdż was born in Częstochowa, Poland, in 966. In 99 he received M.Sc. in electrical engineering from Częstochowa echnical University and since then he has been with Institute of Electronics and Control Systems at Częstochowa echnical University. His research interests include measurement systems and electromagnetic compatibility. Jan Sroka was born in Szczerców in Poland on January 9. He received M.Sc, Ph.D. and D.Sc. degrees in electrical engineering from Warsaw University of echnology in 97, 98 and 99 respectively. Since 99 he has been by SCHAFFNER EMC AG in Switzerland in different departments: Research and echnology, Component Development and est Systems. His current research interests is investigation and experiments in establishing uncertainty budget in EMC calibration and testing. ACKNOWLEDGMEN he authors would like to thank to SCHAFFNER EMC Ltd. for enabling investigation of the presented problem. REFERENCES [] IEC 6--. esting and Measuring echniques. Electrostatic Discharge Immunity est. May, 999. [] J. Sroka (), arget influence on the calibration uncertainty of ESD simulators, th Int. Symposium and Exhibition on EMC Zurich, pp [3] J. Sroka (), Calibration uncertainty of ESD simulator estimated with frequency dependent transfer impedance of the target, 6 th Int. Wrocław Symposium and Exhibition on EMC, Wrocław, pp. 9 3,. [] J. Sroka (3), Oscilloscope influence on the calibration uncertainty of the peak current of ESD simulators. th International Symposium and Exhibition on EMC, Zurich 3 Zürich, February 3, pp [] Dróżdż, Ocena zniekształceń prądu w kalibracji symulatorów wyładowań elektrostatycznych, doctor's thesis, echnical University of Częstochowa, Electrical Engineering Faculty. (in Polish, in printing)