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Methods for Verifying ESD Simulator ComplianceGreg Senko Ensuring simulator performance within the proper limits begins with calculating EMC uncertainty.ESD simulator pulses are notoriously difficult to measure because of their fast rise time and shot-to-shot variations in waveform. When measuring ESD simulators, one must consider all possible error sources and compute the uncertainty—the estimated bounds of the deviation of a measured quantity from its true value. Then a statement of uncertainty should be made to reflect the quality or accuracy of a measured result as compared with the true value,1 which is and will usually remain unknown. The statement of uncertainty is accompanied by a statement of confidence that can be placed in the value of uncertainty. A calculation of uncertainty should be performed for each measured parameter of a calibration. Without these statements of uncertainty and confidence, one cannot be sure that a given simulator's performance falls within acceptable limits. Calculating uncertainty requires an uncertainty budget for each measured parameter. This is a list of the probable sources of error with an estimation of their uncertainty limits, probability distribution, and their influence on the test result. The standard deviations are calculated for each of the sources in this list. The stated uncertainty is then calculated from the root sum of squares of the standard deviations of the individual uncertainty components multiplied by a coverage factor, k. The definitions, procedures, and formulae for calculating uncertainty can be found in the National Association for Measurement and Sampling (NAMAS) publication NIS81, The Treatment of Uncertainty in EMC Measurements.Establishing the Uncertainty Budget Listing all the measured quantities and creating a table for each one is the first step in creating an uncertainty budget. The next step is listing all the probable sources of error for each quantity, including random sources. Each error source must then be evaluated for its bounds and distribution. Sources of information for estimating the uncertainty include manufacturers' specifications, calibration reports, estimates based on experience with the simulator's behavior, and a series of recorded observations (for random sources). If a quantity is measured at more than one point or over a range of points, it is necessary to decide if the uncertainty varies over the range. If desired, the calculation may be simplified by using the worst-case uncertainty for the entire range. The following sections give the methods for estimating the standard deviation for random and systematic effects. Each error source must be evaluated with one of the following methods before calculating the combined and expanded uncertainty. Random Components. Random effects result in errors that vary in an unpredictable way while the measurement is either being made or repeated under the same conditions. The uncertainty associated with these conditions can be evaluated by statistical techniques from a series of repeated measurements. An estimate of the standard deviation, s(qk), of a series of n readings, qk, is obtained from(1)
where q is the mean value of n measurements. The estimation of s(qk) for a random component is part of the process of creating an uncertainty budget. Typically, it is performed just once for each random component. The estimation is only valid if the EUT measurement is made under exactly the same conditions. Establishing a value of standard deviation for each ESD simulator model to be tested may be necessary, as they may behave differently. When testing the EUT, making repeated measurements instead of just a single measurement will reduce the random component of uncertainty. The standard uncertainty, u(xi), for random contributions is calculated from the standard deviation of the mean, s(q), as given by (2)
Normal Distribution. Normal distribution is used when there is a high probability of the true value lying near to the center of the range, and a low probability of the value being near the limits of the range (a Gaussian distribution or bell curve). Normal distribution is assigned to uncertainties derived from multiple contributions—for example, when a NAMAS- or otherwise-certified calibration laboratory provides a total uncertainty value with a stated confidence level for a particular instrument parameter. (3)
where uncertainty is the semirange limit value (±uncertainty). If the uncertainty is not symmetrical, +error  –error, then
(4)
Rectangular Distribution. Rectangular distribution is used where there is an equal probability of the true value lying anywhere within the given range. A rectangular distribution should be assigned where a manufacturer's specification is used as the uncertainty. If there is a statement of confidence associated with the specification, normal distribution may be used instead. If the uncertainty is not symmetrical, +error –error, then
(4)
(5)
U-Shaped Distribution. A U-shaped distribution applies to mismatch uncertainty. Mismatch uncertainty applies to continuous signals, which is not the case with ESD pulses. It is included here, however, for completeness. The value of the limit for the mismatch uncertainty is M, associated with the power transfer at a junction, and is obtained from 20 log10 (1–|Gg| |Gl|) dB where Gg and Gl are the reflection coefficients for the source and load: (6)
Combined Uncertainty Once the uncertainty budget has been completed and a standard deviation value has been assigned to each error source, the combined uncertainty may be calculated. The combined standard uncertainty, uc(y), is calculated by taking the square root of the sum of the squares of the individual standard uncertainties. If any of the standard uncertainties are not already in the same units as the measured result, they must be converted by the appropriate function, ci: ui(y)
= ciu(xi)
(7) Any contributions with known or suspected adverse correlation are added together first, before being entered into the following formula as ui. The combined uncertainty for m contributions is (8)
Expanded Uncertainty The expanded uncertainty, U, is derived from the combined uncertainty and defines an interval around the measured result that encompasses the true value with a specified level of confidence, p%: U=k
• uc(y)
(9) A value of k = 2 approximates a 95% confidence level (recommended by NAMAS for EMC testing); a value of k = 3 approximates a 97.5% confidence level. These are the most-frequently used values of k. If a significant portion of the uncertainty is from random sources, uc(y)/s( (10)
For random effects, the degrees of freedom, vi, are given by vi = n – 1, where n is the number of readings used to calculate s(qk). The effective degrees of freedom of the standard uncertainties based on systematic effects can be assumed to be infinite in most cases. Therefore, they will be reduced to 0,
and can be ignored, leaving only the random contributions. Table I lists the t-distribution values for a 95% confidence level.
Reporting of Result The result of the measurement is y and may be reported as follows: yA ± UA for a confidence level of 95%, (k = 2). If the measured result is compared to a minimum or maximum limit (single-sided limit), and the result including the uncertainty falls within the limit, the confidence in a passing result can be stated as 97.5%. The reason is that the 5% probability of the error lying outside the uncertainty range is symmetric, so half, 2.5%, will also fall within the acceptable range.Applying Uncertainty Calculations The data in this section are given to show how uncertainty calculations are applied. Where possible, the data come from actual data sheets and laboratory measurements. Some of the data were created either to illustrate a particular point or to provide information where none was available. Unless these data exactly match a given EUT's measurement system and simulator performance, they cannot be used for its uncertainty calculations. Simulator Tip Voltage. The following is an example of uncertainty calculation for ESD simulator tip voltage. Creating a table listing all the probable sources of error is the first step. An electrostatic voltmeter measures the tip voltage. Although the electrostatic voltmeter is the only measuring instrument used here, it is not the only probable error source. The resolution of the simulator voltage display is another probable error source that should be included in the table. It has also been observed that in repeating these measurements under the same conditions, the measured voltage changes by a few volts each time the measurement is taken. This variation will be included in the table as a random component of uncertainty (see Table II).
One can estimate the electrostatic voltmeter's
uncertainty range by first looking at the
manufacturer's data sheet. It has a rated
accuracy of ±1% over its entire measuring
range. According to the previous definitions,
rectangular distribution is applied to a manufacturer's
specification. Because the measured quantity
is in volts, one converts 1% to 20 V. The
standard deviation, defined as the semirange
limit value divided by the square root of
three, yields a value of Next, one must assess the uncertainty of the simulator's voltage setting, which has a continuously variable setting. The resolution of the simulator's voltage display is 10 V, which allows the tip voltage to vary as much as 10 V for the same displayed voltage value. Therefore, the semirange limit value is the error range divided by 2 = ±5 V. Because there is an equal probability of the actual tip voltage being anywhere within this range, rectangular distribution is applied. The resolution of the display is the same over the entire voltage range. Therefore, the uncertainty, because of the display, will be highest at low voltages. The lowest IEC test level is 2000 V and has been chosen for our calculation. The last error source to evaluate is measurement repeatability. While using the same instrumentation and general setup will be necessary to minimize random components, small variations in the placement of the simulator relative to the target and in the positioning of its grounding cable relative to the target plane can still cause random variations. The series of measurements to establish the random component must include these variations in positioning. Setting up the simulator once and taking the series of measurements will not take these variations into account. The setup should be taken apart and reestablished between each measurement to include these possible variations. However, the uncertainty of the simulator's voltage setting should not be counted twice. If the voltage setting uncertainty has already been accounted for elsewhere in the table, the setting should not be changed between tests. A series of 10 measurements is taken, and the recorded values are 2000, 2010, 2020, 2000, 1990, 1990, 2000, 1980, 2000, and 2010. The standard deviation is calculated using the formula given in the Random Components section, and its value is 11.6 V. Repeatability should also be checked at other voltage levels; however, this step has been skipped here. Table III shows all of the uncertainty and standard deviation values.
Next, the combined uncertainty is calculated by taking the square root of the sum of squares of the individual uncertainty values. The resulting combined uncertainty value is 17.3 V. One must now evaluate whether a significant portion of the uncertainty is caused by random components, as determined by whether or not
Using the values of combined uncertainty and the standard deviation of the measurement repeatability, the value of veff is 37.7. The value of k is then determined to be 2.08 by linear interpolation between the veff values of 20 and 50 found in Table I. When reporting the measured result of simulator tip voltage at 2000 V, the result y can be stated as y V ± 34.5 V with a confidence level of 95%. By converting the voltage back into a percentage, the uncertainty could also be stated as ±1.7% with a 95% confidence level. Simulator Rise Time (Contact Mode). The next step is to calculate the uncertainty for contact-mode simulator rise-time measurements. The uncertainty components for air-discharge measurements are identical. However, the uncertainty due to the simulator will be greatly increased because of the effects of the arc. Obvious sources of error include the oscilloscope's time measurement accuracy and the simulator repeatability. The rise time uncertainty, however, is much more difficult to estimate than the first example because of some special considerations. First, the simulator's rise time is very fast (0.7–1 ns for IEC 1000-4-2–compliant simulators). If the measurement system's rise time is not much greater than the simulator's rise time (<100 ps is required for a 1% error when measuring 0.7 ns), the measured result can be strongly influenced by the measurement system's rise time. Storage oscilloscopes with rise times <100 ps are uncommon and quite expensive. Most digital oscilloscopes used for ESD measurements have a rise time in the neighborhood of 270–350 ps, and it is the oscilloscope's rise time that usually dominates the system's rise time. The influence of the system's rise time must be included as a probable source of error. Second, it can be seen from the preceding discussion that the influence of the measurement system rise time will vary over the range of measured results. To simplify the calculation, take the worst-case situation for the range that is at the lower limit as set by the IEC simulator standard, 0.7 ns, where the measurement system rise time has the greatest influence. Third, ESD rise time is the time required for the leading edge of the current waveform to increase from 10 to 90% of the peak amplitude. Because these two points are referenced to the peak amplitude, we are not concerned with amplitude errors as long as they remain invariant with frequency. Steps must be taken to minimize any reflections or errors that do vary with frequency, as they can influence the observed rise time. The oscilloscope, attenuators, cables, and target are all probable sources of this type of error. A tutorial on how to measure ESD pulses is beyond the scope of this article; however, such resources are available.2–4 The data sheet rating for the 1-GHz–bandwidth, 5GS/s, oscilloscope's time measurement accuracy is <50 ps. A series of 10 rise-time measurements is taken to assess simulator repeatability, and the recorded values are 804, 721, 768, 778, 772, 753, 697, 731, 759, and 742 ps. The standard deviation is calculated using the formula given in the Random Components section, and its value is 30.9 ps. The influence of the system's rise time is the most difficult quantity to assess. As previously stated, the oscilloscope is usually the most limiting factor in the system's rise time. In a system with a Gaussian impulse response (a smooth roll-off of 20 dB/decade above the –3dB point), the rise time is given by rise_time = 0.35/bandwidth. The system's rise time is composed of the individual rise times of all the components in the system. In a Gaussian system with m components, the system rise time is given by(11)
where rise time (n) is the rise time of each of the system components such as oscilloscope rise time, target rise time, attenuator rise time, etc. For a 1-GHz-bandwidth–rated oscilloscope, the calculated rise time is 350 ps. Most oscilloscopes, however, only approximate this behavior and exhibit a pulse response with a faster rise time and some overshoot. The observed rise time typically approximates a 30% higher bandwidth. In our example of a 1-GHz oscilloscope, this would mean a rise time of 269 ps. The ideal situation for determining the uncertainty would be to measure the actual rise time of the entire target/attenuators/ cable/oscilloscope chain. This is accomplished by driving the measurement system with a pulse of known rise time (100 ps or less is ideal as it will have a minimal influence on the measured result). The measured rise time can be corrected for the contributions of the entire measurement chain, thereby reducing the uncertainty to the accuracy of the system's rise-time measurement. The corrected rise time of the measured result is given by the following equation: (12)
Driving a fast-rise-time pulse into the ESD measurement target requires a special coaxial target adapter. For this reason it may not be possible to measure the entire chain's rise time. Instead, the rated rise time of the target can be used, and the rise time of the attenuators/cable/oscilloscope measured. In this case, the uncertainty of the measurement chain will comprise two components: the tolerance on the target rise time and the uncertainty of the attenuators/cable/oscilloscope chain's rise-time measurement. Rise-time error sources contribute to the measurement error as the square root of the sum of squares. Our example has neither of these specialized instruments and attempts to estimate the uncertainty without the benefit of these measurements. First, let's estimate the worst-case system rise time. We'll assume that our 1-GHz oscilloscope minimally meets its rise-time specification of <350 ps. In all other respects, the measurement system uses high-bandwidth/fast-rise-time components. The cable is manufactured and tested for >20 GHz use. The two attenuators have an 18-GHz bandwidth, and the target has a very flat bandwidth (the target is the new EOS/ESD design, not the IEC target) with a rated rise time of <35 ps. An estimated worst-case contribution of 20 ps for the cable is included: (13)
Next, the influence of the worst-case system rise time on the observed rise time must be calculated. For our ESD simulator with 700-ps rise time, this would produce (14)
Now let's look at the best case. It is expected that the bandwidth of our 1-GHz oscilloscope is nominally 30% high. Let's estimate that it is actually 30% above that, with a rise time of 207 ps. To simplify matters, assume the other components are zero as they have only a small influence on the measured result. The observed rise time for the 700-ps simulator is now as follows: (15)
The error range is 784 – 730 = 54 ps so the semirange limit value is 27 ps. It turns out that the uncertainty due to the estimated range of system rise times is the smallest of the three contributions to the combined uncertainty, and that it is not unreasonable to estimate the uncertainty of the measurement system rise time in this way. The rise-time measured value must be corrected for the nominal system rise time by the following formula: (16)
The uncertainty and standard deviation values are shown in Table V.
The combined uncertainty is 45.1 ps. Now one must evaluate whether a significant portion of the uncertainty is caused by random components, as determined by whether or not
We find that 45.1/30.9 is only 1.46, well below 3; therefore, we cannot simply use k = 2. It is necessary to calculate the effective degrees of freedom so that a value of k based on the t-distribution may be determined. Using the values of combined uncertainty and the standard deviation of the measurement repeatability, the value of veff is 40.8. The value of k is then determined to be 2.07 by linear interpolation between the veff values of 20 and 50 found in Table I. When reporting the measured result of simulator rise time, the result y can be stated as y ps ± 45 ps with a confidence level of 95%. The midrange value of the estimated system rise time is used to correct the observed result for the system rise time and produce the reported value. The examples provided in this section have shown how to estimate the uncertainty for just two of the many parameters normally measured in evaluating a simulator's operation. The general procedure for estimating uncertainty is the same for any measured parameter. The method for creating a table, listing the contributions, and calculating the standard deviation, combined uncertainty, and expanded uncertainty are the same. All that can change is how the uncertainty is estimated for each of the contributions, where some contributions are much more difficult to estimate than others. The tables are created and the calculations are performed as in the examples here.Uncertainty Contributions—All Parameters Table VI lists the simulator parameters and possible contributions to each parameter. The contributions are divided into categories of tip voltage, target-chain dc attenuation, time domain, and random contributions. The following sections explain some of the issues that may be encountered in estimating each of these contributions.
Tip Voltage Amplitude-based measurements are affected by the simulator's tip voltage. Possible contributions to the tip-voltage uncertainty are voltmeter accuracy and simulator voltage-setting resolution, as well as tip-voltage repeatability, which is discussed later in the Random Effects section. Voltmeter Accuracy. Simulator tip voltage is measured either with an electrostatic voltmeter or with a voltmeter plus a high-voltage attenuator. Electrostatic voltmeters typically have several ranges, and the accuracy may not be the same for all of them. If a voltmeter and an attenuator are used, the accuracy of both must be considered. The uncertainty can be taken from the manufacturer's specification or from a calibration report. With high-voltage attenuators, it is necessary to consider the voltage coefficient of resistance in addition to the normal tolerances. The uncertainty values for the scales used during simulator measurements should be selected. If the manufacturer's specification is used, it is considered rectangular distribution and the semirange limit value is divided by. But if a measured value is taken from a calibration report, it is considered normal distribution and the semirange limit value is divided by 2 (or a larger number depending on the stated level of confidence). Division by 2 in the second instance is most likely to produce a lower value of standard deviation. Simulator Voltage Setting Resolution.
The uncertainty of the simulator's voltage setting
may be derived from one of two sources: the
resolution of the display or the resolution
of the voltage setting. If the voltage setting
is continuously variable, the resolution of
the simulator's voltage display will dictate
the uncertainty. For example, if the resolution
of the simulator's voltage display is 10 V,
this allows the setting to be high or low by
as much as 10 V for the same displayed voltage
value. Therefore, the accuracy of the simulator
voltage setting is ±10 V. Because there
is an equal probability of the actual tip voltage
being anywhere within this range, rectangular
distribution is applied. If the resolution of
the voltage setting is incremental and is smaller
than the resolution of the display, the uncertainty
will be the resolution of the voltage setting.
Rectangular distribution is applied because
there is an equal probability of the actual
tip voltage being anywhere within the resolution
of the setting.
Target- and Measurement-Chain Dc Attenuation A dc current source is used to measure the combined dc attenuation of the target and measurement chain (see Figures 1 and 2). Measuring the entire chain simplifies the task of estimating the uncertainty as compared with evaluating the target, attenuators, cables, and oscilloscope separately. It is important that the current applied to the target does not exceed its average power dissipation rating since damage to the target may result. The uncertainty of the current source output contributes directly to the attenuation uncertainty, as well as to the oscilloscope's vertical accuracy. If the dc attenuation measurement is made with the same vertical scale as the simulator measurement, the oscilloscope accuracy has been taken into account and only the vertical resolution must be considered.
Current Source Accuracy. The uncertainty
of the current source output may be derived
from an internal meter, an external measurement,
or the current setting resolution. The uncertainty
can be taken from the manufacturer's specification
or from a calibration report. If the manufacturer's
specification is used, it is considered rectangular
distribution and the semirange limit value
is divided by  . If a measured
value is taken from a calibration report, it
is considered normal distribution and the semirange
limit value is divided by 2 (or a larger number
depending on the stated level of confidence).
The measured values may vary since the settings
(i.e., V/various factors) will be different.
The measured value will probably produce a lower
value of standard deviation.
Time Domain Time domain uncertainty contributions include the oscilloscope's time measurement accuracy and the measurement chain's rise time. The time domain response of the measurement chain is usually dominated by the oscilloscope. Other elements, such as the target, attenuators, and cables, typically make only small contributions to the system response if they have been selected properly. A target with a flat frequency response and high-bandwidth attenuators are required. Long cables, poor attenuators, and the IEC-specified target can contribute significant errors. Recommended performance specifications for these components are available.5 Oscilloscope Time Measurement Accuracy.
The oscilloscope time measurement uncertainty
can be taken from the manufacturer's specification
or from a calibration report. For digital
oscilloscopes, the time measurement accuracy
is usually a fraction of the sampling interval.
If the manufacturer's specification is used,
it is considered rectangular distribution
and the semirange limit value is divided by Measurement System Rise Time and Bandwidth. The measurement system rise time, a function of bandwidth, contributes to amplitude loss and reduced rise time or di/dt in the observed waveform. Rise time and di/dt measurements can be corrected for the system rise time (measured or estimated) as outlined in the Simulator Rise Time section. Amplitude losses are more difficult to estimate, because the actual simulator waveform is complex, with a narrow peak, rather than a square pulse. It varies from shot to shot and remains unknown, as we can only observe the measured waveform. The amplitude losses can be estimated by mathematical simulation using idealized simulator waveforms and a Gaussian filter to represent the system bandwidth. The difference between the idealized waveform and the output of the filter can then be measured to obtain the loss in peak current. A Gaussian filter has no phase shift and an amplitude response of|H(j
 )|
= exp[–0.3466(/c)2]
(17) The Gaussian filter is a good approximation of oscilloscope performance. Equations for the simulator waveforms are provided.6 These idealized waveforms have smooth, rounded peaks and no oscillations. Simulators that have sharper peaks will exhibit higher losses. Overall, the amplitude losses are very low, approximately 1% or even less for the 1-GHz–rated oscilloscope (see Table VII).
Random Effects Possible random effects include tip-voltage repeatability, dc amplitude measurement repeatability, rise-time repeatability, and peak amplitude repeatability. The uncertainty associated with random effects is evaluated by statistical techniques from a series of repeated measurements, as explained in the Random Components section. The estimation is only valid if the EUT measurements are made under exactly the same conditions. Using the same instrumentation and general setup will be necessary to minimize random components. However, small variations in the placement of the simulator relative to the target and in the positioning of its grounding cable relative to the target plane can still cause random variations. The series of measurements to establish the random component must include these variations in positioning. Setting up the simulator once and taking the series of measurements will not take these variations into account. The setup should be taken apart and reestablished between each measurement to include these possible variations. The uncertainty of the simulator's voltage setting, however, should not be counted twice. If the voltage setting uncertainty has been accounted for elsewhere in the table, this setting should not be changed between tests. Shot-to-shot variations in ESD simulators will most likely be the largest contribution to the measurement uncertainty, especially for air discharge. The standard deviation of the variations, even in contact mode, can be several percentage points or more, and can vary considerably across the voltage range because of the operation of the contact-mode relay. These shot-to-shot variations can lead to high values of expanded uncertainty that may approach the specification limit (see Table VIII). According to NIS81, making a statement of compliance with a standard requires that the measured result plus or minus the expanded uncertainty value falls within the specified limits. This has a dramatic effect on the compliance range. For example, the IEC 1000-4-2 specification for peak amplitude is ±10%. If the expanded uncertainty is 4.82%, as in the example, the compliance range is ±10 – ±4.82 = ±5.18%, effectively cutting the compliance range in half. Actual values of expanded uncertainty could be higher, leading to an even smaller compliance range. Conclusion The amplitude measurement uncertainty for ESD simulators can be very significant. The values chosen for this example are low and represent best-case performance. Actual values may be much greater, especially at low-voltage levels where the contact-mode relay contributes significantly to the shot-to-shot variation. It is essential to identify and minimize each contribution to the measurement uncertainty to obtain low levels of expanded uncertainty and to make a statement of compliance with the simulator standard.References
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will
be smaller than s(qk)
and thereby the uncertainty is reduced. It
is advisable to make multiple measurements
whenever the measured result is close to the
specified limit, as this will reduce the measurement
uncertainty. The average value of the repeated
measurements is used as the measured result.
)
3, 
.
The meter has recently been calibrated, and
the uncertainty value could possibly be reduced
if the report gives a lower value of uncertainty
or states a confidence factor in the reported
uncertainty (normal distribution divides the
uncertainty by 2 instead of (check 3). The
calibration report measures the accuracy as
±1%, and no confidence factor has been
stated. Therefore, the uncertainty and standard
deviation values remain 20/
V
