A Method to Calculate Uncertainty of Radiated Measurements

Transcription

1 A Method to Calculate Uncertainty of Radiated Measurements Edward R. Heise Eastman Kodak Company Commercial and Government Systems Rochester, New York Robert E. W. Heise Eastman Kodak Company Business Imaging Systems Rochester, New York Abstract - A simple, practical and straight-forward method to calculate uncertainty of an electric-field radiation test, using standard engineering techniques and data already at hand at a typical electromagnetic interference (EMI) test facility, is presented. Using this model to standardize the calculation of uncertainty for all measurement sites and apparatus will provide a basis to compare different laboratories and will provide insight on what and where to incorporate improvements in existing operations. INTRODUCTION This paper provides an engineering technique to calculate uncertainty, or potential variation, of an electricfield radiation measurement with a given confidence level. The method proposed uses ANSI C63.4 normalized site attenuation (NSA) discrete frequencies and utilizes data normally collected on an annual basis at an EMI test facility as part of equipment calibration protocols. Total uncertainty calculations for radiated electric-field testing must be cognizant of the site, antenna, receiver, calibration sources, and measurement techniques employed in quantifying the elements of the measurement. The three most essential modules in determining the level of uncertainty are shown in Figure 1. Each module represents a combination of elements for a specified function which simplifies the computation of system uncertainty. Modules of a Radiated Uncertainty Calculation OATS Transducer Measuring or 2 (Antenna) 2 (Receiver) equivalent factors system Figure 1. Radiated uncertainty. UNCERTAINTY System uncertainty, as defined here, is the root sum of the squares (RSS) of the uncertainty of each module of the system. Each module, in turn, consists of two types of uncertainty, random (U,) uncertainty and systemic (U,) uncertainty, which are functions of the elements that comprise the individual components in each module. Random uncertainties, (U,), are based upon measured parameters characterizing the equipment and site. If each site, antenna, signal source, and receiver are characterized as separate elements then, applying the module concept, a system uncertainty calculation can be determined for any combination of site or equipment. Consequently, any one facility might have several radiated measurement uncertainty factors dependent on apparatus used. Systemic uncertainties, (U,), are a function of site and equipment endemic error, Ar. Using accepted engineering judgment, analysis, and values derived from data characterizing the site and apparatus these errors are considered to be constant for purposes of determining uncertainty. Note that some factors are an average quantity derived from an analysis of measured data. Uncertainty is a number that when presented with a given confidence level represents the unknown range that a given test result might vary, e.g., U(95%) = uncertainty for an estimated confidence probability of not less than 95%. Normal practice is to use a confidence level of 95%, but because many companies are striving for higher quality and consistency, a confidence level of 99.73% (three sigma) could be more appropriate as a basis to judge correlation between facilities. Uncertainty is expressed in decibels (db) because decibels are the currency of EMC. DESCRIPTION OF TEST SYSTEM This paper discusses an open area test site (OATS) characterized by discrete frequency measurements using tunable dipole antennas. In order to apply the statistics of this paper the specific discrete (27) frequencies of ANSI C63.4 are also used to characterize a calibrated signal source, a tunable receiver, and measurement antennas. The test system example uses two sets of antenna factor calibration data, on the same antennas, provided by a third party calibration service but obtained one year apart. The uncertainty of calibration was not reported nor were any other details provided. To compensate for this omission and to provide reasonable compensation, system uncertainty factors are added which are consistent with estimates for tuned receivers. Two measurement methods are considered, tuned frequency and stepped frequency, which differ with respect to bandpass. A 2% (+1.2 khz) error is calculated for manual tuning methods, e.g., Ar = 0.05 db, while a full 6 db bandwidth (+70 khz) error, Aw = 2.15 db is applied to stepped methods. Stepped methods are considered where a receiver with a nominal 120 khz bandwidth is tuned (stepped) across the frequency range of interest in increments of less than the nominal bandwidth. The sensitivity can vary from a gain of 1.5 db to an attenuation of more than 20 db at any frequency, f /97/$10.00

2 CONVENTIONS Bias (AI,): Average value of the absolute difference of a set of data from the expected reference or mean when measured at the designated (NSA) frequencies. Frequency: The total number of discrete frequencies is 27 in consonance with designated frequencies of ANSI C63.4 for normalized site attenuation (NSA) data. Mean: The statistical mean of data points is replaced by the ideal or standard value (X,) expected at each frequency. An example of an ideal is the C63.4 NSA value or a NIST calibration source. Module: A step in the measurement process that can be isolated and separated from other steps. The RSS of all module uncertainties constitutes total system uncertainty. OATS (open area test site): Use is made of the site NSA as calculated by ANSI C63.4 methods with a tuned dipole antenna. The dipole is probably the best engineering approximation to a standard antenna available to industry. Receiver: A freauencv tunable device conformina with the bandpass characieristics of ANSI C DEFINED TERMS Formulas: System uncertainty: UT = (u,,* + UP2 + ut3 ) Module uncertainty: Ut = (u:+ u:p Random uncertainty: Ur = k(s) + JN Systemic uncertainty: Us = k([za?] + 3) Variance: J12 = Z(Xi - Xn)2 + N Standard deviation: S = [Z(Xi - Xn)2 + (N-1)1! Bias: Ab = CIXi - Xnl + N Average: Av = C(AXr) + N Off set: Ao = C[Xr - X,] + N Definitions: Al General systemic error. f Discrete frequency (ANSI C63.4). k Multiplier dependent on N and % confidence. Xi Individual variable at the iih frequency. X Expected ideal value at the irh frequency. AXi Difference of two variables at a frequency. Total number of measurements, i = 1 -+ N.! Calibration (secondary standard) uncertainty. ut Module uncertainty. Constants: N = 54 measurements, 53 degrees of freedom. k = , for 95% estimated confidence. k = , for 30 estimated confidence. MODULES (1) (2) (3) (4) (5) (6) (7) 03) (9) Calculating the overall system uncertainty can be divided into individual tasks. Each task can be grouped into distinct and unique operations, which are termed modules. These modules are depicted as a line chart in Figure 2. Computing the uncertainty for each line item and applying formula (1) results in total measurement uncertainty. Antenna factors Electric-field Radiation Measurement u I NIST source Figure 2. Chart of uncertainties. An estimate of the uncertainty of an electric-field EMI measurement requires consideration of the attenuation characteristics of the measurement site, the transducer that senses an emanation, the device that determines the magnitude of the sensed signal, and all the peripheral apparatus that is needed to create a system. Numeric values of systemic factors are listed in Table 1. Observe that systemic factor Ab is not included. Ab is a function of measured random data and is a calculated value. Endemic errors values Antenna factor (dioole) Aa = 0.20 db Coaxial cable factor AC = 0.05 db Least significant digit Ad =O.iOdB Least significant digit, NIST Ae = 0.01 db Receiver tuning (2%) Ar = 0.05 db Antenna height variation Ah = 0.10 db Meter linearity A,j, = 0.15 db Antenna polarization AP = 0.02 db Quasipeak detector Ag = 0.01 db Receiver auto attenuator Au =O.l5dB Bandwidth, 6 db Aw = 2.15 db Switch (coaxial) Ax = 0.03 db Antenna azimuth A, = 0.05 db Table 1. Systemic factors Table 2 lists the applicable systemic factors associated with each module and for the signal generator. Applicable Systemic Factors Sianal Gengrator Receiver OATS Dipole factor: - Aa Data bias: Ab Ab Ab Cable factor: AC A, 2Ac LSD: Ad 2& 2& LSD, NIST: Ag - - *Receiver tuning: - At Antenna height: - Ah Meter linearity: - AIll Polarization: - AP Detector: A, Auto attenuator: - Au - *Bandwidth, 6 db: - AW Switch (coaxial): - AX ix Antenna azimuth: - AZ * Mutually exclusive. Table 2. Module systemic factors \ Antenna Factor Aa Ab 2Ac 2Ad At Ah Am AP 360

3 MODULE # 1: Open Area Test Site Figure 3 to Figure 6 shows the measured NSA and the ANSI C63.4 ideal +4 db envelop for a 3 m and a 10 m OATS using the tuned dipole and discrete frequency method. Using the ANSI C63.4 ideal NSA as a mean value and the measured NSA as random data, formulas can be applied for both antenna polarizations at the 27 frequencies to determine the standard deviation, S, and bias of Table 3. Three meter OATS Ten meter OATS Offset (db): Ao = Ao = Bias (d&):. Ab = At, = Standard deviation: S = S = Table 3. NSA statistics From this, using formula (3), the random uncertainty, Ur, can be calculated and applying formula (4) to the bias and appropriate endemic errors listed in Table 2 for OATS, the systemic uncertainty, Us, can be calculated. Selecting the proper constants and applying formula (2) the total module uncertainty, U,, for a given level of confidence can be determined: Three meter (3 m) OATS: Ut(95%) * 0.87 db (Ao = db) Wo) * 1.37 db Ten meter (10 m) OATS: Ut(95%) * 1.33 db (Ao = db) Ut(3o) db Aside: The value of A0 for the 3 m and 10 m site are also calculated. The offset value, in db, provides a measure of the average difference from the ideal NSA for the OATS under consideration. Although not used for uncertainty evaluations it can provide insight to site performance relative to an ideal site. To align the 3 m site data with its ANSI C63.4 NSA ideal the measured data of the example might be reduced by 0.2 db. Similarly, to align the 10 m site data with its ANSI C63.4 NSA ideal the measured data might be increased by 0.37 db. For most OATS this alignment would be relatively insignificant, but for sites with high offset factors this might be a practical way to account for any apparent discrepancy in measured data between sites. A comparison of the calculated uncertainty of 10 m OATS, that are at the 4 db tolerance extremes, (A0 = 4 db), with a normal OATS is shown in Figure 12. Observe that imposition of a U@%) uncertainty factor would still be advantageous to the lossy site but using a Ut(3o) factor could benefit the 10 m OATS. Nevertheless, the low loss OATS is still disadvantaged. It is suggested that, under the present rules, a lossy site has a commercial advantage vis-&-vis other sites. MODULE # 2: Test Antennas Figures 7 and 8 show antenna calibration factors at 3 m and 10 m separations for broadband (biconical and log periodic) antennas, which are used for everyday testing. This data was obtained from independent third patties at discrete frequencies without any other clarification. The antenna factor data shown is typical of the spread to be expected. Using these factors as random data points the bias and standard deviation are calculated and shown in Table 4. Antenna separation Three meter Ten meter Bias (db): &, = Ab = Standard deviation: S = S = Table 4. Antenna factor statistics The major difference in calculating statistical values for these data is that there is no ideal or standard antenna factor that can be used at each test frequency. Consequently the average value of the antenna factor for a given polarization and frequency is used and the bias is taken as the absolute difference from the average. Absent an estimate of the measurement uncertainty, receiver values, U&35%) = 0.37 db and Ut(3o) = 0.58 db are added. Given these differences a similar technique as used for an OATS calculation is followed to determine the random, systemic, and antenna total uncertainty: Three meter (3 m) factors: Ten meter (10 m) factors: U1(95%) =Z db U(30) * 1.59 db U1(95%) * 1.25 db Ut(3o) db MODULE # 3: Receiver The method to calculate uncertainty for a receiver also requires consideration of the signal source used to characterize the receiver. In this case we have chosen a signal generator as a discrete frequency source. The signal generator, in turn, must also be calibrated. Therefore, the signal generator also has an uncertainty which must be taken into account as does the uncertainty of any NIST, or equivalent, traceable standard. Figure 9 shows the signal generator parameters when measured with a calibrated device, traceable to NIST at an uncertainty, Un, of 0.05 db. Two sets of calibration data obtained over a one-year period are used to complete 54 samples. From these the standard deviation, S, and bias, Ab, can be obtained and, applying Table 1 and Table 2, are used to calculate the signal generator total uncertainty, U1(95%) = 0.14 db and U@o) = 0.22 db. Siqnal generator Bias (db): Ai, = Standard deviation: S = Table 5. Signal generator statistics. Figure 10 shows the receiver parameters using the signal generator as a calibrated source. Two sets of data, one year apart, are used to complete 54 data points from which we obtain the Standard deviation, S, and bias, Ab. Applying Tables 1 and 2, we obtain the receiver total uncertainty, Ut(95%) = 0.37 db and Ut(3o) = 0.58 db. Receiver Bias (db): Ab = Standard deviation: S = Table 6. Receiver statistics 361

4 Note: A significant difference in uncertainty is discerned dependent on how a tunable receiver is used to perform a measurement. Using a receiver as a manual device tuned within 2% of a signal results in a systemic error of about 0.05 db, but, if used as a stepped device, using the C63.2 bandpass to bracket a frequency range, the resultant systemic error can be 2.15 db. In Figure 11 calculations of the effect of the nominal receiver bandpass to show the endemic error within 2% of the tuned frequency and the error using the entire 140 khz nominal bandwidth are shown. The total uncertainty of the measurement system module, for both manual tuning and stepping mode, is the RSS of the signal generator, NIST calibrated equipment, and the receiver: Tuned frequency method: Ut(95%) * 0.41 db Ut(3o) db Stepped frequency method: U&Xi%) * 2.53 db U1(30) db TOTAL SYSTEM UNCERTAINTY Applying formula (1) and substituting the uncertainty obtained for each module results in the total uncertainty of the radiated electric-field measurement. Tuned frequencv method: Three meter (3 m) site: Ten meter (10 m) site: ut(%%) db UT(36) =s 2.20 db ut(95%) db UT(3c) db In summary, this paper puts forth the concept of independent modules, use of the ideal or a calibrated value as the statistical mean, suggests N = 54 data samples be used corresponding to ANSI C63.4 frequencies, provides a listing of applicable systemic factors to use for each module, and suggests numerical values for endemic errors. In lieu of tables of numeric data, Figures 3 through 10 present the measured discrete data visually. A set of 54 data sample points are, however, required for application of the formulas to establish a uniform basis for comparison of different test facilities. Notwithstanding the minimum number of test points needed, good engineering practice would not restrict the collection of data to only 27 frequencies nor calibration measurements to once per year. The use of an OATS offset factor, Ao, is best left to the regulators and is not addressed further in this paper. There are many reliable methods of measurement used in industry. This presentation does not intend to preclude continuous scans, spectrum analyzer sweeps or other test methods from consideration. It is suggested that further study with these techniques would be beneficial. ACKNOWLEDGMENT Calculation of uncertainty is traceable to W.S. Gosset who, in 1908, introduced the Student t-distribution. The two-tailed t-distribution is used here to calculate the uncertainty factors. Please note that we use a confidence level of 30 equal to %. Appreciation and thanks is extended for the assistance and support of Steven DeSmitt, John Lynch, Michael Sitarski, Lee Toman and Ronald Willard. Stepped frequency method: Three meter (3 m) site: Ten meter (10 m) site: ut(95%) db UT(3'4 * 4.49 db UT@%) j 3.12 db UT(3CT) db REFERENCE [l] ANSI C , American National Standard for Instrumentation - Electromagnetic Noise and Field Strength, 10 khz to 40 GHz - Specifications. New York: IEEE, SUMMARY The calculation of uncertainty applied to a tuned receiver and the values presented here are consistent with general engineering expectations and the numbers suggested here for a typical test site probably reflects the majority experience of EMI test personnel. The endemic error values listed are realistic numbers, some are based on expected values from specifications, others on estimates of the real world. Consequently, a calculated uncertainty, UT@%) of 1.41 db for a three meter test facility and 1.88 db for a ten meter test facility, or values close to these, are already considered the norm. [2] ANSI C , American National Standard for Methods of Measurement of Radio-Noise Emissions from Low-Voltage Electrical and Electronic Equipment in the Range of 9 khz to 40 GHz. New York: IEEE, [3] Guide to the Expression of Uncertainty in Measurement, International Organization for Standardization-l 993: Switzerland. [4] E. Heise and R. Heise, A Method to Compute Open Area Test Site Uncertainty using ANSI C63.4 NSA Measurement Data IEEE International EMC Symposium Record, p

5 OATS 3 m Attenuation curve w/4 ds tolerance: V&ical dipole. ICC Figure 3. Horizontal 3 m NSA. xx Figure 4. Vertical 3 m NSA. OATS 10 m Attauatim curw w/4 db tolerance Vertical dipole. Figure 5. Horizontal 10 m NSA. Figure 6. Vertical 10 m NSA. Antenna Factors - 3 m 4 Figure 7. Antenna 3 m Factors. Figure 6. Antenna 10 m Factors. 363

6 Signal Generator Calibration Receiver Measurement 0 87 dbuv t I I I II \v I IWII I I I Illlll 86.6 E I I I II 100 Frequency - MHz Figure 9. Signal generator calibration. Figure 10. Tunable receiver. Receiver Tunina Error Effect Of OATS Offset ANSI C63.2 Bandpass Uncertainty at N = 54 de Area (bandpass) = ( ) = -300 (db-khz) Systemic error, Aw = ( ) = db Area (2% tuning) = (db-khz) Systemic error, Am = ( ) = db Confidence - % Figure 11. ANSI C63.2 (6 db) bandpass. Figure 12. Effect of k4 db bias. 364