Antenna Calibration and the Measurement of E-Field Strength
Martin J. Alexander
Aspects of laboratory methods, and lab accreditation issues, are considered in the light of ANSI C63.5 and SAE ARP 958.
Radiated emissions testing for electromagnetic compatibility (EMC) requires the measurement of electric field (E-field) strength, which is compared with a limit level. The output voltage of an antenna is converted to E-field strength via its antenna factor, the measurement of which must include the uncertainty components related to that particular antenna, taking into consideration the environment in which the antenna is to be used for the testing. An unambiguous test is one such that, where different types of antennas overlap in frequency, they must all give the same E-field result at a given frequency, within the antenna factor uncertainties for each type. Uncertainties of antenna factor are not simply the instrumentation uncertainties involved in a particular calibration method. An essential condition for accrediting a calibration laboratory is that the lab has included the relevant uncertainty components in its implementation of the measurement method, such as deviations from the measurement model implied by the standard.
This article reviews aspects of the standard site method in the American National Standards Institute’s ANSI C63.5 and of the Society of Automotive Engineers’ SAE ARP 958 1-m method of antenna calibration.1,2
E-field strength is most commonly measured using an antenna.3 An alternative is to measure an equipment item under test (EUT) in a transverse electromagnetic waveguide in which the output power of the cell can be related to radiated E-field at a given distance from the EUT. There are various possible measurands that would be suitable for radiated EMC testing, such as the power out of a gigahertz transverse electromagnetic cell or reverberation chamber.4,5 However, this article concentrates on the use of antennas.
The International Special Committee on Radio Interference (CISPR) of the International Electrotechnical Commission (IEC) is producing a standard describing methods of antenna calibration. In the first draft of this standard, which was circulated to Working Group 1 of CISPR Subcommittee A on January 6, 2006, FA is proposed as the new notational term for antenna factor.
The main purposes of this article are to help calibration laboratories, as well as technical assessors working for accreditation bodies, be aware of the extent of uncertainty components applicable to antenna factor and to exhort them to make a thorough assessment of the model underlying the method of calibration. To make unrealistic demands for low uncertainties in the measurement of field strength in emission testing is not the aim. Rather, the ultimate intention is that calibration labs should quote realistic uncertainties for FA. The calibration lab should engage in dialog with the test lab to ensure that the method of antenna calibration is appropriate for the use to which the antenna is put—if necessary, helping the test lab to understand the various antenna-related uncertainties.
Antennas are affected by mutual coupling to their environment, which changes FA. Different types of antennas have different directivity, and thus can give different answers for E-field strength for certain measurement geometries. These are uncertainties in E-field strength that should be taken into account by the EMC test laboratory.
Standards. The calibration laboratory calibrates the antenna by a method prescribed in a standard such as those published by the Institute of Electrical and Electronics Engineers, CISPR, ANSI, and SAE. It is the responsibility of the authors of a standard to describe clearly the measurand and, ideally, its purpose, and to devise a calibration method that is able to measure the measurand. If the chosen method of calibration falls short of achieving the measurand in all its aspects—which may be a deliberate shortcoming due to the excessive cost of a complete characterization of a complex measurand—the uncertainties must be identified. To illustrate this by example, the popular standard site method as implemented in ANSI C63.5 is analyzed in the next section.
Sometimes standards are written with reproducibility of measurement as the deliberate first priority and the measurement of a normal physical parameter taking second place. An example is CISPR 25.6 Still, it is incumbent upon the authors to include sufficient guidance in the measurement of the quasi–antenna factor to ensure that it can be reproducibly measured. Ideally, the standard should include an explanation of why reproducibility is preferred to the physical parameter, an itemization of the limitations, and the consequences of misuse of the measurand where it was not intended. For example, it is possible for someone to use the antenna factors of SAE ARP 958 in the measurement of emissions at 10 m, not appreciating that large errors can result. Perhaps there should be a different term for antenna factor as it is used in ARP 958. Aspects of implementing this standard are analyzed later in this article.
The Calibration Laboratory. Several uncertainties should be taken into account by the laboratory that is calibrating the antenna. The calibration lab must thoroughly understand the method described in the antenna calibration standard and any underlying model that this is based on. The lab and the customer should agree on which standard the antenna under calibration (AUC) is being measured to. Also, if necessary, the lab should explain to the customer the limitations of the standard. If the customer wants modifications to the standard method, these should be clearly defined and agreed upon by both parties; and, if the customer wants an accredited calibration, the accreditation body should also accede. If, for convenience, the calibration lab chooses to use a broadband antenna in the measurement of the AUC, any implications of this should be included in the FA uncertainty, for example, by considering the variation of phase center with frequency (see discussion in the next section).
The Accreditation Body. The accreditation body has a number of responsibilities. The ultimate purpose of EMC antenna calibration is to ensure that electronic goods placed on the market adequately protect users of radio services from radio-frequency interference. Various laboratories have established mutual recognition arrangements to recognize one another’s calibration and test results in order to facilitate trade.
For calibrations, the International Bureau of Weights and Measures (BIPM) maintains Key Comparison Databases (KCDB), a compendium of comparative results of the measurement of key physical parameters, such as FA, performed by national calibration laboratories from participating countries.7 The spread in the KCDB values gives a clue as to the achievable uncertainties at the top international level. The BIPM Web site lists the calibration and measurement capabilities of national standards laboratories. An accreditation body can use the uncertainty information, including the spread of KCDB values, to assess the claims made by the laboratory it is accrediting. Relevant comparisons are CCEM.RF-K7.b.F and CCEM.RF-S21.F for broadband EMC antennas.8 CCEM is BIPM’s Consultative Committee for Electricity and Magnetism. CCEM.RF-S21.F is recent and includes monopole antennas; the data may not yet be on the BIPM Web site, but they can be obtained from the British National Physical Laboratory.9
There is a goalpost for an accreditation body. An antenna calibrated by any laboratory that has been accredited (by any recognized accreditation body worldwide) for antenna calibration should have antenna factors that agree within the uncertainties claimed by each laboratory. A calibration laboratory may claim uncertainties that are lower. If lower than those declared by the majority of national laboratories that participate in international intercomparisons, the technical assessor, who is acting on behalf of the accreditation body, will require evidence.
Analysis of ANSI C63.5
ANSI C63.5 has adopted the standard site method (SSM) for the calibration of antennas.10 In order to calculate the uncertainties in E-field strength arising from FA obtained by the C63.5 procedure, one needs to understand the model for calibration and any assumptions made beyond this model.
Figure 1. Two dipole antennas above a ground plane, with a separation R.
The SSM is based on two Hertzian dipoles whose length is less than λ/10 and whose input impedance is negligibly affected by the ground plane. One antenna is height-scanned to find the maximum signal strength, which occurs when the direct ray between Hertzian antennas and the ground-reflected ray are in phase (see Figure 1). The reason for finding the maximum signal is to reduce the sensitivity to site errors. The corollary is that, on a good site, an accurate calibration can be obtained with both antennas at a fixed height and by compensating for the phase misalignment of the two rays. Other aspects of the SSM model to note are that Hertzian dipoles have a phase center at a point that does not vary with frequency and that they have a uniform radiation pattern in the H-plane and a sin θ pattern E-field in the E-plane.
The method of antenna calibration in ANSI C63.5 prescribes certain measurement geometries; for example, for an antenna separation of 10 m, one antenna is set at a fixed height of 2 m above the ground plane and the other antenna is scanned in height from 1 to 4 m. The significant difference from the SSM model is that the antennas are not Hertzian. In addition, they are sensitive to mutual coupling with the ground plane, they do have radiation patterns that differ from sin θ, and some antennas do have phase centers that vary with frequency. This means that the height at which a maximum signal is found may not be the same as the theoretical height used to calculate EDmax (based on the Smith equations).10 EDmax is the maximum E-field strength in μV/m for a half-wave receiving dipole. The dipole is scanned in height in the range of 1–4 m, a given distance away from a half-wave transmitting dipole with 1 pW of radiated power.
Apart from correction of a slightly erroneous EDmax, one could argue that the C63.5 method is tailored to the use to which the antenna is to be put, namely, emissions testing by height scanning. In that case, the mutual-coupling, phase center, and radiation pattern characteristics are properly included in a geometry-specific antenna factor FAgs. This would be true if the EUT were a point source at a 2-m height, using the above geometry, but it breaks down if the EUT has a spread of radiation sources at different heights.
The model assumes a separation of 10 m between the antenna and the face of the EUT. However, in the calibration, a second log-periodic dipole array (LPDA) antenna takes the place of the EUT but, unlike the EUT, it has a phase center that varies with frequency. This variation results in an error in the FA of the first LPDA antenna. For example, for an LPDA operating in the frequency range 200 MHz–1 GHz, and where the distance is measured to the center of the antenna, the error in FAgs of not accounting for the phase center is ±0.3 dB. This increases to ±0.9 dB for a 3-m distance.
The error could be circumvented by using dipole antennas at the fixed-height location, but this would be tedious. An easier option for reducing this uncertainty term is to correct for the phase center variation by using, in EDmax, the distance between the midposition of the scanned LPDA antenna and the phase center position at each frequency of the fixed LPDA antenna. If this is not done, the calibration lab must include this term in the uncertainty budget for FA because the lab is deviating from the model.
Antenna factors can vary on the order of ±1 dB due to mutual coupling with the ground plane. Also, some antennas are directional and deviate substantially from the Hertzian model in both polarizations. If FA is defined as a measurement of field strength, all these issues need to be taken into account in the uncertainties.
ARP 958 Calibration Method
The aim of the SAE ARP 958 antenna calibration method is to give an FA that can be used for measuring field strength at a distance of 1 m from a source in a shielded room. The standard justifies calibrating the antenna with a second identical antenna on the grounds that the second antenna represents a distributed source. The argument here is that the calibration resembles the antenna/source electromagnetic conditions of an emissions test.
Figure 2. The difference in AF2 of a 50-Ω balun biconical antenna using far-field and near-field formulas plotted in comparison with the free-space antenna AF1. AF1m is calculated by ARP 958, AFnf is AF1m using the near-field formula, and AFfs is the free-space FA.
ARP 958 does differentiate the 1-m antenna factor from the far-field antenna factor, acknowledging that they can differ by a few decibels. It calls the former AF2 and the latter AF1. A question worth examining is whether the measurement of field strength at 1 m using AF2 results in lower uncertainties than does the use of AF1.
One virtue of the ARP 958 method of antenna calibration is that it is simpler to implement than a far-field method. In addition, a less costly test site can be used: it is easier to avoid interactions with the antenna surroundings when the antennas only have to be 1 m apart. On the other hand, since most antennas are calibrated for AF1 anyway, to measure AF2 could be an additional expense.
A possible argument that could be used by proponents of ARP 958 is that, as long as an agreed-upon calibration method is used—for application to emissions testing by an agreed method against an agreed limit—it does not matter that there is an error in the measured E-field value, since everyone will experience the same error. In that case, it should be made quite clear that AF2 is to be used only for a particular type of emissions test, with uncertainties for various scenarios laid out. For example, placing an antenna 1 m from the metal side of an automobile would entail a different uncertainty than placing it 1 m from a small EUT in a shielded room would. Furthermore, it would be helpful if ARP 958 quantified the errors that would result if AF2 were mistakenly used instead of AF1 in a far-field emissions test.
Figure 3. Schematic diagram of a biconical antenna with a length of about 1.35 m, a cage width of about 0.5 m, and with one crossbar in each cage.
Biconical Antenna. To find the relative uncertainties of measuring E-field at 1 m using AF1 and AF2 from 20 to 200 MHz using a biconical antenna likely requires a proper study. Nevertheless, some of the answers are advanced in what follows.
The biconical antenna represents an extreme case of the application of the ARP 958 method, which the standard concedes was originally written for log-spiral antennas over the range 200 MHz–1 GHz. Two features of the method stand out.
One is that the extremities of the biconical antenna elements of the opposing antennas are only 0.5 m apart, which implies heavy mutual coupling; when one antenna is removed, the effect of coupling built into AF2 is rarely going to be relevant when the AUC is used for emissions testing. ARP 958 argues that this coupling is realistic, but it may be better to use a calibration method with less coupling and to add an uncertainty to the emissions test result that is appropriate to coupling between the antenna and the item being tested. That the coupling is realistic may be questioned through the use of an example: Placing a biconical antenna 1 m from the metal face of a vehicle means that its reflected image is effectively 2 m away; therefore, placing two biconicals 1 m apart in their calibration exaggerates the mutual coupling effect that could be experienced in an emissions test.
The other noteworthy feature of ARP 958 is that, while the far-field formula is used to derive FA, at 20 MHz a separation of 1 m is only 0.07 wavelength. This is well into the near field. A rule of thumb is that the near field for short dipoles has a large effect on the calculation of FA for distances of less than λ/2π, or 0.16 wavelength; therefore, a point in space 1 m distant from a source is in the near field for frequencies below 47.7 MHz.
The following equation for the dependency of E-field strength on distance, including the near field, has been verified by measurement to predict accurately the E-field strength in the near field of a 10-cm-diameter spherical dipole emitter. The biconical antenna can be considered a short dipole at 20 MHz and, with varying degrees of approximation, up to 47.7 MHz, so it is worth applying this formula in the derivation of FA of two biconicals 1 m apart:
where r is the effective value of distance that is applied to Equation 6 of ARP 958, d is the actual separation distance (that is, 1 m),
λ is the wavelength (all of the preceding are in meters), and β is the result of 2π/λ. At distances larger than a wavelength, r converges with d.
In Figure 2, AF2 is plotted in two forms. AF1m uses r = 1 m, and AFnf uses the above expression for effective r with d = 1 m. The FA changes in the near-field region, and the difference is 7.2 dB at 20 MHz. At 300 MHz the difference is 3.5 dB; this is caused mainly by mutual coupling and by the fact that the length of the antennas at 1.4 m is greater than their 1-m separation. The latter means that the wave front has not formed properly, or is not focused (being in the Fresnel zone), resulting in a general increase in the FA. A common mistake is to assume that a near-field FA is needed when in fact a far-field FA should be used. If the location happens to be in the near field of the source, a near-field formula could be used to extrapolate the field to a greater distance. The process can involve a number of assumptions, including whether the source is primarily electric or magnetic and whether the antenna is a dipole or a loop and what their relative sizes are. Also, the estimate of extrapolated field can involve large uncertainties.
Uncertainty Assessment. Regardless of whether or not AF2 has large uncertainties in the measurement of field strength, it is possible to measure AF2 precisely, according to the method described in the standard and with an accompanying detailed description of how the antennas were set up.
Figure 4. A possible method of calibrating a biconical antenna for AF2 involving the use of a small biconical antenna. This one has a tip-to-tip length of 0.44 m.
Consider the uncertainty that a calibration laboratory can claim in the application of ARP 958 to biconical antennas. First, the antennas are very close to one another, so there will be sensitivity to the separation distance within a centimeter or so. Second, although the angular tip of one biconical facing the tip of the other biconical means the tips will be 0.48 m apart, if the antenna cage is rotated 30°, the tips will be 0.55 m apart (see Figure 3). There is also the question of whether the orientation of the crossbar has any effect on AF2. Since the standard does not specify how the biconical cages are to be oriented, these factors will have to be included in the assessment of uncertainty of AF2.
A way to reduce the influence of mutual coupling on the value of AF2 would be to use two small biconical antennas approximately 0.4 m long in the three-antenna method to calibrate the larger biconical (see Figure 4). This would be a more realistic calibration for many emissions testing setups.
Third, the standard acknowledges the influence of the ground plane on the FA and, accordingly, defines a 3-m height for the center of the antenna above ground. It does not give any guidance on the magnitude of this effect, however. More significantly, it does not specify whether the antennas should have vertical polarization (VP) or horizontal polarization (HP). The two polarizations will yield different values for AF2, and, if the height is different in the emissions test, this will change the FA, making yet another uncertainty in using AF2. The fact that Appendix C of ARP 958 gives EDmax values for HP could be a hint that HP is intended in clause 4. Some labs assume VP because this reduces the influence of the ground (see Figure 5). However, at frequencies where the separations of the antennas and their images are in the near field, there is radiation in the direction of the long axis of the antenna, thereby increasing the ground reflection of a vertically polarized antenna.
Figure 5. A pair of vertically polarized biconical antennas with crossbars facing each other. Their centers are 1 m apart at a height of 1 m above the 60 x 30 m ground plane at the National Physical Laboratory (Teddington, Middx, UK).
A fourth element of uncertainty involves the standard’s stipulation of identical antennas. Two antennas of the same model from the same manufacturer usually will be identical in the context of emissions test uncertainties, but this cannot be taken for granted in the context of antenna calibration uncertainties. Calibration laboratories can get a competitive edge by offering the lowest possible uncertainties. This is not likely to be achieved if the AUC is calibrated by an antenna of a different model unless the uncertainties have been worked out. Even in this case the calibrations of the AUC by the different model and the identical model should be compared. Even an identical model needs to be verified by comparing the transmission loss between each antenna and a third antenna. Any difference must be included in the uncertainty budget.
Guidance on phase center corrections for LPDA antennas has been published.11 An example for 3-m separation was mentioned earlier in this article. It is fortunate that ARP 958 does not mention biconical-log hybrid antennas, because the uncertainties would be excessive.
Uncertainty considerations for monopole calibrations are available.12,13 It is important to bear in mind that the capacitor substitution method of section 5 of ARP 958 is sensitive to stray capacitances, and that the design of a calibration jig is not trivial. The accreditation body should demand proof—for example, through an intercomparison using jigs designed by different calibration labs—if the claimed uncertainties are less than ±1 dB.
Data for the realized gain of a dual-ridged-guide (DRG) horn are presented in Figure 6 for illustrative purposes. The gain has a ripple of ±0.5 dB caused by multiple reflections between the pair of DRG horns. This ripple shows up above 5 GHz. Figure 6 shows that the ripple is virtually eliminated by using WG18 horns, which have a much smaller aperture than the DRG horn (42 x 57 mm as against 140 x 240 mm). Again, the introduction of mutual coupling by the calibration method is artificial and rarely likely to be the same when the AUC is used for emissions testing. The coupling effect could be reduced by calibrating the DRG horn by the three-antenna method and using smaller horns at the higher frequencies.
Annex C of ARP 958 (the three-antenna method at 3 m) makes the erroneous statement that reflection variations are removed by three simultaneous equations.2 In fact, they are included. It is the substitution, or reference, method in which nonuniformities of field caused by site defects cancel out; the lowest uncertainties occur when the AUC and the reference antenna have similar mechanical dimensions. It should also be made clear that Table C1 in the annex applies to horizontally polarized antennas.
Responsibilities of the Interested Parties
The calibration of antennas involves a number of issues affecting the measurement uncertainty, of which all the following parties need to be aware: the customer commissioning the EMC emissions test, the test laboratory that commissions an antenna calibration, the calibration laboratory, and the accreditation body or quality organization.
The customer should be cognizant of the purpose of measuring the radiated emissions of its product and should agree with the test lab that it is either the measurement of field strength or a reproducibility check that is required. The customer and test lab should also share an understanding of the implications for measurement uncertainty. The test lab should be able to advise the customer regarding which test would be suitable.
The test lab should identify the appropriate method of antenna calibration and place reasonable demands on the calibration lab, bearing in mind the differences in the possible methods of calibration. The test lab should communicate with the calibration lab and agree in detail about the method of antenna calibration. For its part, the calibration lab should be able to advise the test lab on a method of calibration that would meet its requirements. It should understand the uncertainties of calibration methods and pass this information on to the test lab, via the calibration certificate or other document.11,14
The quality organization should have an overview of this whole process, keeping in mind the international dimension, so that it can assess whether any uncertainty components have been missed. This organization should fully understand the uncertainties of the proposed method of measurement of FA. It should also decide what additional uncertainties the calibration lab should be pointing out to the test lab in its use of those antenna factors. Some would argue that all antenna-related uncertainties ought to be built into the FA uncertainties to prevent the test lab from underestimating the uncertainty of field strength measurement. A good background to measurement uncertainties is provided by the IEC basic standard CISPR 16-4.15
The calibration lab should quote realistic uncertainties for FA. For this to happen, the calibration lab has to understand the model that applies to the agreed-upon calibration method and must estimate the uncertainties arising from any deviations from that model. For example, in the standard site method, the model assumes a fixed-height antenna with a unique phase center. Thus, when an LPDA antenna is used, FA should be calculated using the appropriate distance at each frequency. If these steps are not taken, corresponding uncertainty terms must be added to the uncertainty of FA.
The SSM can be used to measure geometry-specific antenna factors. The uncertainties can be small for emissions testing of a small EUT placed at the same height as the fixed antenna, but it should be made clear that the uncertainties will increase for a taller EUT. When the SSM is used to measure free-space antenna factors, uncertainty terms must be added to account for the deviations in behavior of the antennas from Hertzian dipoles, such as mutual coupling, radiation pattern, and phase center. An accreditation body should question in depth any calibration laboratory that claims low FA uncertainties for broadband antennas used for emissions testing above a ground plane, making reference to the results of international intercomparisons and data from BIPM. The model for the ARP 958 method of calibration needs to be defined in more detail to avoid understandable differences in implementation that will lead to differences in FA results being obtained by different calibration laboratories. A major example is whether biconical antennas should be horizontally or vertically polarized above a ground plane. ARP 958 should identify the significant contributors to the measurement uncertainty.
Accreditation bodies should ensure that calibration laboratories have estimated uncertainties caused by deviations from the model. Also, they should be wary of uncertainty budgets that include only the instrumentation uncertainty and the setup distance between the antennas. For example, there may be a temptation to use a similar antenna rather than an identical model because the calibration lab does not happen to possess every model that a test lab may submit.
The use of the far-field formula for calculating antenna factors should be reviewed, for the reason discussed in connection with Figure 2, where, in the example, the FA was too low by 7.2 dB at 20 MHz. The example showed that an EUT will be undertested, that is, that the emissions should be 7.2 dB higher than recorded when using AF2.
There is even a case to be made for using free-space antenna factors, based on the fact that the overall uncertainties for emission measurements at a 1-m distance may be comparable to, or less than, the uncertainties involved in using a 1-m separation in the calibration of antennas. The placing of two biconical antennas 1 m apart can hardly claim always to resemble the emissions test setup. It is recommended that calibration using a small biconical antenna be explored.
If the ultimate aim is to know the uncertainty of the E-field strength in an EMC emissions test, it is first necessary to understand the conditions under which the antenna was calibrated. This is in order to distinguish the uncertainty terms already included in the FA from the additional uncertainties that have to be added to account for the differences between the conditions of the calibration and those of the emissions test.
It is incumbent on the calibration laboratory to state clearly in the calibration certificate the calibration conditions. Also, if there could be any ambiguity, it might be necessary to state the calibration method. For example, the term free-space means a truly free-space environment, so if there is any deviation from this, such as ANSI C63.5:2004, the method used should be explicitly mentioned.4 It would be helpful for the calibration laboratory to take the extra step of anticipating the likely use of the antenna and giving estimates of further uncertainties that may be incurred.
It is incumbent upon the accreditation body to understand all of these factors in order to ensure that the calibration laboratory has identified all the uncertainty contributions to the FA as requested by the test laboratory (or in anticipating the test lab’s use of the antenna). An accreditation body may have international responsibilities. A test of their fulfillment is that antennas that have been calibrated by its accredited laboratories anywhere in the world have credible FA uncertainties and give good agreement in the round-robin measurement of field strength of a canonical emitter.
1. ANSI C63.5:2004, “American National Standard for Electromagnetic Compatibility—Radiated Emission Measurements in Electromagnetic Interference (EMI) Control—Calibration of Antennas (9 kHz to 40 GHz)” (Washington, DC: American National Standards Institute, 2004).
2. SAE ARP 958, Rev. D, “Electromagnetic Interference Measurement Antennas—Standard Calibration Method” (Warrendale, PA: Society of Automotive Engineers, 2003).
3. CISPR 16-1-4:2003, “Specification for Radio Disturbance and Immunity Measuring Apparatus and Methods—Part 1-4: Radio Disturbance and Immunity Measuring Apparatus—Ancillary Equipment—Radiated Disturbances” (Brussels: International Electrotechnical Commission, 2003).
4. EN 61000-4-20:2003, “Electromagnetic Compatibility (EMC)—Part 4-20: Testing and Measurement Techniques—Emission and Immunity Testing in Transverse Electromagnetic (TEM) Waveguides” (Brussels: CENELEC, 2003).
5. EN 61000-4-21:2003, “Electromagnetic Compatibility (EMC)—Part 4-21: Testing and Measurement Techniques—Reverberation Chamber Test Methods” (Brussels: CENELEC, 2003).
6. CISPR 25:2002, “Radio Disturbance Characteristics for the Protection of Receivers used Onboard Vehicles, Boats, and on Devices—Limits and Methods of Measurement” (Brussels: International Electrotechnical Commission, 2002).
7. Key Comparison Database [online] (Sèures, France: International Bureau of Weights and Measures, 2002 [cited 3 February 2006]); available from Internet: http://kcdb.bipm.org.
8. M Alexander, “International Comparison CCEM.RF-K7.b.F of Antenna Factors in the Frequency Range 30 MHz to 1 GHz,” Metrologia 39 (2002): 309–317.
9. MD Foegelle, “Site Validation Theory 101: Techniques and Methods,” Compliance Engineering 17, no. 5 (2000): 42–54
10. AA Smith, “Standard-Site Method for Determining Antenna Factors,” IEEE Transactions on EMC 24 (1982): 316–322.
11. MJ Alexander et al., “Measurement Good Practice Guide No. 73: Calibration and Use of Antennas, Focusing on EMC Applications” (Teddington, UK: National Physical Laboratory, 2004), Appendix 4; available from Internet: www.npl.co.uk/electromagnetic/publications/guides.
12. MJ Alexander et al., “Measurement Good Practice Guide No. 73: Calibration and Use of Antennas, Focusing on EMC Applications” (Teddington, UK: National Physical Laboratory, 2004), sect. 9.10; available from Internet: www.npl.co.uk/electromagnetic/publications/guides.
13. DA Knight, A Nothofer, and MJ Alexander, “Comparison of Calibration Methods for Monopole Antennas, with Some Analysis of the Capacitance Substitution Method, NPL Report DEM-EM 005” (Teddington, UK: National Physical Laboratory, 2004).
14. MJ Alexander, “Using Antennas to Measure the Strength of Electric Fields near Equipment,” Compliance Engineering 17, no. 4 (2000): 40–44.
15. CISPR 16-4:2002, “Specification for Radio Disturbance and Immunity Measuring Apparatus and Methods—Part 4: Uncertainty in EMC Measurements” (Brussels: International Electrotechnical Commission, 2002).
Martin J. Alexander is principal research scientist at National Physical Laboratory (Teddington, UK). He can be reached at email@example.com.