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On the use of TEM cells for the calibration of power frequency electric field meters
Measurement 43 (2010) 1282–1290
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On the use of TEM cells for the calibration of power frequency electric field meters Luca Zilberti a,b, Oriano Bottauscio a, Mario Chiampi b, Gabriella Crotti a,* a b
Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, I-10135 Torino, Italy Dip. Ingegneria Elettrica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
a r t i c l e
i n f o
Article history: Received 11 June 2009 Received in revised form 18 May 2010 Accepted 15 July 2010 Available online 21 July 2010 Keywords: Boundary element methods Calibration Electric field measurement TEM cell Uncertainty
a b s t r a c t This paper focuses on the performances of TEM cells when used in the calibration of power frequency environmental electric field meters. The spatial non-uniformity of the electric field inside a TEM cell is analyzed through experimental investigations and three-dimensional Boundary Element modeling to evaluate the field experienced by the sensing elements of actual 3D meter probes. The perturbation caused by the probe support is also taken into account. The uncertainty component associated with the spatial non-uniformity in the volume taken up by typical power and low frequency field probes is estimated. The field non-uniformity is also evaluated in relation to the use of TEM cells of reduced size. Finally, the field non-uniformity is exploited to predict the performance of an actual field meter operating in significant field gradients. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction TEM cells are the recommended set-up for the generation of reference electric fields used in the calibration of probes and sensors in the frequency range from some kilohertz to hundreds of megahertz. A wide literature, see for example [1,2], analyses in detail their behavior and relevant standards precisely define the rules and procedures for a correct execution of the calibration process [3,4] in the specified frequency range. As concern the calibration of power frequency field meters, used for the measurements of environmental fields in the evaluation of human exposure, the recommended configuration is the parallel plate systems [5–7]. The uncertainty associated with the generated field ranges from a few part per thousand to a few percent. Nevertheless, TEM cells are very often used as an alternative generation system. With respect to the recommended devices, TEM
* Corresponding author. E-mail addresses: [email protected] (L. Zilberti), o.bottauscio@ inrim.it (O. Bottauscio), [email protected] (M. Chiampi), g.crotti@ inrim.it (G. Crotti). 0263-2241/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2010.07.005
cells have some practical advantages such as: (i) the possibility of working in a wide frequency range (from DC up to some hundreds megahertz), (ii) the reduced size, (iii) the improved immunity from external disturbances, due to the intrinsic shielding, and the reduced disturbances which can cause interference with other devices. On the other hand, due to their shape, TEM cells show lower electric field uniformity with respect to parallel plate generation systems of the same size. An increase of the cell size improves the field uniformity, but at the same time limits its cutoff frequency. Thus, the possibility of using the cells for the generation of reference electric fields both at high and low frequencies needs a compromise between these two opposite requirements. The paper aim is a quantitative analysis of the performances of a TEM cell, when used in the calibration of electric field meters, which are employed for the measurements of environmental power frequency fields. So, reference is made in the following to the indications given by the relevant standards [5,6]. In comparison with the radiofrequency ones, the low and power frequency field probes are generally characterized by greater dimensions and different internal sensor
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arrangements. The non-uniformity of the spatial field distribution inside the TEM cell and its effect on the indication of the electric field meters under calibration are then investigated. The spatial field distribution inside the cell can be evaluated numerically (e.g. by the moment method as detailed in [8]) or experimentally, by means of calibrated field probes. In the following, a noncommercial three dimensional tool based on the Boundary Element Method (BEM) is adopted to compute the field distribution actually experienced by three-dimensional field probes. In this analysis the probe characteristics (dimensions, number and different arrangement of the field sensing elements) and the possible presence of dielectric material (e.g. probe support) are accounted for. The validation of the computational model is performed by comparison with analytical solutions and experimental data. The measurements are performed in a TEM cell, available at the Istituto Nazionale di Ricerca Metrologica (INRIM). Different configurations are analyzed, such as open or closed cell and field probe placed in the upper or lower section of the cell. An estimation of the size averaging error, which arises because of the non-negligible dimension of the field sensing elements when the probe is introduced in a non-uniform field, is also taken into consideration. Moreover, some comparisons with a parallel plate system are presented. A further effect investigated is the presence, during the calibration, of the field probe support, which can significantly influence the distribution of the electric field in the volume taken up by the meter probe [9,10]. In fact, calibration should be performed in the same configuration used during the measurement, that is with the probe equipped with its own support. In practice, because of their length dielectric supports different from those adopted during the on-site measurements are generally used in the calibration phase. On the basis of the results obtained, an evaluation of the uncertainty contribution that can be associated with the field non-uniformity is carried out, taking into account the finite dimensions and internal field sensors arrangements of actual 3D probes in relation to the TEM cell dimension. Finally, the field non-uniformity of the TEM cell is exploited to estimated the error made by the field meter when used in presence of significant spatial field gradient.
2. Numerical model and experimental setup Under the assumption of quasi-stationary operating conditions, the electric field formulation is developed in an open boundary 3D domain, where the conductive bodies are replaced by Dirichlet conditions, imposing the known potential on the electrodes. This hypothesis allows the description of the electric field E in terms of a scalar potential u (E = grad u), which leads to the boundary value problem:
div ðegraduÞ ¼ 0
ð1Þ
Eq. (1) is solved by means of a standard BEM approach. The surfaces of the bodies included in the domain are divided into N triangles. In each element the potential is
assumed to be linear and its normal derivative to be constant. The electric field distribution is computed by solving the resulting BEM equation in the internal and external regions:
fui ¼
N X j¼1
" ðru nÞj
Z Xj
wds uj
#
Z Xj
ðrw nÞj ds
ð2Þ
where Xj are the triangular elements, w ¼ 1=4pr is the 3D Green function (being r the distance between source point i and computational point j), nj is the normal unit vector and f is 0.5 on the surfaces and 1 elsewhere. The unknowns are the nodal values of the potential and its normal derivatives in each triangle on the surface of the dielectric body (e.g. dielectric support); on the electrodes the only unknowns are the normal derivatives of the potential, while the imposed potential represents the field source. Problem (2) is completed by the interface conditions between internal (a) and external (b) volumes:
(
ðbÞ uðaÞ ¼ uj j eðaÞ ruðaÞ nðaÞ j ¼ eðbÞ ruðbÞ nðbÞ j
ð3Þ
The analysis is developed considering the INRIM TEM cell shown in Fig. 1a, where the origin of the coordinate system is assumed in the central point of the septum. The cell has a square cross-section of side LT = 1.2 m in the xz-plane with a shell-septum distance DT = 0.6 m (ratio LT/DT = 2) and a 2.4 m length along y-axis. The cutoff frequency of the TEM cell, when used for radiofrequency calibrations, is about 125 MHz. A 60 V, 50 Hz voltage, generated by a calibrated voltage source (Fluke 5500A Calibrator), is applied across the electrodes (septum and shell), which corresponds to a nominal value E0 of 100 V/ m in the centre of the lower half-cell P0 (0, 0, 0.3 m) or in the centre of the upper half-cell Q0 (0, 0, +0.3 m). Taking into account the considered frequencies, the magnetic field can be disregarded, since the load terminal of the TEM cell is open. The INRIM parallel plate system, considered for the comparison, is composed of two aluminum square horizontal plates of side LP = 2 m at a vertical distance DP = 1 m (ratio LP/DP = 2); five grading rings improve the field uniformity in the central volume between the plates [11]. The choice of the most suitable BEM discretization of the TEM cell, as a compromise between accuracy and computational cost, is made by increasing the number of triangles in the system of Fig. 1b and by comparing the computed field values in different points of the domain. The obtained results, summarized in Table 1, show that a mesh with about 9700 surface elements is surely sufficient to make the discretization error negligible. The limit error due to the numerical evaluation of the electric field values in the central volume of one half-cell is estimated to be within ±0.5%; it is obtained by considering, besides the discretization error, the comparison with analytical solutions [10,12]. The measured data are obtained using a free-body electric field meter, previously calibrated in the parallel plate generation system. The meter is equipped with a 3D cubic
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Fig. 1. INRIM TEM cell: (a) picture of the cell with probe and plexiglass support; (b) BEM discretization of the lower half-cell, with about 9700 triangles. The considered support configurations are also presented.
Table 1 Electric field amplitude (V/m). Point coordinates (m) x
y
z
0 0 0 0.3 0
0 0 0 0.3 0.6
0.3 0.25 0.35 0.3 0.3
2424 triangles
5832 triangles
9696 triangles
99.6 105.0 94.2 97.8 107.4
99.4 105.0 94.0 97.7 107.0
99.4 105.0 94.0 97.7 107.0
respect to the foam structures typically employed for radiofrequency. In addition, such a cylindrical support is similar to those typically used when measuring on-site. In this investigation, the considered support is made of solid polymethyl methacrylate (plexiglass), with relative permittivity er = 3.5 at 50 Hz and quite large diameter (d = 0.05 m) in order to put in evidence its perturbing effect on the field distribution.
3. Electric field distribution in the calibration volume probe of 0.1 m external side, which is connected to the measuring instrument by optical fiber. The probe is fitted out with five 0.08 m 0.08 m single-axis field sensing elements. Each sensing element is made of two parallel square electrodes closely faced; the field strength orthogonal to their surface is determined by measuring the current induced between them [5,6]. The meter can give, as output indications, both the three orthogonal field components and the resultant field. Two of the orthogonal field components are obtained as the average value given by two single-axis sensing elements, placed at the opposite faces of the cubic probe, whereas the third component is given by only one sensing element, located close to one of the remaining faces of the cube. The field probe can be placed in the considered measurement point either by suspending it through thin plastic threads or by using a support of suitable length. Due to the weight of the low-frequency electric field meters, in this second case usually a hollow rigid support is preferred
With respect to a parallel plate configuration with the same ratio L/D, the electric field distribution inside the
Fig. 2. Distribution of electric potential u and electric field component Ez along a vertical line in the center of the xy-plane.
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Fig. 3. Computed electric field flux lines and electric potential isolevel lines in the middle cross-section of the upper half of the INRIM TEM cell.
Fig. 4. Computed electric potential distribution on a square surface centered in P0 (the imposed potential is 0 on the shell and 60 V on the septum): (a) closed TEM cell; (b) open TEM cell.
TEM cell is only approximately uniform, due to the different shape and size of the two electrodes [11–15]. Fig. 2 shows the electric potential and the field component Ez along the z-axis in the centre of the xy-plane. The electric field decreases from 120 V/m close to the septum, to 80 V/m when moving towards the shell. As a comparison, in the INRIM parallel plate system, which is equipped with grading rings, the field variation along the same line is within 0.2%. This behavior is well put in evidence by Fig. 3, which presents the distributions of the electric field flux lines and electric potential isolevels in the middle cross-section (xz-plane) of the upper half of the TEM cell, where, due to the symmetry, the Ey component is zero.
Disposition
E0
EA
ED
EM
Closed Open
99.4 99.7
99.4 99.8
99.6 99.9
100.2 100.8
The spatial non-uniformity on the xy-plane centered in P0 is shown in Fig. 4a by the distribution of the electric potential over a 0.2 m 0.2 m surface. The potential is about 25 V instead of the expected 30 V; its maximum deviation, with respect to the value in P0, is 0.5 V. As a comparison, the deviation decreases to less than 0.001 V, when considering the same surface in the INRIM parallel plate setup. It can also be observed that, besides an Ex component (up to 12% of Ez), a detectable Ey component up to 2% of Ez is found over the considered area. The potential distribution on the same surface is shown in Fig. 4b for the ‘‘open” cell that is when one of the lateral walls has been removed, for example, to allow the introduction of a probe horizontal support. The results show an evident asymmetrical potential distribution, with, as expected, a higher spatial uniformity towards the removed wall. It must be noted that perturbation due to the presence of external conductive objects is found negligible provided that the cell is not in very close proximity to them. To compare the computed electric field values to those obtained by measurements in a non-uniform field, the finite dimensions of the single-axis sensors and their relative position inside the probe have to be taken into consideration. The field spatial non-uniformity may give rise to discrepancies between the actual value of the field in the probe center (measurement point) and the indication given by the measuring instrument, estimated by averaging the field amplitude on the operating single-axis sensing elements of the probe. Table 2 shows the electric field z-component (E0) computed in P0, the one (EA) averaged on the sensing element area centered in P0 and the mean value (ED) of the two averages on the areas at z = 0.25 m and z = 0.35 m; the corresponding measured value (EM), given by the meter, centered in P0, when the probe is oriented with two single-axis sensors detecting the z-component, is also presented. The data obtained with the open cell configuration are also shown for comparison. The small differences between local and averaged computed values show how a rather satisfactory uniformity is ensured on the sensing element surface centered in P0. Good agreement is also found between the computed mean value ED and the meter output EM, which is the average of the indication of two sensing elements disposed symmetrically with respect to the probe centre. The deviation between measured and computed values can be explained by considering, besides the estimated limit error associated with the numerical procedure, the measurement uncertainty (<1%) of the meter indication. This uncertainty is evaluated by taking into account both the calibration contribution (calibration performed in the parallel plate system) and that due to the vertical positioning of the probe, suspended through a thin plastic thread.
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The insertion of the probe support creates significant modifications of the field distribution, because the flux lines of the electric field are deflected toward the higher permittivity material. If the support is put on the shell in the lower half of the cell (configuration A in Fig. 1b), this effect counteracts the flux enlargement. If the measurements are performed in the upper half-cell, with the support disposed on the septum (configuration B in Fig. 1b), the flux concentration toward the septum is further increased. As a consequence, the results obtained with a support can differ depending on the part of the cell used in the experiment. The curves of Fig. 5a are computed in the center of the xy-plane with the cell closed for both configurations A and B. Fig. 5b shows the analogous behaviors computed in the open cell, along the z-line at x = 0.05 m, y = 0.05 m, towards the removed wall. In Fig. 5a, the presence of the support generates a local field increment up to 65% with respect to the unperturbed field in the region where the probe sensing elements are expected to be. In the case of the results shown in Fig. 5b, the perturbation is lower, because of the higher distance of the considered points with respect to the support. A good agreement is found between computations and experimental values measured by suspending the probe with the z-field single sensing element at increasing distances from the support, starting from 0.05 m to 0.2 m (relative uncertainty of the measured values 5%, with 95% confidence level). The evolution of the field amplitude in proximity to the support is specifically investigated in Fig 6, for configura-
Fig. 6. Component Ez of the electric field along a vertical line starting in close proximity to the support top: (a) configuration A; (b) configuration B.
Fig. 5. Component Ez of the electric field along a vertical line starting from the support top: (a) at the system center (cell closed); (b) at one vertex of the instrument (cell open).
tions A (Fig. 6a) and B (Fig. 6b). The computed Ez components, local value and average on a (0.08 m 0.08 m) area, are compared with those measured by a single sensing element at the two different z heights that correspond to the upper and lower face of the probe, centered in the measurement point (z = ±0.30 m). Because of the high field gradient along the z-axis, the indication given by the field meter can strongly vary as a function of both the position and number of the z-axis sensing elements inside the probe. In fact, a significant difference between computed and measured value is found at z = ±0.30 m (middle height), where the probe indication is actually obtained as the mean value of the outputs given by two z-field sensing elements, positioned on the opposite faces of the cubic probe. The strong non-uniform field distribution at the support surface gives rise, in this case, to a great variation between local and averaged values, well highlighted in Fig. 6. The comparison between the maximum field values computed in both configurations A and B (150 V/m and 175 V/m respectively) suggests the adoption of configuration A when the support is used. Thus, in the following, the analysis will be performed only by considering the probe located in the lower half-cell. Finally, the effects of a probe horizontal support are investigated, introducing in the open cell a 0.6 m long cylindrical stand of solid plexiglass disposed along x-axis (configuration C in Fig. 1b). The computed Ez distribution in the xy-plane, at the shell-septum middle distance, is shown in Fig. 7, where the support end is at x = 0.05 m. The component Ez reduces to about 72 V/m close to the
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L. Zilberti et al. / Measurement 43 (2010) 1282–1290 Table 3 Configuration C: computed Ez component (V/m) in point P0. Position (sensor height)
Local value with support
Averaged value with support
Local value without support
Upper Middle Lower
104.0 96.4 95.2
104.3 95.0 95.7
104.0 99.8 95.7
Considered volume
Surface z-coordinate (m)
FW,min
FWz,min
W1
0.24 0.30 0.36
0.917 0.941 0.921
0.943 0.998 0.943
W2
0.27 0.30 0.33
0.959 0.971 0.960
0.972 0.999 0.972
Table 4 Evaluation of the uniformity index.
Fig. 7. Chromatic map of component Ez of the electric field in proximity to a horizontal support.
support end, due to the field deflection produced by the material permittivity. However, the area significantly perturbed is less than half of the sensor surface. Table 3 summarizes the values of the Ez component (local and averaged value), under the hypothesis of the measurement performed with one sensing element, located at the lower (z = 0.35 m), middle (z = 0.30 m) and upper (z = 0.25 m) height. From the comparison with the data shown in Fig. 6b, it results that the global effect of the horizontal support perturbation is minimal if compared with the solution of a vertical support. However, the configuration with a horizontal support makes the correct positioning of the probe more difficult and has to be performed with the cell open. Moreover, the calibration of a 3D meter becomes problematic with reference to the determination of the behavior of each orthogonal single-axis sensor.
4. Evaluation of the uniformity degree In most cases, the number of single-axis sensing elements and their relative arrangement and position inside a 3D electric field probe are not specified by the manufacturer. Generally, the only information available is the orientation of x, y and z sensors inside the probe and, sometimes, the actual area of the sensing elements. The calibration is usually performed by centering the probe in P0 (or Q0), despite of the actual position of the sensing elements inside it. Taking into account that the dimensions of the electric field sensors range from 0.05 m to 0.1 m, the contribution due to the field spatial non-uniformity cannot be disregarded, when estimating the uncertainty associated with the field actually applied to the sensor. According to [5], when performing a low frequency calibration in a parallel plate system, the difference of the generated field at the centre of the system from the uniform field value should be less than 1%. Different approaches have been adopted to evaluate the electric field uniformity [16–18], which are based on spot measurements or on computed suitable indexes. In particular, the uniformity of vector fields is frequently quantified by means of indexes, since they can give continuous and more detailed information over the considered volume (see for
example [19]). On the basis of these considerations, a uniformity index is here computed as:
F W ðPÞ ¼ 1
! ! j E ðPÞ E0 j E0
ð4Þ
! ! where E 0 is the unperturbed field in P0 and E ðPÞ is the electric field evaluated in the generic point P. The deviation of FW from unity, evaluated over a stated volume, can be used to quantify how the field is far from the full uniformity. A second index FWz is also computed, by replacing ! in (4) vector E with its vertical component Ez; taking into ! account that, due to the symmetry, vector E 0 has only the z-component, provided that the cell is kept closed. By considering the maximum dimensions of the available commercial probes, a volume W1 of side Lm1 = 0.12 m, centered in the lower half-cell is assumed. The minimum values of indexes FW and FWz are computed over three squared surfaces of side Lm1 in the xy-plane with z equal to 0.24 m (upper surface), 0.30 m (medium surface) and 0.36 m (lower surface) respectively. The index computation is then repeated taking into consideration a reduced volume W2 of side Lm2 = 0.06 m and the related upper, medium and lower surfaces. The minimum values of FW and FWz are compared in Table 4. Since separate calibration of each orthogonal single-axis sensor of the probe has to be performed [5,6], the minimum values FWz,min of FWz with reference to W1 and W2 are identified and the quantities ±(1 FWz,min), respectively equal to ±5.7 102 and ±2.8 102, are taken as relative limit variations of the field E0 applied to the z-sensor of a probe, whose z-sensing element number, position and area are not known. Under the simplifying assumption of a rectangular probability distribution of half-width equal to (1 FWz,min)E0, relative standard uncertainty components of 3.3 102 and 1.6 102 are obtained, which are respectively associated with the nonuniform field distribution in the calibration volumes W1 and W2. Lower uncertainty components can be considered, provided that the actual position and sensing element
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arrangements of the single-axis sensor inside the probe are known and the sensor is carefully centered in the system. The uniformity indexes significantly decrease if a solid dielectric support with non-negligible cross-section is used. So, to limit the uncertainty contribution due to the spatial non-uniformity, the use of hollow supports with thin wall is recommended both in the calibration and measurement phase [11]. 5. Influence of the cell size With reference to the use of the TEM cell both at low and high frequency, cells of reduced size with respect to that previously investigated allows the extension of the cutoff frequency. However, it also implies a decrease of the volume where reasonable field uniformity can be ensured, with a consequent possible increase of the uncertainties in the calibration of low frequency instruments with not negligible dimensions. In order to quantify the uncertainty increase, computations are performed considering TEM cells having the same structure as the INRIM one, but with scale of 2/3 and 1/2; the ratio of the probe side to the shell-septum distance then increases from 0.17 to 0.25 and 0.33 respectively. It must be noted that, in order to employ the same TEM cell for radiofrequency calibrations, the corresponding cutoff frequencies increase to 190 MHz and 250 MHz, respectively. Computations are performed by considering the probe centered in the lower half-cell. The average on the area of a single sensing element is computed in correspondence of the half-cell center (middle) and then repeated for the upper and lower probe faces. If present, the support has the same diameter and the same permittivity as in the previous cases; its height is such that the field meter is centered in the lower half-cell, as in configuration A. The computational results are summarized in Tables 5 and 6 respectively for the case without and with the support. They show how the cell reduction, due to the significant increase of the field gradient along the z-axis, produces an increasing trend for the upper surface sensor and a decreasing trend for the lower one. It is worth noting that the presence of the vertical support increases the
Table 5 Computed average value of Ez (V/m) without support. Sensor position
Upper Middle Lower
Scale 1/1
2/3
1/2
105.2 99.6 93.9
108.0 99.5 91.3
110.9 99.4 89.0
Table 6 Computed average value of Ez (V/m) with vertical support. Sensor position
Upper Middle Lower
Scale 1/1
2/3
1/2
107.5 105.8 120.2
109.9 105.2 115.4
113.0 104.6 110.8
averaged value of Ez for the lower sensor position, so that the differences between lower and upper position reduces, in particular for the scale of 1/2. The data in Table 5 shows that, in absence of the support, a cell size reduction does not significantly affect the calibration results, only if the measurement is performed using a single-axis sensor made of one sensing element, positioned in the center of the half-cell. Similar considerations can be extended to the case of a couple of sensing elements symmetrically disposed with respect to the probe center. It must be also remarked that the use of TEM cells of reduced size is further restricted by the proximity of the probe conductive elements to the generation system electrodes [3,5,20]. At the decrease of the cell size, the presence of the support significantly modifies the field distribution and the expected indications, making the calibration process quite unreliable.
6. Field meter behavior in non-uniform field Power frequency environmental electric fields characterized by high spatial non-uniformity often occur in actual situations, for example when carrying out measurements in proximity to non-removable conducting objects, under a high voltage transmission line. Because of its non-negligible dimensions, the instrument indication may be significantly different from the one obtained in a uniform field of amplitude equal to that occurring in the probe geometrical centre (measurement point). The shape of the TEM cell gives rise to an electric field distribution which shows, in proximity of the outer conductor, non-uniformities with quantifiable field gradients along all the three axes. This feature the investigation of the behavior of electric field meters, when measuring a non-uniform field, by posing the probe in suitable positions, where the electric field components and their gradient can be well determined by computations. For such a purpose, the numerical and experimental investigations are performed in two points. The first position, point R (0 m, 0.485 m, 0.3 m), is close to the tapered end; the second one, point S (0.3 m, 0 m, 0.3 m), is toward the lateral wall. The possibility of removing this wall allows the modification of the electric field distribution, with particular reference to point S. The electric field values computed in points R and S, presented in Table 7, show significant y and x components, respectively. Reference is then made to the volume taken up by the considered field meter probe with the cube center located in points R and S. The electric field components (positive or negative) orthogonal to each face of the cube are computed in the center of each face. To quantify the field gradient, only the field component normal to each face is considered, because this is the only quantity detected by the probe sensing elements. The field components in the centre of each cube face are shown in Table 7, where the symbols ‘‘ + ” and ‘‘–” correspond to the greatest and lowest coordinate value with reference to the position of the single sensing element sensor. The discrepancies between ‘‘ + ” and ‘‘” faces put in evidence the presence of a field gradient, that,
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L. Zilberti et al. / Measurement 43 (2010) 1282–1290 Table 7 Computed electric field (V/m) in Points R and S and on the cube faces. Point
Door state
Ex
R
Open Closed
2.9 0.0
S
Open Closed
12.3 42.0
Ey
Value in the point
Value on face (+)
Value in the point
Value on face (+)
Value on face ()
Value in the point
Value on face (+)
Value on face ()
1.12 4.97
7.20 4.97
22.7 21.0
28.30 26.60
18.00 16.40
100.0 99.9
109.0 110.0
91.00 90.10
15.70 53.20
9.12 32.20
0.0 0.0
1.71 0.74
1.71 0.74
95.7 88.7
101.0 101.0
91.30 78.70
Table 8 Measured electric field (V/m) in point R with open cell. Ex
Ey
+ x y z
0.85
Ez
+
6.2 2.6 1.0
+
20.9
101.4 101.4 105.2 97.2
22.4 26.3 21.1
Table 9 Measured electric field (V/m) in point R with closed cell. Ex
x y z
Ey
+
1.0
1.0
Ez
+
1.3 0.91
+
21.0 25.5
101.5 101.2
20.0 20.2
105.4
96.6
Table 10 Measured electric field (V/m) in point S with open cell. Ex
x y z
Ey
+
19.7
15.3
Ez
+
+
0.85
19.1 17.9
2.5
98.1 97.8
2.5 1.1
99.2
95.9
x y z
Ey
+
40.2
29.5 35.9 35.8
Ez
+
+
0.91 0.70
92.8 92.6
0.70 0.94
96.5
tion of the alignment of the single sensing element sensor to the cell x-, y- and z-axis. From the comparison between calculated and measured components, it is possible to verify that the measured field values obtained as a mean of two opposite-face sensing element, provide values quite close to the ones computed in points R and S (Table 7), bringing down the field gradient effect. On the contrary, the results obtained from a single sensor measurement can generally differ in a nonnegligible way with respect to the computed ones. Similar results are obtained with the open cell configuration. The experimental data are clearly affected by an uncertainty mainly due to the finite dimensions of the probes and the positioning of the instrument, which can account for values slightly different for measurements of the same field component performed with different probe orientation. Finally, the measured resultant field is calculated from the data of Tables 8–11 for the considered different probe orientations. Despite the relatively high spatial electric field gradient, the relative deviations of the measured field with respect to the one computed in R and S are found to be within 5%, depending on the measurement point and probe orientation. The deviations which would be given by a similar probe equipped with only three sensing elements orthogonally disposed are then computed. By considering the eight possible combinations of the single sensing element indications deviations up to 7% occur. 7. Conclusion
Table 11 Measured electric field (V/m) in point S with closed cell. Ex
Ez
Value on face ()
87.4
in some cases, gives rise to field components with reversed direction on the opposite cube faces. During the experimental stage, the center of the probe is placed in correspondence of points R and S. In each point, the probe is rotated around its centre so that the electric field components, orthogonal to the six cube faces, are sequentially measured by the probe single-axis sensor made of only one sensing element. For each probe rotation, the output indications of all the three components are recorded. Tables 8–11 summarize the measured data related to point R and S for the close cell configuration, as a func-
The use of the TEM cell for the generation of reference electric fields in the calibration of power frequency electric field meters has been investigated in relation to the field spatial non-uniformity and the specific probe characteristics. The adoption of a validated BEM model has proved to be a useful way to obtain complementary information with respect to those obtained experimentally. With reference to the considered TEM cell, the uncertainty component associated with the electric field nonuniformity in the volume taken up by typical 3D probes of power frequency meters side to has been estimated to range from a few to some percents of the unperturbed field value under the assumption of negligible support influence. Lower uncertainty values can be assumed, provided that the actual position and sensing element arrangements inside the probe are known. With reference to the calibration in cells of reduced size, that is with a ratio probe side to shell-septum distance higher than 0.17, the uncertainty component does not significantly increase, only if calibra-
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tion of a single sensing element sensor positioned in the cell center is performed. The calculations and measurements performed by positioning the probe in specific points of the TEM cells, under conditions of known significant field spatial variations, show that, when using 3D probes, deviation of several percents between measured and actual field can be performed as a function of probe orientation and internal arrangements of the field sensing elements. References [1] M.L. Crawford, Generation of standard EM fields using TEM transmission cells, IEEE Transactions on Electromagnetic Compatibility 16 (4) (1974) 189–195. [2] M. Kanda, R.D. Orr, Generation of Standard Electromagnetic Fields in a TEM cell, NBS Technical Note 1319, Boulder, Colorado, 1988. [3] IEEE Standard for Calibration of Electromagnetic Field Sensors and Probes, Excluding Antennas, from 9 kHz to 40 GHz, IEEE 1309, 2005. [4] Electromagnetic Compatibility (EMC) Part 4–20: Testing and Measurement Techniques – Emission and Immunity Testing in Transverse Electromagnetic (TEM) Waveguides, EN 61000-4-20, 2003. [5] Measurement of Low-frequency Magnetic and Electric Fields with Regard to Exposure of Human Beings – Special Requirements for Instruments and Guidance for Measurements, IEC 61786, 1998. [6] IEEE Recommended Practice for Instrumentation: Specifications for Magnetic Flux Density and Electric Field Strength Meters – 10 Hz– 3 kHz, IEEE 1308, 1994. [7] M. Borsero, G. Crotti, L. Anglesio, G. D’Amore, Calibration and evaluation of uncertainty in the measurement of environmental electromagnetic fields, Radiation Protection Dosimetry 97 (2001) 363–368. [8] R.J. Spiegel, W.T. Joines, C.F. Blackman, A.W. Wood, A method for calculating electric and magnetic fields in TEM cells at ELF, IEEE Transactions on Electromagnetic Compatibility 29 (1987) 265–272.
[9] T. Takuma, T. Kawamoto, S. Sumiyoshitani, M. Akazaki, Effects of an insulating support in AC Electric field measurement, IEEE Transactions on Power Delivery 8 (1993) 2031–2037. [10] O. Bottauscio, M. Chiampi, G. Crotti, L. Zilberti, Perturbing effects of the probe support on the calibration of electric field meters, European Physical Journal – Applied Physics 42 (2008) 345–350. [11] O. Bottauscio, G. Crotti, S. D’Emilio, G. Farina, A. Mantini, Generation of reference electric and magnetic fields for calibration of powerfrequency field meters, IEEE Transactions on Instrumentation and Measurement 42 (1993) 547–552. [12] J.C. Tippet, D.C. Chang, Radiation characteristics of dipole sources located inside a rectangular coaxial transmission line, National Bureau of Standards (USW) NBSIR 12 (January) (1976) 75–829. [13] H.P. Geromiller, A. Kost, Numerically calculated field homogeneity in TEM cells, COMPEL 9 (2) (2000) 268–272. [14] Y. Tanaka, T. Honma, I. Kaji, A boundary-element analysis of TEM cells in three dimensions, IEEE Transactions on Electromagnetic Compatibility 28 (1986) 179–184. [15] X. Cai, G.I. Costache, Theoretical modeling of longitudinal variations of electric field and line impedance in TEM Cells, IEEE Transactions on Electromagnetic Compatibility 35 (1993) 398–401. [16] H. Garbe, M. Koch, H. Haase, Specification of alternative test sites with respect to given EMC field standards, in: Proc. 12th Int. Symp. Tech. Exhibition EMC, Zurich, Switzerland, February 1997, pp. 459– 464. [17] T. Morioka, A Field Uniformity Study of a TEM Cell by Using a Short Wire Scatterer, in: Proc. of the IEEE Int. Symposium on Electromagn. Compat., 2007, pp. 1–5. [18] C. Groth, J.P. Karst, M. Koch, H. Garbe, TEM Waveguides for EMC Measurements, IEEE Transactions on Electromagnetic Compatibility 41 (4) (1999) 440–445. [19] E. Dominguez-Tortajada, J. Monzò-Cabrera, A. Diaz-Morcillo, Uniform electric field distribution in microwave heating applicators by means of genetic algorithms optimization of dielectric multilayer structures, IEEE Transactions on Microwave Theory and Techniques 55 (2007) 85–92. [20] T. Takuma, T. Kawamoto, Y. Sunaga, Analysis of calibration arrangements for ac field strength meters, IEEE Transactions on Power Delivery 8 (1984) 2031–2037.
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
On the use of TEM cells for the calibration of power frequency electric field meters Luca Zilberti a,b, Oriano Bottauscio a, Mario Chiampi b, Gabriella Crotti a,* a b
Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, I-10135 Torino, Italy Dip. Ingegneria Elettrica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
a r t i c l e
i n f o
Article history: Received 11 June 2009 Received in revised form 18 May 2010 Accepted 15 July 2010 Available online 21 July 2010 Keywords: Boundary element methods Calibration Electric field measurement TEM cell Uncertainty
a b s t r a c t This paper focuses on the performances of TEM cells when used in the calibration of power frequency environmental electric field meters. The spatial non-uniformity of the electric field inside a TEM cell is analyzed through experimental investigations and three-dimensional Boundary Element modeling to evaluate the field experienced by the sensing elements of actual 3D meter probes. The perturbation caused by the probe support is also taken into account. The uncertainty component associated with the spatial non-uniformity in the volume taken up by typical power and low frequency field probes is estimated. The field non-uniformity is also evaluated in relation to the use of TEM cells of reduced size. Finally, the field non-uniformity is exploited to predict the performance of an actual field meter operating in significant field gradients. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction TEM cells are the recommended set-up for the generation of reference electric fields used in the calibration of probes and sensors in the frequency range from some kilohertz to hundreds of megahertz. A wide literature, see for example [1,2], analyses in detail their behavior and relevant standards precisely define the rules and procedures for a correct execution of the calibration process [3,4] in the specified frequency range. As concern the calibration of power frequency field meters, used for the measurements of environmental fields in the evaluation of human exposure, the recommended configuration is the parallel plate systems [5–7]. The uncertainty associated with the generated field ranges from a few part per thousand to a few percent. Nevertheless, TEM cells are very often used as an alternative generation system. With respect to the recommended devices, TEM
* Corresponding author. E-mail addresses: [email protected] (L. Zilberti), o.bottauscio@ inrim.it (O. Bottauscio), [email protected] (M. Chiampi), g.crotti@ inrim.it (G. Crotti). 0263-2241/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2010.07.005
cells have some practical advantages such as: (i) the possibility of working in a wide frequency range (from DC up to some hundreds megahertz), (ii) the reduced size, (iii) the improved immunity from external disturbances, due to the intrinsic shielding, and the reduced disturbances which can cause interference with other devices. On the other hand, due to their shape, TEM cells show lower electric field uniformity with respect to parallel plate generation systems of the same size. An increase of the cell size improves the field uniformity, but at the same time limits its cutoff frequency. Thus, the possibility of using the cells for the generation of reference electric fields both at high and low frequencies needs a compromise between these two opposite requirements. The paper aim is a quantitative analysis of the performances of a TEM cell, when used in the calibration of electric field meters, which are employed for the measurements of environmental power frequency fields. So, reference is made in the following to the indications given by the relevant standards [5,6]. In comparison with the radiofrequency ones, the low and power frequency field probes are generally characterized by greater dimensions and different internal sensor
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arrangements. The non-uniformity of the spatial field distribution inside the TEM cell and its effect on the indication of the electric field meters under calibration are then investigated. The spatial field distribution inside the cell can be evaluated numerically (e.g. by the moment method as detailed in [8]) or experimentally, by means of calibrated field probes. In the following, a noncommercial three dimensional tool based on the Boundary Element Method (BEM) is adopted to compute the field distribution actually experienced by three-dimensional field probes. In this analysis the probe characteristics (dimensions, number and different arrangement of the field sensing elements) and the possible presence of dielectric material (e.g. probe support) are accounted for. The validation of the computational model is performed by comparison with analytical solutions and experimental data. The measurements are performed in a TEM cell, available at the Istituto Nazionale di Ricerca Metrologica (INRIM). Different configurations are analyzed, such as open or closed cell and field probe placed in the upper or lower section of the cell. An estimation of the size averaging error, which arises because of the non-negligible dimension of the field sensing elements when the probe is introduced in a non-uniform field, is also taken into consideration. Moreover, some comparisons with a parallel plate system are presented. A further effect investigated is the presence, during the calibration, of the field probe support, which can significantly influence the distribution of the electric field in the volume taken up by the meter probe [9,10]. In fact, calibration should be performed in the same configuration used during the measurement, that is with the probe equipped with its own support. In practice, because of their length dielectric supports different from those adopted during the on-site measurements are generally used in the calibration phase. On the basis of the results obtained, an evaluation of the uncertainty contribution that can be associated with the field non-uniformity is carried out, taking into account the finite dimensions and internal field sensors arrangements of actual 3D probes in relation to the TEM cell dimension. Finally, the field non-uniformity of the TEM cell is exploited to estimated the error made by the field meter when used in presence of significant spatial field gradient.
2. Numerical model and experimental setup Under the assumption of quasi-stationary operating conditions, the electric field formulation is developed in an open boundary 3D domain, where the conductive bodies are replaced by Dirichlet conditions, imposing the known potential on the electrodes. This hypothesis allows the description of the electric field E in terms of a scalar potential u (E = grad u), which leads to the boundary value problem:
div ðegraduÞ ¼ 0
ð1Þ
Eq. (1) is solved by means of a standard BEM approach. The surfaces of the bodies included in the domain are divided into N triangles. In each element the potential is
assumed to be linear and its normal derivative to be constant. The electric field distribution is computed by solving the resulting BEM equation in the internal and external regions:
fui ¼
N X j¼1
" ðru nÞj
Z Xj
wds uj
#
Z Xj
ðrw nÞj ds
ð2Þ
where Xj are the triangular elements, w ¼ 1=4pr is the 3D Green function (being r the distance between source point i and computational point j), nj is the normal unit vector and f is 0.5 on the surfaces and 1 elsewhere. The unknowns are the nodal values of the potential and its normal derivatives in each triangle on the surface of the dielectric body (e.g. dielectric support); on the electrodes the only unknowns are the normal derivatives of the potential, while the imposed potential represents the field source. Problem (2) is completed by the interface conditions between internal (a) and external (b) volumes:
(
ðbÞ uðaÞ ¼ uj j eðaÞ ruðaÞ nðaÞ j ¼ eðbÞ ruðbÞ nðbÞ j
ð3Þ
The analysis is developed considering the INRIM TEM cell shown in Fig. 1a, where the origin of the coordinate system is assumed in the central point of the septum. The cell has a square cross-section of side LT = 1.2 m in the xz-plane with a shell-septum distance DT = 0.6 m (ratio LT/DT = 2) and a 2.4 m length along y-axis. The cutoff frequency of the TEM cell, when used for radiofrequency calibrations, is about 125 MHz. A 60 V, 50 Hz voltage, generated by a calibrated voltage source (Fluke 5500A Calibrator), is applied across the electrodes (septum and shell), which corresponds to a nominal value E0 of 100 V/ m in the centre of the lower half-cell P0 (0, 0, 0.3 m) or in the centre of the upper half-cell Q0 (0, 0, +0.3 m). Taking into account the considered frequencies, the magnetic field can be disregarded, since the load terminal of the TEM cell is open. The INRIM parallel plate system, considered for the comparison, is composed of two aluminum square horizontal plates of side LP = 2 m at a vertical distance DP = 1 m (ratio LP/DP = 2); five grading rings improve the field uniformity in the central volume between the plates [11]. The choice of the most suitable BEM discretization of the TEM cell, as a compromise between accuracy and computational cost, is made by increasing the number of triangles in the system of Fig. 1b and by comparing the computed field values in different points of the domain. The obtained results, summarized in Table 1, show that a mesh with about 9700 surface elements is surely sufficient to make the discretization error negligible. The limit error due to the numerical evaluation of the electric field values in the central volume of one half-cell is estimated to be within ±0.5%; it is obtained by considering, besides the discretization error, the comparison with analytical solutions [10,12]. The measured data are obtained using a free-body electric field meter, previously calibrated in the parallel plate generation system. The meter is equipped with a 3D cubic
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Fig. 1. INRIM TEM cell: (a) picture of the cell with probe and plexiglass support; (b) BEM discretization of the lower half-cell, with about 9700 triangles. The considered support configurations are also presented.
Table 1 Electric field amplitude (V/m). Point coordinates (m) x
y
z
0 0 0 0.3 0
0 0 0 0.3 0.6
0.3 0.25 0.35 0.3 0.3
2424 triangles
5832 triangles
9696 triangles
99.6 105.0 94.2 97.8 107.4
99.4 105.0 94.0 97.7 107.0
99.4 105.0 94.0 97.7 107.0
respect to the foam structures typically employed for radiofrequency. In addition, such a cylindrical support is similar to those typically used when measuring on-site. In this investigation, the considered support is made of solid polymethyl methacrylate (plexiglass), with relative permittivity er = 3.5 at 50 Hz and quite large diameter (d = 0.05 m) in order to put in evidence its perturbing effect on the field distribution.
3. Electric field distribution in the calibration volume probe of 0.1 m external side, which is connected to the measuring instrument by optical fiber. The probe is fitted out with five 0.08 m 0.08 m single-axis field sensing elements. Each sensing element is made of two parallel square electrodes closely faced; the field strength orthogonal to their surface is determined by measuring the current induced between them [5,6]. The meter can give, as output indications, both the three orthogonal field components and the resultant field. Two of the orthogonal field components are obtained as the average value given by two single-axis sensing elements, placed at the opposite faces of the cubic probe, whereas the third component is given by only one sensing element, located close to one of the remaining faces of the cube. The field probe can be placed in the considered measurement point either by suspending it through thin plastic threads or by using a support of suitable length. Due to the weight of the low-frequency electric field meters, in this second case usually a hollow rigid support is preferred
With respect to a parallel plate configuration with the same ratio L/D, the electric field distribution inside the
Fig. 2. Distribution of electric potential u and electric field component Ez along a vertical line in the center of the xy-plane.
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Fig. 3. Computed electric field flux lines and electric potential isolevel lines in the middle cross-section of the upper half of the INRIM TEM cell.
Fig. 4. Computed electric potential distribution on a square surface centered in P0 (the imposed potential is 0 on the shell and 60 V on the septum): (a) closed TEM cell; (b) open TEM cell.
TEM cell is only approximately uniform, due to the different shape and size of the two electrodes [11–15]. Fig. 2 shows the electric potential and the field component Ez along the z-axis in the centre of the xy-plane. The electric field decreases from 120 V/m close to the septum, to 80 V/m when moving towards the shell. As a comparison, in the INRIM parallel plate system, which is equipped with grading rings, the field variation along the same line is within 0.2%. This behavior is well put in evidence by Fig. 3, which presents the distributions of the electric field flux lines and electric potential isolevels in the middle cross-section (xz-plane) of the upper half of the TEM cell, where, due to the symmetry, the Ey component is zero.
Disposition
E0
EA
ED
EM
Closed Open
99.4 99.7
99.4 99.8
99.6 99.9
100.2 100.8
The spatial non-uniformity on the xy-plane centered in P0 is shown in Fig. 4a by the distribution of the electric potential over a 0.2 m 0.2 m surface. The potential is about 25 V instead of the expected 30 V; its maximum deviation, with respect to the value in P0, is 0.5 V. As a comparison, the deviation decreases to less than 0.001 V, when considering the same surface in the INRIM parallel plate setup. It can also be observed that, besides an Ex component (up to 12% of Ez), a detectable Ey component up to 2% of Ez is found over the considered area. The potential distribution on the same surface is shown in Fig. 4b for the ‘‘open” cell that is when one of the lateral walls has been removed, for example, to allow the introduction of a probe horizontal support. The results show an evident asymmetrical potential distribution, with, as expected, a higher spatial uniformity towards the removed wall. It must be noted that perturbation due to the presence of external conductive objects is found negligible provided that the cell is not in very close proximity to them. To compare the computed electric field values to those obtained by measurements in a non-uniform field, the finite dimensions of the single-axis sensors and their relative position inside the probe have to be taken into consideration. The field spatial non-uniformity may give rise to discrepancies between the actual value of the field in the probe center (measurement point) and the indication given by the measuring instrument, estimated by averaging the field amplitude on the operating single-axis sensing elements of the probe. Table 2 shows the electric field z-component (E0) computed in P0, the one (EA) averaged on the sensing element area centered in P0 and the mean value (ED) of the two averages on the areas at z = 0.25 m and z = 0.35 m; the corresponding measured value (EM), given by the meter, centered in P0, when the probe is oriented with two single-axis sensors detecting the z-component, is also presented. The data obtained with the open cell configuration are also shown for comparison. The small differences between local and averaged computed values show how a rather satisfactory uniformity is ensured on the sensing element surface centered in P0. Good agreement is also found between the computed mean value ED and the meter output EM, which is the average of the indication of two sensing elements disposed symmetrically with respect to the probe centre. The deviation between measured and computed values can be explained by considering, besides the estimated limit error associated with the numerical procedure, the measurement uncertainty (<1%) of the meter indication. This uncertainty is evaluated by taking into account both the calibration contribution (calibration performed in the parallel plate system) and that due to the vertical positioning of the probe, suspended through a thin plastic thread.
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The insertion of the probe support creates significant modifications of the field distribution, because the flux lines of the electric field are deflected toward the higher permittivity material. If the support is put on the shell in the lower half of the cell (configuration A in Fig. 1b), this effect counteracts the flux enlargement. If the measurements are performed in the upper half-cell, with the support disposed on the septum (configuration B in Fig. 1b), the flux concentration toward the septum is further increased. As a consequence, the results obtained with a support can differ depending on the part of the cell used in the experiment. The curves of Fig. 5a are computed in the center of the xy-plane with the cell closed for both configurations A and B. Fig. 5b shows the analogous behaviors computed in the open cell, along the z-line at x = 0.05 m, y = 0.05 m, towards the removed wall. In Fig. 5a, the presence of the support generates a local field increment up to 65% with respect to the unperturbed field in the region where the probe sensing elements are expected to be. In the case of the results shown in Fig. 5b, the perturbation is lower, because of the higher distance of the considered points with respect to the support. A good agreement is found between computations and experimental values measured by suspending the probe with the z-field single sensing element at increasing distances from the support, starting from 0.05 m to 0.2 m (relative uncertainty of the measured values 5%, with 95% confidence level). The evolution of the field amplitude in proximity to the support is specifically investigated in Fig 6, for configura-
Fig. 6. Component Ez of the electric field along a vertical line starting in close proximity to the support top: (a) configuration A; (b) configuration B.
Fig. 5. Component Ez of the electric field along a vertical line starting from the support top: (a) at the system center (cell closed); (b) at one vertex of the instrument (cell open).
tions A (Fig. 6a) and B (Fig. 6b). The computed Ez components, local value and average on a (0.08 m 0.08 m) area, are compared with those measured by a single sensing element at the two different z heights that correspond to the upper and lower face of the probe, centered in the measurement point (z = ±0.30 m). Because of the high field gradient along the z-axis, the indication given by the field meter can strongly vary as a function of both the position and number of the z-axis sensing elements inside the probe. In fact, a significant difference between computed and measured value is found at z = ±0.30 m (middle height), where the probe indication is actually obtained as the mean value of the outputs given by two z-field sensing elements, positioned on the opposite faces of the cubic probe. The strong non-uniform field distribution at the support surface gives rise, in this case, to a great variation between local and averaged values, well highlighted in Fig. 6. The comparison between the maximum field values computed in both configurations A and B (150 V/m and 175 V/m respectively) suggests the adoption of configuration A when the support is used. Thus, in the following, the analysis will be performed only by considering the probe located in the lower half-cell. Finally, the effects of a probe horizontal support are investigated, introducing in the open cell a 0.6 m long cylindrical stand of solid plexiglass disposed along x-axis (configuration C in Fig. 1b). The computed Ez distribution in the xy-plane, at the shell-septum middle distance, is shown in Fig. 7, where the support end is at x = 0.05 m. The component Ez reduces to about 72 V/m close to the
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L. Zilberti et al. / Measurement 43 (2010) 1282–1290 Table 3 Configuration C: computed Ez component (V/m) in point P0. Position (sensor height)
Local value with support
Averaged value with support
Local value without support
Upper Middle Lower
104.0 96.4 95.2
104.3 95.0 95.7
104.0 99.8 95.7
Considered volume
Surface z-coordinate (m)
FW,min
FWz,min
W1
0.24 0.30 0.36
0.917 0.941 0.921
0.943 0.998 0.943
W2
0.27 0.30 0.33
0.959 0.971 0.960
0.972 0.999 0.972
Table 4 Evaluation of the uniformity index.
Fig. 7. Chromatic map of component Ez of the electric field in proximity to a horizontal support.
support end, due to the field deflection produced by the material permittivity. However, the area significantly perturbed is less than half of the sensor surface. Table 3 summarizes the values of the Ez component (local and averaged value), under the hypothesis of the measurement performed with one sensing element, located at the lower (z = 0.35 m), middle (z = 0.30 m) and upper (z = 0.25 m) height. From the comparison with the data shown in Fig. 6b, it results that the global effect of the horizontal support perturbation is minimal if compared with the solution of a vertical support. However, the configuration with a horizontal support makes the correct positioning of the probe more difficult and has to be performed with the cell open. Moreover, the calibration of a 3D meter becomes problematic with reference to the determination of the behavior of each orthogonal single-axis sensor.
4. Evaluation of the uniformity degree In most cases, the number of single-axis sensing elements and their relative arrangement and position inside a 3D electric field probe are not specified by the manufacturer. Generally, the only information available is the orientation of x, y and z sensors inside the probe and, sometimes, the actual area of the sensing elements. The calibration is usually performed by centering the probe in P0 (or Q0), despite of the actual position of the sensing elements inside it. Taking into account that the dimensions of the electric field sensors range from 0.05 m to 0.1 m, the contribution due to the field spatial non-uniformity cannot be disregarded, when estimating the uncertainty associated with the field actually applied to the sensor. According to [5], when performing a low frequency calibration in a parallel plate system, the difference of the generated field at the centre of the system from the uniform field value should be less than 1%. Different approaches have been adopted to evaluate the electric field uniformity [16–18], which are based on spot measurements or on computed suitable indexes. In particular, the uniformity of vector fields is frequently quantified by means of indexes, since they can give continuous and more detailed information over the considered volume (see for
example [19]). On the basis of these considerations, a uniformity index is here computed as:
F W ðPÞ ¼ 1
! ! j E ðPÞ E0 j E0
ð4Þ
! ! where E 0 is the unperturbed field in P0 and E ðPÞ is the electric field evaluated in the generic point P. The deviation of FW from unity, evaluated over a stated volume, can be used to quantify how the field is far from the full uniformity. A second index FWz is also computed, by replacing ! in (4) vector E with its vertical component Ez; taking into ! account that, due to the symmetry, vector E 0 has only the z-component, provided that the cell is kept closed. By considering the maximum dimensions of the available commercial probes, a volume W1 of side Lm1 = 0.12 m, centered in the lower half-cell is assumed. The minimum values of indexes FW and FWz are computed over three squared surfaces of side Lm1 in the xy-plane with z equal to 0.24 m (upper surface), 0.30 m (medium surface) and 0.36 m (lower surface) respectively. The index computation is then repeated taking into consideration a reduced volume W2 of side Lm2 = 0.06 m and the related upper, medium and lower surfaces. The minimum values of FW and FWz are compared in Table 4. Since separate calibration of each orthogonal single-axis sensor of the probe has to be performed [5,6], the minimum values FWz,min of FWz with reference to W1 and W2 are identified and the quantities ±(1 FWz,min), respectively equal to ±5.7 102 and ±2.8 102, are taken as relative limit variations of the field E0 applied to the z-sensor of a probe, whose z-sensing element number, position and area are not known. Under the simplifying assumption of a rectangular probability distribution of half-width equal to (1 FWz,min)E0, relative standard uncertainty components of 3.3 102 and 1.6 102 are obtained, which are respectively associated with the nonuniform field distribution in the calibration volumes W1 and W2. Lower uncertainty components can be considered, provided that the actual position and sensing element
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arrangements of the single-axis sensor inside the probe are known and the sensor is carefully centered in the system. The uniformity indexes significantly decrease if a solid dielectric support with non-negligible cross-section is used. So, to limit the uncertainty contribution due to the spatial non-uniformity, the use of hollow supports with thin wall is recommended both in the calibration and measurement phase [11]. 5. Influence of the cell size With reference to the use of the TEM cell both at low and high frequency, cells of reduced size with respect to that previously investigated allows the extension of the cutoff frequency. However, it also implies a decrease of the volume where reasonable field uniformity can be ensured, with a consequent possible increase of the uncertainties in the calibration of low frequency instruments with not negligible dimensions. In order to quantify the uncertainty increase, computations are performed considering TEM cells having the same structure as the INRIM one, but with scale of 2/3 and 1/2; the ratio of the probe side to the shell-septum distance then increases from 0.17 to 0.25 and 0.33 respectively. It must be noted that, in order to employ the same TEM cell for radiofrequency calibrations, the corresponding cutoff frequencies increase to 190 MHz and 250 MHz, respectively. Computations are performed by considering the probe centered in the lower half-cell. The average on the area of a single sensing element is computed in correspondence of the half-cell center (middle) and then repeated for the upper and lower probe faces. If present, the support has the same diameter and the same permittivity as in the previous cases; its height is such that the field meter is centered in the lower half-cell, as in configuration A. The computational results are summarized in Tables 5 and 6 respectively for the case without and with the support. They show how the cell reduction, due to the significant increase of the field gradient along the z-axis, produces an increasing trend for the upper surface sensor and a decreasing trend for the lower one. It is worth noting that the presence of the vertical support increases the
Table 5 Computed average value of Ez (V/m) without support. Sensor position
Upper Middle Lower
Scale 1/1
2/3
1/2
105.2 99.6 93.9
108.0 99.5 91.3
110.9 99.4 89.0
Table 6 Computed average value of Ez (V/m) with vertical support. Sensor position
Upper Middle Lower
Scale 1/1
2/3
1/2
107.5 105.8 120.2
109.9 105.2 115.4
113.0 104.6 110.8
averaged value of Ez for the lower sensor position, so that the differences between lower and upper position reduces, in particular for the scale of 1/2. The data in Table 5 shows that, in absence of the support, a cell size reduction does not significantly affect the calibration results, only if the measurement is performed using a single-axis sensor made of one sensing element, positioned in the center of the half-cell. Similar considerations can be extended to the case of a couple of sensing elements symmetrically disposed with respect to the probe center. It must be also remarked that the use of TEM cells of reduced size is further restricted by the proximity of the probe conductive elements to the generation system electrodes [3,5,20]. At the decrease of the cell size, the presence of the support significantly modifies the field distribution and the expected indications, making the calibration process quite unreliable.
6. Field meter behavior in non-uniform field Power frequency environmental electric fields characterized by high spatial non-uniformity often occur in actual situations, for example when carrying out measurements in proximity to non-removable conducting objects, under a high voltage transmission line. Because of its non-negligible dimensions, the instrument indication may be significantly different from the one obtained in a uniform field of amplitude equal to that occurring in the probe geometrical centre (measurement point). The shape of the TEM cell gives rise to an electric field distribution which shows, in proximity of the outer conductor, non-uniformities with quantifiable field gradients along all the three axes. This feature the investigation of the behavior of electric field meters, when measuring a non-uniform field, by posing the probe in suitable positions, where the electric field components and their gradient can be well determined by computations. For such a purpose, the numerical and experimental investigations are performed in two points. The first position, point R (0 m, 0.485 m, 0.3 m), is close to the tapered end; the second one, point S (0.3 m, 0 m, 0.3 m), is toward the lateral wall. The possibility of removing this wall allows the modification of the electric field distribution, with particular reference to point S. The electric field values computed in points R and S, presented in Table 7, show significant y and x components, respectively. Reference is then made to the volume taken up by the considered field meter probe with the cube center located in points R and S. The electric field components (positive or negative) orthogonal to each face of the cube are computed in the center of each face. To quantify the field gradient, only the field component normal to each face is considered, because this is the only quantity detected by the probe sensing elements. The field components in the centre of each cube face are shown in Table 7, where the symbols ‘‘ + ” and ‘‘–” correspond to the greatest and lowest coordinate value with reference to the position of the single sensing element sensor. The discrepancies between ‘‘ + ” and ‘‘” faces put in evidence the presence of a field gradient, that,
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L. Zilberti et al. / Measurement 43 (2010) 1282–1290 Table 7 Computed electric field (V/m) in Points R and S and on the cube faces. Point
Door state
Ex
R
Open Closed
2.9 0.0
S
Open Closed
12.3 42.0
Ey
Value in the point
Value on face (+)
Value in the point
Value on face (+)
Value on face ()
Value in the point
Value on face (+)
Value on face ()
1.12 4.97
7.20 4.97
22.7 21.0
28.30 26.60
18.00 16.40
100.0 99.9
109.0 110.0
91.00 90.10
15.70 53.20
9.12 32.20
0.0 0.0
1.71 0.74
1.71 0.74
95.7 88.7
101.0 101.0
91.30 78.70
Table 8 Measured electric field (V/m) in point R with open cell. Ex
Ey
+ x y z
0.85
Ez
+
6.2 2.6 1.0
+
20.9
101.4 101.4 105.2 97.2
22.4 26.3 21.1
Table 9 Measured electric field (V/m) in point R with closed cell. Ex
x y z
Ey
+
1.0
1.0
Ez
+
1.3 0.91
+
21.0 25.5
101.5 101.2
20.0 20.2
105.4
96.6
Table 10 Measured electric field (V/m) in point S with open cell. Ex
x y z
Ey
+
19.7
15.3
Ez
+
+
0.85
19.1 17.9
2.5
98.1 97.8
2.5 1.1
99.2
95.9
x y z
Ey
+
40.2
29.5 35.9 35.8
Ez
+
+
0.91 0.70
92.8 92.6
0.70 0.94
96.5
tion of the alignment of the single sensing element sensor to the cell x-, y- and z-axis. From the comparison between calculated and measured components, it is possible to verify that the measured field values obtained as a mean of two opposite-face sensing element, provide values quite close to the ones computed in points R and S (Table 7), bringing down the field gradient effect. On the contrary, the results obtained from a single sensor measurement can generally differ in a nonnegligible way with respect to the computed ones. Similar results are obtained with the open cell configuration. The experimental data are clearly affected by an uncertainty mainly due to the finite dimensions of the probes and the positioning of the instrument, which can account for values slightly different for measurements of the same field component performed with different probe orientation. Finally, the measured resultant field is calculated from the data of Tables 8–11 for the considered different probe orientations. Despite the relatively high spatial electric field gradient, the relative deviations of the measured field with respect to the one computed in R and S are found to be within 5%, depending on the measurement point and probe orientation. The deviations which would be given by a similar probe equipped with only three sensing elements orthogonally disposed are then computed. By considering the eight possible combinations of the single sensing element indications deviations up to 7% occur. 7. Conclusion
Table 11 Measured electric field (V/m) in point S with closed cell. Ex
Ez
Value on face ()
87.4
in some cases, gives rise to field components with reversed direction on the opposite cube faces. During the experimental stage, the center of the probe is placed in correspondence of points R and S. In each point, the probe is rotated around its centre so that the electric field components, orthogonal to the six cube faces, are sequentially measured by the probe single-axis sensor made of only one sensing element. For each probe rotation, the output indications of all the three components are recorded. Tables 8–11 summarize the measured data related to point R and S for the close cell configuration, as a func-
The use of the TEM cell for the generation of reference electric fields in the calibration of power frequency electric field meters has been investigated in relation to the field spatial non-uniformity and the specific probe characteristics. The adoption of a validated BEM model has proved to be a useful way to obtain complementary information with respect to those obtained experimentally. With reference to the considered TEM cell, the uncertainty component associated with the electric field nonuniformity in the volume taken up by typical 3D probes of power frequency meters side to has been estimated to range from a few to some percents of the unperturbed field value under the assumption of negligible support influence. Lower uncertainty values can be assumed, provided that the actual position and sensing element arrangements inside the probe are known. With reference to the calibration in cells of reduced size, that is with a ratio probe side to shell-septum distance higher than 0.17, the uncertainty component does not significantly increase, only if calibra-
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tion of a single sensing element sensor positioned in the cell center is performed. The calculations and measurements performed by positioning the probe in specific points of the TEM cells, under conditions of known significant field spatial variations, show that, when using 3D probes, deviation of several percents between measured and actual field can be performed as a function of probe orientation and internal arrangements of the field sensing elements. References [1] M.L. Crawford, Generation of standard EM fields using TEM transmission cells, IEEE Transactions on Electromagnetic Compatibility 16 (4) (1974) 189–195. [2] M. Kanda, R.D. Orr, Generation of Standard Electromagnetic Fields in a TEM cell, NBS Technical Note 1319, Boulder, Colorado, 1988. [3] IEEE Standard for Calibration of Electromagnetic Field Sensors and Probes, Excluding Antennas, from 9 kHz to 40 GHz, IEEE 1309, 2005. [4] Electromagnetic Compatibility (EMC) Part 4–20: Testing and Measurement Techniques – Emission and Immunity Testing in Transverse Electromagnetic (TEM) Waveguides, EN 61000-4-20, 2003. [5] Measurement of Low-frequency Magnetic and Electric Fields with Regard to Exposure of Human Beings – Special Requirements for Instruments and Guidance for Measurements, IEC 61786, 1998. [6] IEEE Recommended Practice for Instrumentation: Specifications for Magnetic Flux Density and Electric Field Strength Meters – 10 Hz– 3 kHz, IEEE 1308, 1994. [7] M. Borsero, G. Crotti, L. Anglesio, G. D’Amore, Calibration and evaluation of uncertainty in the measurement of environmental electromagnetic fields, Radiation Protection Dosimetry 97 (2001) 363–368. [8] R.J. Spiegel, W.T. Joines, C.F. Blackman, A.W. Wood, A method for calculating electric and magnetic fields in TEM cells at ELF, IEEE Transactions on Electromagnetic Compatibility 29 (1987) 265–272.
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