Transient calibration of electric field sensors M D Judd University of Strathclyde Glasgow, UK Abstract An electric field sensor calibration system that operates in the time-domain is described and its accuracy is assessed. The system makes use of a broadband, unterminated transient test cell that is simple to construct by comparison with matched TEM or GTEM cells. An advantage of the transient technique is that the frequency response of the test equipment does not have to be characterised. Furthermore, given sufficient signal-to-noise ratio, the calibration frequency range can be extended well above the 3 db bandwidth of the measurement equipment. The transient measurement depends for its accuracy on a model for the frequency response of a monopole probe, which is used as a reference. A model for this transfer function is presented. Results for a probe calibrated independently using the swept-frequency method are compared with those measured on the transient calibration system. The level of agreement between the two measurements validates both the transient technique and the model of the reference probe's transfer function. The transient calibration technique offers an alternative means of calibrating non-resonant electric field sensors. 1. Introduction Electric field sensors are usually calibrated using swept-frequency test equipment. To minimise the undesirable effects of standing waves, the test field has to be generated in a matched TEM cell or at an open area test site. In a TEM cell, reflections inevitably occur at geometric transitions, such as those between tapered and straight sections of the transmission line. The useful upper frequency limit can be extended by using only the tapered section of the line, a form that has become known as the GTEM cell [1]. Ideally, the GTEM should be both large (to maximise the useable test volume) and terminated in such a way that reflections are minimised up to the highest possible frequency. However, increasing the size of the structure increases both the difficulty and cost of matching the GTEM at higher frequencies. An alternative to the swept-frequency approach is to use a fast transient signal [2], obtaining the frequency response of a sensor using a fast Fourier transform (FFT). In this paper, the frequency response of a monopole sensor measured using this time-domain approach is compared with an independently calibrated swept-frequency response. The results are in good agreement, indicating that the transient calibration is a valid test technique capable of yielding accurate results using relatively simple test equipment. 2. Monopole transfer function model The transient calibration system requires a reference sensor with a known transfer function. The monopole is a good choice for this purpose as it is easy to mount in a ground plane. A loaded monopole probe acting as a receiving antenna is shown together with its equivalent page 1 of 9
circuit in Fig. 1. In the frequency-domain, the transfer function of the loaded probe in this configuration [3] can be expressed as H V h Z L e L = = (1) EI Z + Z L where E I is the incident electric field normal to the ground plane and V L is the output voltage into the load impedance Z L. The probe's effective height h e and impedance Z are both frequency dependent functions of its dimensions. The monopole used in the experiments was made from a readily available SMA connector with a centre pin of radius r = 0.65 mm. The length h = 25 mm was selected to avoid any resonances below 2 GHz. Using these dimensions, Z and h e can be obtained from values for the corresponding dipole [4] because the ground plane of the monopole forms a plane of symmetry between the probe and its image. The effective half-length of the dipole then becomes the effective height of the monopole while the monopole's impedance is half that of the corresponding dipole. (a) E I 2r h ground plane (b) Z h e E I V L Z L Fig. 1: (a) Monopole probe as an electric field sensor. (b) Equivalent circuit. The data in [4] is tabulated as a function of the parameter Ω = 2 ln( 2h r). Substituting the monopole dimensions gives Ω=8.686. This value lies between two sets of results, as tables are only given for integral values of Ω. The parameters of the monopole model were therefore obtained by interpolating the data as a function of Ω, yielding the values listed in Table 1. At frequencies below those listed in the table, coupling between the probe and the electric field tends towards a capacitive behaviour and in this region, the probe impedance was represented by a fixed capacitance. An effective height of 11.6 mm and a capacitance at 0.596 pf were used to generate a transfer function that interpolates smoothly with the first set of data in Table 1. page 2 of 9
Table 1 - Parameters used to model the transfer function of the 25 mm monopole. frequency ( MHz ) effective height h e ( mm ) impedance Z ( Ω ) real part imaginary part real part imaginary part 954 11.6 0.0 2.5-280.0 1336 12.0-0.1 5.2-179.7 1718 12.6-0.1 9.2-115.5 2099 13.3-0.2 15.2-68.5 2290 13.7-0.1 19.2-48.1 2481 14.4 0.3 24.2-28.9 The resulting magnitude response H of the monopole when used as an electric field probe is shown in Fig. 2. This model has been used previously to record the time-domain electric fields in a coaxial chamber [5], where it produced results in close agreement with the calculated fields. 10 sensitivity H ( mv/vm -1 ) 1.0 0.1 0 500 1000 1500 2000 frequency ( MHz ) Fig. 2: Theoretical magnitude response of the 25 mm monopole. 3. Time-domain measurement system 3.1 The transient test cell In previous work, a time-domain calibration system using an unshielded transmission line was described [2]. The measurement technique was proposed as a means of evaluating the frequency response of UHF couplers used to detect the signals radiated by partial discharges in high voltage electrical apparatus. Although serving to demonstrate the principle of time-domain calibration, the system suffered from high radiation losses and reflections at discontinuities in the structure. To overcome these problems, a device similar to a GTEM cell was constructed. This tapered transmission line, shown in Fig. 3, differs from a conventional GTEM device in the following ways: 1) An array of wires is used for the septum instead of a solid sheet conductor. 2) No attempt is made to match the device at its output. 3) The characteristic impedance of the cell is not designed to match a particular value. page 3 of 9
input removable hatch TOP wire septum 1.5 m 1.5 m SIDE Fig. 3: The transient test cell. When wave-guiding structures have dimensions that are not insignificant compared to the wavelength at frequencies of interest, impedance matching at geometric discontinuities is not sufficient to eliminate reflections. This is illustrated by the resonances that degrade the performance of a TEM cell above a certain frequency [6]. The function of the transient test cell is to guide an electromagnetic transient from the input to the output. The electric field generated normal to one of the walls of the cell is the incident field used to calibrate the sensor. The cell is 3 m long, with a hatch at its mid-point to which various test plates can be fitted. Using wires to form the septum eliminates the need for internal supports (an equivalent metal sheet would sag under its own weight). The wires are soldered to a brass support at the input of the cell and attached to a steel rod with tensioning screws at the other end. This rod is earthed as a precaution against electrostatic discharge. Reflections at the cell output make it unsuitable for swept-frequency measurements. However, by using a fast transient as the incident waveform, the response of a sensor can be captured before the arrival of the reflected signal. A characteristic impedance of 50 Ω for the cell would maximise the amplitude of the signal coupled into it from the signal source. However, the precise value of this impedance is not critical and a mismatch between the 50 Ω impedance of the signal source and the cell input can be tolerated provided that: 1) The output of the signal source is sufficiently well matched to absorb the reflected signal. 2) The mismatch occurs only at the transition between the 50 Ω system and the cell input. No other mismatches can be tolerated, as they would give rise to multiple reflections, causing unwanted signals to enter the cell. The time window during which the sensor response must be captured is equal to twice the propagation delay between the position of the sensor under test and the end of the cell. In this case, the duration of the window is 10 ns, and the significant part of the sensor response must be contained within this window. In general, this means that the sensor under test should have a broadband characteristic rather than being highly resonant. The measurement page 4 of 9
window could be extended by using a longer cell, but beyond about 20 ns the size of the cell becomes impractical. 3.2 Input signal The particular shape of the incident transient signal is not critical, but for optimum system performance, it should satisfy two requirements: 1) The signal spectrum should be broadband, extending to high frequencies with the maximum amplitude that can reasonably be achieved. 2) The duration of the transient should be as short as possible. The first condition ensures a good signal-to-noise ratio at high frequencies in view of the fact that the sensitivity of the measurement system will be decreasing in this region. The second condition helps to maximise the measurement time available between the end of the incident transient and the arrival of the first unwanted reflection. For a given signal risetime the realistic choices are a pulse, which has spectral advantages, or a step, which occupies less time. In this instance, a step was chosen because it results in simpler waveforms. For example, when testing small electric field sensors whose response is essentially of a timederivative nature, the output in response to an incident step will be a pulse. However, if the incident signal were a pulse, the sensor output would be a double (bipolar) pulse. 3.3 Measurement equipment The transient calibration system is shown in Fig. 4. The signal source produces a 10 V step with a quoted risetime of less than 50 ps. This signal is connected to the input of the cell and generates an electric field that reaches a peak amplitude of about 35 Vm -1 over the test hatch. The output signal from the sensor is captured using a 1 GHz bandwidth digitiser that acquires the voltage as a 10 ns record with 256 sampling points. The digitiser timebase is triggered by a reference signal from the pulse driver unit. Trigger delay is adjusted so that the sensor response begins just after the start of the 10 ns acquisition window. Consistent triggering combined with averaging helps to reduce the background noise floor of the system. fast step module sensor transient field pulse driver unit PC timing signal digitiser Fig. 4: Block diagram of the transient calibration system. page 5 of 9
Using a computer, the digitised records are extended to 80 ns (2048 points) by the addition of augmenting zeros. This reduces the spacing of the calculated frequency response points from 100 to 12.5 MHz when using the FFT, improving the resolution. The computer displays a continuously updated frequency response for the sensor under test. Alternatively, the data can be printed or saved to disk for future use. 3.4 Principle of operation The measurement procedure can be explained with reference to Fig. 5. All quantities in this diagram are taken to be in the frequency-domain. V I is the cell input voltage, E I is the electric field incident at the test hatch, V O is the true output voltage and V M is the measured output voltage (including the effects of cables, connectors and the measurement equipment's frequency response). The purpose of the calibration is to find the unknown response of the sensor VOs VMs H sens = = (2) EI H sys EI Instead of calibrating the incident electric field, the response V Mr of the reference probe to the transient field E I is first recorded. The sensor to be tested is then mounted in the transient test cell and its output signal V Ms is measured. Now the incident field can be expressed as VMr E I = (3) H sys H ref and substituting (3) into (2) allows the frequency response of the sensor to be calculated in terms of the measured voltages as VMs H sens = H ref (4) VMr This expression is implemented using FFT software. An advantage of the relative measurement is that the frequency response H sys of the test equipment need not be known, because its effect is common to both measurements and cancels when the ratio is taken. In addition, the measurement technique is insensitive to distortion of the incident waveform E I relative to the input voltage V I because the effect is common to both measured signals. (a) V I H cell E I H ref V Or H sys V Mr (b) V I H cell E I H sens V Os H sys V Ms? Fig. 5: Transfer functions of the cell, sensor and measurement system: (a) initial measurement using the standard reference probe. (b) testing a sensor with an unknown frequency response. page 6 of 9
From (4) it can be seen that an accurate modelled or measured transfer function H ref for the reference probe is fundamental to the accuracy of the calibration. The 25 mm monopole described in Section 2 has been adopted as a reference for the calibration system [7] and other sensors have been calibrated relative to its theoretical response shown in Fig. 2. To provide traceability to recognised national standards, the reference probe was sent to the National Physical Laboratory (NPL) in the UK for calibration. The calibration was carried out using a network analyser and appropriate TEM cells. Subsequently, it has been possible to compare the results of this standard swept-frequency measurement with the probe response obtained using the transient test cell. 4. Results When used as a reference in the transient test cell, the monopole probe is mounted as shown in Fig. 6(a). For the swept-frequency calibration at NPL the probe was housed in a mounting block as shown in Fig. 6(b). This avoids having to drill a hole in the ground plane of the TEM cell. The mounting block will increase the electric field strength at the probe and we should therefore expect its sensitivity in this configuration to be greater than for the flat ground plane. 25 mm Aluminium mounting block 25 mm 25 mm (a) (b) 60 mm Fig. 6: Mounting arrangements for the 25 mm monopole: (a) Reference sensor for the transient calibration system. (b) Swept-frequency calibration. To compare the transient calibration with the swept-frequency results, the probe and mounting block arrangement of Fig. 6(b) (as calibrated at NPL) was tested as an unknown sensor in the transient test cell. The results are shown in Fig. 7, in which data from the swept-frequency calibration is plotted at 100 MHz intervals and the dashed lines represent the upper and lower limits of the measurement uncertainty (± 2.5 db). The solid line, which is the result of the transient calibration, lies within the uncertainty limits of the sweptfrequency results over the full 100-2000 MHz frequency range. As expected, the presence of the block increases the sensitivity of the probe. Comparing Figs. 2 and 7, it can be seen that H is approximately doubled when the sensor is mounted in the block rather than directly at the ground plane. Although the bandwidth of the digitiser used in the transient calibration system is 1 GHz, Fig. 7 indicates that the results obtained using this equipment are valid up to at least 2 GHz. In fact, tests have shown that the measurements are stable and repeatable up to 2.4 GHz. This bandwidth can only be achieved because of the relative nature of the measurements on which the technique relies. page 7 of 9
sensitivity H ( mv/vm-1) 20 10 1.0 0.1 0 500 1000 1500 2000 frequency ( MHz ) NPL swept-frequency calibration calibration uncertainty limits transient measurement Fig. 7: Comparing swept-frequency and transient measurements of the frequency response of the monopole and mounting block. 5. Discussion and conclusions The transient calibration system was originally developed for calibrating UHF couplers that are used to detect partial discharges in high voltage equipment [7]. Fig. 8 shows the measurement system being used to calibrate a disc type coupler. In addition to its own uncertainties, the transient measurement is directly affected by any inaccuracy in the model of the reference probe that is used. This study has confirmed that both the transient calibration technique and the theoretical model for the reference probe response are in agreement with measurements to national standards. The maximum difference between the swept and transient calibration results over the frequency range 100-2000 MHz is 1.7 db. This figure lies within the overall uncertainty of ± 2.5 db for the swept-frequency calibration and is comparable with the accuracy achieved by EMC test houses [8]. Fig. 8: The transient calibration system being used to test a UHF coupler. page 8 of 9
The transient test cell can form the basis of a relatively simple system for testing broadband electric field sensors. The accuracy of the transient calibration technique is not dependent on a knowledge of the incident field or the frequency response of the measurement equipment. By first storing the time-domain response of a reference probe, the transfer function of other sensors can be calculated relative to this reference, provided that no other components in the signal path are changed. The frequency range of the calibration is primarily governed by the signal-to-noise ratio of the FFT of the recorded sensor output voltages. Calibration can therefore be carried out at frequencies beyond the normal upper limit of the measurement equipment. 6. Acknowledgement This work was funded by an EPSRC research grant (GR/L34785). 7. References [1] D Koenigstein and D Hansen, "A new family of TEM-cells with enlarged bandwidth and optimized working volume", Proc. 7th Int. Symp. and Technical Exh. on EMC (Zurich), pp. 127-132, 1987 [2] M D Judd, O Farish and J S Pearson, "UHF couplers for gas insulated substations - a calibration technique", IEE Proc. Science, Measurement and Technology, Vol. 144, No. 3, pp. 117-122, May 1997 [3] H J Schmitt, C W Harrison and C S Williams, "Calculated and experimental response of thin cylindrical antennas to pulse excitation", IEEE Trans. Antennas and Propagation, Vol. AP-14, No. 2, pp. 120-127, March 1966 [4] C W Harrison, "The radian effective half-length of cylindrical antennas less than 1.3 wavelengths long", IEEE Trans. Antennas and Propagation, Vol. AP-11, No. 6, pp. 657-660, 1963 [5] M D Judd, O Farish and B F Hampton, "The excitation of UHF signals by partial discharges in GIS", IEEE Trans. Dielectrics and Electrical Insulation, Vol. 3, No. 2, pp. 213-228, 1996 [6] M L Crawford, J L Workman and C L Thomas, "Expanding the bandwidth of TEM cells for EMC measurements", IEEE Trans. Electromagnetic Compatibility, Vol. 20, No. 3, pp. 368-375, August 1978 [7] M D Judd, O Farish and P F Coventry, "UHF couplers for GIS - sensitivity and specification", Proc. 10th Int. Symp. on High Voltage Engineering (Montreal), Vol. 6, August 1997 [8] M J Alexander, "European intercomparison of antenna factors in the frequency range 30 MHz to 1 GHz", IEE Proc., Science, Measurement and Technology, Vol. 143, No. 4, pp. 229-240, July 1996 page 9 of 9