Digital fluxgate magnetometer for the Astrid-2 satellite

Transcription

1 Meas. Sci. Technol. 10 (1999) N124 N129. Printed in the UK PII: S (99) DESIGN NOTE Digital fluxgate magnetometer for the Astrid-2 satellite Erik B Pedersen, Fritz Primdahl, Jan R Petersen, J M G Merayo, Peter Brauer and O V Nielsen TERMA Elektronik AS, Hovmarken 4 6, 8520 Lystrup, Denmark Department of Automation, Building 327, Technical University of Denmark, DK-2800 Lyngby, Denmark Received 23 April 1999, in final form and accepted for publication 20 August 1999 Abstract. The design and performance of the Astrid-2 magnetometer are described. The magnetometer uses mathematical routines, implemented by software for commercially available digital signal processors, to determine the magnetic field from the fluxgate sensor. The sensor is from the latest generation of amorphous metal sensors developed by the Department of Automation at the Technical University of Denmark. Keywords: magnetic field, fluxgate magnetometer, digital signal processing, amorphous metal sensors, satellite instrumentation for Astrid-2 1. Introduction Modern fluxgate magnetometers have until now been based solely on analogue signal processing. However, with the encouraging results reported by Primdahl et al (1994), Piil- Henriksen et al (1996) and Auster et al (1995), it seems feasible to use an early sampling of the fluxgate sensor signal and replace some of the analogue circuitry with mathematical routines executed in high-performance digital signal processors (DSPs). The development of the Astrid-2 magnetometer is based on technology and knowledge from the Ørsted magnetometer. This involves using ring core sensors and all-even detection. Instead of analogue signal processing, the sensor signal is sampled directly after the input amplifier and processed in a DSP. Feedback is generated by a digitalto-analogue converter (DAC). The Astrid-2 magnetometer is based on DSPs from Analog Devices. Each axis has its own 16-bit fixed-point DSP and operates autonomously. The magnetometer is part of the EMMA (Electrical and Magnetic Monitoring of the Aurora) instrument developed by the Alfvén Laboratory at the Royal Institute of Technology, Stockholm, Sweden, and it is controlled through this instrument. The fluxgate sensor is based on the technology developed at the Department of Automation of the Technical University of Denmark. It is a single-axis compensated sensor (Brauer et al 1999). 2. Design of the Astrid magnetometer The magnetometer is designed for a full-field range of approximately 65 µt. It is based on the principle first described by Henriksen et al (1996). It samples the raw fluxgate sensor signal with an analogue-to-digital converter (ADC), and then uses a DSP to perform the field extraction and generation of the feedback signal for the sensor. This signal is converted into an analogue signal by a DAC. The structure of the Astrid-2 magnetometer is shown in figure 1. The excitation frequency has been set to 8 khz, and the excitation circuit uses parametric amplification in order to save power (Acuña 1974). The excitation level is adjusted to approximately 1 A pp, which should ensure stable operation. The actual design is based on the Ørsted magnetometer (Nielsen et al 1995). The sensor signal is amplified and converted to a voltage by a current feedback operational amplifier used in shortcircuit mode (Primdahl et al 1989). The amplifier is followed by a first-order RC filter with a 50 khz 3 db cut-off frequency. A 12-bit ADC is used to sample the sensor signal. The sampling rate is set to 16f exc = 128 khz. The quantization step is determined by the fluxgate feedthrough signal, since the magnetometer operates as a feedback system compensating for the external field. This leaves the sensor feedthrough signal as the main signal seen by the ADC. For the Astrid-2 sensor, the size of this signal corresponds to approximately 2 µt. With an adequate margin in the input amplifier, the quantization step can be calculated to be 1.32 nt. The ADC quantization noise is transferred unattenuated to the output (see below), therefore the noise contribution from the ADC (in the case of an ideal ADC) will be 1.51 pt rms /root (Hz). Even if the ADC performs less than perfectly, the noise it produces will be insignificant. The DSP is an Analog Devices ADSP2173, which is a 16-bit fixed-point processor. The processor runs at 10 MHz, delivering 10 MIPS sustained and peak 20 MIPS. The telemetry output is 20-bit 2 s complement. The instrument /99/ $ IOP Publishing Ltd

2 DC-blocking Input amp ADC Matched filter Integrator Decimation/TM TM out V/I conv. DAC Dac interpolator Fluxgate sensor ADSP2173 Exc. driver Timing/excitation Figure 1. Digital fluxgate magnetometer. uses one DSP per axis. Each axis runs independently, and the synchronization between the X, Y and Z axes is controlled externally. The timing is also controlled externally, reducing jitter on the excitation and the sampling signal, which could otherwise result in added noise. The output signal is generated with an 18-bit DAC using the same update frequency as the ADC sampling. The DAC is an audio type, constructed as a resistor ladder type. The output from the DAC is converted to a current. This eliminates the sensitivity to changes in resistance in the feedback coil due to temperature fluctuations. The complete triaxial instrument is mounted on two printed circuit boards, one containing channel Z and the excitation, and the other containing channels X and Y. As part of the EMMA box, the magnetometer is controlled by the EMMA data handling system, and the output is part of the EMMA telemetry packets. When the power is switched on, the magnetometer is loaded with software from the data handling system. Initialization of the software is performed after booting, while the execution of the magnetometer function waits for an external synchronization signal. To summarize, the instrument characteristics are as follows. Power consumption, 2 W; range, ± nt; resolution, 20 bit DSP routines The core of the magnetometer is the routines executed by the DSP. Four major routines are executed: field extraction, integration, feedback generation and filtering of the data for the telemetry output. The field-extraction algorithm corresponds to the analogue phase detector in the classical instrument. It calculates a field estimate by filtering the fluxgate sensor signal by a set of coefficients which represent the expected measured field output from the sensor. This reference signal has been constructed by measuring the response from the sensor with a field applied in two opposite directions (Henriksen et al 1996). Figure 2 shows the reference function. The field estimate is calculated for every half cycle (once every eight samples). This raises the maximum theoretical frequency to 8 khz and reduces the inband quantization noise from the DAC due to the faster update rate. The frequency response from the matched filter allows even harmonics of Reference coefficient Sensor reference Sample number Figure 2. Reference function for field extraction. the excitation frequency to pass (the field-dependent part of the signal), while odd harmonics are attenuated. The fieldextraction algorithm corresponds to a cross-correlation, e.g.: r(i) = [S(i N + n)r(n)]. n S(n) is the sensor signal and R(n) is the reference function. Viewed in the frequency domain, the function of the field extraction can be interpreted as a matched filter followed by a resampling. The output of the matched filter is sampled twice during every excitation period, at the maximum correlation value. The matched filter takes care of the attenuation of odd harmonics and the suppression of DC offsets in the sensor signal. The resampling process demodulates the even harmonics of the sensor signal down to DC (the even harmonics contain the field information). The resampling process corresponds to a folding in the frequency domain with a delta function. 1 Y(f) = M(f) δ (f 1 ). n T mn T This equation can be reduced to Y(f) = 1 N N 1 m= (N 1) ( M f ± m 1 ). N T N125

3 2kf 0 Magnetometer output MAG out Sensor R1 External field B ext A Z -1 2f 0 N-bit R0 B-bits D/A B-N+1 bit Lowpass filter Figure 4. Functional diagram for determination of loop function. B Figure 3. Resolution enhancement for DAC. T is the time between two samples and N is the number of harmonics used in the matched filter. It can be seen that only the even harmonics are converted to DC. The integrator, which in discrete signal processing corresponds to a summation, is updated twice every excitation period. The output of the integrator is representative of the current field seen by the fluxgate sensor. The feedback generator uses the output from the integrator and processes it with an interpolator routine. The main purpose of this function is to reduce the quantization noise of the DAC. Figure 3 shows a functional diagram of this function. The actual signal processing effect on the noise spectrum can be calculated by N(f) = E 1 (z)(1 z 1 ) where E 1 (z) is the spectral density of the quantization noise. This results in a high-pass filtering of the noise, lowering it within the frequency band of interest. Filtering of the telemetry output is described in detail below Loop function At low frequencies (below a few hundred hertz), the magnetometer loop can be approximated by a first-order loop. Figure 4 illustrates the set-up. The approximation ignores the effects of both the zero-order hold filter created by the DAC and the RC low-pass filter in the output of the DAC (with a cut-off frequency of 6 khz) and the frequency response of the sensor itself (roll-off around each harmonic). The reason for ignoring these effects is that they all occur at least a factor of ten above the area of interest. The gain factor A is a combination of the sensor scale factor, the input amplifier gain and a digital correction factor. B is determined by the conversion factor in the V/I converter in the output, and the coil constant for the feedback coil. Two interesting transfer functions are the external B-field (B ext ) to the digital output (MAG out ) and the DAC noise to the digital output. B ext to MAG out : H Bext MAG out (z) = DAC noise to MAG out : H DAC MAGout (z) = Az 1 1 (1+AB)z 1. BAz 1 1 (1+AB)z 1. From ADC To DAC Extraction/summation Interpolation 2048Hz filter 256Hz filter 16Hz filter Figure 5. Structure used for the decimation filters. 2048Hz filtered 256Hz filtered 16Hz filtered Unfiltered Both functions are low-pass functions with a pole determined by A B. The equations show that it is possible to control the bandwidth by adjusting the digital correction factor A. In the Astrid magnetometer it is adjusted to approximately 300 Hz. Experiments show that the instrument is stable if the bandwidth is kept below 1000 Hz. At higher frequencies the loop gain gets too high and the instrument becomes sensitive to noise. To get an accurate determination of the behaviour at higher frequencies, it is necessary to incorporate the effects mentioned above. Due to the low-pass function from the DAC to the telemetry output, noise and nonlinearities generated by the DAC will be transferred unattenuated to the telemetry output. The effect of this is described below Decimation filters The output from the magnetometer loop can be filtered through a chain of decimation filters. Figure 5 shows how the different output rates are generated. All output rates are calculated in parallel, allowing a shift between them without rebooting the magnetometer. The output can be set at 2048, 256 and 16 Hz, with or without filter. All three filters are finite impulse response (FIR) filters and they are linear phase filters within the passband. Figures 6 8 show the frequency response for the filters. The cut-off frequencies are: (a) stage: 700 Hz (b) stage: 85 Hz (c) stage: 7 Hz. The delays through the filters are: (a) stage: 3.75 ms (b) stage: 49.1 ms ms (c) stage: 0.74 s ms ms. DC gains are: (a) stage: (b) stage: (c) stage: N126

4 Amplitude (db) Frequency (Hz) Figure 6. First-stage decimation filter Temperature drifts The flight electronics has been tested in a thermal chamber at different temperatures between 5 and 35 C. Offset and gain drifts have been derived. The following equation illustrates the use of the parameters. F = (offset + α(t nominal T actual )) +gain(1+β(t nominal T actual )) field. Values for the three axes are given in table 1. Table 1. Values for the three axes (EU are engineering units in bits). Axis a β X 0.92 EU/ C / C Y 6.18 EU/ C / C Z 8.25 EU/ C / C 0 Amplitude (db) The conversion factor (gain) between engineering units and nanoteslas has been determined (Merayo et al 1998). The values are approximately: X = nt/eu Y = nt/eu Z = nt/eu Frequency (Hz) 0 Figure 7. Second-stage decimation filter. The offsets are: X = EU Y =3648.3EU Z= EU. 50 Amplitude (db) 100 The temperature for the electronics is believed to be within 10 C of the nominal temperature, when in orbit. The primary source for temperature drift in the magnetometer electronics is the DAC, and according to the data sheet the total drift due to gain, offset and linearity is 25 ppm of the fullscale range per degree. The measured drift is approximately 83 ppm for the worst channel. The remaining drift can be attributed to voltage references and operational amplifiers in the output (gain and offset drift). Drifts in the input circuit will only result in a change in the instrument bandwidth Frequency (Hz) Figure 8. Third-stage decimation filter. The data have to be corrected by the DC gain factor before any further data processing takes place. Due to the delay in the filters, a shift between two filters will result in a jump in time. Going from a lower sampling rate to a higher rate will result in lost data, while the opposite will produce redundant data until the filter catches up DAC nonlinearities During test and calibration it was discovered that the feedback DAC suffered from nonlinearities of the order of several LSBs. Since the DAC is a resistor-ladder type the nonlinearities are generated by a mismatch between the resistors. The nonlinearities have been measured at the Alfvén Laboratory at the Royal Institute of Technology, Stockholm, Sweden. The measurements are available as a correction table, which can be used to decrease the resulting residuals (Merayo et al 1998) for further information. N127

5 Figure 9. Polar passage of the Astrid-2 satellite. 3. Performance With the sensor inside a magnetic shield, the overall noise from the magnetometer is quite low. At the 16 Hz filtered output it has been measured to be below 50 pt rms. The overall calibration shows residuals in the order of 1.3 nt rms after compensating for the DAC nonlinearities. This is clearly higher than the best analogue magnetometers and depends mainly on the choice of DAC. However, transverse effects from the sensor have some influence as well. Parameter drift is quite small, but it might get worse with an accumulated radiation dose. 4. Future developments The major source of error in the digital magnetometer design is clearly the DAC. Due to its position inside the feedback loop, both quantization noise and nonlinearities are transferred, unattenuated, to the digital output. Quantization noise can be dealt with by using an oversampling scheme, as described above. However, nonlinearities are difficult to remove. To achieve a linearity of greater than 20 bits requires an equally linear DAC, but with the present DAC technology, this is not possible with commercially available circuits. The only way to handle this problem is to use a one-bit converter, which is inherently linear. However, it might prove difficult to achieve the required noise level without using extremely high sampling rates. 5. Data from the Astrid-2 satellite Astrid-2 was launched into a 1000 km circular 83 inclination orbit on 10 December 1998, and the magnetometer was successfully switched on shortly after. On 11 January 1999, the hinged boom with the sensor was deployed, also successfully, and the near 90 rotation of the sensor during boom deployment was verified from the magnetic data. For more information on Astrid-2, consult the Swedish Space Corporation s website ( Figure 9 shows data from a polar passage. The data from the magnetometer has been despun into an inertial coordinate system and the satellite orientation has been derived. The IGRF magnetic field model has been subtracted from the B field and the residuals are plotted together with the E field. The plot clearly shows the passages of the auroral zones. 6. Conclusion The Astrid-2 magnetometer demonstrates that it is possible to construct a fluxgate magnetometer using digital signal processing, and that this magnetometer can achieve performance comparable to that of analogue magnetometers. The design has shown a robustness and performance that look promising for the future. One advantage of the digital magnetometer design is that it reduces the need for manual adjustments of the electronics. The only part that needs to be optimized is the excitation circuit. Bandwidth and phase can be adjusted in the software. This will reduce both the test and manufacturing time of the magnetometer. Acknowledgments The development of the Astrid-2 magnetometer is funded in part by the Danish Technical Scientific Research Council. The development has been made in close collaboration with the Finnish Sodankylä Geophysical Observatory, the Alfvén Laboratory at the Royal Institute of Technology, Stockholm, Sweden, and TERMA Elektronik AS, in part funded by the Danish Academy of Technical Sciences. We wish to thank L Blomberg, G Marklund and N Ivchenko from the Alfvén N128

6 Laboratory for their support, and for kindly providing the reduced data from the Astrid-2 satellite. References Acuña M H 1974 Fluxgate magnetometers for outer planets exploration IEEE Trans. Magn Auster H-U, Lichopoj A, Rustenbach J, Bitterlich H, Fornacon K H, Hillenmaier O, Krause R, Schenk HJand Auster V 1995 Concept and first results of a digital fluxgate magnetometer Meas. Sci. Technol Brauer P 1997 The ring core fluxgate sensor PhD Thesis Department of Automation, Technical University of Denmark Brauer P, Risbo T, Merayo JMGandNielsen O V 1999 Fluxgate sensor of the vector magnetometer onboard the Astrid-2 satellite Sensors Actuators A at press Candy J C and Huynh An-Ni 1986 Double interpolation for digital-to-analog conversion IEEE Trans. Commun. COM Merayo J, Brauer P, Risbo T, Pedersen E B, Petersen JRand Primdahl F 1998 Astrid-2 EMMA magnetic calibration final report Department of Automation, Technical University of Denmark Nielsen O V, Petersen J R, Primdahl F, Brauer P, Hernando B, Fernandez A, MerayoJMGandRipka P 1995 Development, construction and analysis of the Ørsted fluxgate magnetometer Meas. Sci. Technol Piil-Henriksen J, Merayo JMG,Nielsen O V, Petersen H, Petersen J R and Primdahl F 1996 Digital detection and feedback fluxgate magnetometer Meas. Sci. Technol Primdahl F, Hernando B, Petersen J R and Nielsen O V 1994 Digital detection of the flux-gate sensor output signal Meas. Sci. Technol Primdahl F, Petersen J R, Olin C and Harboe Andersen K 1989 The short-circuited fluxgate output current J. Phys. E: Sci. Instrum Smith RWM,Freeston I L, Brown B H and Sinton A M 1992 Design of a phase-sensitive detector to maximize signal-to-noise ratio in the presence of Gaussian wideband noise Meas. Sci. Technol N129