1. 1 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Digital Signal Processing Approaches for Varying Magnetic Field Measurements through a Rotating Coils System L. Angrisani, R. Schiano Lo Moriello L. Bottura, A. Masi

2. 2 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Outline Introductive notes Limitations of the standard Fourier analysis in the presence of analog bucking Proposals:  Quadrature demodulation-based method  Extrapolation-based method Performance comparison in simulated conditions Results in actual experiments Conclusions

3. 3 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Introduction In superconducting magnets, dynamic effects like snapback can be estimated only through measurements in ramping conditions. Due to current variation, field harmonics are both time and ramp rate dependent (e.g. decay phenomena). The conventional Fourier analysis does not work properly. Being addressed to DC measurements, it assumes field harmonics to be constant during a coil turn.

4. 4 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Introduction Increasing coil speed is often impracticable, and it could prove unsuccessful in the presence of high ramp rates of the current. To measure varying magnetic fields through a rotating coils system, two new digital signal-processing methods are proposed. They both assume continuous coil rotation.

5. 5 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland The standard Fourier analysis Magnetic flux as a function of the angular position Integration of V coil in the angular domain Constant during a coil turn Field Harmonics

6. 6 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Problems with the standard Fourier analysis A periodic, magnetic flux characterized by constant envelope…..

7. 7 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland The envelope of the main component (fundamental) increases linearly with the angular position, B 3 and B 5 being constant ….. Imposed values DFT results Problems with the standard Fourier analysis

8. 8 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Hardware solution: analog bucking Problems with the standard Fourier analysis Measurement problems with B 5 still survive. Measurement problems with B 3 still survive.

9. 9 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Standard Fourier analysis characterization LHC Cycle Typical test current evolution

10. 10 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Standard Fourier analysis characterization

11. 11 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Standard Fourier analysis characterization Difference greater than 1 unit for a 10A/s linear ramp 4000500060007000800090001000011000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 x 10 -3 R=10A/s R=20A/s R=30A/s Absolute difference for B 1 Current [A] Abs(B 1 -B 1 avg) [T] R=40A/s R=50A/s R=60A/s R=70A/s R=80A/s R=90A/s R=100A/s Linear ramp: different ramp rates have been simulated

12. 12 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Standard Fourier analysis characterization 010203040 0 1 2 3 4 5 x 10 -5 Number of coil turns abs[(B1-B1avg) [T] B1B1 010203040 0 0.2 0.4 0.6 0.8 1 x 10 -4 Number of coil turns abs[(B3-B3avg) [T] B3B3 Parabolic ramp

13. 13 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Standard Fourier analysis characterization Exponential ramp

14. 14 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Proposal 1: quadrature demodulation-based method Ф(t) sin(2πft) FIR tg -1 x2 Unwrap Phase Modulus cos(2πft) Residual C 1 evaluation: digital bucking Quadrature demodulation scheme

15. 15 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Sliding window FFT Overlap ratio: Proposal 1: quadrature demodulation-based method

16. 16 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Proposal 1: typical results Difference (  ) between estimated and nominal evolution of B 1. Comparison of the nominal evolution of B 3 (green) to those obtained through STFT (red) and demodulation+STFT (violet).

17. 17 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Proposal 2 : extrapolation-based method For each angular position, the flux samples (red dots) acquired in the last four coil turns are used to extrapolate the flux samples related to the next turn for different sampling times (black dots).

18. 18 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Proposal 2 : extrapolation-based method

19. 19 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Performance comparison: linear ramp 10 20 30 40 50 1,00E-05 1,00E-04 1,00E-03 1,00E-02 Absolute RMS error [T] Ramp Rate [A/s] B1B1 Standard analysis STFT Extrapolation

20. 20 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Performance comparison: linear ramp B5B5 B3B3

21. 21 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Performance comparison: parabolic ramp B 1 -B 7 A 1 -A 8

22. 22 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Performance comparison: exponential ramp B 1 -B 7 A 1 -A 8

23. 23 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Proposal 2: experimental results Some measurements have been carried out on a reference, resistive magnetic dipole. Continuous coil rotation has been assured. Coil speed has been equal to 1 turn/s. Different ramp rates have been considered: 5A/s, 10A/s, 20A/s.

24. 24 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Proposal 2: experimental results As expected for the reference magnet measured, the first results seem to highlight that harmonic coefficients are independent of ramp rate.

25. 25 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Comparison Blue trace: proposal 1 Black trace: proposal 2 The evolution versus time of harmonic coefficients gained from proposal 2 result smoother than those from proposal 1.

26. 26 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Conclusions Characterization of the standard Fourier analysis when applied to compensated magnetic fluxes in non-stationary conditions. A quadrature demodulation-based method for a reliable digital bucking has been proposed (proposal 1).  Harmonic coefficients are gained from the application of the standard Fourier analysis to digitally compensated flux samples. An alternative method that extrapolates, for a given time instant, the flux value for each angular position in a coil turn has also been presented (proposal 2).

27. 27 / 27 L.Angrisani University of Naples Federico II, ITALY angrisan@unina.it 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Conclusions Many tests in simulated dynamic conditions have been carried out to assess and compare the performance of the proposed methods.  Proposal 1 allows more accurate estimate of harmonic coefficients, but B 1, than that granted by standard Fourier analysis.  Proposal 2 performs much better even in the presence of high ramp rates.  The reduced computational burden of proposal 2 make real-time tracking of harmonic coefficients feasible. The first results obtained in actual experiments seem to confirm the reliability of proposal 2.