1. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Dynamic Characterization of Nonlinear Magnets by Modeling and Measuring Magnetic Field Phase Spectrum Pasquale Arpaia (1), Alessandro Masi (2), Giovanni Spiezia (2), Antonio Zanesco (1) (1)Università del Sannio, Dipartimento di Ingegneria, Italy (2)CERN, AT-MTM Group, Switzerland

2. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland State of the art investigation of magnet macroscopic behavior in industrial applications New digital measurement systems to determine magnetic characteristics Development of adequate nonlinear models for transfer functions when imposing a flux for generating currents

3. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Measurement method: basic ideas l Analytic relationship between dynamic hysteresis and current phase spectrum l Decomposition of nonlinear material behavior in a hysteretic component and a non-hysteretic component

4. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Relationship between hysteresis and current phase spectrum Non-hysteretic behaviorSymmetrical hysteretic behavior Asymmetrical hysteretic behavior  i  i =  i=1…n k

5. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Material non linearity decomposition ymmetrical h Asymmetrical hysteretic characteristic Common-mode componentDifferential component

6. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Dynamic model of hysteretic material

7. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Characterization of the measurement method NI(t) nhnh Measurement uncertainty Noise Model estimate MEASUREMENT METHOD rms[NI-NI] ^

8. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Simulation results rms of the model error in estimating NI for an added white noise Sigma=0.0010 Sigma=0.0008 Sigma=0.0005 Sigma=0.0003 Sigma=0.0001

9. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Simulation results Sigma=0.001 Sigma=0.0008 Sigma=0.0005 Sigma=0.0003 Sigma=0.0001 rms of the model error in estimating NI for an added LF noise

10. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Simulation results Sigma=0.001 Sigma=0.0008 Sigma=0.0005 Sigma=0.0003 Sigma=0.0001 rms of the model error in estimating NI for an added HF noise

11. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Comparison with classical algorithm Comparison between polynomial interpolation and proposed method in case of white noise Classical method Proposed method n h = 15 n = 30 Noise Standard Deviation Classical method Proposed method

12. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Comparison with classical algorithm Comparison between polynomial interpolation and proposed method in case of LF noise Noise Standard Deviation Classical method Proposed method Classical method Proposed method n h = 15 n = 30

13. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Comparison with classical algorithm Comparison between polynomial interpolation and proposed method in case of HF noise Classical method Proposed method n h = 15 n = 30 Classical method Proposed method Noise Standard Deviation

14. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Experimental results Lab measurement station

15. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Method application to an actual case l Ferrite (Mn-Zn) l Frequency 200 Hz l Maximum flux density l n h = 15 l f c = 25.6 kHz  f=25 Hz  f=25 Hz l n c = 1024 Measurement conditions B max = 0.08 T B max = 0.17 T B max = 0.28 T

16. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Results Proposed method performance for B max = 0.08T Induzione magnetica B (T) Campo magnetico H (A/m) Experimental points Proposed method Magnetic flux density - B(T) Magnetic Field - H Magnetic Field – H (A/m)

17. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Results Proposed method performances for Bmax= 0.17T Induzione magnetica B(T) Campo magnetico H (A/m) Experimental points Proposed method Magnetic flux density - B(T) Magnetic Field – H (A/m)

18. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Results Proposed method performances for Bmax= 0.28T Campo magnetico H (A/m) Experimental points Proposed method Magnetic Field – H (A/m) Magnetic flux density - B(T)

19. IMMW 14 - 14 th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland Conclusions Conclusions o Method to characterize magnet dynamic behavior by modeling and measuring current phase spectrum o Preliminary validation on digital signals affected by different noises o Comparison in simulation with results obtained by a classical estimation method o Experimental verification by a lab measurement station o Satisfactory results  Good alternative at classical methods suitable for DSP implementation