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Emmanuele Ravaioli LHC-CM Thanks to Hugues Thiesen, Guy Deferne, Christian Giloux,

Frequency Transfer Function of a dipole What is it Why is it important How to calculate it How to model it How to measure it. Emmanuele Ravaioli LHC-CM Thanks to Hugues Thiesen, Guy Deferne, Christian Giloux, Bernard Dubois, Emmanuel Garde , Miguel Cerqueira Bastos 11-11-2011.

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Emmanuele Ravaioli LHC-CM Thanks to Hugues Thiesen, Guy Deferne, Christian Giloux,

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  1. Frequency Transfer Functionof a dipoleWhat is itWhy is it importantHow to calculate it How to model itHow to measure it Emmanuele Ravaioli LHC-CM Thanks to Hugues Thiesen, Guy Deferne, Christian Giloux, Bernard Dubois, Emmanuel Garde, Miguel Cerqueira Bastos 11-11-2011

  2. Simulation of the electrical behavior of the LHC dipole circuits • Model of a dipole • Frequency Transfer Function • Measurements in SM18: Set-up and results • Comments on the results… • Conclusions & Further Work Frequency Transfer Function of a dipole Emmanuele Ravaioli LHC-CM 11-11-2011

  3. Simulation of the electrical behavior of the LHC dipole circuits • For more info: • TE-Magnet-Seminary - Circuit simulations of the main LHC dipoles and the case of the 'unbalanced' dipoles – Ravaioli • 5JO-3_Ravaioli_20110916 • Modeling of the voltage waves in the LHC main dipole circuits Emmanuele Ravaioli LHC-CM 11-11-2011

  4. L = Laperture = 49 mH C = Cground = 150 nF Rp = Rparallel = 100 Ω Cp = 1 pF (for the moment) k = 0.75 7 Ω < R1,2 < 10 Ω Model of a dipole Inhomogeneous AC behavior of the two apertures of the dipole Different frequency response Phase-velocity of the wave changing along the dipole chain Each aperture shifts the wave of a different angle Eddy Currents in the coils Magnetization Effects Parasitic Coil-to-Ground Capacitance Parasitic Turn-to-Turn Capacitance • For more info: • 5JO-3_Ravaioli_20110916 • Modeling of the voltage waves in the LHC main dipole circuits Emmanuele Ravaioli LHC-CM 11-11-2011

  5. Frequency Transfer Function Example: L = 2*Laperture = 98 mH C = 2*Cground = 300 nF R = Rparallel = 100 Ω Matlab application for the study of the parameters of the proposed model of a dipole aperture Impedance of a stand-alone aperture model: (C/2) // [ (1-k)*L + (k*L // R) ] (second Z/2 bypassed by a short-circuit) Impedance of a series of aperture models: (Cp, Rp ignored here for simplicity) (C/2) // ∑Nmodules { [ (1-k)*L + (k*L // R) ] + C // [ (1-k)*L + (k*L // R) ] } Emmanuele Ravaioli LHC-CM 11-11-2011

  6. Measurements in SM18: Set-up • Two power converters in parallel, one providing the current level I_max and the other one providing a sinusoidal oscillation of ±4 V at a frequency sweeping between 30 and 2 kHz. • The gain-phase analyzer measures two differential voltages: one coming directly from the voltage taps of the dipole (Umag) and one proportional to the current flowing through the DCCT, ie through the dipole (Imag); this latter signal is acquired through an AC coupled differential amplifier with a gain of 1000. • Test without current (only Gain-Phase Analyzer and dipole, no PCs; frequency range: 1-20 kHz) • Tests at different I_max: 0 A ; 50 A ; 1 kA ; 2 kA ; 3 kA ; 4 kA ; 5 kA ; 6 kA . • Tests at different dI/dt(varying current): 0 A/s ; ±10 A/s ; 20 A/s ; 30 A/s ; 40 A/s ; ±50 A/s . • Tests measuring two separate apertures. • Tests measuring four separate poles. • Test after disconnecting Rparallel. Emmanuele Ravaioli LHC-CM 11-11-2011

  7. Imax = 0* dI/dt = 0 A/s Magnet * Without Power Converters Measurements in SM18: Results No PCs – Impedance Emmanuele Ravaioli LHC-CM 11-11-2011

  8. Imax = 0* dI/dt = 0 A/s Magnet * Without Power Converters Measurements in SM18: Results Different Imax – Phase Emmanuele Ravaioli LHC-CM 11-11-2011

  9. Imax = 0*, 50, 1000, 2000, 3000, 4000, 5000, 6000 A dI/dt = 0 A/s Magnet * Without Power Converters Measurements in SM18: Results Different Imax – Impedance Emmanuele Ravaioli LHC-CM 11-11-2011

  10. Imax = 0*, 50, 1000, 2000, 3000, 4000, 5000, 6000 A dI/dt = 0 A/s Magnet * Without Power Converters Measurements in SM18: Results Different Imax – Phase Emmanuele Ravaioli LHC-CM 11-11-2011

  11. Imax = 50, 1000, 2000, 3000, 4000, 5000, 6000 A dI/dt = 10 A/s Magnet Measurements in SM18: Results Different Imax – Impedance Emmanuele Ravaioli LHC-CM 11-11-2011

  12. Imax = 50, 1000, 2000, 3000, 4000, 5000, 6000 A dI/dt = 10 A/s Magnet Measurements in SM18: Results Different Imax – Phase Emmanuele Ravaioli LHC-CM 11-11-2011

  13. Imax = 50, 1000, 2000, 3000, 4000, 5000, 6000 A dI/dt = -10 A/s Magnet Measurements in SM18: Results Different Imax – Impedance Emmanuele Ravaioli LHC-CM 11-11-2011

  14. Imax = 50, 1000, 2000, 3000, 4000, 5000, 6000 A dI/dt = -10 A/s Magnet Measurements in SM18: Results Different Imax – Phase Emmanuele Ravaioli LHC-CM 11-11-2011

  15. dI/dt = 0, ±10, 20, 30, 40, ±50 A/s Imax > 50 Magnet Measurements in SM18: Results Different Imax – Impedance Emmanuele Ravaioli LHC-CM 11-11-2011

  16. dI/dt = 0, ±10, 20, 30, 40, ±50 A/s Imax > 50 Magnet Measurements in SM18: Results Different Imax – Phase Emmanuele Ravaioli LHC-CM 11-11-2011

  17. Imax = 0*, 50 A dI/dt = 0 A/s Apertures * Without Power Converters Measurements in SM18: Results Different Imax – Impedance Emmanuele Ravaioli LHC-CM 11-11-2011

  18. Imax = 0*, 50 A dI/dt = 0 A/s Apertures * Without Power Converters Measurements in SM18: Results Different Imax – Phase Emmanuele Ravaioli LHC-CM 11-11-2011

  19. Imax = 0*, 0 A dI/dt = 0 A/s Poles * Without Power Converters Measurements in SM18: Results Different Imax – Impedance Emmanuele Ravaioli LHC-CM 11-11-2011

  20. Imax = 0*, 0 A dI/dt = 0 A/s Poles * Without Power Converters Measurements in SM18: Results Different Imax – Phase Emmanuele Ravaioli LHC-CM 11-11-2011

  21. Imax = 0*, 50**, 1000, 2000 A dI/dt = 0 A/s Magnet, No Rparallel * Without Power Converters, With Rparallel ** With Rparallel Measurements in SM18: Results Different Imax – Impedance Emmanuele Ravaioli LHC-CM 11-11-2011

  22. Imax = 0*, 50**, 1000, 2000 A dI/dt = 0 A/s Magnet, No Rparallel * Without Power Converters, With Rparallel ** With Rparallel Measurements in SM18: Results Different Imax – Phase Emmanuele Ravaioli LHC-CM 11-11-2011

  23. Imax = 0*, 50**, 1000 A dI/dt = 0 A/s Apertures, No Rparallel * Without Power Converters, With Rparallel ** With Rparallel Measurements in SM18: Results Different Imax – Impedance Emmanuele Ravaioli LHC-CM 11-11-2011

  24. Imax = 0*, 50**, 1000 A dI/dt = 0 A/s Apertures, No Rparallel * Without Power Converters, With Rparallel ** With Rparallel Measurements in SM18: Results Different Imax – Phase Emmanuele Ravaioli LHC-CM 11-11-2011

  25. The measured Frequency Transfer Function (FTF) is not fitting with the expected one, and corresponds to parameters different from the nominal ones: • L 49 mH→ 35 mH • k 0.75 → 0.45-0.55 • Rparallel 100 Ω→ 80 Ω• R 10 Ω→ 30 Ω • The shape of the measured Frequency Transfer Function does not correspond to the expected curve calculated with the adopted electrical model. • Possible explanation: The model has been tailored on the measurements during Fast Power Aborts, when the main excitation frequency is ~28.5 Hz. Therefore it is possible that the model fits well the behavior of the dipoles, but only around 30 Hz. (see the qualitative example below: measurement, old model, new model) Comments on the results... -1 Emmanuele Ravaioli LHC-CM 11-11-2011

  26. Development of a new electrical model of the dipole apertures, fitting their behavior in a wider range of frequency, and test of its capability to simulate the actual behavior of the dipole circuit. Such a model could be developed by fitting the curve of the impedance of an aperture without Rparallel , and may include the splitting of the inductance in 3 parts (4 free parameters: k1, k2, R1, R2). Fitting already started with Matlab. Comments on the results... -1b Emmanuele Ravaioli LHC-CM 11-11-2011

  27. The AC inductance of the dipole even at low frequency (0.1 Hz) is about 35-40 mH, whereas the measured DC value is close to the nominal ~100 mH. This phenomenon has been observed in the past. The AC inductance was measured with two independent systems (without PCs between 0.1 Hz and 20 kHz; with PCs between 30 Hz and 2 kHz) with similar outcome. It would be interesting to perform this measurement also for the new configuration between 0.1 Hz and 30 Hz. (first attempt on Wednesday, still problems; Hugues is taking care of it). → At which frequency is the dipole changing its inductance? FTF almost independent on the current level (!) → Why do the dipoles exhibit a different behavior at different current? FTF almost independent on the current ramp-rate (!) FTF of the two apertures is very similar → Did we spot a perfectly balanced dipole? Comments on the results... -2 Emmanuele Ravaioli LHC-CM 11-11-2011

  28. The measurement system seems to work fine, and the results have physical significance. • The initial problems related to the poor quality of the measurement of the DCCT current have been solved (Miguel). • Thanks to the SM18 team for the kind support! • Further Work • Measurements of the FTF with the current configuration (parallel PCs) between 0.1 Hz and 30 Hz. To be done modulating a sinusoidal signal with the large PC, and measuring the impedance corresponding to different frequencies (manually). • Repeat the same measurements on another available spare dipole, hoping to spot an unbalanced dipole. • Development of a new electrical model of the dipole apertures, fitting their behavior in a wider range of frequency, and test of its capability to simulate the actual behavior of the dipole circuit. Such a model could be developed by fitting the curve of the impedance of an aperture without Rparallel , and may include the splitting of the inductance in 3 parts (4 free parameters: k1, k2, R1, R2). Fitting already started with Matlab. • Enlightened by the new results and model, check that the expected change of FTF is theoretically visible (With the old model, changing R1,2 between 7 and 10 Ω leads to a difference of ~1 dB of the impedance of two unbalanced apertures... With the new?). • Analysis of the past FTF measurements (at cold, no PCs, 0 current). • Analysis of the measurements of the FTF of the whole chain of 154 dipoles (Report Interpretation of the TFM tests of dipole circuits, PJK (?), 5 March 2008), and comparison with the calculated FTF of the series of 308 aperture models. Conclusions & Further Work Emmanuele Ravaioli LHC-CM 11-11-2011

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