1. 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

2. Frequency Transfer Function of a dipole
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
Emmanuele Ravaioli LHC-CM

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_
Modeling of the voltage waves in the LHC main dipole circuits
Emmanuele Ravaioli LHC-CM

4. Model of a dipole 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
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_
Modeling of the voltage waves in the LHC main dipole circuits
Emmanuele Ravaioli LHC-CM

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

25. Comments on the results... -1
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 →
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)
Emmanuele Ravaioli LHC-CM

26. Comments on the results... -1b
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.
Emmanuele Ravaioli LHC-CM

27. Comments on the results... -2
The AC inductance of the dipole even at low frequency (0.1 Hz) is about 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?
Emmanuele Ravaioli LHC-CM

28. Conclusions & Further Work
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.
Emmanuele Ravaioli LHC-CM