I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do Magnetic field measurement system based on rotating PCB coils Author: Gianluca Nicosia Politecnico di Milano Supervisor: Joseph DiMarco Fermilab TD September 26, 2014 1 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do Section 1 I NTRODUCTION 2 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do A IM OF THE INTERNSHIP Developing a magnetic field measurement system in LabVIEW and MATLAB implementing preexisting scripts and using it to analyze the performances of rotating PCB coils comparing them to more traditional machine-wound harmonic coils. 3 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do R OTATING COIL IN MAGNETIC FIELD The system is based on Faraday’s Law: �� E = − d φ dt = − d B · n d A = (1) dt A �� �� d B − dt · n d A − v × B d l (2) A ∂ A � �� � � �� � Time-varying field Displacement or deformation of the coil If the geometry and the position of the coil are known, integrating the voltage, the flux is obtained. t � Φ − Φ 0 = − E d t (3) 0 The field harmonics (multipoles) are derived using knowledge of the coil geometry. 4 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do H ARMONIC DECOMPOSITION Let’s consider a region of space free of charges and current. ∇ · B = 0 (4) ∇ × B = 0 (5) A magnetic field B = ( B x , B y , B z ) with B z constant and the other two components given by B y + iB x = C n ( x + iy ) n − 1 = C n z n − 1 C n ∈ C , n ∈ N (6) satisfies 4 and 5 5 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do H ARMONIC DECOMPOSITION A generic field is given by � z � n − 1 ∞ � B y + iB x = C n (7) R r n = 1 Harmonics can be easily measured starting form the flux �� � C n K n e in θ Φ( θ ) = Re (8) n = 1 K n is the winding sensitivity and is defined as: N wires � x j + iy j � n L j R r � ( − 1 ) j K n = (9) n R r j = 1 Flux Fourier coefficients F n C n = F n (10) K n 6 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do B UCKING To accurately measure higher order harmonics it is necessary to connect the coils in such a fashion as to suppress the signal of the main field component. This will consequently suppress spurious harmonics due to coil vibrations. This technique is called bucking . i UB ≈ 1 k Ω DB ≈ 1 k Ω i 7 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do Section 2 S ET -U P AND NOISE ANALYSIS 8 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do W ORKING BENCH 9 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do M ORGAN P ROBE 10 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do DAQ (PXI-4462) ◮ Maximum sampling frequency: 204 . 8 kHz ◮ Differential inputs ◮ ADC resolution: 24 bit ◮ Input dynamic range set to ± 0 . 316 V − → 30 dB gain ◮ Input resistance: 1 M Ω LSB = ∆ = 0 . 316 V × 2 ≈ 37 . 67 nV 2 24 Quantization noise: ∆ σ = √ ≈ 10 . 87 nV 12 Not infinite input resistance leads to signal loss of 1 M Ω PCB ≈ 1 − 10 k Ω + 1 M Ω ≈ 1 % 1 M Ω Morgan ≈ 1 − 10 Ω + 1 M Ω ≈ ǫ 11 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do DAQ N OISE Channel Mean [µV] Standard deviation [µV] AI0 -10.24 -11.24 -12.04 0.39 0.44 0.46 AI1 5.42 5.35 5.34 0.35 0.36 0.36 AI2 0.57 0.87 0.53 0.39 0.38 0.44 AI3 4.63 4.64 4.64 7.18 7.12 7.08 12 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do DAQ N OISE Power Coil 1 1E-13 1E-14 1E-15 1E-16 1E-17 Power [V^2] 1E-18 1E-19 1E-20 1E-21 1E-22 1E-23 0.1 1 10 100 1000 Frequency [Hz] Figure 2 : AI0 Noise Spectrum 13 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do S ENSORS ◮ PCB probe 5 signals: Unbucked (UB), Dipole Bucked (DB), Dipole Quadrupole Bucked (DQB), Dipole Quadrupole Sextupole Bucked (DQSB) and Unbucked Low Gain (UBL) ◮ Morgan probe 6 signals: Dipole (2P1), Quadrupole (4P1), Sextupole (6P1), Decapole (10P1) and Dodecapole (12P1) sensitive ◮ Rotary encoder 2 signals: index and encoder pulses 14 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do PCB PROBE PROPER NOISE Power Coil 1 1E-11 1E-12 1E-13 1E-14 1E-15 1E-16 Power [V^2] 1E-17 1E-18 1E-19 1E-20 1E-21 1E-22 1E-23 0.1 1 10 100 1000 Frequency [Hz] Figure 3 : UB coil 15 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do PCB PROBE PROPER NOISE Power Coil 3 1E-11 1E-12 1E-13 1E-14 1E-15 Power [V^2] 1E-16 1E-17 1E-18 1E-19 1E-20 1E-21 1E-22 0.1 1 10 100 1000 Frequency [Hz] Figure 4 : DQB coil 16 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do M ORGAN PROBE PROPER NOISE −12 10 −14 2 /Hz) 10 Power/Frequency (V −16 10 −18 10 −20 10 −22 10 0 1 2 3 10 10 10 10 Frequency (Hz) Figure 5 : 2P1 17 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do M ORGAN PROBE PROPER NOISE 10 -12 10 -13 10 -14 Power/Frequency (V 2 /Hz) 10 -15 10 -16 10 -17 10 -18 10 -19 10 -20 10 -21 10 -2 10 -1 1 10 1 10 2 10 3 Frequency (Hz) Figure 6 : 12P1 18 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do P ROBE NOISE COMPARISON White noise level appears to be almost almost the same in both probes. ◮ DAQ : � S f ≈ 1 nV √ Hz √ � ◮ UB : � S f = 4 kT × 1 k Ω ≈ 4 nV 4 kTR coil ≈ Hz difficult to √ see on a log graph. √ � ◮ DQB : � S f = 4 kT × 4 . 5 k Ω ≈ 8 . 5 nV 4 kTR coil ≈ Hz slight √ increase visible ◮ 2P1 and 12p1 : resistance in the order of few Ω . Thermal noise negligible with respect to DAQ noise Conclusion: PCB coils are slightly noisier than Morgan coils. 19 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do S TEPPER MOTOR Probes are spun using a stepper motor. This kind of actuators are quite noisy. −5 −10 10 10 2 /Hz) 2 /Hz) −12 10 −10 Power/Frequency (V Power/Frequency (V 10 −14 10 −15 10 −16 10 −20 −18 10 10 0 1 2 3 0 1 2 3 10 10 10 10 10 10 10 10 Frequency (Hz) Frequency (Hz) (a) UB (b) 2P1 Noise raised from � S f ≈ 1 nV Hz , to � S f ≈ 1 µ V Hz . No relation √ √ with the spinning frequency was found. 20 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do S TEPPER MOTOR Power spectra obtained spinning the probe manually confirm that the stepper motor is a dominant source of noise −5 −5 10 10 2 /Hz) 2 /Hz) −10 −10 Power/Frequency (V Power/Frequency (V 10 10 −15 −15 10 10 −20 −20 10 10 0 1 2 3 0 1 2 3 10 10 10 10 10 10 10 10 Frequency (Hz) Frequency (Hz) (a) UB (b) DQB 21 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do P OWER SUPPLY Magnets were powered using a Kepco BOP 36-12M DC bipolar power supply. Random fluctuations of the current generated by it can increase the uncertainty of the measures. 22 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do P OWER SUPPLY Power Coil 1 1E-9 1E-10 1E-11 1E-12 1E-13 1E-14 Power [V^2] 1E-15 1E-16 1E-17 1E-18 1E-19 1E-20 1E-21 1E-22 0.1 1 10 100 1000 Frequency [Hz] Figure 9 : UB coil. Power supply on 23 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do M AGNETS Two magnets were employed to test the probes: ◮ Dipole magnet : 10 A → C 1 ≈ 71 mT R ref = 10 mm ◮ Quadrupole magnet : 5 A → C 2 ≈ 2 mT R ref = 10 mm 24 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do LABV IEW VI Fluxes displayed after each turn almost in real-time. Harmonic analysis performed at the end of data acquisition. 25 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do LABV IEW VI 26 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do LABV IEW VI 27 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do Section 3 H ARMONIC ANALYSIS 28 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do D IPOLE MAGNET : HARMONICS B n A n 4 1 10 10 Morgan Morgan DBUCK DBUCK DQBUCK DQBUCK 3 10 DQSBUCK DQSBUCK 2 0 10 10 1 10 Units Units 0 −1 10 10 −1 10 −2 −2 10 10 −3 10 −4 −3 10 10 2 3 4 5 6 2 3 4 5 6 Harmonic Order Harmonic Order Dipole harmonics comparison: normal component B n and skew component A n . Error as ± σ 29 / 36
I NTRODUCTION S ET -U P AND NOISE ANALYSIS H ARMONIC ANALYSIS To Do D IPOLE MAGNET : HARMONICS B n A n 4 1 10 10 Morgan Morgan UBUCK UBUCK UBUCKL UBLUCK 3 10 2 0 10 10 1 10 Units Units 0 −1 10 10 −1 10 −2 −2 10 10 −3 10 −4 −3 10 10 2 3 4 5 6 2 3 4 5 6 Harmonic Order Harmonic Order Dipole harmonics comparison: normal component B n and skew component A n . Error as ± σ 30 / 36
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