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S. Simrock & Z. Geng, 7th International Accelerator School for Linear Colliders, India, 2012
Cavity Field Control - RF Signal Detection and Actuation
LLRF Lecture Part 3.4
S. Simrock, Z. Geng
ITER / SLAC
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 2
Outline
• Requirements to RF field detector
• RF field detection methodology
• Reduce the noises and compensate the drifts in RF field detection
• RF actuation
• Appendix
– Typical hardware for RF field detection • Mixer
• Analog to Digital Converter (ADC)
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 3
Requirements to RF Field Detector
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 4
Context of the RF Field Detector
ttQttI
tttAtVc
sincos
cos
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 5
Recall: Transfer Function from Detector Noise to
Cavity Field
101
102
103
104
105
106
107
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
Frequency / Hz
Ma
gn
itu
de
/ d
B
Cavity bandwidth
Closed loop bandwidth
Input noise transfer A(s)->Y(s)
Detector noise transfer D(s)->Y(s)
• Low frequency noise of
detector is transferred
directly to the cavity
output; high frequency
noise is filtered by
closed loop bandwidth
and detector bandwidth
• Reducing the detector
noise will be essential to
get highly stable cavity
field!
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 6
Requirements to the RF Field Detector
• The requirements of the RF field detector should be
derived from the overall requirements to LLRF system
• Functional requirements: detect the amplitude and
phase of RF field for each cavity in real time
• Quality requirements:
– Field detection bandwidth
– Amplitude and phase error
– Non-linearity
Example for FLASH:
• Field detection bandwidth: 10 MHz
• Amplitude and phase error: < 10^-4
• Non-linearity: at full scale of the measurement, the amplitude compression
should be less than 1% and phase shift should be less than 0.5 degree
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 7
RF Field Detection Methodology
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 8
Direct Amplitude and Phase Detection
• Simple system structure
• Linear for small phase errors
• Phase measurement is influenced by the amplitude error of the RF or LO signal
tAtV LOLO cos)(
0sin)( tAtV RFRF
Mixer input:
Mixer output:
) small(for 2
sin2
2sinsin2
cossin
000
000
LORFLORFmixer
LORFLORFmixer
AAAAVLPF
tAA
tAtAV
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 9
Analog I/Q Detection
tAtV LOLO cos)(
0cos)( tAtV RFRF
00 cos4
cos2
cos2
LORFLORF AAt
At
ALPFI
Inputs:
00 sin4
sin2
cos2
LORFLORF AAt
At
ALPFQ
Outputs:
I
Q1
0 tan 22 QIA
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 10
Analog I/Q Detection
• Phase measurement is linear for the whole range of 360º
• Low efforts of digital processing
• Disadvantages:
– Phase and amplitude imbalance
– DC offset
Amplitude
imbalance
Phase
imbalance
DC
offset
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 11
IQ Sampling
• Digital I/Q detection
• IF and clock signal should be
synchronized
• Alternating sample give I and
Q components of the cavity
field
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 12
IQ Sampling at FLASH
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 13
IQ Sampling
• Advantages
– Get rid of the imbalance effect compared with the analog I/Q demodulator
• Problems
– DC offset caused by the mixer
– Nonlinearities in the analog front-end or the ADC generate harmonics, which will be aliased to the IF frequency
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1.5
-1
-0.5
0
0.5
1
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 14
IQ Sampling
Vector of 1st
Harmonic
Vectors of
Aliased
Harmonics
Measured
Vector of 1st
Harmonic
• The phase of nth harmonic changes
n times faster than the fundamental
phase
• Phase shifts in the cavity due to
microphonics and Lorenz force
detuning will lead to a time
dependent error
A
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 15
Non-IQ Sampling
• Compared with IQ sampling, non-IQ sampling is aimed to avoid the
harmonics aliasing by shifting the sampling frequency slightly from
4 times of the IF frequency
2n
m
Example: m=4, n=15
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 16
Non-IQ Sampling
• Fourier series decomposition of the RF signal
• Demodulation algorithm:
1
0
1
0
sin2
cos2 n
i
i
n
i
i ixn
Qixn
I ,
,...2,1,
2sin2
2cos2
2sin2cos2
2sin2cos2sin
0
0
1
0
k
dttfktsT
b
dttfktsT
a
tfkbtfkaa
ts
tfQtfItfAts
T
IFk
T
IFk
k
IFkIFk
IFIFIF
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 17
Non-IQ Sampling
• Most harmonics no longer line up with IF frequency. Influence
due to the higher order harmonics and DC offset can be
reduced with band pass filter.
• The algorithm for demodulation need more computation power
and will cause larger latency
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 18
Direct Sampling
• Example for available ADC: ADS5474, 14 bits,
400MSPS, 1.4GHz bandwidth
• Under-sampling
• Non-IQ sampling (m,n have the same meaning as the
discussion of non-IQ sampling)
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 19
Direct Sampling
• Advantage: no down converter needed
• Essential problems: ADC measurement noise is sensitive to the clock jitter due to the high input RF frequency
rmsjitterRFjitter tfSNR _10 2log20
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 20
Digital Down Conversion
• Principle same as analog I/Q demodulator
• NCO: Numerical Controlled Oscillator
• Digital mixer: multiplication operation in processors (in FPGA can be multiplier cores)
• Digital low pass filter, can be IIR, FIR or CIC filter
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 21
Reduce the Noises and Compensate
the Drifts in RF Field Detection
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 22
Noise and Drift Sources for RF Detection
• Slow phase and amplitude drifts:
– Cavity pick up cables
– Down converter
– LO low frequency phase noise
• Fast phase and amplitude jitters:
– Thermal noise
– LO high frequency phase noise
– ADC noise
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 23
Reduce the High Frequency Noise
• Select components of
down converter with
low noise level
• Filtering in RF side
• ADC oversampling
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 24
Drift and Fluctuation Correction
Reference tracking
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Drift and Fluctuation Correction
Measurement chain drift calibration
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 26
RF Actuation
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 27
RF Actuator
• Change the amplitude and phase of RF driving signal
and perform frequency up-conversion
• Widely used solutions:
– Direct up-conversion
– IF up-conversion
– Single sideband up-conversion
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 28
Direct Up-conversion
I
QQIA
tAtQtIRF
122
000
tan,
cossincos
• Easy to implement
• Suffer from the DC offset in I/Q base band signals
and the phase and amplitude imbalance of the vector
modulator
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 29
IF Up-conversion
• Band pass filter after the DAC can remove the DC offset
• Band pass filter after the mixer is necessary
• If IF is small, filter design will be critical
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 30
Single Sideband Up-conversion
tAttAttARF IFLOIFLOIFLO cossinsincoscos
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 31
Summary
In this part, we have learnt:
• Principles and characteristics of several RF field detection methods
• Ideas to correct the noise and drift of the RF field detector
• Principles for several RF actuation (up-conversion) methods
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 32
Reference
[1] Z. Geng. Design and Construction of the Phasing System for
BEPCII Linac. Ph.D. thesis of Chinese Academy of Sciences, 2007
[2] T. Schilcher. Vector Sum Control of Pulsed Accelerating Fields in
Lorentz Force Detuned Superconducting Cavities. Ph. D. Thesis of
DESY, 1998
[3] M. Hoffmann. Development of A Multichannel RF Field Detector
for the Low-Level RF Control of the Free-Electron Laser at Hamburg.
Ph.D. Thesis of DESY, 2008
[4] L. Doolittle. Digital Low-Level RF Control Using Non-IQ Sampling.
LINAC2006, Knoxville, Tennessee USA
[5] Z. Geng, S. Simrock. Evaluation of Fast ADCs for Direct Sampling
RF Field Detector for the European XFEL and ILC. LINAC2008,
Victoria, BC, Canada
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 33
Appendix:
Typical Hardware for RF Field
Detection
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 34
Mixer
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 35
Mixer
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 36
Mixer
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 37
Mixer
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 38
Analog to Digital Converter
What is an ADC?
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 39
Analog to Digital Converter
Least Significant Bit (LSB) and Most Significant Bit (MSB)
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 40
Analog to Digital Converter
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 41
Analog to Digital Converter
ADC noise source: Quantization noise
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 42
Analog to Digital Converter
ADC noise source: Clock jitter
rmsjitterRFjitter tfSNR _10 2log20
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 43
Analog to Digital Converter
ADC noise source: Noisy components or circuitry
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 44
Analog to Digital Converter
Signal to Noise Ratio (SNR) of ADC:
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 45
Analog to Digital Converter
Differential Non-Linearity (DNL): “small scale” code to
code errors
S. Simrock & Z. Geng, 6th International Accelerator School for Linear Colliders, USA, 2011 46
Analog to Digital Converter
Integral Non-Linearity (INL): “large scale” overall transfer
function error
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