González, J

Johnston, S

Schulte, E C

Gonzalez, J

Schulte, E

CERN Document Server

Fast Q-measurement for the PS by FFT Analysis

April 1994 OCR OutputGeneva, SwitzerlandJune 27 - July 1, 1994, London, United Kingdom.Paper to be presented at the 1994 European Particle Accelerator Conferencebeam samples for subsequent sliding-FFT analysis.Q-value every 1.8 ms. The Digital Signal Processor memory can store up to 106 ms worth ofrapid changes of machine parameters, e. g. at transition, interleaving of measurements yields aa coherence time of 80 tts the precision is still 1 0.001 over a 35 dB input range. To followprecision of 1 0.0001 is thus obtained over a 30 dB input range, whilst for an oscillation withbased on (sin x)/x tit. Frequency interpolation is then applied. For a pure sine-wave, aAmplitude distortion due to rectangular windowing is corrected using amplitude-interpolationposition measurements from one pick—up, sampled at the revolution frequency (~ 0.5 MHz).Transform analyser, has been developed. The Q-value is calculated in 2.8 ms from 512 beamFor speedier and more precise Q-measurements, a new System, based on a Fast FourierABSTRACTPS Division, CERN, CH-1211 Geneva 23J. Gonzalez, S. Johnston and E. SchulteFAST Q-MEASUREMENT Fon THE PS BY FFT ANALYSISW {Y2 6P00023996CERN/PS ea|i|||||N|||l||||Nllllllillllllll||I||||¢|||lU|||CEM LIBRARIES, GENEVAEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHlength to one revolution period.not represent the true amplitude of the signal but is a point OCR Outputcore kicker receiving a capacitor discharge pulse equal inmain lobe. The fact that the tallest of these two lines doesFor each Q-measurement the beam is excited by an airwill be the well known (sin x)/x containing two lines in the2. HARDWARE the betatron oscillation, the shape of the resulting spectrumAssuming a sine wave as a first-order approximation ofusing a fast Digital Signal Processor (DSP) system. offp.using beam position modulation. This has been achieved DSP for the tallest spectral line within the frequency rangerapid Q-changes, e.g. during chromaticity measurements spectrum will be fm X q. Thus a search is performed by theThe system must be fast enough to allow measurement of a sufficient kick, the strongest component of the beambetatron frequency fp is based on the assumption that, given20 kHz< fB <2l5 kl-Iz The selection of the spectral line which contains thewhich the four Zoran ZR34l61s perform in 0.63 ms [4].be measured is512-point magnitude-squared Fast Fourier Transform (FFT),using the values in Table 1, the betauon frequency range tocontained in a rectangular window and are treated using aThe value of Q in the PS lies in the range 6.1 to 6.45, andderived from the beam pick-up signal. The samples arecalculation of the fraction q or its complement 1-q [2].Q-calculation, using the machine revolution frequency askicker. The use of a single pick-up, however, only allows512 beam-position samples are acquired by the DSP forwhich is achieved by exciting the beam with a magneticcoherent betatron oscillation fp of sufficient amplitude, 3. SIGNAL PROCESSHQGTo calculate the Q-value it is necessary to obtain aconcurrent with processing of the other.* Deceleration for injection into LEAR data memories, allowing data acquisition in one memoryprocessors. An arbitration unit govems access to the twoPbI 95_4 Mgv/u I 4.25 GeV/u I 200.8 I 469.3”*`processing is performed by four Zoran ZR34l6l vectorthe I 0.6 Gev | 3.5 Gev | 477.1 | 477.1controlled by a Texas TMS320C25 processor, and signalD, P | 200* MeV | 26 GeV I 270.2 I 476.8 the VASP-16 DSP [3] via a custom 16-bit bus. The board isEmin Emax Ibn (min) frev (max) Data are transferred into one of the two data memories offrequency (kHz)Figure l. Hardware for the PS Q-measurement system.RevolutionParticle | Kinetic energyTable 1.MVME147‘€§i‘§h.a3.;..m1.[1l·Motorolacycle information,particles and the corresponding revolution frequencies fmleptons and ions. Table 1 shows the total energy E of theseBI I 4xDB416lThe PS accelerates several types of particle : hadrons,1. 1NrRo1>UcT1oNAI Imsszocxworth of beam samples for subsequent sliding-FI-'I` analysis.. . VME-based DSP Pick-up Amptirier A“é‘l;:rh“‘ ADCThe Digital Signal Processor memory can store up to 106 msfrequencies.interleaving of measurements yields a Q-value every 1.8 ms.interpolation and can accept some lightly attenuated imagerapid changes of machine parameters, e.g. at transition,steep since the processing system uses amplitudeprecision is still :0.001 over a 35 dB input range. To followthe case of Q-calculation the tilter does not need to be verywhilst for an oscillation with a coherence time of 80 ps theanti-aliasing filter is selected depending upon the choice. Inprecision w.OO01 is thus obtained over a 30 dB input range,higher modes of oscillation. A fixed-frequency or trackinginterpolation is then applied. For a pure sine-wave, abe perfonned using the accelerating frequency fgp to observeamplitude-interpolation based on (sin x)/x tit. Frequencyalways performed using fm,. but spectral analysis may alsodistortion due to rectangular windowing is corrected usingtype of signal analysis to be performed. Q-measurement isat the revolution frequency (~ 0.5 MHz). AmplitudeThe sample clock of the ADC is selected according to the512 beam position measurements from one pick-up, sampledDigital Converter (ADC) (see Figure 1).been developed. The Q-value is calculated in 2.8 ms frombefore being digitised by a 10 MI-lz, 12-bit Analogue tosystem, based on a Fast Fourier Transform analyser, haselectric signal. The signal is then amplified and filteredFor speedier and more precise Q-measurements, a newup which senses the beam position and converts it into anAbstract The acquisition system consists of an electrostatic pickPS Division, CERN, CH-1211 Geneva 23J. Gonzalez, S. Johnston, and E. SchulteOCR OutputFast Q-measurement for thc PS by FFF Analysistwo data banks and the access—arbitration unit allows a OCR Outputinterpolated from the FFT usingfurther 0.4 ms. The division of the DSP data memory intoas representing the betatron oscillation, and the q value is2.8 ms. Amplitude interpolation by the TMS320C25 takes aConsequently the stronger of the two signals is selectedand interpolation of the q value, is performed by the DSP inconsisting of an acquisition, data pre-processing [4], FFTGi +Q}Ui-1(5) 'l`he execution time of a single Q-measurement,JG;] k =k·—— I m Iwhere may exhibit for the q error to be less than 0.001.Figure 4. Maximum coherence time which a sine wavei f“"°“*“*" Si¤(#¤(kr — km) Initial peak amplitude of sine wave (bits)4 ( )3 4 S 6 7 8 9 10 ll¢=(/q - km) A = ·—;—JZ0.05amplitude is found fromline of the main lobe lies to the left of the peak, the u·ueFor the case of the coupling signal, in which the second 0.15kp; respectively.aj and aj+1 are the amplitudes of the specual lines kj and0.25time (ms)G + Q}(1j+‘ (3)Coherencek —k-+ M"] M Iin this region.whereamplifier gains can be selected to keep the signal amplituderange (see Figure 4). Beam excitation voltages and. s1n(1t(k,,, —— ki)<2> obtained for a coherence time of 80 us over a 35 dB inputAf =t/Z °the system, to obtain an error less than 0.001, has beenn(km ' kj)using [5] results in increased measurement errors. The design goal ofdata window, the true amplitude of the signal fp is calculated Coherence-loss reduces the oscillation amplitude andFor a power spectrum, performed using a rectangular calculations (2)..(5).storage in the DSP. introducing errors into the results ofbut which appears to be taller in the spectrum. amplitudes of the spectral lines are truncated to integer forwith 10% less amplitude than the signal of interest fp, floating point arithmetic during FFT calculation but theFigure 2. Power spectrum showing a signal fwcaupled) oscillation, it is less than 0.0005. The Zoran processors use30 dB input range, and even with only 3 bits (peak)The error of the system remains below 0.0001 over a fullsine wave input.Figure 3. Absolute error in the q calculation for a pure3 a-1Amplitude of sine input (bits)3 A 5 6 7 8 9 10 ll. B<¤>¤p1¤¢> ill0.0lX)l§ l0.0002i "` a M—··—i at0.00030.0w43 1 ———é0.0005Absoluteamplitude of the input signal.former. shows the plot of the absolute error in q, dependent upon thefrom the other plane, with 90% of the amplitude of the values and the results calculated by the system. Figure 3measured, while the second peak could be a coupled signal oscillation allows a study of the error between known qsignal on the right is the actual betatron oscillation being The use of a pure sine wave to simulate the betatronspectrum [5],[6]. In the example shown in Figure 2, the4. Rtzsuursis employed on the two most prominent signals in theTo reduce the risk of such errors, amplitude interpolation where N = Number of points in FFT.plane, could appear taller than the signal of interest.signal, e.g. a coupled betatron oscillation from the other q =(6)on thc (sin x)/x cuwc, introduces thc risk that another strong

Fast Q-measurement for the PS by FFT analysis

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